State Estimation With Trajectory Shape Constraints Using Pseudomeasurements

• Published in: IEEE transactions on aerospace and electronic systems Vol. 55; no. 5; pp. 2395 - 2407
• Main Authors: Zhou, Gongjian, Li, Keyi, Kirubarajan, Thiagalingam, Xu, Linfeng
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Computer simulation; Constrained state estimation; Corresponding states; Covariance matrices; cubature Kalman filter (CKF); Fixed incomes; Gain measurement; Kalman filters; Noise measurement; Performance enhancement; Position measurement; pseudomeasurement; Redundancy; Shape; Smoothing; state augmentation; State estimation; State vectors; target tracking; Time measurement; Trajectory; Trajectory analysis; trajectory constraint
• ISSN: 0018-9251; 1557-9603
• DOI: 10.1109/TAES.2018.2887180

In this paper, a trajectory shape constraint on target motion is investigated, and the corresponding state estimation method is presented. This type of constraint occurs when only the shape of the target trajectory is known a priori, without any other necessary information to exactly describe the specific trajectory. For example, one may only know that the target moves along a straight line. This prior knowledge of trajectory can be considered as a constraint to improve tracking performance. To describe the shape constraint arising from the straight line assumption, the state vector is augmented by the states at previous time steps. This facilitates the description of the shape constraint using the components of the state vector. Pseudomeasurements are then constructed based on these relationships to incorporate the constraint into an estimation process to improve the performance. The redundancy of the complete set of pseudomeasurements for a given augmented state vector is analyzed, and the minimal set of pseudomeasurements, which describes the constraint exactly, is proposed. The time evolution equation for the augmented state and the measurement equation using the minimal pseudomeasurement set are formulated. A trajectory shape constraint Kalman filter (TSCKF) is then proposed for simultaneous filtering and smoothing. Since both the measurement vector and the state vector are high dimensional, the cubature Kalman filter is used in the proposed TSCKF to deal with the strong nonlinearity in this problem. Monte Carlo simulations illustrate the effectiveness of the proposed TSCKF and the improvement in both filtering and smoothing accuracies by incorporating the trajectory shape constraint.