Fixed lag smoothing of scalar diffusions .1. The filtering-smoothing equation

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:64

Article

Liptser, RS ; Steinberg, Y ; Bobrovsky, BZ

关键词: filtering;    smoothing;    Kushner and Zakai equations;   

DOI  :  10.1016/S0304-4149(96)00086-5

来源: Elsevier

【 摘 要 】

The problem of optimal fixed lag smoothing of a diffusion process, x(t) is to estimate x(t-tau) for t > tau, given the output of a nonlinear noisy sensor up to time t. The nonlinear filtering-smoothing problem is to estimate both x(t) and x(t-tau). The optimal estimators are the conditional expectations of the processes, given the measurements. We derive evolution equations for both the normalized and unnormalized versions of the joint probability density function of x(t) and x(t-tau), given the noisy measurements. The former is an equation of Kushner's type and the latter is of Zakai's type.

【 授权许可】

Free