Nonlinear estimation, detection, and fault-tolerant control

This dissertation proposes solutions to several nonlinear estimation and detection problems via fault detection methods. The problems considered are the integer resolution problem for GPS, the exact solution of the GPS measurement equations, and the bearings-only radar track association problem. The dissertation also investigates when time-varying control laws may be appropriate for controlling time-invariant systems in the presence of failures.; To obtain highly accurate relative position estimates between two GPS antennae using carrier phase measurements, one must estimate integer-valued parameters in the measurement equations. We estimate the values of these parameters with nonlinear filters called multiple hypothesis sequential probability ratio tests (MHSPRTs). The Wald MHSPRT can estimate the initial value of the integer parameters, and the Shiryayev MHSPRT can monitor the parameters for jumps. Since MHSPRTs assume independent measurement residual sequences, we construct independent measurement residuals using special projection matrices.; Even though the exact solution to the noiseless GPS measurement equations has long been known, the noisy version of this problem has remained unsolved. We solve it by using a special projection to transform the m nonlinear measurement equations into m − 1 linear equations and one nonlinear equation. We then compute an initial linear estimate, which we refine with information present in the remaining nonlinear equation.; Although the problem of associating radar tracks between several physically separated stations has been investigated before, no research has been conducted on performing this task using only angular measurements. Such measurements are nonlinear, but special Modified Gain Extended Kalman Filters (MGEKFs) can track targets accurately using them. We propose a unique configuration of MGEKFs, operating cooperatively as detection filters, to perform bearings-only track association.; Prior work in fault tolerant controller design has focused solely on the issue of reconfiguring the controller once a fault has been detected. For certain classes of systems, stability in the presence of an undetected fault requires a stable controller. We introduce a test that determines whether a stable periodically time-varying controller can deliver performance superior to a stable time invariant controller.; Experimental results are provided for each problem.