State Estimation for Kinematic Model Over Lossy Network

Abstract

The major benefit of the kinematic Kalman filter (KKF), i.e., the state estimation based on kinematic model is that it is immune to parameter variations and unknown disturbances regardless of the operating conditions. In carrying out complex motion tasks such as the coordinated manipulation among multiple machines, some of the motion variables measured by sensors may only be available through the communication layer, which requires to formulate the optimal state estimator subject to lossy network. In contrast to standard dynamic systems, the kinematic model used in the KKF relies on sensory data not only for the output but also for the process input. This paper studies how the packet dropout occurring from the input sensor as well as the output sensor affects the performance of the KKF. When the output sensory data are delivered through the lossy network, it has been shown that the mean error covariance of the KKF is bounded for any non-zero packet arrival rate. On the other hand, if the input sensory data are subject to lossy network, the Bernoulli dropout model results in an unbounded mean error covariance. More practical strategy is to adopt the previous input estimate in case the current packet is dropped. For each case of packet dropout models, the stochastic characteristics of the mean error covariance are analyzed and compared. Simulation results are presented to illustrate the analytical results and to compare the performance of the time varying (optimal) filter gain with that of the static (sub-optimal) filter gain.