Observability Analysis for Target Tracking Systems with Bearing Measurements

This paper is concerned with the problem of estimating the position and velocity of targets with noise-corrupted bearing information. Instead of traditional models on targets with a constant velocity, a more general model for the bearings-only target tracking problem is discussed. Firstly, a equivalent transformation is proposed such that the nonlinearity of measurements can be transferred to the dynamical systems. Then, some sufficient and necessary conditions for the locally weak observability of the systems are given by using Lie algebra tools. Finally, the Consistent Extended Kalman Filter(CEKF) algorithm is designed to estimate the state vector and some numerical simulations are carried out.