The over-extended Kalman filter - don't use it!
D.F. Bizup, Donald E. Brown · 2003
Some target tracking filters ignore the radar range rate measurements because they are highly nonlinear in Cartesian space. A linearized mea-surement equation, composed of range rate’s partial derivatives with re-spect to the track state, is sometimes used in an extended Kalman filter. Unfortunately, this naive linearization biases the posterior estimates. The origins of these biases are investigated and found to lie in the linearized measurement’s functional dependence on the state’s position elements. An alternative linearization having no functional dependence on the state’s position elements is derived. Analyses and numerical evaluations show that the new linearization leads to filters with lower biases. 1 1