Estimation and Control for Linear Systems with Additive Cauchy Noise.

摘要

A new class of scalar and vector-state estimators and stochastic controllers for linear dynamic systems with additive Cauchy process and measurement noises has been developed. The Kalman filter and the linear- quadratic-Gaussian controller have been the main estimation and control paradigms in modern engineering. However, many practical system noises, such as radar glint, are better described by heavy tailed probability density functions (pdf). Although the Cauchy pdf has an infinite variance, the conditional density of a Cauchy random variable, given a linear measurement with an additive Cauchy noise, has a conditional mean and a finite conditional variance, both being functions of the measurement. Over the last three years, a theory of estimation and stochastic control has been developed for the vector state linear dynamic system. The methodology for scalar state systems entailed propagation of the conditional pdf, while the vector state case was addressed by developing a recursion for the analytic propagation of the character function of the unnormalized conditional pdf (ucpdf). Through a spectral transformation, the character function of the ucpdf is used explicitly in the development of stochastic controllers for vector-state systems.