Optimal Observer Path Planning For Bearings-Only Moving Targets Tracking Using Chebyshev Polynomials

In this paper, an optimization problem for the observer trajectory in the bearings-only surface moving target tracking (BOT) is studied. The BOT depends directly on the observability of the target's position in the target/observer geometry or the optimal observer maneuver. Therefore, the maximum lower band of the Fisher information matrix is opted as an independent criterion of the target estimator. First, modeling of the optimal control problem of the observer path is presented based on the orthogonal Chebyshev polynomial. Then, a control law for the observer direction, which is independent of the initial conditions, is obtained using the direct numerical optimization. The advantages of the proposed model include maximization of the total maneuver time, calculation of the control law at the start time of the maneuver, and high flexibility in applying the tracking constraints of the observer's motion. The efficiency of the proposed algorithm is compared with the conventional path optimization methods using the Monte Carlo. In addition, the performance of the algorithm is evaluated in different scenarios for target tracking, including remote, near, moving, and stationary, and its reliability is investigated. It is also applied in the surface submarine tracking problem using sonar.