The recent advances in wireless communication, micro-fabrication, and integration have led to the rise of multi-agent networks such as wireless sensor networks, drone swarms, and satellite arrays. These multi-agent networks comprise multiple agents, which cooperate to solve a problem collectively, beyond the individual knowledge of a single agent. Multi-agent networks are also known for improving overall system performance, especially in terms of scalability, robustness, and flexibility.

Multi-agent networks are tasked with a variety of tasks e.g., target tracking, surveillance, traffic control, and environmental monitoring. Traditionally these tasks are solved using distributed state-space filtering methods, however under the assumptions of linear models with underlying Gaussian noise. However, in general, the models could be Non-linear, and the underlying stochastic noise is not necessarily Gaussian in nature. To address this limitation, Distributed particle filters (DPF) have been investigated in recent years. Depending on the quantities exchanged in the network, DPFs can be categorized as weight-based, likelihood-based, or posterior-based.

One of the key challenges for effective implementation of the DPF is the need for approximation strategies to reduce the burden on communication and computation resources to suit engineering applications. To this end, we review two state-of-the-art DPF, (a) one based on applying the Graph Laplacian (GL) approximation to weights, and (b) the other using the Gaussian mixture model (GMM) to represent the local posteriors. These two algorithms significantly reduce the communication burden; however, the main limitation is the synchronization and heavy computational burden, which places high demands on hardware and software implementation of agents.

To improve on these existing methods, we propose the use of Gaussian process (GP) enhanced resampling algorithm, which reduces the particle set size, while ensuring an acceptable filter performance. Based on this GP-enhanced resampling scheme, we propose a novel Distributed particle filtering algorithm. Secondly, based on the proposed GP-enhanced sampling, we propose several metaheuristic optimization algorithms (i.e., genetic algorithm and firefly algorithm) to fuse the information across the whole network to improve the estimation performance (i.e., to seek the global optimal particle set as we can treat particles as “parents” or “fireflies”).

We compare our proposed algorithms and study their performance against the state-of-the-art DPFs in terms of time, space, and communication complexity, for a target tracking application. We use time-averaged root mean square error (ARMSE), which is used to quantify the performance of each DPF. Our numerical results demonstrate the superiority of our proposed algorithms under the condition of limited communication and computational resources, and still maintaining the optimality of particle filter.

For example, to achieve a certain ARMSE for a target tracking application, the traffic for existing GL and GMM based DPFs, is 12000 scalars/second/agent and 600 scalars/second/agent respectively, while our proposed GP-enhanced resampling and firefly algorithm uses only 900scalars/second/agent. In terms of the computation runtime, the GL and GMM based approaches take 40 and 300 seconds (about 5 minutes) respectively, while our proposed algorithm takes just 1.5 seconds, and thus shows significant improvement. Finally, we propose research directions to further improve our proposed algorithms in the future.