This book offers an analytical rather than measure-theoretical approach to the derivation of the partial differential equations of nonlinear filtering theory. The basis for this approach is the discrete numerical scheme used in Monte-Carlo simulations of stochastic differential equations and Wiener's associated path integral representation of the transition probability density. Furthermore, it presents analytical methods for constructing asymptotic approximations to their solution and for synthesizing asymptotically optimal filters. It also offers a new approach to the phase tracking problem, based on optimizing the mean time to loss of lock. The book is based on lecture notes from a one-semester special topics course on stochastic processes and their applications that the author taught many times to graduate students of mathematics, applied mathematics, physics, chemistry, computer science, electrical engineering, and other disciplines. The book contains exercises and worked-out examples aimed at illustrating the methods of mathematical modeling and performance analysis of phase trackers.
Author(s): Zeev Schuss (auth.)
Series: Applied Mathematical Sciences 180
Edition: 1
Publisher: Springer US
Year: 2012
Language: English
Pages: 262
Tags: Probability Theory and Stochastic Processes;Theoretical, Mathematical and Computational Physics;Partial Differential Equations
Front Matter....Pages i-xviii
Diffusion and Stochastic Differential Equations....Pages 1-59
Euler’s Simulation Scheme and Wiener’s Measure....Pages 61-83
Nonlinear Filtering and Smoothing of Diffusions....Pages 85-106
Low-Noise Analysis of Zakai’s Equation....Pages 107-145
Loss of Lock in Phase Trackers....Pages 147-184
Loss of Lock in Radar and Synchronization....Pages 185-225
Phase Tracking with Optimal Lock Time....Pages 227-246
Back Matter....Pages 247-262
