The main objective of this dissertation is to develop mean-squared error performance predictions for multiple target tracking. Envisioned as an approximate Cramer-Rao lower bound, these performance predictions allow a tracking system designer to quickly and efficiently predict the general performance trends of a tracking system. The symmetric measurement equation (SME) approach to multiple target tracking (MTT) lies at the heart of our method. The SME approach, developed by Kamen et al., offers a unique solution to the data association problem. Rather than deal directly with this problem, the SME approach transforms it into a nonlinear estimation problem. In this way, the SME approach sidesteps report-to-track associations. Developing performance predictions using the SME approach requires work in several areas: (1) extending SME tracking theory, (2) developing nonlinear filters for SME tracking, and (3) understanding techniques for computing Cramer-Rao error bounds in nonlinear filtering. First, on the SME front, we extend SME tracking theory by deriving a new set of SME equations for motion in two dimensions. We also develop the first realistic and efficient method for SME tracking in three dimensions. Second, we apply, for the first time, the unscented Kalman filter (UKF) and the particle filter to SME tracking. Using Taylor series analysis, we show how different SME implementations affect the performance of the EKF and UKF and show how Kalman filtering degrades for the SME approach as the number of targets rises. Third, we explore the Cramer-Rao lower bound (CRLB) and the posterior Cramer-Rao lower bound (PCRB) for computing MTT error predictions using the SME. We show how to compute performance predictions for multiple target tracking using the PCRB, as well as address confusion in the tracking community about the proper interpretation of the PCRB for tracking scenarios.

In this thesis several non-causal offline algorithms are developed and evaluated for a vision system used for pedestrian and vehicle traffic. The reason was to investigate if the performance increase of non-causal offline algorithms alone is enough to evaluate the performance of vision system. In recent years the vision systems have become one of the most important sensors for modern vehicles active security systems. The active security systems are becoming more important today and for them to work a good object detection and tracking in the vicinity of the vehicle is needed. Thus, the vision system needs to be properly evaluated. The problem is that modern evaluation techniques are limited to a few object scenarios and thus a more versatile evaluation technique is desired for the vision system. The focus of this thesis is to research non-causal offline techniques that increases the tracking performance without increasing the number of sensors. The Unscented Kalman Filter is used for state estimation and an unscented Rauch-Tung-Striebel smoother is used to propagate information backwards in time. Different motion models such as a constant velocity and coordinated turn are evaluated. Further assumptions and techniques such as tracking vehicles using fix width and estimating topography and using it as a measurement are evaluated. Evaluation shows that errors in velocity and the uncertainty of all the states are significantly reduced using an unscented Rauch-Tung-Striebel smoother. For the evaluated scenarios it can be concluded that the choice of motion model depends on scenarios and the motion of the tracked vehicle but are roughly the same. Further the results show that assuming fix width of a vehicle do not work and measurements using non-causal estimation of topography can significantly reduce the error in position, but further studies are recommended to verify this.

The Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF) and Ensemble Kalman Filter (EnKF) are commonly implemented practical solutions for solving nonlinear state space estimation problems; all based on the linear state space estimator, the Kalman Filter. Often, the UKF and EnKF are cited as a superior methods to the EKF with respect to error-based performance criteria. The UKF in turn has the advantage over the EnKF of smaller computational complexity. In practice however the UKF often fails to live up to this expectation, with performance which does not surpass the EKF and estimates which are not as robust as the EnKF. This work explores the geometry of alternative sigma point sets, which form the basis of the UKF, contributing several new sets along with novel methods used to generate them. In particular, completely novel systems of sigma points that preserve higher order statistical moments are found and evaluated. Additionally a new method for scaling and problem specific tuning of sigma point sets is introduced as well as a discussion of why this is necessary, and a new way of thinking about UKF systems in relation to the other two Kalman Filter methods. An Iterated UKF method is also introduced, similar to the smoothing iterates developed previously for the EKF. The performance of all of these methods is demonstrated using problem exemplars with the improvement of the contributed methods highlighted.

The first loudspeaker was invented almost 150 years ago and even though much has changed regarding the manufacturing, the main idea is still the same. To produce clean sound, modern loudspeaker consist of expensive materials that often need advanced manufacturing equipment. The relatively newly established company Actiwave AB uses digital signal processing to enhance the audio for loudspeakers with poor acoustic properties. Their algorithms concentrate on attenuating the linear distortion but there is no compensation for the loudspeakers' non-linear distortion, such as harmonic distortion. To attenuate the harmonic distortion, this thesis presents controllers based on exact input-output linearisation. This type of controller needs an accurate model of the system. A loudspeaker model has been derived based on the LR-2 model, an extension of the more common Thiele-Small model. A controller based on exact input-output linearisation also needs full state feedback, but since feedback risk being expensive, state estimators were used. The state estimators were based on feed-forward or observers using the extended Kalman filter or the unscented Kalman filter. A combination of feed-forward state estimation and a PID controller were designed as well. In simulations, the total harmonic distortion was attenuated for all controllers up to 180 Hz. The simulations also showed that the controllers are sensitive to inaccurate parameter values in the loudspeaker model. During real-life experiments, the controllers needed to be extended with a model of the used amplifier to function properly. The controllers that were able to attenuate the harmonic distortion were the two methods using feed-forward state estimation. Both controllers showed improvement compared to the uncontrolled case for frequencies up to 40 Hz.

The goal of this thesis was to evaluate sensors and motor speed control methods for BLDC/PMSM motors in Aerospace applications. The sensors and methods were evaluated by considering accuracy, robustness, cost, development gain and parameter sensitivity. The sensors and methods chosen to simulate were digital Hall sensors and sensorless control of BLDC motors. Using Matlab Simulink/Simscape some motor speed control methods and motor speed estimation methods were simulated using the Hall sensors and sensorless control as a basis. It was found that the sensorless control methods for BLDC motors couldn't estimate the speed accurately during dynamic loads and that the most robust and accurate solution based on the simulations was using the digital Hall sensors for both speed estimation and commutation and this was tested on a hardware setup.

The purpose of this paper was to implement Kalman filtering in the form of pre-existing Simulink blocks into a CubeSat attitude determination and control system simulation and to evaluate their performance. In recent versions of Simulink, the block library has been expanded, providing a new level of abstraction for simulation engineers. The capabilities of such library filter blocks have previously not been explored for space applications and could offer a faster and more simplified filter integration process. Three types of filter implementations have been realized, being classic Kalman filter, extended Kalman filter and unscented Kalman filter. These have been applied to the outputs of the coarse Sun sensor and Earth horizon sensor, as well as to the simulation attitude estimate. State propagation functions have been defined in the form of constant and linear approximations in addition to state propagation following the same structure as the simulation reference truth. Filter efficiency was evaluated using control error, pointing knowledge, pointing accuracy and variance as performance measures. Furthermore, interventions were introduced in the form of sensor data loss and solar panel deployment. The Kalman filter blocks were successfully integrated into the simulation. Performance measures revealed that constant state transition functions provided the best performance in most cases, exceptions being the extended Kalman filter and unscented Kalman filter of the attitude estimate application. Here, the true state propagation instead outperformed the other filters. Signal data loss showed that the true state propagation was the only one that could accurately predict the attitude state in a scenario when sensors fail to provide data. Solar panel deployment could not be utilized to evaluate the filter performance as the filter implementation did not support prediction of a dynamic attitude state. Results suggest that the pre-existing Simulink filter blocks can provide an easier alternative to defining filters from scratch. However, great care needs to be taken when tuning block parameters and constructing state transition functions to assure proper behavior. / Syftet med arbetet har varit att implementera Kalmanfilter i formen av fördefinierade Simulink-block i en simulering av ett system för attitydbestämning och styrning för en CubeSat, och utvärdera prestandan. I nyare versioner av Simulink har blockbiblioteken utökats, vilket har introducerat nya nivåer av abstraktion för simuleringsingenjörer. Möjligheterna hos filterblock i sådana bibliotek har ännu inte utforskats för rymdtekniska tillämpningar, och skulle kunna leda till snabbare och enklare integrering av filter. Tre typer av filterimplementationer har genomförts: klassiska Kalmanfilter, utökat Kalmanfilter och oparfymerat Kalmanfilter. Dessa har applicerats till utdata från solsensor och jordhorisontsensor, samt till simuleringens uppskattade attityd. Funktioner för tillståndspropagering har definierats i formen av konstanta och linjära approximationer tillsammans med den verkliga tillståndspropageringen, som har samma struktur som simuleringens sanna referensvärde. Effektiviteten hos filtren har utvärderats genom kontrollfel, riktningskunskap, riktningsnoggrannhet och varians som prestandamått. Vidare har interventioner introducerats i form av förlust av sensordata och utfällning av solpaneler. Kalmanfilterblocken integrerades med framgång i simuleringen. Prestandamåtten visade att de konstanta funktionerna för tillståndspropagering gav bäst prestanda i de flesta fallen, förutom i fallet av utökat Kalmanfilter och oparfymerat Kalmanfilter i appliceringen på den uppskattade attityden. I det sistnämnda fallet var det den verkliga tillståndspropageringen som presterade bättre än de andra filtren. Förlust av signaldata visade att den verkliga tillståndspropageringen är den enda som med säkerhet kan förutsäga utvecklingen av attityden i ett läge där sensorerna inte längre levererar data. Utfällningen av solpanelerna kunde inte utnyttjas för att utvärdera prestandan hos filtren, då implementeringen av filtren inte kan förutsäga utvecklingen av ett dynamiskt attitydtillstånd. Resultaten antyder att fördefinierade Simulink-filter kan erbjuda ett enklare alternativ till att definiera filter helt från början. Dock så krävs noga omsorg vid inställning av blockparametrar och vid konstruktion av funktioner för tillståndspropagering för att säkerställa korrekt beteende

For over a decade, Brigham Young University's Microwave Earth Remote Sensing (MERS) team has been developing SAR systems and SAR processing algorithms. In order to create the most accurate image reconstruction algorithms, detailed aircraft motion data is essential. In 2008, the MERS team purchased a costly inertial measurement unit (IMU) coupled with a high precision global positioning system (GPS) from NovAtel, Inc. In order to lower the cost of obtaining detailed motion measurements, the MERS group decided to build a system that mimics the capability the NovAtel system as closely as possible for a much lower cost. As a first step, the same sensors and a simplified set of flight dynamics are used. This thesis presents a standalone motion sensor recording system (MOTRON), and outlines a method of utilizing the square-root Unscented Kalman filter (SR-UKF) to estimate aircraft flight dynamics, based on recorded flight data, as an alternative to the extended Kalman filter. While the results of the SR-UKF are not as precise as the NovAtel results, they approach the accuracy of the NovAtel system despite the simplified dynamics model.

In order to overcome the various disadvantages of standalone INS and GPS, these systems are integrated using nonlinear estimation techniques and benefits of the two complementary systems are obtained at the same time. The standard and most widely used estimation algorithm in the INS/GPS integrated systems is Extended Kalman Filter (EKF). Linearization step involved in the EKF algorithm can lead to second order errors in the mean and covariance of the state estimate. Another nonlinear estimator, Unscented Kalman Filter (UKF) approaches this problem by carefully selecting deterministic sigma points from the Gaussian distribution and propagating these points through the nonlinear function itself leading third order errors for any nonlinearity. Scaled Unscented Transformation (SUT) is one of the sigma point selection methods which gives the opportunity to adjust the spread of sigma points and control the higher order errors by some design parameters. Determination of these parameters is problem specific. In this thesis, effects of the SUT parameters on integrated navigation solution are investigated and an &ldquo / Adaptive UKF&rdquo / is designed for a tightly-coupled INS/GPS integrated system. Besides adapting process and v measurement noises, SUT parameters are adaptively tuned. A realistic fighter flight trajectory is used to simulate IMU and GPS data within Monte Carlo analysis. Results of the proposed method are compared with standard EKF and UKF integration. It is observed that the adaptive scheme used in the sigma point selection improves the performance of the integrated navigation system especially at the end of GPS outage periods.

This thesis details several applications of Gaussian processes (GPs) for enhanced time series modeling. We first cover different approaches for using Gaussian processes in time series problems. These are extended to the state space approach to time series in two different problems. We also combine Gaussian processes and Bayesian online change point detection (BOCPD) to increase the generality of the Gaussian process time series methods. These methodologies are evaluated on predictive performance on six real world data sets, which include three environmental data sets, one financial, one biological, and one from industrial well drilling. Gaussian processes are capable of generalizing standard linear time series models. We cover two approaches: the Gaussian process time series model (GPTS) and the autoregressive Gaussian process (ARGP).We cover a variety of methods that greatly reduce the computational and memory complexity of Gaussian process approaches, which are generally cubic in computational complexity. Two different improvements to state space based approaches are covered. First, Gaussian process inference and learning (GPIL) generalizes linear dynamical systems (LDS), for which the Kalman filter is based, to general nonlinear systems for nonparametric system identification. Second, we address pathologies in the unscented Kalman filter (UKF).We use Gaussian process optimization (GPO) to learn UKF settings that minimize the potential for sigma point collapse. We show how to embed mentioned Gaussian process approaches to time series into a change point framework. Old data, from an old regime, that hinders predictive performance is automatically and elegantly phased out. The computational improvements for Gaussian process time series approaches are of even greater use in the change point framework. We also present a supervised framework learning a change point model when change point labels are available in training.

In vehicle control practice, there are some variables, such as lateral tire force, body slip angle and yaw rate, that cannot or is hard to be measured directly and accurately. Vehicle model, like the bicycle model, offers an alternative way to get them indirectly, however due to the widely existent simplification and inaccuracy of vehicle models, there are always biases and errors in prediction from them. When developing advanced vehicle control functions, it is necessary and significant to know these variables in relatively high precision. Kalman filter offers a choice to estimate these variables accurately with measurable variables and with vehicle model together. In this thesis, estimation models based on Extended Kalman Filter (EKF) and Uncented Kalman Filter (UKF) are built separately to evaluate the lateral tire force, body slip angel and yaw rate of two typical passenger vehicles. Matlab toolbox EKF/UKF developed by Simo Särkkä, et al. is used to implement the estimation models. By comparing their principle, algorithm and results, the better one for vehicle state estimation will be chosen and justified. The thesis is organized in the following 4 parts: First, EKF and UKF are studied from their theory and features. Second, vehicle model used for prediction in Kalman filter is build and justified. Third, algorithms of EKF and UKF for this specific case are analysed. EKF and UKF are then implemented based on the algorithms with the help of Matlab toolbox EKF/UKF. Finally, comparisons between EKF and UKF are presented and discussed.