Analysis of the Compressed Distributed Kalman Filter Over Markovian Switching Topology

Area of Science:

• Control Systems Engineering
• Signal Processing
• Information Theory

Background:

• Distributed estimation of high-dimensional sparse states in stochastic dynamic systems is challenging due to complex communication topologies.
• Randomly switching communication links governed by Markovian chains introduce non-stationarity and non-independence in system matrices.

Purpose of the Study:

• To develop a novel compressed distributed Kalman filter (CDKF) for accurate state estimation in stochastic dynamic systems with time-varying communication topologies.
• To analyze the stability and performance of the proposed CDKF under weaker conditions than existing methods.

Main Methods:

• Utilizing compressed sensing (CS) theory for data compression at each sensor.
• Employing a diffusion strategy and covariance intersection fusion in a compressed low-dimensional space.
• Applying reconstruction techniques to recover the original high-dimensional sparse state vector.
• Leveraging stochastic stability theory, Markov chain theory, and CS theory for stability analysis.

Main Results:

• The proposed CDKF effectively estimates high-dimensional sparse state vectors.
• Stability analysis established an upper bound for estimation error under a compressed cooperative excitation condition.
• This condition is significantly weaker than traditional uncompressed collective observability conditions.

Conclusions:

• The CDKF offers a robust and efficient solution for distributed estimation in dynamic systems with complex communication environments.
• The theoretical framework provides a rigorous stability analysis, paving the way for practical applications.