This master thesis investigates the performance of a car navigation system using lateral accelerometers, yaw rate and bearings relative three known radio beacons. Accelerometer, gyroscope and position data has been collected by an IMU combined with a GPS receiver, where the IMU was installed in the approximate motion center of a car. The bearing measurements are simulated using GPS data and the measurement noise model is derived from an experiment where the direction of arrival to one transmitter was estimated by an antenna array and the signal processing algorithm MUSIC. The measurements are fused in a multi-rate extended Kalman filter which assumes that all measurement noise is Gaussian distributed. This is not the case for the bearing measurement noise which contains outliers and therefore is modelled as a Gaussian uniform noise mixture. Different methods to deal with this have been investigated where the main focus is on the principle to use the Kalman filter’s innovation for each bearing measurement as an indication of its quality and discarding measurements with a quality above a certain threshold.

When the primary measurement sensor is passive in nature--by which we mean that it does not directly measure range or range rate--there are well-documented challenges for target state estimation. Most estimation schemes rely on variations of the Extended Kalman Filter (EKF), which, in certain situations, suffer from divergence and/or covariance collapse. For this and other reasons, we believe that the Kalman filter is fundamentally ill-suited to the problems that are inherent in target state estimation using passive sensors. As an alternative, we propose a bounded-error (or set-membership) approach to the target state estimation problem. Such estimators are nearly as old as the Kalman filter, but have enjoyed much less attention. In this study we develop a practical estimator that bounds the target states, and apply it to the two-dimensional case of a submarine tracking a surface vessel, which is commonly referred to as Target Motion Analysis (TMA). The estimator is robust in the sense that the true target state does not escape the determined bounds; and the estimator is not unduly pessimistic in the sense that the bounds are not wider than the situation dictates. The estimator is--as is the problem itself--nonlinear and geometric in nature. In part, the simplicity of the estimator is maintained by using redundant states to parameterize the target's velocity. These redundant states also simplify the incorporation of other measurements that are frequently available to the system. The estimator's performance is assessed in a series of simulations and the results are analyzed. Extensions of the algorithm are considered.

Particle filters are a class of sequential Monte-Carlo methods which are used commonly when estimating various unknowns of the time-varying signals presented in real time, especially when dealing with nonlinearity and non-Gaussianity in BOT applications. This thesis work is designed to perform one such estimate involving tracking a person using the road information available from an IR surveillance video. In this thesis, a parallel custom hardware is implemented in Altera cyclone IV E FPGA device utilizing SIRF type of particle filter. This implementation has accounted how the algorithmic aspects of this sampling based filter relate to possibilities and constraints in a hardware implementation. Using 100MHz clock frequency, the synthesised hardware design can process almost 50 Mparticles/s. Thus, this implementation has resulted in tracking the target, which is defined by a 5-dimensional state variable, using the noisy measurements available from the sensor.

Angles-only navigation is simple, robust, and well proven in many applications. However, it is sometimes ill-conditioned for orbital rendezvous and proximity operations because, without a direct range measurement, the distance to approaching satellites must be estimated by firing thrusters and observing the change in the target's bearing. Nevertheless, the simplicity of angles-only navigation gives it great appeal. The viability of this technique for relative navigation is examined by building a high-fidelity simulation and evaluating the sensitivity of the system to sensor errors. The relative performances of square-root filtering methods, including Potter, Carlson, and UD factorization filters, are compared to the conventional and Joseph formulations. Filter performance is evaluated during closed-loop "station keeping" operations in simulation.

The basic problem with angle-only or bearings-only tracking is to estimate the trajectory of a target (i.e., position and velocity) by using noise corrupted sensor angle data. In this thesis, the tracking platform is an Aerial Vehicle and the target is simulated as another Aerial Vehicle. Therefore, the problem can be defined as a single-sensor bearings only tracking. The state consists of relative position and velocity between the target and the platform. In the case where both the target and the platform travel at constant velocity, the angle measurements do not provide any information about the range between the target and the platform. The platform has to maneuver to be able to estimate the range of the target. Two problems are investigated and tested on simulated data. The first problem is tracking non-maneuvering targets. Extended Kalman Filter (EKF), Range Parameterized Kalman Filter and particle filter are implemented in order to track non-maneuvering targets. As the second problem, tracking maneuvering targets are investigated. An interacting multiple model (IMM) filter and different particle filter solutions are designed for this purpose. Kalman filter covariance matrix initialization and regularization step of the regularized particle filter are discussed in detail.

In this study, accurate target tracking for bearings-only tracking problem is investigated. A new tracking filter for this nonlinear problem is designed where both range parameterization and Rao-Blackwellized (marginalized) particle filtering techniques are used in a Gaussian mixture formulation to track both constant velocity and maneuvering targets. The idea of using target turn rate in the state equation in such a way that marginalization is possible is elaborated. Addition to nonlinear nature, unobservability is a major problem of bearings-only tracking. Observer trajectory generation to increase the observability of the bearings-only tracking problem is studied. Novel formulation of observability measures based on mutual information between the state and the measurement sequences are derived for the problem. These measures are used as objective functions to improve observability. Based on the results obtained better understanding of the required observer trajectory for accurate bearings-only target tracking is developed.

This thesis contributes new algorithms and implementations for particle filter-based target tracking. From an algorithmic perspective, modifications that improve a batch-based acoustic direction-of-arrival (DOA), multi-target, particle filter tracker are presented. The main improvements are reduced execution time and increased robustness to target maneuvers. The key feature of the batch-based tracker is an image template-matching approach that handles data association and clutter in measurements. The particle filter tracker is compared to an extended Kalman filter~(EKF) and a Laplacian filter and is shown to perform better for maneuvering targets. Using an approach similar to the acoustic tracker, a radar range-only tracker is also developed. This includes developing the state update and observation models, and proving observability for a batch of range measurements. From an implementation perspective, this thesis provides new low-power and real-time implementations for particle filters. First, to achieve a very low-power implementation, two mixed-mode implementation strategies that use analog and digital components are developed. The mixed-mode implementations use analog, multiple-input translinear element (MITE) networks to realize nonlinear functions. The power dissipated in the mixed-mode implementation of a particle filter-based, bearings-only tracker is compared to a digital implementation that uses the CORDIC algorithm to realize the nonlinear functions. The mixed-mode method that uses predominantly analog components is shown to provide a factor of twenty improvement in power savings compared to a digital implementation. Next, real-time implementation strategies for the batch-based acoustic DOA tracker are developed. The characteristics of the digital implementation of the tracker are quantified using digital signal processor (DSP) and field-programmable gate array (FPGA) implementations. The FPGA implementation uses a soft-core or hard-core processor to implement the Newton search in the particle proposal stage. A MITE implementation of the nonlinear DOA update function in the tracker is also presented.