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This thesis provides a novel approach to the problem of state estimation for discrete-time nonlinear systems in the presence of large model uncertainties. Though classical nonlinear Kalman filters such as the extended Kalman filter (EKF) can handle uncertainties by increasing the value of noise covariances, this is only applicable to systems with small uncertainties. To this end, a discretetime robust extended Kalman filter (REKF) is formulated and applied to examples from the fields of aerospace engineering and signal processing with an emphasis on attitude estimation for small unmanned aerial vehicles (UAVs) and image processing under the influence of atmospheric turbulence. The robust filter is an approximate set-valued state estimator where the Riccati and filter equations are obtained as an approximate solution to a reverse-time optimal control problem defining the set-valued state estimator. The advantages of the REKF over the classical EKF are investigated for examples from the fields aerospace engineering and signal processing where large model uncertainties are introduced. In the case of small UAVs, an alternative attitude estimation algorithm based on the REKF is proposed in the event of gyroscopic failure and the inability of the vehicle to carry redundant sensors due to limited payload capabilities. In the case of image reconstruction under atmospheric turbulence, a robust pixel-wandering (random shifts) scheme is proposed to aid the process of image reconstruction. Also, problems pertaining to platform vibration analysis for aerospace vehicles and a frequency demodulation process in the presence of channel-induced uncertainties is also discussed.

<p>Sensor fusion deals with the merging of several signals into one, extracting a better and more reliable result. Traditionally the Kalmanfilter is used for this purpose and the aircraft navigation has benefited tremendously from its use. This thesis considers the merge of two navigation systems, the GPS positioning system and the Saab developed Synthetic Attitude and Heading Reference System (SAHRS). The purpose is to find a model for such a fusion and to investigate whether the fusion will improve the overall navigation performance. The non-linear nature of the navigation equations will lead to the use of the extended Kalman filter and the model is evaluated against both simulated and real data. The results show that this strategy indeed works but problems will arise when the GPS signal falls away.</p>

Sensor fusion deals with the merging of several signals into one, extracting a better and more reliable result. Traditionally the Kalmanfilter is used for this purpose and the aircraft navigation has benefited tremendously from its use. This thesis considers the merge of two navigation systems, the GPS positioning system and the Saab developed Synthetic Attitude and Heading Reference System (SAHRS). The purpose is to find a model for such a fusion and to investigate whether the fusion will improve the overall navigation performance. The non-linear nature of the navigation equations will lead to the use of the extended Kalman filter and the model is evaluated against both simulated and real data. The results show that this strategy indeed works but problems will arise when the GPS signal falls away.

Design of nonlinear observers has received considerable attention since the early development of methods for linear state estimation. The most popular approach is the extended Kalman filter (EKF), that goes through significant degradation in the presence of nonlinearities, particularly if unmodeled dynamics are coupled to the process and the measurement. For uncertain nonlinear systems, adaptive observers have been introduced to estimate the unknown state variables where no priori information about the unknown parameters is available. While establishing global results, these approaches are applicable only to systems transformable to output feedback form. Over the recent years, neural network (NN) based identification and estimation schemes have been proposed that relax the assumptions on the system at the price of sacrificing on the global nature of the results. However, most of the NN based adaptive observer approaches in the literature require knowledge of the full dimension of the system, therefore may not be suitable for systems with unmodeled dynamics. We first propose a novel approach to nonlinear state estimation from the perspective of augmenting a linear time invariant observer with an adaptive element. The class of nonlinear systems treated here are finite but of otherwise unknown dimension. The objective is to improve the performance of the linear observer when applied to a nonlinear system. The approach relies on the ability of the NNs to approximate the unknown dynamics from finite time histories of available measurements. Next we investigate nonlinear state estimation from the perspective of adaptively augmenting an existing time varying observer, such as an EKF. EKFs find their applications mostly in target tracking problems. The proposed approaches are robust to unmodeled dynamics, including unmodeled disturbances. Lastly, we consider the problem of adaptive estimation in the presence of feedback control for a class of uncertain nonlinear systems with unmodeled dynamics and disturbances coupled to the process. The states from the adaptive EKF are used as inputs to the control law, which in target tracking usually takes the form of a guidance law. The applications of this approach lie in the areas of missile-target tracking, formation flight control and obstacle avoidance.

Vehicle motion and tire forces have been estimated using extended Kalman filters for many years. The use of extended Kalman filters is primarily motivated by the simultaneous presence of nonlinear dynamics and sensor noise. Two versions of extended Kalman filters are employed in this thesis: one using a deterministic tire-force model and the other using a stochastic tire-force model. Previous literature has focused on linear stochastic tire-force models and on linear deterministic tire-force models. However, it is well known that there exists a nonlinear relationship between slip variables and tire-force variables. For this reason, it is suitable to use a nonlinear deterministic tire-force model for the extended Kalman filter, and this is the novel aspect at this work. The objective of this research is to show the improvement of the extended Kalman filter using a nonlinear deterministic tire-force model in comparison to linear stochastic tire-force model. The simulation model is a seven degree-of-freedom bicycle model that includes vertical suspension dynamics but neglects the roll motion. A comparison between the linear stochastic tire-force model and the nonlinear deterministic tire-force model confirms the expected results. Simulation studies are performed on some illustrative examples obtaining good tracking performance.