Convergence of the Distributed SG Algorithm Under Cooperative Excitation Condition

Area of Science:

• Distributed systems
• Signal processing
• Control theory

Background:

• Distributed sensors generate noisy measurements for parameter estimation.
• Existing algorithms often require independent and stationary data, limiting applicability.

Purpose of the Study:

• To propose a novel distributed stochastic gradient (SG) algorithm for parameter estimation.
• To analyze the algorithm's convergence properties under less restrictive conditions.

Main Methods:

• Combining consensus strategies with diffusion of regression vectors.
• Utilizing graph theory and martingale theory for theoretical analysis.
• Introducing a cooperative excitation condition for convergence.

Main Results:

• The proposed distributed SG algorithm converges without requiring independent or stationary regression vectors.
• Convergence rate of the algorithm is established.
• Simulation demonstrates cooperative estimation surpassing individual sensor capabilities.

Conclusions:

• The developed distributed SG algorithm effectively estimates parameters from noisy, distributed sensor data.
• The cooperative excitation condition is key to achieving convergence guarantees.
• The algorithm enables collective estimation tasks unachievable by individual sensors.