Gaussian Filtering with Stochastically Composed Current and Past Measurements

Abstract

The presence of irregularities in measurement causes poor filtering performance to well-celebrated Gaussian filters. The reason is that these filters are traditionally designed with an ideal measurement model, ignoring the possibility of any irregularity in the measurements. In this paper, we address a new measurement irregularity wherein an inaccurate measurement is received, which is stochastically composed of the current and past hypothetically true measurements. The proposed method reformulates the measurement model for incorporating the possible existence of the concerned irregularity. Subsequently, it re-derives the traditional Gaussian filtering method for the reformulated measurement model, resulting into the proposed filtering method. In summary, the paper first proposes a new measurement equation to model the concerned irregularity, resulting into a new state-space model. With the new measurement model, the parameters associated to the measurement update step of Gaussian filtering, i.e., measurement estimate, covariance, and cross-covariance are re-derived accordingly. Interestingly, any of the existing Gaussian filters, such as the extended Kalman filter (EKF) and cubature Kalman filter (CKF), can be designed under the proposed filtering method. We study the stability of the proposed method for its EKF-based formulation. The improved accuracy of the proposed method is validated for two nonlinear filtering problems. © 2004-2012 IEEE.