[Paper Review] Information-driven Fully Distributed Kalman Filter for Sensor Networks in Presence of Naive Nodes

Shaocheng Wang, Wei Ren+1 more|arXiv (Cornell University)|Oct 1, 2014

Distributed Control Multi-Agent Systems6 references13 citations

TL;DR

This paper proposes the Information-driven Fully Distributed Kalman Filter (IFDKF), a novel distributed estimation algorithm for sensor networks that operates without requiring global information such as network size or maximum node degree. By using a local weighted least squares estimator based on generalized measurements—including local estimates and neighbor data—the IFDKF effectively mitigates performance degradation from naive nodes (those not observing the target or neighbors), achieving superior tracking accuracy and robustness under dynamic topologies and node failures compared to existing consensus-based filters like ICF and GKCF.

ABSTRACT

We consider the distributed Kalman filtering problem for sensor networks where each node takes the measurement, communicates with its local neighbors, and updates its local estimate and estimation error covariance at the same frequency. In such a scenario, if the target is not directly observed by neither a certain node nor its local neighbors, this node is naive about the target. The well-known Kalman Consensus filter (KCF) has been shown to perform well if there exists no naive node in the network. The case in presence of naive nodes has been considered by the generalized KCF (GKCF) and the Information Weighted Consensus filter (ICF) later on. However, all these consensus-embedded filters require some global information such as the maximum degree of the graph, or the total number of the nodes. If these global information are changing over the time, such as time-varying topologies or unexpected sensor failures in the network, the performance of the GKCF or the ICF might be degraded. With communication topology changes, node failures, or addition of new nodes, the filter performance would be adversely affected. In this paper, we consider a novel local Weighted Least Square estimator for each node that utilizes its generalized measurement formed by not only its own and local neighbors' measurements but their prior local estimates to track the target. With some approximations in the derivation of the covariance matrix, we propose the Information-driven Fully Distributed Kalman filter (IFDKF), which is able to deal with the existence of naive nodes without knowing any global information. Experimental results show that the proposed algorithm performs better than the existing algorithms in the considered realistic scenario.

Motivation & Objective

• To address the performance degradation of existing distributed Kalman filters in sensor networks when naive nodes—nodes not observing the target or their neighbors—exist.
• To develop a distributed filtering algorithm that operates without relying on global information such as total number of nodes, maximum node degree, or consensus step sizes.
• To ensure robustness against dynamic network changes, including topology shifts, node failures, and additions, without reconfiguration or parameter tuning.
• To achieve estimation performance close to the centralized optimal solution even in the presence of naive nodes and changing network conditions.

Proposed method

• Each node performs local measurements, communicates with its immediate neighbors, and updates its local state estimate and error covariance in real time.
• A local weighted least squares estimator is formulated using generalized measurements that combine the node's own measurement and prior local estimates from neighbors.
• The algorithm approximates the error covariance matrix using information-theoretic principles to enable fully distributed computation without global knowledge.
• The filter design incorporates information-weighted consensus principles, dynamically adjusting influence based on local estimation uncertainty rather than fixed weights.
• The method avoids reliance on global parameters by deriving local update rules that self-adapt to network changes and maintain consistency.
• Theoretical analysis and simulations validate the filter’s stability, optimality, and convergence properties under various network dynamics.

Experimental results

Research questions

• RQ1 How can distributed Kalman filtering be made robust to naive nodes that do not observe the target or their neighbors?
• RQ2 Can a fully distributed Kalman filter be designed without requiring global network parameters such as total node count or maximum node degree?
• RQ3 How does the proposed algorithm maintain performance under dynamic network changes like topology shifts or node failures?
• RQ4 What is the relative performance of the proposed IFDKF compared to existing filters like ICF, GKCF, and KCF in realistic, dynamic scenarios?

Key findings

• The IFDKF achieves lower steady-state mean absolute error than both ICF and GKCF in the presence of naive nodes, demonstrating superior tracking accuracy.
• The IFDKF converges to the centralized optimal solution faster after disturbances, such as process noise at k=90, outperforming ICF in transient response.
• When network topology changes at k=65, the IFDKF maintains stable performance, while the ICF degrades due to outdated consensus parameter ε not adapting to the new maximum degree.
• After node failures at k=65 (nodes 5 and 6), the IFDKF converges to the centralized solution, whereas the ICF fails to converge due to overestimation of neighbor confidence from unchanged global parameters.
• The IFDKF exhibits consistent performance under dynamic conditions, proving its adaptability and robustness without requiring reconfiguration or global information.