A new smooth variable structure Tobit filter for systems with censored measurements and model parameters uncertainty

Abstract

The smooth variable structure filter (SVSF) is an effective state estimation strategy for systems with model parameters uncertainty. The superiority of SVSF, however, depends on accurate sensor measurements. In practice, the accuracy of traditional SVSF algorithm will be degraded or even diverge for censored measurements. To solve this problem, in this paper, firstly, the Tobit censored model is introduced to describe censored phenomenon for systems with model parameters uncertainty and censored measurements. The innovation, residual, innovation covariance and state prediction error cross-covariance are revised based on cumulative probability density. Then, the near optimal smooth boundary layer (SBL) is recalculated based on the minimum trace principle of estimation error covariance. A robust filter gain is redesigned based on the convergence of estimation error absolute, and the necessary conditions for the convergence of the proposed filter are proved. In the end, oscillators, distributed target tracking and the Udacity self-driving data-set are used to verify that the proposed algorithm has higher accuracy and better robustness under model parameters uncertainty and censored measurements.