Fixed-Point Nonlinear Smoothing.
CALIFORNIA UNIV IRVINE SYSTEMS ENGINEERING AND OPERATIONS RESEARCH GROUP
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Smoothing is a generic term describing any technique that estimates a state or parameter at a point in time prior to a most recent noisy measurement which is related to the state. Attention in this dissertation is focused on the derivation and application of a recursive forward-time fixed-point smoothing algorithm. This algorithm is for discrete-time nonlinear dynamic systems driven by Gaussian, white noise wherein the measurements are nonlinear functions of the state in the presence of additive Gaussian white noise. Using the marginal maximum likelihood approach, the author obtains the smoothing algorithm. It is found that the derived algorithm depends on the past filtered estimates thus the fixed-point smoothing problem is solved by simultaneously implementing the filtering and smoothing algorithms. The smoothing algorithm contains terms involving the second-order partial derivatives of the system dynamics. The associated filtering algorithm includes the second-order partial derivatives of the nonlinear measurement function. Both filtering and smoothing estimates are computed recursively by iterative solution of the algorithms. A nontrivial example in data smoothing is presented to illustrate the application of the theory. Modified author abstract
- Statistics and Probability