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Non-myopic GOSPA-driven Gaussian Bernoulli Sensor Management

George Jones, Angel Garcia-Fernandez, Christian Blackman

TL;DR

This work develops a non-myopic, MSGOSPA-driven sensor management framework for Bernoulli filtering, enabling an agile sensor to track a single target and search for new ones within a POMDP setting. By deriving a Gaussian-Bernoulli model and an efficient MSGOSPA upper bound, the authors formulate a Bellman-like planning problem and solve it approximately with Monte Carlo Tree Search. The approach is validated in simulations showing that non-myopic planning can outperform myopic and KL-based strategies, particularly in obstacle-rich environments where foresight enables successful target maintenance and re-acquisition. These results offer a practically efficient, interpretable method for sensor management under uncertain single-target dynamics, with potential extensions to multi-target scenarios and learning-based enhancements.

Abstract

In this paper, we propose an algorithm for non-myopic sensor management for Bernoulli filtering, i.e., when there may be at most one target present in the scene. The algorithm is based on selecting the action that solves a Bellman-type minimisation problem, whose cost function is the mean square generalised optimal sub-pattern assignment (GOSPA) error, over a future time window. We also propose an implementation of the sensor management algorithm based on an upper bound of the mean square GOSPA error and a Gaussian single-target posterior. Finally, we develop a Monte Carlo tree search algorithm to find an approximate optimal action within a given computational budget. The benefits of the proposed approach are demonstrated via simulations.

Non-myopic GOSPA-driven Gaussian Bernoulli Sensor Management

TL;DR

This work develops a non-myopic, MSGOSPA-driven sensor management framework for Bernoulli filtering, enabling an agile sensor to track a single target and search for new ones within a POMDP setting. By deriving a Gaussian-Bernoulli model and an efficient MSGOSPA upper bound, the authors formulate a Bellman-like planning problem and solve it approximately with Monte Carlo Tree Search. The approach is validated in simulations showing that non-myopic planning can outperform myopic and KL-based strategies, particularly in obstacle-rich environments where foresight enables successful target maintenance and re-acquisition. These results offer a practically efficient, interpretable method for sensor management under uncertain single-target dynamics, with potential extensions to multi-target scenarios and learning-based enhancements.

Abstract

In this paper, we propose an algorithm for non-myopic sensor management for Bernoulli filtering, i.e., when there may be at most one target present in the scene. The algorithm is based on selecting the action that solves a Bellman-type minimisation problem, whose cost function is the mean square generalised optimal sub-pattern assignment (GOSPA) error, over a future time window. We also propose an implementation of the sensor management algorithm based on an upper bound of the mean square GOSPA error and a Gaussian single-target posterior. Finally, we develop a Monte Carlo tree search algorithm to find an approximate optimal action within a given computational budget. The benefits of the proposed approach are demonstrated via simulations.
Paper Structure (42 sections, 1 theorem, 62 equations, 10 figures, 3 tables)

This paper contains 42 sections, 1 theorem, 62 equations, 10 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Problem Formulation & Background
  3. Bernoulli Dynamic & Measurement Model
  4. Bernoulli Filtering
  5. The GOSPA metric
  6. Non-myopic Planning using the time-discounted predicted MSGOSPA Error
  7. Non-myopic Gaussian Bernoulli Sensor Management
  8. Gaussian Predicted Density
  9. Predicted Measurement Density
  10. Gaussian Posterior
  11. For ${Z}_k = \emptyset$
  12. For ${Z}_k = \{\hat{z}_{a_k}\}$
  13. Upper Bound on the MSGOSPA error
  14. The Bellman Equation
  15. Monte Carlo Tree Search Implementation
  16. ...and 27 more sections

Key Result

Lemma 1

Let $(r_{k|k,a_k}^j, P^j_{k|k,a_k} )$ be the updated probability of existence and covariance matrix of the target for $|Z_k|=j, j\in \{0,1\}$. An upper bound on the MSGOSPA error for a given measurement set $Z_k$ is where A proof of this lemma is provided in Appendix Appendix B.

Figures (10)

  • Figure 1: Selection stage of the MCTS. Top node representing the current time-step with the green nodes indicating which have been selected from the pre-existing tree (black nodes).
  • Figure 2: Expansion stage of the MCTS with green nodes indicating those that have been used to get to the point where the tree has been expanded (lowest green node).
  • Figure 3: Simulation phase of the MCTS where the green nodes indicate which nodes have been selected (or expanded - lowest green node) and the blue nodes indicating a random path, as governed by the rollout policy, down to the planning horizon.
  • Figure 4: Back-propagation phase of the MCTS with the yellow nodes indicating which node statistics are set to be updated, stating from the lowest yellow node and propagating back up the tree.
  • Figure 5: The sensor movement model where the number of available actions is equal to six.
  • ...and 5 more figures

Theorems & Definitions (1)

  • Lemma 1