Bayesian Filtering with Unknown Sensor Measurement Losses

Abstract: This work studies the state estimation problem of a stochastic nonlinear system with unknown sensor measurement losses. If the estimator knows the sensor measurement losses of a linear Gaussian system, the minimum variance estimate is easily computed by the celebrated intermittent Kalman filter (IKF). However, this will no longer be the case when the measurement losses are unknown and/or the system is nonlinear or non-Gaussian. By exploiting the binary property of the measurement loss process and the IKF, we design three suboptimal filters for the state estimation, i.e., BKF-I, BKF-II and RBPF. The BKF-I is based on the MAP estimator of the measurement loss process and the BKF-II is derived by estimating the conditional loss probability. The RBPF is a particle filter based algorithm which marginalizes out the loss process to increase the efficiency of particles. All the proposed filters can be easily implemented in recursive forms. Finally, a linear system, a target tracking system and a quadrotor's path control problem are included to illustrate their effectiveness, and show the tradeoff between computational complexity and estimation accuracy of the proposed filters.