<p>In this thesis Sequential Monte Carlo filters, or particle filters, applied to aircraft navigation is considered. This report consists of two parts. The first part is an illustration of the theory behind this thesis project. The second and most important part evaluates the algorithm by using real flight data.</p><p>Navigation is about determining one's own position, orientation and velocity. The sensor fusion studied combines data from an inertial navigation system (INS) with measurements of the ground elevation below in order to form a terrain aided positioning system (TAP). The ground elevation measurements are compared with a height database. The height database is highly non-linear, which is why a marginalized particle filter (MPF) is used for the sensor fusion.</p><p>Tests have shown that the MPF delivers a stable and good estimate of the position, as long as it receives good data. A comparison with Saab's NINS algorithm showed that the two algorithms perform quite similar, although NINS performs better when data is lacking.</p>

<p>In this work a particle filter (PF) that uses a one-dimensional dynamic model to estimate the position of vehicles traveling on a road is derived. The dynamic model used in the PF is a second order linear-Gaussian model. To be able to track targets traveling both on and off road two different multiple model filters are proposed. One of the filters is a modified version of the Efficient Interacting Multiple Model (E-IMM) and the other is a version of the Multiple Likelihood Models (MLM). Both of the filters uses two modes, one for the on road motion and one for the off road motion. The E-IMM filter and the MLM filter are compared to the standard PF to be able to see the performance gain in using multiple models. This result indicates that the multiple model filters have better performance, at least when the true mode switching probabilities are used.</p> / <p>Den här arbetet presenterar ett partikelfilter som använder sig av en endimensionell dynamisk modell för att skatta positionen på fordon som befinner sig på någon väg. Den dynamiska modellen som används i partikelfiltret är en andra ordningens linjär-gaussisk modell. För att kunna spåra fordon som befinner sig både på och utanför vägen så föreslås två olika multipla filter. Ena filtret är en modifierad</p><p>variant av Efficient Interacting Multiple Model (E-IMM) och den andra är en version a Multiple Likelihood Models (MLM). Båda filtren använder sig av två moder, en för rörelse på vägen och en för rörelse utanför vägen. E-IMM filtret och MLM filtret jämförs med ett standard partikelfilter för att kunna se förbättringen vid använding av multipla modeller. Resultatet visar att båda multipla modell filtren ger bättre resultat, i varje fall då rätt sannolikheter för modbyte används.</p>

With advances in micro-electronic complexity and fabrication, sophisticated algorithms for source localisation and tracking can now be deployed in cost sensitive appliances for both consumer and commercial markets. As a result, such algorithms are becoming ubiquitous elements of contemporary communication, robotics and surveillance systems. Two of the main requirements of acoustic localisation and tracking algorithms are robustness to acoustic disturbances (to maximise localisation accuracy), and low computational complexity (to minimise power-dissipation and cost of hardware components). The research presented in this thesis covers both advances in robustness and in computational complexity for acoustic source localisation and tracking algorithms. This thesis also presents advances in modelling of sound propagation in indoor environments; a key to the development and evaluation of acoustic localisation and tracking algorithms. As an advance in the field of tracking, this thesis also presents a new method for tracking human speakers in which the problem of the discontinuous nature of human speech is addressed using a new state-space filter based algorithm which incorporates a voice activity detector. The algorithm is shown to achieve superior tracking performance compared to traditional approaches. Furthermore, the algorithm is implemented in a real-time system using a method which yields a low computational complexity. Additionally, a new method is presented for optimising the parameters for the dynamics model used in a state-space filter. The method features an evolution strategy optimisation algorithm to identify the optimum dynamics’ model parameters. Results show that the algorithm is capable of real-time online identification of optimum parameters for different types of dynamics models without access to ground-truth data. Finally, two new localisation algorithms are developed and compared to older well established methods. In this context an analytic analysis of noise and room reverberation is conducted, considering its influence on the performance of localisation algorithms. The algorithms are implemented in a real-time system and are evaluated with respect to robustness and computational complexity. Results show that the new algorithms outperform their older counterparts, both with regards to computational complexity, and robustness to reverberation and background noise. The field of acoustic modelling is advanced in a new method for predicting the energy decay in impulse responses simulated using the image source method. The new method is applied to the problem of designing synthetic rooms with a defined reverberation time, and is compared to several well established methods for reverberation time prediction. This comparison reveals that the new method is the most accurate.

The GPS tracking in sprint orienteering is often a poor supplement to the viewer experience during events taking place in urban areas because of multipath effects. Since the GPS tracking of runners is an important means to making the sport more spectator friendly, it is of interest to make it more accurate. In this thesis project, the information provided by the map of a competition is fused with the GPS tracker position measurements and punch time data in a particle filter to create estimates of the runner trajectories. The map is used to create constraints and to predict motion of runners, as well as to create a model of the GPS reliability depending on map position. A simple observation model is implemented, using the map to decide if a GPS measurement is reliable or not depending on the distance to the closest building. A rather complex motion model is developed to predict the runner motion within the constraints given by the map. The results show that given certain conditions the improvements are vast compared to the traditional GPS tracking. The estimates are bound to possible routes, and they are often very good given that alternative route choices are easily separable. It is however principally difficult to generally improve the tracking using this method. Better measurements or observation models are needed in order to receive a fully satisfying tracking.

Mobile systems, such as ground robots and electric vehicles, inherently operate in stochastic environments where load demands are largely unknown. Onboard energy storage, most commonly an electrochemical battery system, can significantly constrain operation. As such, mission planning and control of mobile systems can benefit from a priori knowledge about battery dynamics and constraints, especially the rate-capacity and recovery effects. To help overcome overly conservative predictions common with most existing battery remaining run-time algorithms, a prediction scheme was proposed. For characterization of a priori unknown power loads, an unsupervised Gaussian mixture routine identifies/clusters the measured power loads, and a jump-Markov chain characterizes the load transients. With the jump-Markov load forecasts, a model-based particle filter scheme predicts battery remaining run-time. Monte Carlo simulation studies demonstrate the marked improvement of the proposed technique. It was found that the increase in computational complexity from using a particle filter was justified for power load transient jumps greater than 13.4% of total system power. A multivariable reliability method was developed to assess the feasibility of a planned mission. The probability of mission completion is computed as the reliability integral of mission time exceeding the battery run-time. Because these random variables are inherently dependent, a bivariate characterization was necessary and a method is presented for online estimation of the process correlation via Bayesian updating. Finally, to abate transient shutdown of mobile systems, a model predictive control scheme is proposed that enforces battery terminal voltage constraints under stochastic loading conditions. A Monte Carlo simulation study of a small ground vehicle indicated significant improvement in both time and distance traveled as a result. For evaluation of the proposed methodologies, a laboratory terrain environment was designed and constructed for repeated mobile system discharge studies. The test environment consists of three distinct terrains. For each discharge study, a small unmanned ground vehicle traversed the stochastic terrain environment until battery exhaustion. Results from field tests with a Packbot ground vehicle in generic desert terrain were also used. Evaluation of the proposed prediction algorithms using the experimental studies, via relative accuracy and [alpha]-[lambda] prognostic metrics, indicated significant gains over existing methods. / text

Analysis of circular data becomes more and more popular in many fields of studies. In this report, I present two statistical analysis of circular data using von Mises distributions. Firstly, the maximization-expectation algorithm is reviewed and used to classify and estimate circular data from the mixture of von Mises distributions. Secondly, Forward Filtering Backward Smoothing method via particle filtering is reviewed and implemented when circular data appears in the dynamic state-space models. / text

The standard ensemble filtering schemes such as Ensemble Kalman Filter (EnKF) and Sequential Monte Carlo (SMC) do not properly represent states of low priori probability when the number of samples is too small and the dynamical system is high dimensional system with highly non-Gaussian statistics. For example, when the standard ensemble methods are applied to two well-known simple, but highly nonlinear systems such as a one-dimensional stochastic diffusion process in a double-well potential and the well-known three-dimensional chaotic dynamical system of Lorenz, they produce erroneous results to track transitions of the systems from one state to the other.In this dissertation, a set of new parametric resampling methods are introduced to overcome this problem. The new filtering methods are motivated by a general H-theorem for the relative entropy of Markov stochastic processes. The entropy-based filters first approximate a prior distribution of a given system by a mixture of Gaussians and the Gaussian components represent different regions of the system. Then the parameters in each Gaussian, i.e., weight, mean and covariance are determined sequentially as new measurements are available. These alternative filters yield a natural generalization of the EnKF method to systems with highly non-Gaussian statistics when the mixture model consists of one single Gaussian and measurements are taken on full states.In addition, the new filtering methods give the quantities of the relative entropy and log-likelihood as by-products with no extra cost. We examine the potential usage and qualitative behaviors of the relative entropy and log-likelihood for the new filters. Those results of EnKF and SMC are also included. We present results of the new methods on the applications to the above two ordinary differential equations and one partial differential equation with comparisons to the standard filters, EnKF and SMC. These results show that the entropy-based filters correctly track the transitions between likely states in both highly nonlinear systems even with small sample size N=100.

Scania CV AB is a large manufacturer of heavy duty trucks that, with an increasingly stricter emission legislation, have a rising demand for an effective On Board Diagnosis (OBD) system. One idea for improving the OBD system is to employ a model for the construction of an observer based diagnosis system. The proposal in this report is, because of a nonlinear model, to use a nonlinear filtering method for improving the needed state estimates. Two nonlinear filters are tested, the Particle Filter (PF) and the Extended Kalman Filter (EKF). The primary objective is to evaluate the use of the PF for Fault Detection and Isolation (FDI), and to compare the result against the use of the EKF. With the information provided by the PF and the EKF, two residual based diagnosis systems and two likelihood based diagnosis systems are created. The results with the PF and the EKF are evaluated for both types of systems using real measurement data. It is shown that the four systems give approximately equal results for FDI with the exception that using the PF is more computational demanding than using the EKF. There are however some indications that the PF, due to the nonlinearities, could offer more if enough CPU time is available.

In this thesis Sequential Monte Carlo filters, or particle filters, applied to aircraft navigation is considered. This report consists of two parts. The first part is an illustration of the theory behind this thesis project. The second and most important part evaluates the algorithm by using real flight data. Navigation is about determining one's own position, orientation and velocity. The sensor fusion studied combines data from an inertial navigation system (INS) with measurements of the ground elevation below in order to form a terrain aided positioning system (TAP). The ground elevation measurements are compared with a height database. The height database is highly non-linear, which is why a marginalized particle filter (MPF) is used for the sensor fusion. Tests have shown that the MPF delivers a stable and good estimate of the position, as long as it receives good data. A comparison with Saab's NINS algorithm showed that the two algorithms perform quite similar, although NINS performs better when data is lacking.

In this work a particle filter (PF) that uses a one-dimensional dynamic model to estimate the position of vehicles traveling on a road is derived. The dynamic model used in the PF is a second order linear-Gaussian model. To be able to track targets traveling both on and off road two different multiple model filters are proposed. One of the filters is a modified version of the Efficient Interacting Multiple Model (E-IMM) and the other is a version of the Multiple Likelihood Models (MLM). Both of the filters uses two modes, one for the on road motion and one for the off road motion. The E-IMM filter and the MLM filter are compared to the standard PF to be able to see the performance gain in using multiple models. This result indicates that the multiple model filters have better performance, at least when the true mode switching probabilities are used. / Den här arbetet presenterar ett partikelfilter som använder sig av en endimensionell dynamisk modell för att skatta positionen på fordon som befinner sig på någon väg. Den dynamiska modellen som används i partikelfiltret är en andra ordningens linjär-gaussisk modell. För att kunna spåra fordon som befinner sig både på och utanför vägen så föreslås två olika multipla filter. Ena filtret är en modifierad variant av Efficient Interacting Multiple Model (E-IMM) och den andra är en version a Multiple Likelihood Models (MLM). Båda filtren använder sig av två moder, en för rörelse på vägen och en för rörelse utanför vägen. E-IMM filtret och MLM filtret jämförs med ett standard partikelfilter för att kunna se förbättringen vid använding av multipla modeller. Resultatet visar att båda multipla modell filtren ger bättre resultat, i varje fall då rätt sannolikheter för modbyte används.