Stability Analysis of Multi-Sensor Kalman Filtering over Lossy Networks

Area of Science:

• Control Systems Engineering
• Information Theory
• Stochastic Processes

Background:

• Distributed systems with multiple sensors present challenges in remote Kalman filtering.
• Packet loss in communication channels between sensors and filters can degrade estimation accuracy.
• Existing methods for ensuring filter stability under data loss often impose restrictive conditions.

Purpose of the Study:

• To develop a robust remote Kalman filtering method for distributed systems with lossy communication channels.
• To establish a necessary and sufficient condition for the stability of the mean estimation error covariance.
• To propose a method with less restrictive conditions compared to prior work.

Main Methods:

• Modeling communication channel behavior using time-homogeneous Markov chains.
• Deriving a stability condition based on the Markov model for packet delivery and loss.
• Expressing the stability condition as an explicit inequality involving system and channel parameters.

Main Results:

• A necessary and sufficient condition for the stability of the mean estimation error covariance was derived.
• The stability condition is presented as a simple inequality dependent on the spectral radius and Markov chain transition probabilities.
• The proposed method demonstrates less restrictive conditions than existing approaches.

Conclusions:

• The derived stability condition effectively guarantees the performance of remote Kalman filters in distributed systems with packet loss.
• The method offers a more flexible and less restrictive approach to robust filtering under communication uncertainties.
• Simulation examples validate the theoretical findings and the practical applicability of the proposed method.