Likelihood Consensus and Its Application to Distributed Particle Filtering (1108.6214v4)

Abstract: We consider distributed state estimation in a wireless sensor network without a fusion center. Each sensor performs a global estimation task---based on the past and current measurements of all sensors---using only local processing and local communications with its neighbors. In this estimation task, the joint (all-sensors) likelihood function (JLF) plays a central role as it epitomizes the measurements of all sensors. We propose a distributed method for computing, at each sensor, an approximation of the JLF by means of consensus algorithms. This "likelihood consensus" method is applicable if the local likelihood functions of the various sensors (viewed as conditional probability density functions of the local measurements) belong to the exponential family of distributions. We then use the likelihood consensus method to implement a distributed particle filter and a distributed Gaussian particle filter. Each sensor runs a local particle filter, or a local Gaussian particle filter, that computes a global state estimate. The weight update in each local (Gaussian) particle filter employs the JLF, which is obtained through the likelihood consensus scheme. For the distributed Gaussian particle filter, the number of particles can be significantly reduced by means of an additional consensus scheme. Simulation results are presented to assess the performance of the proposed distributed particle filters for a multiple target tracking problem.

• The paper proposes Likelihood Consensus (LC), a novel method enabling decentralized state estimation and particle filtering in wireless sensor networks by approximating the joint likelihood function across nodes.
• The method relies on the assumption that local likelihoods belong to the exponential family, facilitating efficient decomposition and consensus-based computation of the joint likelihood.
• Numerical simulations show that distributed particle filters using LC achieve near-centralized performance while offering enhanced energy efficiency, robustness, and scalability in multi-target tracking.

Overview of "Likelihood Consensus and Its Application to Distributed Particle Filtering"

The paper "Likelihood Consensus and Its Application to Distributed Particle Filtering" introduces a novel approach to distributed state estimation in wireless sensor networks (WSNs), emphasizing decentralized operations that eliminate the need for a fusion center. Each sensor node performs global estimation tasks leveraging local processing and communications with adjacent nodes, thereby enhancing robustness and scalability.

Key Concepts and Methods

The paper discusses the use of consensus algorithms to approximate the joint likelihood function (JLF) across all sensors in the network. This method, termed "likelihood consensus" (LC), facilitates distributed computation by enabling each sensor to possess an approximate version of the JLF, critical for sequential Bayesian estimation and particle filtering applications.

Exponential Family Assumption

The approach is predicated on local likelihood functions that subscribe to the exponential family of distributions. This assumption allows for a systematic decomposition and subsequent consensus-based computation of the JLF. The exponential family framework permits efficient representation of likelihood functions in terms of sufficient statistics, which are essential for consensus computations.

Distributed Particle Filtering

The authors apply LC to develop distributed versions of particle filters and Gaussian particle filters. In these implementations, each sensor runs a local particle filter that computes a global state estimate by evaluating the JLF approximation obtained via consensus. This decentralized approach reduces communication overhead and avoids the potential single point of failure inherent in centralized systems with a fusion center.

Numerical Results and Simulation

Simulations involving multiple target tracking with acoustic sensors are employed to evaluate the performance of the proposed distributed particle filters. The results indicate that these filters, particularly when using LC, achieve performance close to centralized approaches while providing advantages in terms of energy efficiency and robustness due to reduced communication requirements and enhanced scalability.

Implications and Speculation

The LC method has significant implications for the deployment of sensor networks, particularly in environments where centralized control is impractical or undesirable due to power constraints or reliability concerns. By decentralizing the estimation process and enabling sensors to operate more autonomously, the approach opens avenues for more resilient and adaptive networks.

Future Directions

Future research could explore optimization of the consensus process to further reduce computational and communication costs. Moreover, extending LC to a broader class of likelihood functions, beyond those in the exponential family, remains a promising direction to expand applicability. With advancements in hardware and network protocols, integrating LC with emerging AI frameworks may offer enhanced decision-making capabilities in distributed sensor networks.

In summary, the paper contributes a valuable methodology for distributed state estimation using particle filters, leveraging the power of the consensus algorithm in WSNs, with promising applications across multiple domains where decentralized control is crucial.