Improving results of rational non-linear observation functions using a Kalman filter correction

This article deals with the divergence of the Kalman filter when used on non-linear observation functions. The Kalman filter allows to update some parameters according to observations and their uncertainties. The observation model which links the parameters to the observations is often non-linear and has to be linearized. An improper linearization leads to a divergence effect that could be contained by increasing the observation noise. When the observation model can be written as a quotient of two linear functions, the presented method allows to reduce the divergence effect without modifying the observation noise. This method is similar to a proportional correction in the Kalman update step and is more efficient than the unscented Kalman filter or particle filter.