Parzen Particle Filters

Using a Parzen density estimator any distribution can be approximated arbitrarily close by a sum of kernels. In particle filtering this fact is utilized to estimate a probability density function with Dirac delta kernels; when the distribution is discretized it becomes possible to solve an otherwise intractable integral. In this work we propose to extend the idea and use any kernel to approximate the distribution. The extra work involved in propagating small kernels through the nonlinear function can be made up for by decreasing the number of kernels needed, especially for high dimensional problems. A further advantage of using kernels with nonzero width is that the density estimate becomes continuous.