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GOSPA-Driven Non-Myopic Multi-Sensor Management with Multi-Bernoulli Filtering

George Jones, Angel Garcia-Fernandez

TL;DR

A non-myopic sensor management algorithm for multi-target tracking, with multiple sensors operating in the same surveillance area, based on multi-Bernoulli filtering and selects the actions that solve a non-myopic minimisation problem, over a future time window.

Abstract

In this paper, we propose a non-myopic sensor management algorithm for multi-target tracking, with multiple sensors operating in the same surveillance area. The algorithm is based on multi-Bernoulli filtering and selects the actions that solve a non-myopic minimisation problem, where the cost function is the mean square generalised optimal sub-pattern assignment (GOSPA) error, over a future time window. For tractability, the sensor management algorithm actually uses an upper bound of the GOSPA error and is implemented via Monte Carlo Tree Search (MCTS). The sensors have the ability to jointly optimise and select their actions with the considerations of all other sensors in the surveillance area. The benefits of the proposed algorithm are analysed via simulations.

GOSPA-Driven Non-Myopic Multi-Sensor Management with Multi-Bernoulli Filtering

TL;DR

A non-myopic sensor management algorithm for multi-target tracking, with multiple sensors operating in the same surveillance area, based on multi-Bernoulli filtering and selects the actions that solve a non-myopic minimisation problem, over a future time window.

Abstract

In this paper, we propose a non-myopic sensor management algorithm for multi-target tracking, with multiple sensors operating in the same surveillance area. The algorithm is based on multi-Bernoulli filtering and selects the actions that solve a non-myopic minimisation problem, where the cost function is the mean square generalised optimal sub-pattern assignment (GOSPA) error, over a future time window. For tractability, the sensor management algorithm actually uses an upper bound of the GOSPA error and is implemented via Monte Carlo Tree Search (MCTS). The sensors have the ability to jointly optimise and select their actions with the considerations of all other sensors in the surveillance area. The benefits of the proposed algorithm are analysed via simulations.

Paper Structure

This paper contains 29 sections, 1 theorem, 52 equations, 5 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background & Objective
  3. Dynamic & Measurement Model
  4. Multi-Bernoulli Filtering
  5. MB Filter Prediction Step
  6. MB Filter Update Step
  7. The GOSPA metric
  8. Non-myopic Planning with Time-discounted MSGOSPA Error
  9. Multi-sensor Management
  10. Assumptions of the Sensor Management Algorithm
  11. Measurement Density
  12. MSGOSPA Error for a Given MB Posterior
  13. MSGOSPA Error Upper Bound in One Time Step
  14. Multi-sensor Update for sensor management
  15. Non-myopic Planning
  16. ...and 14 more sections

Key Result

Lemma 1

Let $r_{k|k,a_{k}}^{i,|Z_{k}^{i}|}$ and $P_{k|k,a_{k}}^{i,|Z_{k}^{i}|}$ be the updated probability of existence and covariance matrix of the $i$-th Bernoulli for the sequence of detections/misdetections $|Z_{k}^{i}|=\left(|Z_{k}^{1,i}|,...,|Z_{k}^{S,i}|\right)$ where $|Z_{k}^{s,i}|\in\{0,1\}$ with $ Lemma 1 is proved in Appendix appendix_A.

Figures (5)

  • Figure 1: The four stages of the MCTS algorithm. Where $\Delta$ is the cost returned from the simulation phase. Figure adapted from BostroemRost2021Browne2012.
  • Figure 2: Sensor movement model, showing seven possible actions for an individual sensor. Six actions cause the sensor to move and one action cause the sensor to hold its position.
  • Figure 3: Number of targets alive at each time step in the simulation. Starting with zero targets and a maximum number of four at time steps 75 and 125. The total number of targets in the simulation is 8.
  • Figure 4: Frame 152 in one Monte Carlo run, number of targets alive: 2. Top - myopic KLD scenario snapshot. Both sensors are stuck behind the obstacle as they do not have the ability to plan further ahead. Bottom - MCTS3 scenario snapshot. Sensors have navigated around the obstacle and are maintaining track of the two targets alive at this time step. Purple outline on each sensor indicates they are planning with a non-myopic policy, purple line between the two sensors indicates they are being jointly optimised at this time step. Birth density is centred at the origin.
  • Figure 5: GOSPA error breakdown for the obstacles scenario. The top plot shows the overall GOSPA error across each MC run for each time step. The second, third and fourth plots show the localisation, missed and false errors that contribute to the overall GOSPA error. Result set for $\overline{\lambda}^C_{a_k} = 1$.

Theorems & Definitions (1)

  • Lemma 1