  We analyze the performance of different resampling strategies for the
regularized particle filter regarding parameter estimation. We show in
particular, building on analytical insight obtained in the linear Gaussian
case, that resampling systematically can prevent the filtered density from
converging towards the true posterior distribution. We discuss several means to
overcome this limitation, including kernel bandwidth modulation, and provide
evidence that the resulting particle filter clearly outperforms traditional
bootstrap particle filters. Our results are supported by numerical simulations
on a linear textbook example, the logistic map and a non-linear plant growth
model.
