In search for improved auxiliary particle filters

In designing a particle filter, the most important task is choosing the importance function that can generate good particles. If the importance function, also called proposal, does a satisfactory job, the particles of the filter are placed in parts where the explored state space has high probability mass. Further, the weights of these particles are not too disparate in values. An important class of particle filtering that uses a clever approach to create good importance functions is known as auxiliary particle filtering. In this paper, we first analyze the approximations used for computing the particle weights of the standard auxiliary particle filter. We show that these approximations can be detrimental to the performance of the auxiliary particle filter. Further, we propose a more comprehensive evaluation of the weights, which leads to a much enhanced performance of the auxiliary particle filter. We also demonstrate the improvements with computer simulations.