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A Distributed Consensus Particle Filter for Target Tracking using Autonomous Surface Vessels

Carter Noh, Kyle Crandall, Connor Yates, Corbin Wilhelmi

arXiv:2609.09066v1cs.RO

TL;DR

Intermittent communication in distributed maritime tracking can leave agents with overly confident local estimates. The paper adds particle spreading along the measurement manifold to a distributed particle filter, and reports comparable nominal performance with improved performance in certain communication-dropout edge cases.

  • Problem

    Distributed maritime tracking requires independent estimates and opportunistic communication, but local filters can become overly confident without external updates.

    Source: §I · p. 1, C. Particle Spreading Heuristic · p. 2

  • Method

    The method spreads particles along the measurement manifold during communication dropouts to reduce the influence of outdated consensus updates.

    Source: C. Particle Spreading Heuristic · p. 2

  • Results

    The spreading filter performs comparably to the unaugmented filter nominally and outperforms it in certain dropout edge cases.

    Source: C. Effect of Dropout on Performance · p. 6, §V · p. 6

  • Takeaways & Limitations

    The heuristic did not significantly worsen nominal performance and marginally improved recovery time relative to the standard particle filter.

    Source: C. Effect of Dropout on Performance · p. 6

    Further work will examine dropout durations, target behavior during dropouts, parameter tuning, and larger teams with heterogeneous sensing.

    Source: §V · p. 6

Abstract

from arXiv · show

Maritime target tracking over large distances often requires multi-agent teams without centralized coordination, and intermittent communication. Each agent must maintain an independent estimate that can take advantage of opportunistic communications availability when possible. This can lead to overly confident local estimates in the absence of external data. In this work, we propose an augmentation to a classical particle filter implementation that accounts for this potential source of error by forcing particles to spread strategically in the absence of informative updates from other sensor nodes. We demonstrate our method using Unmanned Surface Vessels (USVs) on a lake, and show that our augmentations do not deteriorate nominal performance, and provide an advantage in some specific edge cases.

I. INTRODUCTION

Maritime tracking over large distances calls for distributed teams that maintain local estimates while coordinating over intermittent communications. This work introduces particle spreading to reduce overconfidence in local estimates during communication gaps and evaluates it with USVs on a lake.

I. INTRODUCTION

  • Distributed maritime tracking must support independent local estimates and opportunistic information sharing when communications are noisy or intermittent.Existing distributed particle-filter approaches often have stringent communication requirements.Source: §I · p. 1
  • Without external updates, filters can over-rely on prior information and produce overly confident local estimates.Distributed consensus approaches also struggle with large communication gaps without additional heuristics.Source: §I · p. 1
  • The proposed heuristic spreads particles along the sensor manifold during communication gaps; lake field tests found no nominal performance degradation and faster recovery in certain dropout edge cases.The tests used a team of USVs.Source: §I · p. 1

II. METHODS

The agents estimate target position using local sensing and opportunistic communication over a changing network. The paper compares a tiled Bayes filter baseline with its main focus, a distributed particle filter that shares estimates rather than measurements.

A. Problem Formulation

  • Agents estimate a target’s position from noisy direction-of-arrival measurements while communicating only when within range, with dropouts possible.Each agent estimates its own global position and orientation.Source: A. Problem Formulation · p. 1
  • A changing communication graph supports opportunistic estimate sharing; agents exchange estimates, not measurements, and perform Bayesian updates as information arrives.The approach avoids forwarding measurements and tracking which measurements have already been applied.Source: A. Problem Formulation · p. 2

B. Distributed Particle Filter

1) Prediction Update:

The filter predicts target motion by randomly moving each particle, then incorporates bearing measurements by weighting and resampling particles.

1) Prediction Update:

  • The prediction update samples a movement distance and direction for the target’s random-walk model, with a unique update for each particle.Distance is sampled uniformly from 0 to rmax, and angle uniformly from −π to π.Source: 1) Prediction Update · p. 2

2) Measurement Update:

  • The bearing likelihood uses the predicted angle for each particle and measurement-noise variance.The supplied passages identify the likelihood model as Gaussian.Source: 2) Measurement Update · p. 2
  • For a direction-of-arrival bearing measurement, the filter weights particles by measurement likelihood and resamples using normalized weights.The measurement likelihood is computed for each particle.Source: 2) Measurement Update · p. 2

3) Consensus Update:

At communication windows, agents exchange uniformly sampled subsets of their particles. Receiving agents weight the incoming particles and resample them together with their current particles.

3) Consensus Update:

  • At each communication window, an agent shares a uniformly sampled subset of its particles with neighboring agents.This is an estimate-sharing update rather than forwarding measurements.Source: 3) Consensus Update · p. 2
  • A receiving agent assigns each incoming particle a weight based on the sizes of its own particle set and the received subset.The own-set size is M, and the received-subset size is Mj.Source: 3) Consensus Update · p. 2
  • The receiving agent resamples from the incoming particles and its current particles, using the assigned weights for incoming particles and weight 1 for current particles.Resampling forms a Bernoulli distribution, as in the measurement update.Source: 3) Consensus Update · p. 2

C. Particle Spreading Heuristic

During communication dropout, particles can remain tightly clustered despite growing uncertainty along the measurement manifold, producing falsely certain estimates. The heuristic spreads particles along that manifold until another consensus update arrives.

C. Particle Spreading Heuristic

  • Without consensus updates, particles may stay tightly clustered as uncertainty grows along the measurement manifold, leaving a falsely certain estimate and a difficult-to-recover distribution after communication resumes.The distribution may become multimodal or otherwise deteriorated when a consensus update arrives at the end of a dropout period.Source: C. Particle Spreading Heuristic · p. 2
  • For a DoA sensor, the measurement manifold is the bearing line: angle is constrained, while uncertainty in target distance along the line grows during dropout.The movement distance is directed along the agent-to-particle unit vector toward the corresponding Voronoi cell center.Source: C. Particle Spreading Heuristic · pp. 2–3
  • The heuristic adds a prediction-step movement that spreads particles along the measurement manifold, reducing the influence of prior consensus updates.Particles are projected onto the manifold, assigned Voronoi cells, and moved toward their respective cell centers before projection back into target state space.Source: C. Particle Spreading Heuristic · p. 2, Figure 2 · p. 3

1) Scaling & Convergence:

The spreading movement is scaled using a convergence metric, while a singularity score distinguishes poorly conditioned agent-target geometry from better-conditioned geometry.

1) Scaling & Convergence:

  • The largest eigenvalue of the inter-set dispersion matrix is used as the convergence metric for scaling particle spreading.The matrix is defined as the second-moment matrix of pairwise displacements between particle sets; spreading defaults to a scale of 1 during inter-agent dropout.Source: 1) Scaling & Convergence · p. 3

D. Geometric Singularity

  • The singularity score is small near agent-target collinearity and approaches 1 when the geometry is well-conditioned for localizing the target.The score is used to distinguish nominal estimates from singular cases, where tracking is expected to deteriorate.Source: D. Geometric Singularity · p. 3

E. Distributed Bayes Filter

The distributed Bayes filter provides a tiled baseline for comparison with the continuous-space particle filter.

E. Distributed Bayes Filter

  • The distributed Bayes filter tracks target-position probabilities over one-meter hexagonal tiles, diffuses them according to a behavioral model, and combines consensus messages by multiplying and normalizing probabilities.Its position estimate is the probability-weighted average of tile centers.Source: E. Distributed Bayes Filter · p. 3
  • For direct comparison, particle estimates are converted into tile probabilities and then averaged over tile centers, matching the Bayes filter’s estimate procedure.The Bayes filter’s performance is bounded by tile size, whereas the particle filter operates in continuous space.Source: E. Distributed Bayes Filter · p. 3

III. EXPERIMENTS

The field test used two USV agents and a target at a lake, with four missions covering different motion and geometry scenarios. Data were replayed with simulated communication dropout to compare estimation methods on the same baseline data.

III. EXPERIMENTS

  • Two SeaRobotics HYCAT USV agents tracked a target at a lake, communicating over WiFi with a base station that controlled the experiment.Each vehicle used station-keeping and waypoint controllers to execute position commands.Source: §III · p. 3

A. Missions

  • The four missions varied target and agent motion, including a far-target scenario with consistently low singularity and a Mission 3 crossing designed to create geometric singularities.Mission 4 kept the target stationary while the agents moved around it; Fig. 3 shows agent and target trajectories across the missions.Source: A. Missions · p. 4, Figure 3 · p. 4

B. Data Processing

  • The team collected full data without dropout, then replayed it with artificially induced dropout to compare methods using the same baseline data.Dropout was simulated by ignoring other agents’ consensus messages while a dropout command was active.Source: B. Data Processing · p. 4, §III · p. 4

IV. RESULTS

Across four missions, the filters had nearly identical overall RMSE, while performance worsened in geometrically singular regions. Singularity scores also tracked estimation error, which rose as singularity increased.

A. Performance Across All Missions

  • On Mission 1, the filters’ Agent 1 estimates deviated from the true target at similar points and had similar noise levels.Fig. 4 shows the target-position estimates.Source: A. Performance Across All Missions · p. 4, Figure 4 · p. 4
  • Across four missions, RMSE differed by only 0.11 m between the best and worst filters, a statistically negligible difference below the standard deviation.The reported standard deviations were near the 1 m tile radius, which the paper identifies as a lower bound on filter performance.Source: Table I · p. 4, A. Performance Across All Missions · p. 4

B. Effect of Geometric Singularity on Performance

C. Effect of Dropout on Performance

During communication dropouts, the Bayes filter outperformed both particle filters on peak-to-base error ratio and recovery time. Longer dropouts increased peak error ratios and recovery times, while particle spreading modestly improved particle-filter results.

C. Effect of Dropout on Performance

  • During dropout, agents used only their own DoA measurements, error accumulated, and estimates returned to normal levels after communication resumed.Peak error was measured against the mean error in the five seconds before dropout; recovery meant returning within 1.1x baseline, across dropout durations from 2.5 to 15 seconds.Source: C. Effect of Dropout on Performance · p. 5
  • As dropout duration increased, mean peak-to-base error ratios rose and recovery times also increased, though recovery-time changes were less predictable.The particle-spreading heuristic consistently reduced peak error by a small amount and marginally improved recovery time without performing significantly worse than the standard particle filter.Source: C. Effect of Dropout on Performance · pp. 5–6
  • The Bayes filter outperformed both particle filters in peak-to-base error ratio and recovery time during communication dropout.The paper attributes an inherent dropout advantage to the Bayes filter’s coverage of the whole space, while its minimum error remains bounded by tile size.Source: C. Effect of Dropout on Performance · pp. 5–6, Figure 7 · p. 5

V. CONCLUSION

The spreading augmentation has comparable performance to a no-spreading filter in nominal conditions and outperforms it in some communication-dropout edge cases; its performance is also comparable to a baseline Bayes filter. Future work will examine edge cases and larger, heterogeneous teams.

V. CONCLUSION

  • The spreading filter performs comparably to a no-spreading filter in nominal conditions and outperforms it in some communication-dropout edge cases; both are comparable to a baseline Bayes filter.These findings are based on experimental data from real-world USV tests.Source: §V · p. 6
  • When communication drops, the augmentation spreads particles along the sensor manifold to de-emphasize outdated external measurements and focus on locally available data.Source: §V · p. 6
  • Future work will examine dropout durations, target behavior during dropouts, parameter tuning, and extension to larger teams with heterogeneous sensing capabilities.Source: §V · p. 6
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