Abstract: Aiming at the incomplete observability problem of bearing-only tracking system with single sensor, the optimal motion trajectory of the sensor is presented under the condition of maximizing variational evidence lower bound to accumulate more information from measurement. Firstly, assuming that sensor’s speed is a constant, a joint optimization framework with the super-parameters of sensor’s heading, state estimation and its estimation error covariance is established by using variational Bayesian inference. On this basis, Fisher information matrix with respect to sensor’s heading is derived by maximizing evidence lower bound, so that the optimal heading can be computed at the point of Fisher information accumulation maximization. Meanwhile, considering the robustness of estimated system, a weighted Kullback- Leibler divergence between variational distribution and the posteriori is taken as a regularization to constructed an optimization function, in which state estimation and the associated error covariance are set as variational super-parameters. Furthermore, the partial derivatives of optimization function with respect to state estimation and the associated error covariance arepresented to compute estimation update. Simulations of bearing-only tracking system arepresented showing that the proposed algorithm can accumulate information from measurement efectively and achieve a higher estimation performance of accuracy by changing sensor’s heading.

Key words: sensor trajectory planning, variational Bayesian inference, nonlinear filtering, adaptive filtering, Fisher information matrix