[Paper Review] Randomized Consensus based Distributed Kalman Filtering over Wireless Sensor Networks

Jiahu Qin, Wang Jie+2 more|arXiv (Cornell University)|Oct 5, 2018

Distributed Control Multi-Agent Systems36 references4 citations

TL;DR

This paper proposes a randomized gossip-based distributed Kalman filtering algorithm for wireless sensor networks that enables each sensor to estimate system states using only local neighbor information, reducing communication and energy costs. The method achieves mean square convergence and outperforms noncooperative decentralized filtering in estimation accuracy under energy and resource constraints.

ABSTRACT

This paper is concerned with developing a novel distributed Kalman filtering algorithm over wireless sensor networks based on randomized consensus strategy. Compared with the centralized algorithm, distributed filtering techniques require less computation per sensor and lead to more robust estimation since they simply use the information from the neighboring nodes in the network. However, poor local sensor estimation caused by limited observability and network topology changes which interfere the global consensus are challenging issues. Motivated by this observation, we propose a novel randomized gossip-based distributed Kalman filtering algorithm. Information exchange and computation in the proposed algorithm can be carried out in an arbitrarily connected network of nodes. In addition, the computational burden can be distributed for a sensor which communicates with a stochastically selected neighbor at each clock step under schemes of gossip algorithm. In this case, the error covariance matrix changes stochastically at every clock step, thus the convergence is considered in a probabilistic sense. We provide the mean square convergence analysis of the proposed algorithm. Under a sufficient condition, we show that the proposed algorithm is quite appealing as it achieves better mean square error performance theoretically than the noncooperative decentralized Kalman filtering algorithm. Besides, considering the limited computation, communication, and energy resources in the wireless sensor networks, we propose an optimization problem which minimizes the average expected state estimation error based on the proposed algorithm. To solve the proposed problem efficiently, we transform it into a convex optimization problem. And a sub-optimal solution is attained. Examples and simulations are provided to illustrate the theoretical results.

Motivation & Objective

• Address the challenge of limited observability and dynamic network topologies in distributed Kalman filtering over wireless sensor networks.
• Reduce computational and communication burdens per sensor by avoiding centralized processing and minimizing data exchange.
• Develop a robust, scalable filtering framework suitable for energy-constrained, ad-hoc sensor networks with arbitrary connectivity.
• Optimize sensor scheduling to minimize average expected state estimation error under resource limitations.
• Establish theoretical convergence guarantees in a probabilistic sense for stochastic information exchange and state update mechanisms.

Proposed method

• Utilizes a randomized gossip protocol where each sensor stochastically selects a neighbor to exchange information at each time step.
• Integrates a consensus-based framework with Kalman filtering dynamics, updating state estimates using local measurements and neighbor data.
• Models the error covariance evolution as a stochastic process, with convergence analyzed in expectation using matrix theory and contraction mapping principles.
• Employs symmetric stochastic weight matrices to ensure consensus and stability in the distributed estimation process.
• Transforms the sensor scheduling optimization problem into a convex program to find a sub-optimal solution minimizing expected estimation error.
• Applies trace inequalities and conditional expectation techniques to prove that the expected error covariance is bounded by the centralized case.

Experimental results

Research questions

• RQ1 Can a distributed Kalman filtering algorithm achieve better mean square estimation performance than noncooperative decentralized filtering under the same resource constraints?
• RQ2 How can information exchange be minimized in wireless sensor networks while maintaining estimation accuracy and robustness to topology changes?
• RQ3 What conditions ensure mean square convergence of the distributed filtering algorithm when updates occur stochastically over time?
• RQ4 How can sensor scheduling be optimized to minimize the average expected state estimation error in energy-constrained networks?
• RQ5 Can the proposed algorithm maintain performance in arbitrarily connected networks without requiring full network knowledge or centralized coordination?

Key findings

• The proposed algorithm achieves better mean square error performance than noncooperative decentralized Kalman filtering under a sufficient condition.
• The error covariance matrix evolves stochastically, and the algorithm is proven to converge in expectation using a contraction mapping argument.
• The trace of the expected error covariance is bounded above by the centralized error covariance trace, ensuring estimation quality is preserved.
• A convex optimization formulation is derived to minimize the average expected state estimation error, enabling efficient sub-optimal sensor scheduling.
• Theoretical analysis confirms that the algorithm maintains stability and consistency even under arbitrary network connectivity and stochastic communication patterns.
• Simulations validate the theoretical results, demonstrating improved estimation accuracy and energy efficiency in practical WSN scenarios.