Minimum Upper Bound Estimation With Colored Measurement Noise in the Presence of Generalized Unknown Disturbance

A recursive minimum upper bound estimator (UBE) is proposed in this article for stochastic systems with colored measurement noise (CMN) in the presence of generalized unknown disturbance (UD), which is motivated by noncooperative target tracking in the environment of continuous external interference. The CMN causes system noises to be correlated in time dimension, and the UD makes online calculation of estimate error covariance intractable, both of which give rise to deterioration of classical Kalman-like filtering and smoothing. By considering that constructing the upper bound of estimate error covariance requires looser conditions than directly calculating the theoretical covariance, an UBE is first defined, to obtain the filtered estimate and smoothed estimate together. Then, based on the reconstructed measurement model containing multiple state vectors due to measurement differencing to whiten system noises, the recursive structure of the defined UBE is derived in the case of CMN (CUBE) by introducing a free parameter to be optimized, and the existence condition of CUBE is also discussed. Finally, the minimum UBE with CMN, i.e., CMUBE, is presented by pursuing the minimum upper bound of estimate error covariance online through parameter optimization, in order to further suppress the peak of estimate errors. The advantages of estimation accuracy of the proposed CMUBE over Kalman filter (KF)/smoother, KF with CMN and minimum upper bound filter (MUBF) are demonstrated by an example of noncooperative target tracking in persistent interference environment, in terms of filtering versus smoothing, different values of the initial estimate error covariance and the positive-definite matrix setting a priori, sensor accuracies and different levels of UD.