Networked State Estimation with Delayed and Irregularly Spaced Time-Stamped Observations

We analyze the performance of a networked multisensor continuous-discrete Kalman filter in the presence of random observation delay and irregular sampling. The primary cause for irregular intersample intervals is the occasional loss of information packets. Additional causes include lack of synchrony between sensors, difference in their sampling rates, and the superposition of multiple sampling patterns. We rely on time stamping of all sensor packets to accurately determine, at the estimation hub, both transmission delay and sensor sampling instants. We relate the average (steady-state) error covariance to two moment-generating functions: 1) we provide lower and upper bounds on the average error covariance in the presence of irregular sampling, expressed in terms of the moment-generating function of the sampling intervals; 2) we obtain a stability condition that depends on the region of convergence of this moment-generating function; and 3) we derive an expression for the added error caused by transmission delay, which depends on the moment-generating function of the delay. We also demonstrate that the average error covariance depends primarily on the average sampling interval, with a very minor dependence on the variance and higher order moments of the multisensor intersample interval.