Learning Flock: Enhancing Sets of Particles for Multi~Sub-State Particle Filtering with Neural Augmentation

TL;DR

This work introduces Learning Flock (LF), a permutation-equivariant neural augmentation for particle filters that jointly corrects the entire flock of particles and their weights in multi-substate tracking. By processing all sub-particles with self-attention and dedicated embeddings, LF leverages inter-particle relationships to produce a richer, more accurate posterior with fewer particles, and it supports both supervised and unsupervised training while remaining transferable across PF implementations. The authors define a dual-component loss combining state-estimation accuracy (OSPA) and a heatmap-based pdf alignment against an oracle distribution, and they provide a practical training framework with grid-based pdf reconstruction. Experiments on synthetic state estimation and radar multi-target tracking demonstrate that LF improves accuracy, robustness to observation-model mismatch, and latency, often matching or surpassing high-particle baselines and enabling significant particle-efficiency gains in challenging MT tracking scenarios.

Abstract

A leading family of algorithms for state estimation in dynamic systems with multiple sub-states is based on particle filters (PFs). PFs often struggle when operating under complex or approximated modelling (necessitating many particles) with low latency requirements (limiting the number of particles), as is typically the case in multi target tracking (MTT). In this work, we introduce a deep neural network (DNN) augmentation for PFs termed learning flock (LF). LF learns to correct a particles-weights set, which we coin flock, based on the relationships between all sub-particles in the set itself, while disregarding the set acquisition procedure. Our proposed LF, which can be readily incorporated into different PFs flow, is designed to facilitate rapid operation by maintaining accuracy with a reduced number of particles. We introduce a dedicated training algorithm, allowing both supervised and unsupervised training, and yielding a module that supports a varying number of sub-states and particles without necessitating re-training. We experimentally show the improvements in performance, robustness, and latency of LF augmentation for radar multi-target tracking, as well its ability to mitigate the effect of a mismatched observation modelling. We also compare and illustrate the advantages of LF over a state-of-the-art DNN-aided PF, and demonstrate that LF enhances both classic PFs as well as DNN-based filters.

Figures (11)

• Figure 1: lf block architecture block diagram. A set of $N$ particle-weight pairs $\{\breve{{\boldsymbol{x}}}_i^k, \breve{w_i}^k\}_{i=1}^N$ is decomposed into $N \times t$ sub-particles $\{\breve{{\boldsymbol{x}}}_{j,i}^k,\breve{w_i}^k\}_{j,i=1}^{t,N}$, and processed by $J$flock-update blocks in parallel. Each block contains two parallel embedding networks in series with two sa blocks and fc layers, outputting a correction term to each full-particle.
• Figure 2: The construction of the actual pdf $c)$ using the adapting kernels functions $b)$ based on the desired pdf $a)$.
• Figure 3: staged meshgrid: The heatmap loss is calculated as the sum of $L$ squared error between $L$ pairs of heatmaps grids, desired (top row) and actual (bottom row), on different resolutions and scales.
• Figure 4: lf particles and weights adjustment example with the lfsispf in the \ref{['itm:UniformNoise']} settings of Subsection \ref{['ssec:StateEstimation']}. Top: reconstructed pdf cross-section and particles at the input (Fig. \ref{['fig:heatmap_rand_grid_before_nn3']}) and output (Fig. \ref{['fig:heatmap_rand_grid_after_nn3']}) of the lf block. The particles projection on $[x_1,x_2]$ plane are marked with red dots, and the desired state's and its estimate's projections are marked with green and red crosses, respectively. Bottom: the particles' sorted weights (Fig. \ref{['fig:sorted_wts_rand_grid']}) and weights histograms (Fig. \ref{['fig:wts_hists_rand_grid']}) at the input and output of the lf module.
• Figure 5: Overall (top) and last time-step $k=\kappa$ (bottom) tracking accuracy for settings \ref{['itm:LinGauss']}-\ref{['itm:UniformNoise']} over $\kappa=12$ time-steps trajectories. urpf is utilized for overall and last time-step accuracy with its respective task oriented trained parameters ${\boldsymbol{\xi}}_1$ or ${\boldsymbol{\xi}}_2$. ($\_Rs$) implies resampling with $N_{\rm th}=N//3$, and ($LF-$) or ($LF_{(-1)}-$) implies the utilization of the lf including or excluding the last time-step. $SISPF\_Rs\_300$ was tested with $N=300$ particles, while all other benchmarks were tested with $N=25$.