Sampling and quantization in nonlinear filtering and control

The thesis describes contributions made in two areas, namely, aspects of nonlinear filtering and control over communication channels. Specifically, the thesis is concerned with addressing the impact of temporal and spatial quantization on the performance of estimation and control algorithms. Regarding nonlinear filtering, emphasis is placed on technical and theoretical issues regarding the impact of sampling and spatial quantization. New techniques of upsampling and downsampling are developed to address specific computational issues. Also, extensions to Lebesgue sampling are explored. In addition, a new class of nonlinear filtering algorithms, called Minimum Distortion Filters, is developed based on the use of Vector Quantization. The effectiveness of the new filtering algorithms are illustrated, by using it on a wide variety of problems including system identification, state estimation for chemical processes and radar tracking. Regarding control over communication channels, the focus is primarily on the practical problem of inner loop power control in broadband WCDMA. This control loop is characterized by the use of a one-bit-per-sample control law. This restriction severely limits the achievable performance. To address the problem, a novel adaptive quantizer is developed in the thesis. The scheme is shown to lead to significant performance improvements. The scheme has also been extended and applied to the problem of stabilizing an open loop unstable system over a bit rate constrained channel. Other control problems in WCDMA are also explored including the use of the "Happy Bit" to signal buffer sizes for the purposes of scheduling. This control loop is also subject to a one-bit-per-sample constraint. Typically, the one bit is used for a different purpose in current implementations. Here we develop an adaptive scheme based on the Happy Bit for communicating the buffer size.