Techn. Universiẗat, Diss., 2001--Berlin.

Master-Arbeit Univ. St. Gallen, 2005.

abstract: This study focuses on state estimation of nonlinear discrete time systems with constraints. Physical processes have inherent in them, constraints on inputs, outputs, states and disturbances. These constraints can provide additional information to the estimator in estimating states from the measured output. Recursive filters such as Kalman Filters or Extended Kalman Filters are commonly used in state estimation; however, they do not allow inclusion of constraints in their formulation. On the other hand, computational complexity of full information estimation (using all measurements) grows with iteration and becomes intractable. One way of formulating the recursive state estimation problem with constraints is the Moving Horizon Estimation (MHE) approximation. Estimates of states are calculated from the solution of a constrained optimization problem of fixed size. Detailed formulation of this strategy is studied and properties of this estimation algorithm are discussed in this work. The problem with the MHE formulation is solving an optimization problem in each iteration which is computationally intensive. State estimation with constraints can be formulated as Extended Kalman Filter (EKF) with a projection applied to estimates. The states are estimated from the measurements using standard Extended Kalman Filter (EKF) algorithm and the estimated states are projected on to a constrained set. Detailed formulation of this estimation strategy is studied and the properties associated with this algorithm are discussed. Both these state estimation strategies (MHE and EKF with projection) are tested with examples from the literature. The average estimation time and the sum of square estimation error are used to compare performance of these estimators. Results of the case studies are analyzed and trade-offs are discussed. / Dissertation/Thesis / M.S. Electrical Engineering 2013

The goal of this paper is to suggest suitable method for angle measuring of mobile robot. There are being analyzed 3 different sensors – gyroscope, accelerometer and electronic compass in the prologue. Their advantages and disadvantages in the theoretical way are being explained in this part and also their opportunities of use in the practical way. In the following parts the work is focused on MEMS gyroscopes and their opportunities of use in the practical way with regard to achievable exactness and to the application for development of its exactness. The application of device together with main SW for microcontroller and the valuation of achievable exactness and determined facts are being described in the conclusion part.

Kamerabasierte Verfahren zur Steuerung autonomer mobiler Roboter wurden in den letzten Jahren immer populärer. In dieser Arbeit wird der Einsatz eines Stereokamerasystems und eines Mono-Kamera-SLAM Verfahrens hinsichtlich der Unterstützung der Navigation eines autonomen Luftschiffes untersucht. Mit Hilfe von Sensordaten aus IMU, GPS und Kamera wird eine Positionsschätzung über eine Sensorfusion mit Hilfe des Extended und des Unscented Kalman Filters durchgeführt.

As the technology is advances the reduced size of hardware gives rise to an additive 1/f baseband noise. This additive 1/f noise is a system noise generated due to miniaturization of hardware and affects the lower frequencies. Though 1/f noise does not show much effect in wide band channels because of its nature to affect only certain frequencies, 1/f noise becomes a prominent in OFDM communication systems where narrow band channels are used. in this thesis, I study the effects of 1/f noise on the OFDM systems and implement algorithms for estimation and suppression of the noise using Kalman filter. Suppression of the noise is achieved by subtracting the estimated noise from the received noise. I show that the performance of the system is considerably improved by applying the 1/f noise suppression.

A critical ability of any aircraft is to be able to detect potential collisions with other airborne objects, and maneuver to avoid these collisions. This can be done by utilizing sensors on the aircraft to monitor the sky for collision threats. However, several problems face a system which aims to use multiple sensors for target tracking. The data collected from sensors needs to be clustered, fused, and otherwise processed such that the flight control system can make accurate decisions based on it. Raw sensor data, while filled with useful information, is tainted with inaccuracies due to limitations and imperfections of the sensor. Combined use of different sensors presents further issues in how to handle disagreements between sensor data. This thesis project tackles the problem of processing data from multiple sensors (in this application, a radar and an infrared sensor) on an airborne platform in order to allow the aircraft to make flight corrections to avoid collisions.

As computing power becomes more and more available, robotic systems are moving away from active sensors for environmental awareness and transitioning into passive vision sensors.  With the advent of teleoperation and real-time video tracking of dynamic environments, the need to stabilize video onboard mobile robots has become more prevalent. This thesis presents a digital stabilization method that incorporates inertial fusion with a Kalman filter.  The camera motion is derived visually by tracking SIFT features in the video feed and fitting them to an affine model.  The digital motion is fused with a 3 axis rotational motion measured by an inertial measurement unit (IMU) rigidly attached to the camera. The video is stabilized by digitally manipulating the image plane opposite of the unwanted motion. The result is the foundation of a robust video stabilizer comprised of both visual and inertial measurements.  The stabilizer is immune to dynamic scenes and requires less computation than current digital video stabilization methods. / Master of Science

Indiana University-Purdue University Indianapolis (IUPUI) / With passage of time and repeated usage of a system, component values that make up the system parameters change, causing errors in its functional output. In order to ensure the fidelity of the results derived from these systems it is thus very important to keep track of the system parameters while being used. This thesis introduces a method for tracking the existing system parameters while the system was being used using the inherent noise of its signal source. Kalman filter algorithm is used to track the inherent noise response to the system and use that response to estimate the system parameters. In this thesis this continuous characterization scheme has been used on a Universal Invertible Amplifier (UIA). Current biomedical research as well as diagnostic medicine depend a lot on shape profile of bio-electric signals of different sources, for example heart, muscle, nerve, brain etc. making it very important to capture the different event of these signals without the distortion usually introduced by the filtering of the amplifier system. The Universal Invertible Amplifier extracts the original signal in electrodes by inverting the filtered and compressed signal while its gain bandwidth profile allows it to capture from the entire bandwidth of bioelectric signals. For this inversion to be successful the captured compressed and filtered signals needs to be inverted with the actual system parameters that the system had during capturing the signals, not its original parameters. The continuous characterization scheme introduced in this thesis is aimed at knowing the system parameters of the UIA by tracking the response of its source noise and estimating its transfer function from that. Two types of source noises have been tried out in this method, an externally added noise that was digitally generated and a noise that inherently contaminates the signals the system is trying to capture. In our cases, the UIA was used to capture nerve activity from vagus nerve where the signal was contaminated with electrocardiogram signals providing us with a well-defined inherent noise whose response could be tracked with Kalman Filter and used to estimate the transfer function of UIA. The transfer function estimation using the externally added noise did not produce good results but could be improved by means that can be explored as future direction of this project. However continuous characterization using the inherent noise, a bioelectric signal, was successful producing transfer function estimates with minimal error. Thus this thesis was successful to introduce a novel approach for system characterization using bio-signal contamination.

<p> Bayesian filtering refers to the process of sequentially estimating the current state of a complex dynamic system from noisy partial measurements using Bayes' rule. This thesis considers Bayesian filtering as applied to an important class of state estimation problems, which is describable by a discrete-time nonlinear state-space model with additive Gaussian noise. It is known that the conditional probability density of the state given the measurement history or simply the posterior density contains all information about the state. For nonlinear systems, the posterior density cannot be described by a finite number of sufficient statistics, and an approximation must be made instead.</p> <p> The approximation of the posterior density is a challenging problem that has engaged many researchers for over four decades. Their work has resulted in a variety of approximate Bayesian filters. Unfortunately, the existing filters suffer from possible divergence, or the curse of dimensionality, or both, and it is doubtful that a single filter exists that would be considered effective for applications ranging from low to high dimensions. The challenge ahead of us therefore is to derive an approximate nonlinear Bayesian filter, which is theoretically motivated, reasonably accurate, and easily extendable to a wide range of applications at a minimal computational cost.</p> <p> In this thesis, a new approximate Bayesian filter is derived for discrete-time nonlinear filtering problems, which is named the cubature Kalman filter. To develop this filter, it is assumed that the predictive density of the joint state-measurement random variable is Gaussian. In this way, the optimal Bayesian filter reduces to the problem of how to compute various multi-dimensional Gaussian-weighted moment integrals. To numerically compute these integrals, a third-degree spherical-radial cubature rule is proposed. This cubature rule entails a set of cubature points scaling linearly with the state-vector dimension. The cubature Kalman filter therefore provides an efficient solution even for high-dimensional nonlinear filtering problems. More remarkably, the cubature Kalman filter is the closest known approximate filter in the sense of completely preserving second-order information due to the maximum entropy principle. For the purpose of mitigating divergence, and improving numerical accuracy in systems where there are apparent computer roundoff difficulties, the cubature Kalman filter is reformulated to propagate the square roots of the error-covariance matrices. The formulation of the (square-root) cubature Kalman filter is validated through three different numerical experiments, namely, tracking a maneuvering ship, supervised training of recurrent neural networks, and model-based signal detection and enhancement. All three experiments clearly indicate that this powerful new filter is superior to other existing nonlinear filters. </p> / Thesis / Doctor of Philosophy (PhD)