Fast Inference and Update of Probabilistic Density Estimation on
  Trajectory Prediction
Takahiro Maeda Norimichi Ukita
Safety-critical applications such as autonomous vehicles and social robots
require fast computation and accurate probability density estimation on
trajectory prediction. To address both requirements, this paper presents a new
normalizing flow-based trajectory prediction model named FlowChain. FlowChain
is a stack of conditional continuously-indexed flows (CIFs) that are expressive
and allow analytical probability density computation. This analytical
computation is faster than the generative models that need additional
approximations such as kernel density estimation. Moreover, FlowChain is more
accurate than the Gaussian mixture-based models due to fewer assumptions on the
estimated density. FlowChain also allows a rapid update of estimated
probability densities. This update is achieved by adopting the \textit{newest
observed position} and reusing the flow transformations and its
log-det-jacobians that represent the \textit{motion trend}. This update is
completed in less than one millisecond because this reuse greatly omits the
computational cost. Experimental results showed our FlowChain achieved
state-of-the-art trajectory prediction accuracy compared to previous methods.
Furthermore, our FlowChain demonstrated superiority in the accuracy and speed
of density estimation. Our code is available at
\url{https://github.com/meaten/FlowChain-ICCV2023}