WP2: Distributed Multi-Sensor Processing

The objective of this research theme is to address challenges in detecting and tracking targets with networked sensor platforms of various modalities. In order to meet with the requirements of performance, flexibility and fault tolerance under resource constraints such as limited communication bandwidth and energy, we investigate distributed solutions which avoid a single designated processing centre. We are also interested in providing scalable solutions in centralised settings to facilitate multi-sensor exploitation.

WP2.1 Distributed Fusion and Registration

Cooperative Self-Localisation for Distributed Fusion Networks

Recently, we developed an algorithm by using the platforms which in a distributed fusion network can locate themselves in GPS denying environments. The measurements used for localisation are the detection's nodes collected from non-cooperative targets. The algorithm avoids the transmission of these measurements in the network to other sensor platforms [1].

One key to our algorithm is parameter likelihoods with the node-wise separability property: The conventional parameter estimation in state space models perspective [2] leads to a likelihood which is updated at every time step based on all the target detections collected across the network. In distributed fusion, however, filtered target distributions are exchanged among the nodes, as opposed to target detections [3]. We propose node-wise separable likelihoods for sensor pairs which are products of terms locally computable at the fusion nodes. These local terms are found using only the local target detections and the incoming target distributions. Hence, the resulting likelihoods are node-wise separable, and, are highly informative for estimation tasks (Figure 1).

Figure 1. Node-wise separable localisation likelihood for a pair of sensors: (left) 2 range-bearing sensors collect noisy measurements from multiple targets (green tracks) with false alarms and imperfect detection probabilities (black and blue crosses). They perform local multi-target filtering and exchange their posteriors (here, Sequential Monte Carlo (SMC) Probability Hypothesis Density (PHD) filtering [4] is used and the multi-target posteriors are multi-object Poisson distributions). Starting from time step k=1, we observe the change of the parameter likelihood. (Central graph) The update term at k=45 for the likelihood of the respective location of Sensor 2 in Sensor 1’s coordinate system. (right) The node-wise separable likelihood obtained through the updates from k=1 to k=45.

The second key to our algorithm is a pairwise Markov Random Field model for the parameter posterior that has node-wise separable likelihoods as edge potentials. We select the underlying communication topology as the corresponding graph. Since the likelihoods (the edge potentials of the model) are updated at every time step, the model is a dynamic Markov Random Field. Belief Propagation (BP) on this model leads to sensor self-localisation in a distributed fusion network (Figure 2).

Figure 2. Demonstration of the online likelihood update – BP messaging scheme: The nodes of the network (upper left) perform local filtering (SMC-PHD) of the target measurements (coloured crosses are detections from the targets with green tracks) and exchange posterior with their neighbours. For a selected time window T, they update node-wise separable localisation likelihoods. These local updates are in linear complexity with the number of detections. At the end of T, they iterate BP messaging for a selected number of steps (here, we use Non-parametric Belief Propagation [5] which is a particle algorithm compatible with the filtering performed). Here, the scatter plots of the particles generated from the local position densities are presented over time (upper left through lower right).

We have recently derived bounds on the Kullback-Leibler Divergence between the centralised and the node-wise separable likelihoods for a pair of sensors. These details will appear in a journal manuscript, soon.

Scalable Centralised Sensor Localisation and Target Tracking

A degree of centralisation might be inevitable if individual sensors do not have a good degree of target observability but joint filtering of sensor histories can provide the desired accuracy. We recently considered simultaneous localisation and tracking for bearing-only sensors and developed an online algorithm that scales with the number of sensors [6].

Our algorithm partitions the problem into sub-problems of a solvable size and then merges the solutions in a coherent fashion with scalable computational complexity.  We achieve this by assuming a Junction Tree model for the parameter posterior (Figure 3). This model decomposes the problem and specifies how the partial solutions can be merged (i.e., the Junction tree algorithm) [7]. From a computational perspective, our algorithm works as a Gibbs sampler for individual sensor locations. Specifically, we window the measurement histories and generate samples from single sensor distributions for consecutive windows. The complexity of the sampler is controlled by selecting the width of the Junction Tree (i.e., the number of variables in the variable nodes). This framework also allows us to exploit additional localisation information such as the received signal strength at the fusion centre for improving the robustness and accuracy of the algorithm (Figure 4).

Figure 3. An example Junction Tree model for the locations of bearing-only sensors with respect to the cluster head. (right) A sensor cluster. (middle) An example triangulated Markov graph. (right) The Junction Tree corresponding to the selected triangulation.

Figure 4. A demonstration of the proposed algorithm: (a) A target (green track) inducing bearing-only measurements on the peripheral sensors (S1-S4) as well as the cluster head (S0).  (b) Scatter plot of the particles generated from the location distributions for time window n=1,  (c) n=5, (d) n=10, ( e) n=15.

Figure 5. Comparison of the tracking errors for using only the bearing measurements at the cluster head (red) and the proposed online algorithm (black).

WP2.2 Distributed Decentralised Detection

The second stage of this work package tackles the problems surrounding the concept of a network as a sensor and considers distributed detection in networks constituted of sensors comparably less homogenous in their capabilities. We aim to close the gap between the potential that the literature offers and the applications of such systems.

There is a strong potential for collaboration with the other work packages of this research programme. The fusion and multi-modality aspects of this work package provide an ample ground for joint work with E_WP3 and E_WP4, respectively. Issues related to sensor management should be considered in cooperation with E_WP5. The second stage of this work package has the potential to interact with E_WP1 to exploit sparsity concepts in distributed detection settings. The algorithms developed within this work package should be implemented in liaison with E_WP6.

References

• [1] M. Uney, B. Mulgrew, D.E. Clark, “Cooperative sensor localisation in distributed fusion networks by exploiting non-cooperative targets,” in IEEE Workshop on Statistical Signal Processing (SSP) 2014, Gold Coast, Australia.
• [2] N. Kantas, A. Doucet, S. Singh, and J. Maciejowski, “An overview of Sequential Monte Carlo methods for parameter estimation on general state space models,” in Proceedings of the 15^th IFAC Symposium on System Identification, 2009, pp. 774—785.
• [3] M. Uney, D.E. Clark, S.J. Julier, “Distributed fusion of PHD filters via Exponential Mixture Densities,” IEEE Journal of Selected Topics in Signal Processing, vol.7, no.3, pp.521-531, June 2013.
• [4] B. Ristic, D. Clark, B.-N. Vo, B.-T. Vo, “Adaptive target birth intensity for PHD and CPHD filters,” IEEE Transactions on Aerospace and Electronic Systems, vol. 48, no. 2, pp. 1656—1668, 2012.
• [5] E.B. Sudderth, A.T. Ihler, M. Isard, W.T. Freeman, and A.S. Willsky, “Nonparametric Belief Propagation,” Communications of the ACM, vol. 53, no. 10, pp. 95—103, Oct. 2010.
• [6] M. Uney, B. Mulgrew, D.E. Clark, “Target aided online sensor localisation for bearing only clusters,” in Sensor Signal Processing for Defence (SSPD) 2014, Edinburgh, UK.
• [7] R. G. Cowell, A. P. Dawid, S. L. Lauritzen, and D. J. Spiegelhalter, Probabilistic Networks and Expert Systems. Springer, 1999.

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