A signal-of-opportunity-based method to automatically calibrate the orientations and shapes of a set of hydrophone arrays using the sound emitted from nearby ships is presented. The calibration problem is formulated as a simultaneous localization and mapping problem, where the locations, orientations, and shapes of the arrays are viewed as the unknown map states, and the position, velocity, etc., of the source as the unknown dynamic states. A sequential likelihood ratio test, together with a maximum a posteriori source location estimator, is used to automatically detect suitable sources and initialize the calibration procedure. The performance of the proposed method is evaluated using data from two 56-element hydrophone arrays. Results from two sea trials indicate that: 1) signal sources suitable for the calibration can be automatically detected; 2) the shapes and orientations of the arrays can be consistently estimated from the different data sets with shape variations of a few decimeters and orientation variations of less than 2(degrees) and 3) the uncertainty bounds calculated by the calibration method are in agreement with the true calibration uncertainties. Furthermore, the bearing time record from a sea trial with an autonomous mobile underwater signal source also shows the efficacy of the proposed calibration method. In the studied scenario, the root-mean-square bearing tracking error was reduced from 4(degrees) to 1(degrees) when using the calibrated array shapes compared to assuming the arrays' to be straight lines. Also, the beamforming gain increased by approximately 1 dB.

This letter investigates relationships between iterated filtering algorithms based on statistical linearization, such as the iterated unscented Kalman filter (IUKF), and filtering algorithms based on quasi–Newton (QN) methods, such as the QN iterated extended Kalman filter (QN–IEKF). Firstly, it is shown that the IUKF and the iterated posterior linearization filter (IPLF) can be viewed as QN algorithms, by finding a Hessian correction in the QN –IEKF such that the IPLF iterate updates are identical to that of the QN–IEKF. Secondly, it is shown that the IPLF/ IUKF update can be rewritten such that it is approximately identical to the QN–IEKF, albeit for an additional correction term. This enables a richer understanding of the properties of iterated filtering algorithms based on statistical linearization.

A static world assumption is often used when considering the simultaneous localization and mapping (SLAM) problem. In reality, especially when long-term autonomy is the objective, this is not valid. This paper studies a scenario where uniquely identifiable landmarks can attend multiple discrete positions, not known a priori . Based on a feature based multi-hypothesis map representation, a multi-hypothesis SLAM algorithm is developed inspired by target tracking theory. The creation of such a map is merged into the SLAM framework allowing any available SLAM method to solve the underlying mapping and localization problem for each hypothesis. A recursively updated hypothesis score allows for hypothesis rejection and prevents exponential growth in the number of hypotheses. The developed method is evaluated in an underground mine application, where physical barriers can be moved in between multiple distinct positions. Simulations are conducted in this environment showing the benefits of the multi-hypothesis approach compared to executing a standard SLAM algorithm. Practical considerations as well as suitable approximations are elaborated upon and experiments on real data further validates the simulated results and show that the multi-hypothesis approach has similar performance in reality as in simulation.

Robust and highly accurate position estimation in underground mines is investigated by considering a vehicle equipped with 2D laser scanners. A survey of available methods to process data from such sensors is performed with focus on feature extraction methods. Pros and cons of the usage of different methods for the positioning application with 2D laser data are highlighted, and suitable methods are identified. Three state-of-the-art feature extraction methods are adapted to the scenario of positioning in a predefined map and the methods are evaluated through experiments conducted in a simulated underground mine environment. Results indicate that feature extraction methods perform in parity with the method of matching each ray individually to the map, and better than the point cloud scan matching method of a pure ICP, assuming a highly accurate map is available. Furthermore, experiments show that feature extraction methods more robustly handle imperfections or regions of errors in the map by automatically disregarding these regions.

This paper presents and experimentally evaluates an algorithm named Multiple Generalized Likelihood Ratio (MGLR) for detecting and estimating multiple consecutive measurement biases appearing frequently, in the case of non-redundant sensors; typically the case for a small drone or remotely piloted aerial vehicle. The algorithm itself is based on the Generalized Likelihood Ratio (GLR) algorithm by Willsky for bias detection and estimation, and introduces additional steps for continuously estimating, compensating, and eliminating measurement biases after detection. An experimental campaign using a car-mounted IMU and GNSS receiver in an urban environment shows the effectiveness of the approach to increase accuracy, consistency, and integrity of the estimate in non-redundant estimation with position measurements subject to time-varying bias.

This article introduces a Poisson multi-Bernoulli mixture (PMBM) filter in which the intensities of target birth and undetected targets are grid-based. A simplified version of the Rao-Blackwellized point mass filter is used to predict the intensity of undetected targets and to initialize tracks of targets detected for the first time. The grid approximation can efficiently represents intensities with abrupt changes with relatively few grid points compared to the number of Gaussian components needed in conventional PMBM implementations. This is beneficial in scenarios where the sensors field of view is limited. The proposed method is illustrated in a sensor management setting, where trajectories of sensors with limited fields of view are controlled to search for and track the targets in a region of interest.

A novel method for accurate speed estimation of a vehicle using a deep learning convolutional neural network (CNN), with accelerometer and gyroscope measurements as input, is presented. It does not suffer from the fundamental drift problem present in all dead reckoning methods, and yet yields about 2 m/s in accuracy. Efficient drift-free vehicle speed estimates are essential in many automotive applications, where internal wheel speed sensors or GPS are unavailable. Using extensive experimental data, the proposed CNN method is compared to an existing frequency analysis method. The proposed method is shown to perform significantly better, particularly during low speed and rapid speed changes where the frequency method struggles.

The problem of joint classification of gait and device mode from inertial measurement units (IMU) measurements is considered. For this, an approach for computing unique gait signature using measurements collected from body-worn inertial measurement units (IMUs) is proposed.The gait signature represents one full cycle of the human gait, and is suitable for off-line or on-line classification of the gait mode. The signature can also be used to jointly classify the gait mode and the device mode. The device mode identifies how the IMU-equipped device is being carried by the user. The method is based on precise segmentation and resampling of the measured IMU signal, as an initial step, further tuned by minimizing the variability of the obtained signature within each gait cycle. Finally, a Fourier series expansion of the gait signature is introduced which provides a low-dimensional feature vector well suited for classification purposes. The proposed method is evaluated on a large dataset involving several subjects, each one containing two different gait modes and four different device modes.

Tracked targets often exhibit common behaviors due to influences from the surrounding environment, such as wind or obstacles, which are usually modeled as noise. Here, these influences are modeled using sparse Gaussian processes that are learned online together with the state inference using an extended Kalman filter. The method can also be applied to time-varying influences and identify simple dynamic systems. The method is evaluated with promising results in a simulation and a real-world application.

Novel features for joint classification of gait and device modes are proposed and multiple machine learning methods are adopted to jointly classify the modes. The classification accuracy as well as the F₁ score of two standard classification algorithms, K-nearest neighbor (KNN) and Gaussian process (GP), are evaluated and compared against a proposed neural network (NN)-based classifier. The proposed features are the correlation scores of a detected gait cycle relative to a set of unique gait signatures as well as the gait cycle time, all extracted from handheld inertial measurement units (IMUs). Each gait signature is defined such that it contains one full cycle of the human gait. In order to take the temporal correlation between classes into account, the initial classifiers’ estimates are fed into a hidden Markov model (HMM) unit to obtain the final class estimates. The performance of the proposed method is evaluated on a large data set, including two classes of gait modes (walking and running) and four classes of device modes (fixed and face-up in the hand, swinging in the hand, in the pocket, and in the backpack). The experimental results validate the reliability of the considered features and effectiveness of the HMM unit. The initial classification accuracy of the NN-based approach is 91%, which is further improved to 99% after the smoothing stage on the validation set and 98% on the test set.

An Informed Path Planning algorithm for multiple agents is presented. It can be used to efficiently utilize available agents when surveying large areas, when total coverage is unattainable. Internally the algorithm has a Probability Hypothesis Density (PHD) representation, inspired by modern multi-target tracking methods, to represent unseen objects. Using the PHD, the expected number of observed objects is optimized. In a sequential manner, each agent maximizes the number of observed new targets, taking into account the probability of undetected objects due to previous agents actions and the probability of detection, which yields a scalable algorithm. Algorithm properties are evaluated in simulations, and shown to outperform a greedy base line method. The algorithm is also evaluated by applying it to a sea ice tracking problem, using two datasets collected in the Arctic, with reasonable results. An implementation is provided under an Open Source license.

We consider a linear state estimation problem, where, in addition to the usual timestamped measurements, observations with uncertain timestamps are available. Such observations could, e.g., come from traces left by a target in a tracking scenario or from witnesses of an event and have the potential to improve the estimation accuracy significantly. We derive the posterior distribution and point estimators for a linear Gaussian smoothing formulation of this problem and illustrate with two numerical examples.

The ensemble Kalman filter (EnKF) is a Monte Carlo-based implementation of the Kalman filter (KF) for extremely high-dimensional, possibly nonlinear, and non-Gaussian state estimation problems. Its ability to handle state dimensions in the order of millions has made the EnKF a popular algorithm in different geoscientific disciplines. Despite a similarly vital need for scalable algorithms in signal processing, e.g., to make sense of the ever increasing amount of sensor data, the EnKF is hardly discussed in our field. This self-contained review is aimed at signal processing researchers and provides all the knowledge to get started with the EnKF. The algorithm is derived in a KF framework, without the often encountered geoscientific terminology. Algorithmic challenges and required extensions of the EnKF are provided, as well as relations to sigma point KF and particle filters. The relevant EnKF literature is summarized in an extensive survey and unique simulation examples, including popular benchmark problems, complement the theory with practical insights. The signal processing perspective highlights new directions of research and facilitates the exchange of potentially beneficial ideas, both for the EnKF and high-dimensional nonlinear and non-Gaussian filtering in general.

1 Migratory songbirds carry an inherited capacity to migrate several thousand kilometers each year crossing continental landmasses and barriers between distant breeding sites and wintering areas. How individual songbirds manage with extreme precision to find their way is still largely unknown. The functional characteristics of biological compasses used by songbird migrants has mainly been investigated by recording the birds directed migratory activity in circular cages, so-called Emlen funnels. This method is 50 years old and has not received major updates over the past decades. The aim of this work was to compare the results from newly developed digital methods with the established manual methods to evaluate songbird migratory activity and orientation in circular cages. 2 We performed orientation experiments using the European robin (Erithacus rubecula) using modified Emlen funnels equipped with thermal paper and simultaneously recorded the songbird movements from above. We evaluated and compared the results obtained with five different methods. Two methods have been commonly used in songbirds orientation experiments; the other three methods were developed for this study and were based either on evaluation of the thermal paper using automated image analysis, or on the analysis of videos recorded during the experiment. 3 The methods used to evaluate scratches produced by the claws of birds on the thermal papers presented some differences compared with the video analyses. These differences were caused mainly by differences in scatter, as any movement of the bird along the sloping walls of the funnel was recorded on the thermal paper, whereas video evaluations allowed us to detect single takeoff attempts by the birds and to consider only this behavior in the orientation analyses. Using computer vision, we were also able to identify and separately evaluate different behaviors that were impossible to record by the thermal paper. 4 The traditional Emlen funnel is still the most used method to investigate compass orientation in songbirds under controlled conditions. However, new numerical image analysis techniques provide a much higher level of detail of songbirds migratory behavior and will provide an increasing number of possibilities to evaluate and quantify specific behaviors as new algorithms will be developed.

Safety and security applications benefit from better situational awareness. Radar micro-Doppler signatures from an observed target carry information about the target's activity, and have potential to improve situational awareness. This article describes, compares, and discusses two methods to classify human activity based on radar micro-Doppler data. The first method extracts physically interpretable features from the time-velocity domain such as the main cycle time and properties of the envelope of the micro-Doppler spectra and use these in the classification. The second method derives its features based on the components with the most energy in the cadence-velocity domain (obtained as the Fourier transform of the time-velocity domain). Measurements from a field trial show that the two methods have similar activity classification performance. It is suggested that target base velocity and main limb cadence frequency are indirect features of both methods, and that they do often alone suffice to discriminate between the studied activities. This is corroborated by experiments with a reduced feature set. This opens up for designing new more compact feature sets. Moreover, weaknesses of the methods and the impact of non-radial motion are discussed.

Today, the workflows that are involved in industrial assembly and production activities are becoming increasingly complex. To efficiently and safely perform these workflows is demanding on the workers, in particular when it comes to infrequent or repetitive tasks. This burden on the workers can be eased by introducing smart assistance systems. This article presents a scalable concept and an integrated system demonstrator designed for this purpose. The basic idea is to learn workflows from observing multiple expert operators and then transfer the learnt workflow models to novice users. Being entirely learning-based, the proposed system can be applied to various tasks and domains. The above idea has been realized in a prototype, which combines components pushing the state of the art of hardware and software designed with interoperability in mind. The emphasis of this article is on the algorithms developed for the prototype: 1) fusion of inertial and visual sensor information from an on-body sensor network (BSN) to robustly track the user’s pose in magnetically polluted environments; 2) learning-based computer vision algorithms to map the workspace, localize the sensor with respect to the workspace and capture objects, even as they are carried; 3) domain-independent and robust workflow recovery and monitoring algorithms based on spatiotemporal pairwise relations deduced from object and user movement with respect to the scene; and 4) context-sensitive augmented reality (AR) user feedback using a head-mounted display (HMD). A distinguishing key feature of the developed algorithms is that they all operate solely on data from the on-body sensor network and that no external instrumentation is needed. The feasibility of the chosen approach for the complete action-perception-feedback loop is demonstrated on three increasingly complex datasets representing manual industrial tasks. These limited size datasets indicate and highlight the potential of the chosen technology as a combined entity as well as point out limitations of the system.

This paper addresses one of the main challenges in physical activity monitoring, as indicated by recent benchmark results: The difficulty of the complex classification problems exceeds the potential of existing classifiers. Therefore, this paper proposes the ConfAdaBoost.M1 algorithm. This algorithm is a variant of the AdaBoost.M1 that incorporates well-established ideas for confidence-based boosting. ConfAdaBoost.M1 is compared to the most commonly used boosting methods using benchmark datasets from the UCI machine learning repository.  Moreover, it is evaluated on an activity recognition and an intensity estimation problem, including a large number of physical activities from the recently released PAMAP2 dataset. The presented results indicate that the proposed ConfAdaBoost.M1 algorithm significantly improves the classification performance on most of the evaluated datasets, especially for larger and more complex classification tasks. Finally, two empirical studies are designed and carried out to investigate the feasibility of ConfAdaBoost.M1 for physical activity monitoring applications in mobile systems.

The unscented Kalman filter (UKF) has become a popular alternative to the extended Kalman filter (EKF) during the last decade. UKF propagates the so called sigma points by function evaluations using the unscented transformation (UT), and this is at first glance very different from the standard EKF algorithm which is based on a linearized model. The claimed advantages with UKF are that it propagates the first two moments of the posterior distribution and that it does not require gradients of the system model. We point out several less known links between EKF and UKF in terms of two conceptually different implementations of the Kalman filter: the standard one based on the discrete Riccati equation, and one based on a formula on conditional expectations that does not involve an explicit Riccati equation. First, it is shown that the sigma point function evaluations can be used in the classical EKF rather than an explicitly linearized model. Second, a less cited version of the EKF based on a second-order Taylor expansion is shown to be quite closely related to UKF. The different algorithms and results are illustrated with examples inspired by core observation models in target tracking and sensor network applications.

The particle filter (PF) has during the last decade been proposed for a wide range of localization and tracking applications. There is a general need in such embedded system to have a platform for efficient and scalable implementation of the PF. One such platform is the graphics processing unit (GPU), originally aimed to be used for fast rendering of graphics. To achieve this, GPUs are equipped with a parallel architecture which can be exploited for general-purpose computing on GPU (GPGPU) as a complement to the central processing unit (CPU). In this paper, GPGPU techniques are used to make a parallel recursive Bayesian estimation implementation using particle filters. The modifications made to obtain a parallel particle filter, especially for the resampling step, are discussed and the performance of the resulting GPU implementation is compared to the one achieved with a traditional CPU implementation. The comparison is made using a minimal sensor network with bearings-only sensors. The resulting GPU filter, which is the first complete GPU implementation of a PF published to this date, is faster than the CPU filter when many particles are used, maintaining the same accuracy. The parallelization utilizes ideas that can be applicable for other applications.

Localization is an enabling technology in many applications and services today and in the future. Satellite navigation often works fine for navigation, infotainment and location based services, and it is today the dominating solution in commercial products. A nice exception is the localization in Google Maps, where radio signal strength from WiFi and cellular networks are used as complementary information to increase accuracy and integrity. With the on-going trend with more autonomous functions being introduced in our vehicles and with all our connected devices, most of them operated in indoor enviroments where satellite signals are not available,there is an acute need for new solutions.

At the same time, our smartphones are getting more sophisticated in their sensor configuration. Therefore, in this chapter we present a freely available Sensor Fusion app developed in-house, how it works, how it has been used, and how it can be used based on a variety of applications in our research and student projects.

It is a well-known fact that exercising helps people improve their overall well-being; both physiological and psychological health. Regular moderate physical activity improves the risk of disease progression, improves the chances for successful rehabilitation, and lowers the levels of stress hormones. Physical fitness can be categorized in cardiovascular fitness, and muscular strength and endurance. A proper balance between aerobic activities and strength exercises are important to maximize the positive effects. This balance is not always easily obtained, so assistance tools are important. Hence, ambient assisted living (AAL) systems that support and motivate balanced training are desirable. This chapter presents methods to provide this, focusing on the methodologies and concepts implemented by the authors in the physical activity monitoring for aging people (PAMAP) platform. The chapter sets the stage for an architecture to provide personalized activity monitoring using a network of wearable sensors, mainly inertial measurement units (IMU). The main focus is then to describe how to do this in a personalizable way: (1) monitoring to provide an estimate of aerobic activities performed, for which a boosting based method to determine activity type, intensity, frequency, and duration is given; (2) supervise and coach strength activities. Here, methodologies are described for obtaining the parameters needed to provide real-time useful feedback to the user about how to exercise safely using the right technique.

Accurate localization is a part of most autonomous systems. GNSS is today the go to solution for localization but is unreliable due to jamming and is not available indoors. Inertial navigation aided by visual measurements, e.g., optical flow, offers an alternative. Traditional feature-based optical flow is limited to scenes with good features, current development of deep neural network derived dense optical flow is an interesting alternative. This paper proposes a method to evaluate the result of dense optical flow on real image sequences using traditional feature-based optical flow and uses this to compare six different dense optical flow methods. The results of the dense methods are promising, and no clear winner amongst the methods can be determined. The results are discussed in the context of how they can be used to support localization.

Underwater surveillance using passive sonar and track-before-detect technology requires accurate models of the tracked signal and the background noise. However, in an underwater environment, the signal channel is time-varying and prior knowledge about the spatial distribution of the background noise is unavailable. In this paper, an autoregressive model that captures a time-varying signal level caused by multi-path propagation is presented. In addition, a multi-source model is proposed to describe spatially distributed background noise. The models are used in a Bernoulli filter track-before-detect framework and evaluated using both simulated and sea trial data. The simulations demonstrate clear improvements in terms of target loss and improved ability to discern the target from the noisy background. An evaluation of the track-before-detect algorithm on the sea trial data indicates a performance gain when incorporating the proposed models in underwater surveillance and tracking problems.

A new class of iterated linearization-based nonlinear filters, dubbed dynamically iterated filters, is presented. Contrary to regular iterated filters such as the iterated extended Kalman filter (IEKF), iterated unscented Kalman filter (IUKF) and iterated posterior linearization filter (IPLF), dynamically iterated filters also take nonlinearities in the transition model into account. The general filtering algorithm is shown to essentially be a (locally over one time step) iterated Rauch-Tung-Striebel smoother. Three distinct versions of the dynamically iterated filters are especially investigated: analogues to the IEKF, IUKF and IPLF. The developed algorithms are evaluated on 25 different noise configurations of a tracking problem with a nonlinear transition model and linear measurement model, a scenario where conventional iterated filters are not useful. Even in this “simple” scenario, the dynamically iterated filters are shown to have superior root mean-squared error performance as compared with their respective baselines, the EKF and UKF. Particularly, even though the EKF diverges in 22 out of 25 configurations, the dynamically iterated EKF remains stable in 20 out of 25 scenarios, only diverging under high noise.

The Particle filter can in theory estimate the state of any nonlinear system, but in practice it suffers from an exponential complexity in terms of the number of particles as the dimension of the state increases. The marginalized particle filter can potentially reduce this problem by improving the estimates, particularly for lower number of particles. However, it turns out that for certain systems, it does not provide any improvement in the accuracy of the estimate. The core cause of degeneracy is linked to when the uncertainty of the linear state conditioned on the nonlinear state is 0. Conditions for determining when this occurs are presented and applied to common constant velocity, constant acceleration and constant jerk models with various sampling methods. Interestingly, some combinations are useful while others should be avoided. These findings are supported using simulated systems.

Conventional direction of arrival (DOA) estimators are based on array processing using either time differences or beam-forming. The proposed approach is based on the received power at each microphone, which enables simple hardware, low sampling frequency and small arrays. The problem is recast into a linear regression framework where the least squares method applies, and the main drawback is that different sound sources are not readily separable.Our proposed approach is based on a training phase where the directional sensitivity of each microphone element is estimated. This model is then used as a fingerprint of the observed power vector in a real-time estimator. The learned power vector is here modeled by a Fourier series expansion, which enables Cramér-Rao lower bound computations. We demonstrate the performance using a circular array with eight microphones with promising results.

The classical SIR model is a fundamental building block in most epidemiological models. Despite its widespread use, its properties in filtering and estimation applications are much less well explored. Independently of how the basic SIR model is integrated into more complex models, the fundamental question is whether the states and parameters can be estimated from a fusion of available numeric measurements. The problem studied in this paper focuses on the parameter and state estimation of a stochastic SIR model from assumed direct measurements of the number of infected people in the population, and the generalisation to other measurements is left for future research. In terms of parameter estimation, two components are discussed separately. The first component is model parameter estimation assuming that the all states are measured directly. The second component is state estimation assuming known parameters. These two components are combined into an iterative state and parameter estimator. This iterative method is compared to a straightforward approach based on state augmentation of the unknown parameters. Feasibility of the problem is studied from an information-theoretic point of view using the Cramer Rao Lower Bound (CRLB). Using simulated data resembling the first wave of Covid-19 in Sweden, the iterative method outperforms the state augmentation approach.

Linearized Direction of Arrival (LinDoA) is a method for sound source localization that is designed for use with wearable microphone arrays. The method uses a Taylor series expansion of the sound source signal in the time domain to beamform and estimate the direction of arrival. The original method is limited to spatial sampling, but is here generalized to also consider temporal sampling for improved performance and usability. The proposed generalization allows for time-domain formulations of the Delay-and-Sum and Minimum-Variance Distortionless Response beamformers in addition to the original formulation by implementing interpolation and estimating the noise covariance. A number of variants of the method are described and the design choices are discussed. The methods are evaluated on data gathered by a head-worn array in real and simulated experiments and are compared to conventional methods. They are shown to perform on par with conventional methods at a reduced computational cost.

Marginalization enables the particle filter to be applied to high-dimensional problems by invoking the Kalman filter to estimate a larger part of the state vector. The marginalized (a.k.a. Rao-Blackwellized) particle filter (MPF) has found many use cases in tracking and navigation applications. These are characterized by having position and its derivatives as states. Here, we take a closer look at the MPF for the constant velocity motion model, which well represents the basic properties of most motion models used in this context. In particular, how the Kalman filter (KF)-part depends on how the continuous time state noise is sampled in the discrete time model.

We find that for many of the most common sampling approaches, the KF-part of the MPF degenerates, meaning that the covariance approaches 0. Further, we show that for those same sampling approaches there is no performance increase by switching from a particle filter to an MPF in this situation.

A tightly integrated magnetic-field aided inertial navigation system is presented. The system uses a magnetometer sensor array to measure spatial variations in the local magnetic-field. The variations in the field are - via a recursively updated polynomial magnetic-field model - mapped into displacement and orientation changes of the array, which in turn are used to aid the inertial navigation system. Simulation results show that the resulting navigation system has three orders of magnitude lower position error at the end of a 40 seconds trajectory as compared to a standalone inertial navigation system. Thus, the proposed navigation solution has the potential to solve one of the key challenges faced with current magnetic-field simultaneous localization and mapping (SLAM) systems - the very limited allowable length of the exploration phase during which unvisited areas are mapped.

The unscented Kalman filter (UKF) is a method to solve nonlinear dynamic filtering problems, which internally uses the unscented transform (UT). The behavior of the UT is controlled by design parameters, seldom changed from the values suggested in early UT/UKF publications. Despite the knowledge that the UKF can perform poorly when the parameters are improperly chosen, there exist no wide spread intuitive guidelines for how to tune them. With an application relevant example, this paper shows that standard parameter values can be far from optimal. By analyzing how each parameter affects the resulting UT estimate, guidelines for how the parameter values should be chosen are developed. The guidelines are verified both in simulations and on real data collected in an underground mine. A strategy to automatically tune the parameters in a state estimation setting is presented, resulting in parameter values inline with developed guidelines.

A belief-space planning problem for GNSS-denied areas is studied where the location and number of landmarks available are unknown when performing the planning. To be able to plan an informative path in this situation, an algorithm using virtual landmarks to position the platform during the planning phase is studied.  The virtual landmarks are selected to capture the expected information available in different regions of the map, based on the beforehand known landmark density. The main contribution of this work is a better approximation of the obtained information from the virtual landmarks and a theoretical study of the properties of the approximation. Furthermore, the proposed approximation, in itself and its use in a path planner, is investigated with successful results.

This paper addresses the problem of change detection for a quadcopter in the presence ofwind disturbances. Different aspects of the quadcopter dynamics and various flight conditions have beeninvestigated. First, the wind is modeled using the Dryden wind model as a sum of a low-frequent and aturbulent part. Since the closed-loop control can compensate for system changes and disturbances andthe effect of the wind disturbance is significant, the residuals obtained from a standard simulation modelcan be misleading. Instead, a sensor-to-sensor submodel of the quadcopter is selected to detect a changein the payload using the Instrumental Variables (IV) cost function. It is shown that the mass variationcan be detected using the IV cost function in different flight scenarios.

Modern maritime navigation is heavily dependent on satellite systems. Availability of an accurate position is critical for safe operations, but satellite-based navigation systems are vulnerable to interference, jamming, and spoofing. In this work, we propose a method for maritime navigation independent of GNSS, able to provide absolute positioning of the vessel based on marine radar scans.

A measurement model is presented where a Digital Elevation Model is used to predict the output of a marine radar, given a hypothetical position. The model, as used by an on-line particle filter, is used to track the movements of a ship from real recorded data. This demonstrates the feasibility of this method for robust positioning, without the need of external positioning signals, in a maritime environment. The tracking only uses sensors commonly available on maritime vessels, and demonstrates its application using freely available elevation data.

Lidar-based positioning in a 2D map is analyzed as a method to provide a robust, high accuracy, and infrastructure-free positioning system required by the automation development in underground mining. Expressions are derived that highlight separate information contributions to the obtained position accuracy. This is used to develop two new methods that efficiently select which subset of available lidar rays to use to reduce the computational complexity and allow for online processing with minimal loss of accuracy. The results are verified in simulations of a mid-articulated underground loader in a mine. The methods are shown to be able to reduce the number of rays needed without considerably affecting the performance, and to be competitive with currently used methods. Furthermore, simulations highlight the effects of errors in the map and other map properties, and how imperfect maps degrades the performance of different selection strategies.

We consider a decentralized sensor network of multiple nodes with limited communication capability where the cross-correlations between local estimates are unknown. To reduce the bandwidth the individual nodes determine which subset of local information is the most valuable from a global perspective. Three information selection methods (ISM) are derived. The proposed ISM require no other information than the communicated estimates. The simulation evaluation shows that by using the proposed ISM it is possible to determine which subset of local information is globally most valuable such that both reduced bandwidth and high performance are achieved.

For a given radar system on an unmanned air vehicle, this work proposes a method to find the optimal tracking rangeand the optimal beamwidth for tracking a maneuvering target.  An inappropriate optimal range or beamwidth is indicative ofthe need for a redesign of the radar system. An extended Kalman filter (EKF) is employed to estimate the state of the target using measurements of the range and bearing from the sensor to the target. The proposed method makes use of an alpha-beta filter to predict the expected tracking performanceof the EKF. Using an assumption of the maximum acceleration of the target, the optimal tracking range (or beamwidth) is determined as the one that minimizes the maximum mean squared error (MMSE) of the position estimates while satisfying a user-defined constraint on the probability of losing track of the target.The applicability of the design method is verified using Monte Carlo simulations.

This paper considers the problem of gathering information about features of interest in adversarial environments using mobile robots equipped with sensors. The problem is formulated as an informative path planning problem where the objective is to maximize the gathered information while minimizing the tracking performance of the adversarial observer. The optimization problem, that at first glance seems intractable to solve to global optimality, is shown to be equivalent to a mixed-integer semidefinite program that can be solved to global optimality using off-the-shelf optimization tools.

The unscented Kalman filter (UKF) is a very popular solution for estimation of the state in nonlinear systems. Similar to the extended Kalman filter (EKF) and contrary to the Kalman filter (KF) for linear systems, the UKF provides no guarantees that the filter updates will improve the filtered state estimate. In the past, the iterated EKF (IEKF) has been suggested as a way to online monitor the filter performance and try to improve it using optimization techniques. In this paper we do the same for the UKF, deriving six iterated UKF (IUKF) variations based on two cost functions and three optimization algorithms. The methods are evaluated and compared to IEKF versions and to two versions of the iterative posterior linearization filter (IPLF) in three benchmark simulation studies. The results show that IUKF algorithms can be used as a derivative free alternative to IEKF, and provide insights about the different design choices available in IUKF algorithms.

The number of sensors used in tracking scenariosis constantly increasing, this puts high demands on the trackingmethods to handle these data streams. Central processing (ideallyoptimal) puts high demands on the central node, is sensitive toinaccurate sensor parameters, and suffers from the single pointof failure problem. Decentralizing the tracking can improve this,but may give considerable performance loss. The newly presentedinverse covariance intersection method, proven to be consistent,even under unknown track cross correlations, is benchmarkedagainst alternatives. Different track-to-track methods, includingsmoothed association over a window, are compared. A scenariowith objects tracked in multiple cameras, not necessarily opti-mized for tracking, are used to give realism to the evaluations.

Classification of motion mode (walking, running, standing still) and device mode (hand-held, in pocket, in back-pack) is an enabler in personal navigation systems for the purpose of saving energy and design parameter settings and also for its own sake. Our main contribution is to publish one of the most extensive datasets for this problem, including inertial data from eight users, each one performing three pre-defined trajectories carrying four smartphones and seventeen inertial measurement units on the body. All kind of metadata is available such as the ground truth of all modes and position. A second contribution is the first study on a joint classifier of motion and device mode, respectively, where preliminary but promising results are presented.

Many positioning systems rely on accuratetime of arrival measurements. In this paper, we addressnot only the accuracy but also the relevance of Time ofArrival (TOA) measurement error modeling. We discusshow better knowledge of these errors can improve relativedistance estimation, and compare the impact of differentlydetailed measurement error information. These models arecompared in simulations based on models derived froman Ultra Wideband (UWB) measurement campaign. Theconclusion is that significant improvements can be madewithout providing detailed received signal information butwith a generic and relevant measurement error model.

In this work, we estimate a model of the vertical dynamics of a quadcopter and explain how this model can be used for mass estimation and diagnosis of system changes. First, a standard thrust model describing the relation between the calculated control signals of the rotors and the thrust that is commonly used in literature is estimated. The estimation results are compared to those using a refined thrust model and it turns out that the refined model gives a significant improvement. The combination of a nonlinear model and closed-loop data poses some challenges and it is shown that an instrumental variables approach can be used to obtain accurate estimates. Furthermore, we show that the refined model opens up for fault detection of the quadcopter. More specifically, this model can be used for mass estimation and also for diagnosis of other parameters that might vary between and during missions.

Acoustic frequency tracking of a harmonic signalwith continuously varying frequency is considered. The Rao-Blackwellized point mass filter (RBPMF), previously proposed bythe authors for mechanical vibration tracking, is applied to the problem. The RBPMF is compared with two periodogram-based methods, and the similarities and differences between them are explained. Both experimental and simulation results in a Doppler frequency tracking scenario are presented, and the results show that the RBPMF can have significantly less estimation error than the competing methods.

The safe fusion algorithm is benchmarked againstthree other methods in distributed target tracking scenarios. Safefusion is a fairly unknown method similarly to, e.g., covarianceintersection, that can be used to fuse potentially dependentestimates without double counting data. This makes it suitablefor distributed target tracking, where dependencies are oftenunknown or difficult to derive. The results show that safe fusionis a very competitive alternative in five evaluated scenarios, whileat the same time easy to implement and compute compared tothe other evaluated methods. Hence, safe fusion is an attractivealternative in track to track fusion systems.

We consider a target tracking problem where, in addition to the usual sensor measurements, accurate observations with uncertain timestamps are available. Such observations could, \eg, come from traces left by a target or from witnesses of an event, and have the potential in some scenarios to improve the accuracy of an estimate significantly. The Bayesian solution to the smoothing problem for one observation with uncertain timestamp is derived for a linear Gaussian state space model. The joint and marginal distributions of the states and uncertain time are derived, as well as the minimum mean squared error (MMSE) and maximum a posteriori (MAP) estimators. To attain an intuition for the problem in consideration a simple first-order example is presented and its posterior distributions and point estimators are compared and examined in some depth.

We consider personal navigation systems in devices equipped with inertial sensors and GPS, where we propose an improved Pedestrian Dead Reckoning (PDR) algorithm that learns gait parameters in time intervals when position estimates are available, for instance from GPS or an indoor positioning system (IPS). A novel filtering approach is proposed that is able to learn internal gait parameters in the PDR algorithm, such as the step length and the step detection threshold. Our approach is based on a multi-rate Kalman filter bank that estimates the gait parameters when position measurements are available, which improves PDR in time intervals when the position is not available, for instance when passing from outdoor to indoor environments where IPS is not available. The effectiveness of the new approach is illustrated on several real world experiments. 

The speed of a wheeled vehicle is usually estimatedusing wheel speed sensors (WSS) or GPS. If these signals are unavailable, other methods must be used. We propose a novelapproach exploiting the fact that vibrations from rotating axles,with fundamental frequency proportional to vehicle speed, aretransmitted via the vehicle chassis. Using an accelerometer, these vibrations can be tracked to estimate vehicle speed whileother sources of vibrations act as disturbances. A state-space model for the dynamics of the harmonics is presented andformulated such that there is a conditional linear-Gaussiansubstructure, enabling efficient Rao-Blackwellized methods. Avariant of the Rao-Blackwellized point-mass filter is derived, significantly reducing computational complexity, and reducingthe memory requirements from quadratic to linear in thenumber of grid points. It is applied to experimental data from the sensor cluster of a car and validated using therotational frequency from WSS data. The proposed methodshows improved performance and robustness in comparisonto a Rao-Blackwellized particle filter implementation and afrequency spectrum maximization method.

This paper investigates the usefulness of multi-frequency received signal strength (RSS) for indoor localization. Acollected set of data from four sites containing 7 frequencies fromdual receivers and a high accuracy reference positioning systemis presented. The collected data is also made publicly availablethrough ResearchGate. The data is analyzed with respect tospatial variations using Gaussian processes ( GP ). The resultsshow that there are more rapid signal variations across corridorsthan along them. The uniqueness of RSS fingerprints is analyzedsuggesting that sequences of measurements in smoothing, orsmoothing-like, algorithms that can handle temporary positionambiguities are likely the best choice for localization applications.

This paper presents a method for global pose estimation using inertial sensors, monocular vision, and ultra wide band (UWB) sensors. It is demonstrated that the complementary characteristics of these sensors can be exploited to provide improved global pose estimates, without requiring the introduction of any visible infrastructure, such as fiducial markers. Instead, natural landmarks are jointly estimated with the pose of the platform using a simultaneous localization and mapping framework, supported by a small number of easy-to-hide UWB beacons with known positions. The method is evaluated with data from a controlled indoor experiment with high precision ground truth. The results show the benefit of the suggested sensor combination and suggest directions for further work.

The extended Kalman filter (EKF) has been animportant tool for state estimation of nonlinear systems sinceits introduction. However, the EKF does not possess the same optimality properties as the Kalman filter, and may perform poorly. By viewing the EKF as an optimization problem it is possible to, in many cases, improve its performance and robustness. The paper derives three variations of the EKF by applying different optimisation algorithms to the EKF costfunction and relate these to the iterated EKF. The derived filters are evaluated in two simulation studies which exemplify the presented filters.

Visual animal tracking is a challenging problem generally requiring extended target models, group tracking and handling of clutter and missed detections. Furthermore, the dolphin tracking problem we consider includes basin constraints, shadows, limited field of view and rapidly changing light conditions. We describe the whole pipeline of a solution based on a ceiling-mounted fisheye camera that includes foreground segmentation and observation extraction in each image, followed by a target tracking framework. A novel contribution is a potential field model of the basin edges as a part of the motion model, that provides a robust prediction of the dolphin trajectories in phases with long segments of missed detections. The overall performance on real data is quite promising.

The Kalman filter has been the work horse in model based filtering for five decades, and basic knowledge and understanding of it is an important part of the curriculum in many Master of Science programs. It is therefore important to combine theoretical studies with practical experience to allow the students to deepen their understanding of the filter. We have developed a lab where the students implement a Kalman filter in a real-time Matlab framework, to which data are streamed from the smartphone over WiFi. The goal of the lab is to estimate the orientation of the smartphone, which can be nicely visualized graphically and also be compared to the built-in filters in the smartphone. The filter can accept any combination of sensor data from accelerometers, gyroscopes, and magnetometer, with different performance.  Different tunings and tricks in the Kalman filter are easily evaluated on-line. The smartphone app is also a stand-alone tool to visualize the sensor data graphically. So far the lab seems tohave been successful in reaching the pedagogic goals and to engage the students.

Nonlinear Kalman filter adaptations such as extended Kalman filters (EKF) or unscented Kalman filters (UKF) provide approximate solutions to state estimation problems in nonlinear models. The algorithms utilize mean values and covariance matrices to represent the probability densities in the otherwise intractable Bayesian filtering equations. As a consequence, their estimation performance can show significant dependence on the choice of state coordinates. The here considered problem of tracking maneuvering targets using coordinated turn (CT) models is one practically relevant example: The velocity in the target state can either be formulated in Cartesian or polar coordinates. We extend a previous study to a broader range of CT models that allow for changes in target speed and turn rate, and investigate UKF as well as EKF variants in terms of their performance and sensitivity to noise parameters. The results advocate for the use of polar CT models.

The Markov modulated (switching) state space is an important model paradigm in statistical signal processing. In this article, we specifically consider Markov modulated nonlinear state-space models and address the online Bayesian inference problem for such models. In particular, we propose a new Rao-Blackwellized particle filter for the inference task which is our main contribution here. A detailed description of the problem and an algorithm is presented.

Physical activity monitoring has recently become an important topic in wearable computing, motivated by e.g. healthcare applications. However, new benchmark results show that the difficulty of the complex classification problems exceeds the potential of existing classifiers. Therefore, this paper proposes the ConfAdaBoost.M1 algorithm. The proposed algorithm is a variant of the AdaBoost.M1 that incorporates well established ideas for confidence based boosting. The method is compared to the most commonly used boosting methods using benchmark datasets from the UCI machine learning repository and it is also evaluated on an activity recognition and an intensity estimation problem, including a large number of physical activities from the recently released PAMAP2 dataset. The presented results indicate that the proposed ConfAdaBoost.M1 algorithm significantly improves the classification performance on most of the evaluated datasets, especially for larger and more complex classification tasks.

The monitoring of physical activities under realistic, everyday life conditions - thus while an individual follows his regular daily routine - is usually neglected or even completely ignored. Therefore, this paper investigates the development and evaluation of robust methods for everyday life scenarios, with focus on the task of aerobic activity recognition. Two important aspects of robustness are investigated: dealing with various (unknown) other activities and subject independency. Methods to handle these issues are proposed and compared, a thorough evaluation simulates usual everyday scenarios of the usage of activity recognition applications. Moreover, a new evaluation technique is introduced (leave-one-other-activity-out) to simulate when an activity recognition system is used while performing a previously unknown activity. Through applying the proposed methods it is possible to design a robust physical activity recognition system with the desired generalization characteristic.

Optimal estimation problems for general state space models do not typically admit a closed form solution. However, modern Monte Carlo methods have paved the way to solve such complex inference problems. Particle filters (PF) are a popular class of such Monte Carlo based Bayesian algorithms, which solve the estimation problems numerically in a sequential manner.

PF in general, assume a prior knowledge of the (process and observation) noise distributions involving the state space model, whereas the properties of the noise processes are often unknown for many practical problems. Furthermore, the unknown noise distributions may be state dependent or even non-stationary, which prevent the offline noise calibrations.

In this article, the unknown noises are assumed to be slowly varying in time. The article then proposes a hierarchical noise adaptive PF where a two tier PF is run, the top tier PF estimates the latent states from the streaming observations and the bottom tier PF estimates the noise statistics conditioned on the top tier PF output together with the observations. The estimates are statistically fused together for the inference purpose. In essence, it is an implementation of approximate Rao-Blackwellized PF, where the later is achieved through local Monte Carlo integration. This approach is very generic for different noise classes and importantly, it enhances the level of parallelism in PF implementations.

This paper addresses two fundamental requirements of full body motion monitoring: (a) the ability to sense the input of the user and (b) the means to interpret the captured input. Appropriate technology in both areas is required for an interactive virtual reality system to provide feedback in a useful and natural way. This paper combines technologies for both areas: It develops a sensor fusion approach for capturing user input based on miniature on-body inertial and magnetic motion sensors. Furthermore, it presents work in progress to automatically generate models for motion patterns from the captured input. The technology is then used and evaluated in the context of a personalized virtual rehabilitation trainer application.

Egomotion tracking is since the last decades an often addressed problem and hybrid approaches evidentially have potential to provide accurate, efficient and robust results. Simultaneous localisation and mapping (SLAM) - in contrast to a model-based approach - is used to enable tracking in unknown environments. However, it also suffers from high computational complexity. Moreover, in many applications, the map itself is not needed and the target environment is partiall known, e.g. in a few 3D anchor points. In this paper, rather than using SLAM, optical flow measurements are introduced into a model-based system. With these measurements, a modified visual-inertial tracking method is derived, which in Monte Carlo simulations reduces the need for 3D points and thus allows tracking during extended gaps of 3D point registrations.

Visual simultaneous localisation and mapping (SLAM) is since the last decades an often addressed problem. Online mapping enables tracking in unknown environments. However, it also suffers from high computational complexity and potential drift. Moreover, in augmented reality applications the map itself is often not needed and the target environment is partially known, e.g. in a few 3D anchor or marker points. In this paper, rather than using SLAM, measurements based on optical flow are introduced. With these measurements, a modified visual-inertial tracking method is derived, which in Monte Carlo simulations reduces the need for 3D points and allows tracking for extended periods of time without any 3D point registrations.

For performance gain and efficiency it is important to utilize model structure in particle filtering. Applying Bayes- rule, present linear Gaussian substructure can be efficiently handled by a bank of Kalman filters. This is the standard formulation of the Rao-Blackwellized particle filter (RBPF), by some authors denoted the marginalized particle filter (MPF), and usually presented in a way that makes it hard to implement in an object oriented fashion. This paper discusses how the solution can be rewritten in order to increase the understanding as well as simplify the implementation and reuse of standard filtering components, such as Kalman filter banks and particle filters. Calculations show that the new algorithm is equivalent to the classical formulation, and the new algorithm is exemplified in a target tracking simulation study.

In this paper, several recursive Bayesian filtering methods for target tracking are discussed. Performance for target tracking problems is usually measured using the second-order moment. For nonlinear or non-Gaussian applications, this measure is not always sufficient. The Kullback divergence is proposed as an alternative to mean square error analysis, and it is extensively used to compare estimated posterior distributions for various applications. The important issue of efficient software development, for nonlinear and non-Gaussian estimation, is also addressed. A new framework in C++ is detailed. Utilizing modern design techniques an object oriented filtering and simulation framework is provided to allow for easy and efficient comparisons of different estimators. The software environment is extensively used in several applications and examples.

The performance of nonlinear fault detection schemes is hard to decide objectively, so Monte Carlo simulations are often used to get a subjective measure and relative performance for comparing different algorithms. There is a strong need for a constructive way of computing an analytical performance bound, similar to the Cramér-Rao lower bound for estimation. This paper provides such a result for linear non-Gaussian systems. It is first shown how a batch of data from a linear state-space model with additive faults and non-Gaussian noise can be transformed to a residual described by a general linear non-Gaussian model. This also involves a parametric description of incipient faults. The generalized likelihood ratio test is then used as the asymptotic performance bound. The test statistic itself may be impossible to compute without resorting to numerical algorithms, but the detection performance scales analytically with a constant that depends only on the distribution of the noise. It is described how to compute this constant, and a simulation study illustrates the results.

Recursive triangulation, using a bearings-only sensor, is investigated for a fly-by scenario. In a simulation study, several estimators are compared, fundamental estimation limits are calculated for different measurement noise assumptions. The quality of the estimated state distributions is evaluated.

The Kalman filter is known to be the optimal linear filter for linear non-Gaussian systems. However, nonlinear filters such as Kalman filter banks and more recent numerical methods such as the particle filter are sometimes superior in performance. Here a procedure to a priori decide how much can be gained using nonlinear filters, without having to resort to Monte Carlo simulations, is outlined. The procedure is derived in terms of the posterior Cramér-Rao lower bound. Results are shown for a class of standard distributions and models in practice.

I många fall är det viktigt att kunna få ut så mycket och så bra information som möjligt ur tillgängliga mätningar. Att utvinna information om till exempel position och hastighet hos ett flygplan kallas för filtrering. I det här fallet är positionen och hastigheten exempel på tillstånd hos flygplanet, som i sin tur är ett system. Ett typiskt exempel på problem av den här typen är olika övervakningssystem, men samma behov blir allt vanligare även i vanliga konsumentprodukter som mobiltelefoner (som talar om var telefonen är), navigationshjälpmedel i bilar och för att placera upplevelseförhöjande grafik i filmer och TV -program. Ett standardverktyg som används för att extrahera den information som behövs är olineär filtrering. Speciellt vanliga är metoderna i positionerings-, navigations- och målföljningstillämpningar. Den här avhandlingen går in på djupet på olika frågeställningar som har med olineär filtrering att göra:

* Hur utvärderar man hur bra ett filter eller en detektor fungerar?

* Vad skiljer olika metoder åt och vad betyder det för deras egenskaper?

* Hur programmerar man de datorer som används för att utvinna informationen?

Det mått som oftast används för att tala om hur effektivt ett filter fungerar är RMSE (root mean square error), som i princip är ett mått på hur långt ifrån det korrekta tillståndet man i medel kan förvänta sig att den skattning man får är. En fördel med att använda RMSE som mått är att det begränsas av Cramér-Raos undre gräns (CRLB). Avhandlingen presenterar metoder för att bestämma vilken betydelse olika brusfördelningar har för CRLB. Brus är de störningar och fel som alltid förekommer när man mäter eller försöker beskriva ett beteende, och en brusfördelning är en statistisk beskrivning av hur bruset beter sig. Studien av CRLB leder fram till en analys av intrinsic accuracy (IA), den inneboende noggrannheten i brus. För lineära system får man rättframma resultat som kan användas för att bestämma om de mål som satts upp kan uppnås eller inte. Samma metod kan också användas för att indikera om olineära metoder som partikelfiltret kan förväntas ge bättre resultat än lineära metoder som kalmanfiltret. Motsvarande metoder som är baserade på IA kan även användas för att utvärdera detektionsalgoritmer. Sådana algoritmer används för att upptäcka fel eller förändringar i ett system.

När man använder sig av RMSE för att utvärdera filtreringsalgoritmer fångar man upp en aspekt av filtreringsresultatet, men samtidigt finns många andra egenskaper som kan vara intressanta. Simuleringar i avhandlingen visar att även om två olika filtreringsmetoder ger samma prestanda med avseende på RMSE så kan de tillståndsfördelningar de

producerar skilja sig väldigt mycket åt beroende på vilket brus det studerade systemet utsätts för. Dessa skillnader kan vara betydelsefulla i vissa fall. Som ett alternativ till RMSE används därför här kullbackdivergensen som tydligt visar på bristerna med att bara förlita sig på RMSE-analyser. Kullbackdivergensen är ett statistiskt mått på hur mycket två fördelningar skiljer sig åt.

Två filtreringsalgoritmer har analyserats mer i detalj: det rao-blackwelliserade partikelfiltret (RBPF) och den metod som kallas unscented Kalman filter (UKF). Analysen av RBPF leder fram till ett nytt sätt att presentera algoritmen som gör den lättare att använda i ett datorprogram. Dessutom kan den nya presentationen ge bättre förståelse för hur algoritmen fungerar. I undersökningen av UKF ligger fokus på den underliggande så kallade unscented transformation som används för att beskriva vad som händer med en brusfördelning när man transformerar den, till exempel genom en mätning. Resultatet består av ett antal simuleringsstudier som visar på de olika metodernas beteenden. Ett annat resultat är en jämförelse mellan UT och Gauss approximationsformel av första och andra ordningen.

Den här avhandlingen beskriver även en parallell implementation av ett partikelfilter samt ett objektorienterat ramverk för filtrering i programmeringsspråket C ++. Partikelfiltret har implementerats på ett grafikkort. Ett grafikkort är ett exempel på billig hårdvara som sitter i de flesta moderna datorer och mest används för datorspel. Det används därför sällan till sin fulla potential. Ett parallellt partikelfilter, det vill säga ett program som kör flera delar av partikelfiltret samtidigt, öppnar upp för nya tillämpningar där snabbhet och bra prestanda är viktigt. Det objektorienterade ramverket för filtrering uppnår den flexibilitet och prestanda som behövs för storskaliga Monte-Carlo-simuleringar med hjälp av modern mjukvarudesign. Ramverket kan också göra det enklare att gå från en prototyp av ett signalbehandlingssystem till en slutgiltig produkt.

This report aims to describe the latest research and method developmentof image-based multi sensor fusion navigation and summarizes open aerialdatasets which can support the latest research related to this project. Itsupports the initial setting of the direction of the algorithm development inthe early stage of the project.The Multi Sensor Image-based Navigation project aims to study and developthe methods focusing on image-based multisensor navigation in orderto acquire a precise localization of the aircraft. GNSS-based localizationand navigation systems are sensitive to disturbances and jamming, hencethe capability to provide reliable position accuracy without GNSS is a keyelement to develop the navigation systems.The output of this project can be utilized in a wide range of applications,such as aircraft operation in GNSS denied environments or urban air mobilitycontext.

For performance gain and efficiency it is important to utilize model structure in particle filtering. Applying Bayes- rule, present linear Gaussian substructure can be efficiently handled by a bank of Kalman filters. This is the standard formulation of the Rao-Blackwellized particle filter (RBPF), by some authors denoted the marginalized particle filter (MPF), and usually presented in a way that makes it hard to implement in an object oriented fashion. This paper discusses how the solution can be rewritten in order to increase the understanding as well as simplify the implementation and reuse of standard filtering components, such as Kalman filter banks and particle filters. Calculations show that the new algorithm is equivalent to the classical formulation, and the new algorithm is exemplified in a target tracking simulation study.

A class of nonlinear transformation-based filters (NLTF) for state estimation is proposed. The nonlinear transformations that can be used include first (TT1) and second (TT2) order Taylor expansions, the unscented transformation (UT), and the Monte Carlo transformation (MCT) approximation. The unscented Kalman filter (UKF) is by construction a special case, but also nonstandard implementations of the Kalman filter (KF) and the extended Kalman filter (EKF) are included, where there are no explicit Riccati equations. The theoretical properties of these mappings are important for the performance of the NLTF. TT 2 does by definition take care of the bias and covariance of the second order term that is neglected in the TT 1 based EKF. The UT computes this bias term accurately, but the covariance is correct only for scalar state vectors. This result is demonstrated with a simple example and a general theorem, which explicitly shows the difference between TT 1, TT 2, UT, and MCT.

Performance for many filtering problems is usually measured using the second order moment. For non-Gaussian application this measure is not always sufficient. In the paper the Kullback divergence is extensively used to compare distributions. Several estimation techniques are compared, and methods such as the particle filter are shown to give superior performance over some classical second-order estimators.

The performance of nonlinear fault detection schemes is hard to decide objectively, so Monte Carlo simulations are often used to get a subjective measure and relative performance for comparing different algorithms. There is a strong need for a constructive way of computing an analytical performance bound, similar to the Cramér-Rao lower bound for estimation. This paper provides such a result for linear non-Gaussian systems. It is first shown how a batch of data from a linear state-space model with additive faults and non-Gaussian noise can be transformed to a residual described by a general linear non-Gaussian model. This also involves a parametric description of incipient faults. The generalized likelihood ratio test is then used as the asymptotic performance bound. The test statistic itself may be impossible to compute without resorting to numerical algorithms, but the detection performance scales analytically with a constant that depends only on the distribution of the noise. It is described how to compute this constant, and a simulation study illustrates the results.

Sophisticated fault detection (FD) algorithms often include nonlinear mappings of observed data to fault decisions, and simulation studies are used to support the methods. Objective statistically supported performance analysis of FDalgorithms is only possible for some special cases, including linear Gaussian models. The goal here is to derive general statistical performance bounds for any FD algorithm, given a nonlinear non-Gaussian model of the system. Recent advances in numerical algorithms for nonlinear filtering indicate that such bounds in many practical cases are attainable. This paper focuses on linear non-Gaussian models. A couple of different fault detection setups based on parity space and Kalman filter approaches are considered, where the fault enters a computable residual linearly. For this class of systems, fault detection can be based on the best linear unbiased estimate (BLUE) of the fault vector. Alternatively, a nonlinear filter can potentially compute the maximum likelihood (ML) state estimate, whose performance is bounded by the Cramér-Rao lower bound (CRLB). The contribution in this paper is general expressions for the CRLB for this class of systems, interpreted in terms offault detectability. The analysis is exemplified for a case with measurements affected by outliers.

The Kalman filter is known to be the optimal linear filter for linear non-Gaussian systems. However, nonlinear filters such as Kalman filter banks and more recent numerical methods such as the particle filter are sometimes superior in performance. Here a procedure to a priori decide how much can be gained using nonlinear filters, without having to resort to Monte Carlo simulations, is outlined. The procedure is derived in terms of the posterior Cramer-Rao lower bound. Results are shown for a class of standard distributions and models in practice.

To develop and maintain a modern combat aircraft it is important to have simple, yet accurate, threat models to support early stages of functional development. Therefore this thesis develops and evaluates a model of an active radio frequency (RF) seeker for a missile with data-link capability. The highly parametrized MATLAB-model consists of a pulse level radar model, a tracker using either interacting multiple models (IMM) or particle filters, and a guidance law.

Monte Carlo simulations with the missile model indicate that, under the given conditions, the missile performs well (hit rate>99%) with both filter types, and the model is relatively insensitive to lost data-link transmissions. It is therefore under normal conditions not worthwhile to use the more computer intense particle filter today, however when the data-link degrades the particle filter performs considerably better than the IMM filter. Analysis also indicate that the measurements generated by the radar model are neither independent, white nor Gaussian. This contradicts the assumptions made in this, and many other radar applications. However, the performance of the model suggests that the assumptions are acceptable approximations of actual conditions, but further studies within this are recommended to verify this.