Improved auxiliary and Unscented Particle Filter variants

This paper proposes some modifications to the Auxiliary Particle Filter and the Unscented Particle Filter. For the APF, based on some error bound considerations it is suggested that the auxiliary weights are taken into account not proportionally but nonlinearly. An improved way to compensate for the auxiliary weights after the resampling is also proposed. For the UPF, a method is introduced to compute the covariance matrices of the particles not using the UKF equations for each particle separately, but so as to optimize the characteristics of the total distribution. The application of the modified filters to an example shows that the proposed changes lead to performance increase.