  Resampling is a key component of sample-based recursive state estimation in
particle filters. Recent work explores differentiable particle filters for
end-to-end learning. However, resampling remains a challenge in these works, as
it is inherently non-differentiable. We address this challenge by replacing
traditional resampling with a learned neural network resampler. We present a
novel network architecture, the particle transformer, and train it for particle
resampling using a likelihood-based loss function over sets of particles.
Incorporated into a differentiable particle filter, our model can be end-to-end
optimized jointly with the other particle filter components via gradient
descent. Our results show that our learned resampler outperforms traditional
resampling techniques on synthetic data and in a simulated robot localization
task.
