The objective of this paper is concerned with the estimation problem for linear discrete-time stochastic systems with mixed uncertainties involving random one-step sensor delay, stochastic-bias measurements, and missing measurements. Three Bernoulli distributed random variables are employed to describe the uncertainties. All the three uncertainties in the measurement have certain probability of occurrence in the target tracking system. And then, an adaptive Kalman estimation is proposed to deal with this problem. The adaptive filter gains can be obtained in terms of solutions to a set of recursive discrete-time Riccati equations. Examples in three scenarios of target tracking are exploited to show the effectiveness of the proposed design approach. 1. Introduction In practical target tracking, the missing phenomenon of the sensor measurement often occurs. For example, the measurement value may contain noise only due to the shelter of the obstacles, a high noise environment, a failure in the measurement, intermittent sensor failures, high maneuverability of tracked target, and so forth. Thus, the estimation for systems with missing measurements has received much attention during the few years. In general, there are two ways to describe the missing phenomenon. One way is to model the uncertainty by using a stochastic Bernoulli binary switching sequence taking on values of 0 and 1 (see, e.g., [1–18] and the references therein). The suboptimal filtering algorithm [2] in the minimum variance sense with only missing measurements has been proposed and the robust filter [14] is designed. In [3] Sinopoli et al. studied the statistical behavior of the Kalman filter error covariance with varying Kalman gain with missing measurements and the existence of a critical value has been shown for the arrival rate of the observations. The stochastic stability of the extended kalman filter with missing measurements is analyzed in [8], while stochastic stability of the unscented kalman filter with missing measurements is studied in [13]. For benchmarking the performance of any estimation algorithm with missing measurements in advance, the modified Cramer-Rao bound (CRLB) and modified Riccati equation have been studied in [1, 15–18]. Another way is to model the uncertainty as a Markovian jumping sequence (see [19–21] and the references therein). The convergence for semi-Markov chains has been studied in [20], where the exponential filter is designed in [21]. For the case of random delayed measurements, the delays will cause performance degradation or instability with
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