Nadjiasngar, Roaldje. On Improving the Performance of the Gauss-Newton Filter. PhD Thesis. Department of Electrical Engineering, University of Cape Town, 2013.
The Gauss-Newton filter is a tracking filter developed by Norman Morrison around the same time as the celebrated Kalman filter. It received little attention, primarily due to the computation requirements at the time. Today computers have vast processing capacity and computation is no longer an issue. The filter finite memory length is identified as the key element in the Gauss-Newton filter adaptability and robustness.
This thesis focuses on improving the performance of the Gauss-Newton. We incorporate the process noise statistics into the filter algorithm to obtain a filter which explains the error covariance inconsistency of the Kalaman filter. In addition, a biased version of the linear Gauss-Newton filter, with lower mean squared error than the unbiased filter, is proposed. Furthermore, the Gauss-Newton filter is adapted using the Levenberg Marquardt method for improved convergence. In order to improve the computation requirements, a recursive version of the filter is obtained. The recursive version of the filter has an exponential forgetting factor, a substitute of the non recursive filter memory length.
It is shown that the recursive Gauss-Newton filter is equivalent to the iterated extended Kalman filter when the forgetting factor is equal to one. Stability analysis has demonstrated the necessity of having finite memory length, thus imposing a less than unity forgetting factor. The forgetting factor is updated by means of a memory control algorithm, similar to Morrison’s master control algorithm (MCA). The new compact filter retains the robustness and adaptability of the non recursive filter, and stands out as a good candidate for tracking highly manoeuvrable targets. The recursive filter is also adapted using the Levenberg Marquardt method.