Characteristic Function Approach for Estimation of Scalar Systems with Cauchy Noises
Moshe Idan, Jason Lee Speyer · 2010
variable, given a scalar linear measurement with an additive Cauchy noise, has a conditional mean and a nite conditional variance, both being functions of the measurement. For scalar discrete linear systems with additive process and measurement noises that have Cauchy probability density functions, characteristic functions are used to generate a recursive process from which the conditional mean and variance are easily obtained. The conditional mean and variance are generated by a growing sum that at each measurement update increases by one term, constructed from four new parameters. In particular, the characteristic function of the un-normalized conditional probability density function is considered where the dynamics of the parameters are propagated by linear dynamics. These parameters are shown to decay, allowing an approximate nite dimensional recursion. Since radar measurement noise and target motion process noise are not Gaussian, but are better characterized by heavy tailed density functions, a simple homing missile problem using proportional navigation is used to demonstrate the Cauchy estimator.