A technique to improve the performance of a nonlinear filter with an application to satellite-aided aircraft navigation

This paper evaluates performance of a filter that transforms nonlinear measurements in the coordinate system of the state before using in the filter. The bias and computational performance of this mechanization are compared with the conventional extended Kalman (EK) filter. The bias in the EK filter is a function of the covariance of the estimation error, while in the state-coordinate-system (SCS) it depends on variance of the transformed measurement noise, which is independent of the estimation error and depends only on the nonlinearity. Thus when the initial covariance of the state is large, the SCS filter has less bias than the EK filter. This reduction in the bias is achieved at a cost of additional computations required to implement the transformation. The improved performance of the filter due to the coordinate transformation is then demonstrated with an example of satellite-aided aircraft navigation.