Distributed Multi-Object Tracking Under Limited Field of View Heterogeneous Sensors with Density Clustering

TL;DR

This work proposes an efficient distributed multi-object tracking algorithm that performs track-to-track fusion using a clustering-based analysis of the state space transformed into a density space to mitigate the complexity of the assignment problem.

Abstract

We consider the problem of tracking multiple, unknown, and time-varying numbers of objects using a distributed network of heterogeneous sensors. In an effort to derive a formulation for practical settings, we consider limited and unknown sensor field-of-views (FoVs), sensors with limited local computational resources and communication channel capacity. The resulting distributed multi-object tracking algorithm involves solving an NP-hard multidimensional assignment problem either optimally for small-size problems or sub-optimally for general practical problems. For general problems, we propose an efficient distributed multi-object tracking algorithm that performs track-to-track fusion using a clustering-based analysis of the state space transformed into a density space to mitigate the complexity of the assignment problem. The proposed algorithm can more efficiently group local track estimates for fusion than existing approaches. To ensure we achieve globally consistent identities for tracks across a network of nodes as objects move between FoVs, we develop a graph-based algorithm to achieve label consensus and minimise track segmentation. Numerical experiments with synthetic and real-world trajectory datasets demonstrate that our proposed method is significantly more computationally efficient than state-of-the-art solutions, achieving similar tracking accuracy and bandwidth requirements but with improved label consistency.

Figures (18)

• Figure 1: A distributed heterogeneous sensor network with limited FoVs and bandwidth-limited communication links.
• Figure 2: CDP algorithm illustration. Different colours denote different clusters of data. (a) Example set of data points. (b) Data points are converted to ($\rho,\delta$) coordinates. Cluster centres can be identified by data with high $(\rho, \delta)$ values (those above the dashed line in our example).
• Figure 3: An example illustrating the analysis of labelled estimates with the ModifiedCDP Algorithm, resulting in label associations from the cluster analysis and the derivation of the kinematic consensus state. a) Consider ten 2D spatial locations of labelled local estimates from three sensor nodes: $\boldsymbol{X}^{(\text{local})} = [\boldsymbol{x}_1^{(1)},\boldsymbol{x}_2^{(1)},\boldsymbol{x}_3^{(1)},\boldsymbol{x}_1^{(2)},\boldsymbol{x}_2^{(2)},\boldsymbol{x}_3^{(2)},\boldsymbol{x}_4^{(2)},\boldsymbol{x}_1^{(3)},\boldsymbol{x}_2^{(3)},\boldsymbol{x}_3^{(3)}]$. After applying the ModifiedCDP Algorithm, $6$ cluster centres are identified. Now, the resulting clustering index vector for the input $\boldsymbol{X}^{(\text{local})}$ is $D = [5,2,1,3,2,5,4,6,2,3]$. This vector signifies that $\boldsymbol{x}^{(1)}_1$ is associated with $\boldsymbol{x}^{(2)}_3$ (clustering index $5$), $\boldsymbol{x}^{(1)}_2$ is associated with both $\boldsymbol{x}^{(2)}_2$ and $\boldsymbol{x}^{(3)}_2$ (clustering index $2$), $\boldsymbol{x}^{(2)}_1$ is associated with $\boldsymbol{x}^{(3)}_3$ (clustering index $3$), whilst the remaining local estimates are not associated with any others. b) Illustrates the label associations between local estimates based on the clustering indices $D$ obtained from the ModifiedCDP Algorithm. This information is used to update the weighted graph to achieve global label consensus.
• Figure 4: An overview of the proposed CDP-WGL algorithm for Distributed MOT (DMOT). Each Sensor Node tracks objects within its sensor's FoV using a local MOT Filter and shares the local labelled estimates $\mathbf{X}^{(n)}$ via a communication network with other nodes. Global fused, labelled estimates $\mathbf{X}^{(\text{global})}$ or tracks are computed at each sensor node using the local and shared information using DMOTFusion described in Algorithm \ref{['algo:compute_glob_est']} where: i) Kinematic Consensus is supported by the proposed CDP cluster analysis based algorithm, ModifiedCDP, described in Algorithm \ref{['algo:modified_CDP']}; and ii) Global Label Consensus is supported by the weighted graph labelling method using UpdateGraph described in Algorithm \ref{['algo:update_graph']}.
• Figure 5: A simple illustration of the weighted graph label consensus method compared to the unweighted method in the presence of an incorrect label association assertion resulting from the clustering analysis. a) Object 1 and Object 2 enter the common FoV of sensor node 1 and node 2. The label graph shows the correct label association between each sensor node's labels. b) A clustering error occurs when object 1 crosses Object 2 at a similar space-time dimension and leads to grouping local estimates of Object 1 and 2 from nodes 1 and 2 into a single cluster. c) Result of unweighted graph label consensus method. After the label graph update, new edges $\{\ell_{1}^{(1)}, \ell_{2}^{(2)}\}$ and $\{\ell_{2}^{(1)}, \ell_{1}^{(2)}\}$ are added as a result of the clustering error. The smallest label $\ell_{1}^{(1)}$ in terms of lexicographic order is then permanently associated with Object 2 and causes a label switch while object 1's label is not affected. d) Effect of weighted graph label consensus method. After the graph update, the same edges are added with an initial weight of $5$ while all other edges' weights remain at $0$ (due to the graph update prior to the cluster error). The edge weight provides evidence to support a label association, effectively isolating Object 1 and 2's label graphs and preventing a label switch for Object 2.

Theorems & Definitions (2)

• Remark 1
• Remark 2