Bearings-only tracking: a hybrid coordinate system approach

A bearings-only tracking algorithm is described. The algorithm is an extended Kalman filter (EKF) which combines the linear-in-state properties of the Cartesian state variable definition with the linear-in-measurement properties of the modified polar (MP) state variable definition. This hybrid approach uses the Cartesian system for state and state covariance extrapolation and uses the MP system for state and state covariance updating. Accurate state and state covariance extrapolation is achieved without numerical integration. The filter equations of this EKF are, furthermore, derived using a line-of-sight algebra which yields equations which are nonlinear algebraic rather than transcendental. This approach allows for easier of the filter equations and provides for greater insight into the bearings-only tracking problem. Applying recent results from differential geometric system theory, observability is analyzed by applying the Lie bracket criteria to the algebraic filter equations