  Multi-object state estimation is a fundamental problem for robotic
applications where a robot must interact with other moving objects. Typically,
other objects' relevant state features are not directly observable, and must
instead be inferred from observations. Particle filtering can perform such
inference given approximate transition and observation models. However, these
models are often unknown a priori, yielding a difficult parameter estimation
problem since observations jointly carry transition and observation noise. In
this work, we consider learning maximum-likelihood parameters using particle
methods. Recent methods addressing this problem typically differentiate through
time in a particle filter, which requires workarounds to the non-differentiable
resampling step, that yield biased or high variance gradient estimates. By
contrast, we exploit Fisher's identity to obtain a particle-based approximation
of the score function (the gradient of the log likelihood) that yields a low
variance estimate while only requiring stepwise differentiation through the
transition and observation models. We apply our method to real data collected
from autonomous vehicles (AVs) and show that it learns better models than
existing techniques and is more stable in training, yielding an effective
smoother for tracking the trajectories of vehicles around an AV.
