  We introduce an auxiliary technique, called residual nudging, to the particle
filter to enhance its performance in cases that it performs poorly. The main
idea of residual nudging is to monitor, and if necessary, adjust the residual
norm of a state estimate in the observation space so that it does not exceed a
pre-specified threshold. We suggest a rule to choose the pre-specified
threshold, and construct a state estimate accordingly to achieve this
objective. Numerical experiments suggest that introducing residual nudging to a
particle filter may (substantially) improve its performance, in terms of filter
accuracy and/or stability against divergence, especially when the particle
filter is implemented with a relatively small number of particles.
