  We consider the problem of designing efficient particle filters for twisted
Feynman--Kac models. Particle filters using twisted models can deliver low
error approximations of statistical quantities and such twisting functions can
be learnt iteratively. Practical implementations of these algorithms are
complicated by the need to (i) sample from the twisted transition dynamics, and
(ii) calculate the twisted potential functions. We expand the class of
applicable models using rejection sampling for (i) and unbiased approximations
for (ii) using a random weight particle filter. We characterise the average
acceptance rates within the particle filter in order to control the
computational cost, and analyse the asymptotic variance. Empirical results show
the mean squared error of the normalising constant estimate in our method is
smaller than a memory-equivalent particle filter but not a
computation-equivalent filter. Both comparisons are improved when more
efficient sampling is possible which we demonstrate on a stochastic volatility
model.
