Stability of Diffusion Adaptive Filters

Abstract In this paper, we consider the diffusion adaptive filters where a set of sensors is required to collectively estimate time-varying signals (or parameters) from noisy measurements in a way of information diffusion. We will establish the stability of the diffusion least mean square (DLMS) algorithm, without requiring stationarity, independency, and boundedness assumptions of the system signals, which means that our results can be applied to more general and practical class of stochastic systems than those studied in the literature. We will present theoretical results concerning stability and bounds on the mean square error(MSE) of the filtering. We will also show that the network of sensors can cooperate to guarantee the stability of the filtering, even though any single sensor does not have such a capability. This clearly reveals the advantages of the DLMS algorithm vs. standard least mean square (LMS) algorithm. Numerical simulations will also be presented to support the theoretical justifications.

[1]  Shoulie Xie,et al.  Distributed LMS estimation over networks with quantised communications , 2013, Int. J. Control.

[2]  Ali H. Sayed,et al.  Diffusion recursive least-squares for distributed estimation over adaptive networks , 2008, IEEE Transactions on Signal Processing.

[3]  Lei Guo,et al.  Stability of Recursive Stochastic Tracking Algorithms , 1994 .

[4]  Azam Khalili,et al.  Performance analysis of quantized incremental LMS algorithm for distributed adaptive estimation , 2010, Signal Process..

[5]  Wheyming Tina Song,et al.  Variance Reduction Techniques on Generating M/M/1 Processes in Simulation Output Analysis , 2013, IEEE Transactions on Automatic Control.

[6]  H. Vincent Poor,et al.  Distributed Linear Parameter Estimation: Asymptotically Efficient Adaptive Strategies , 2011, SIAM J. Control. Optim..

[7]  Han-Fu Chen,et al.  Lp‐stability of estimation errors of kalman filter for tracking time‐varying parameters , 1991 .

[8]  Ioannis D. Schizas,et al.  Distributed LMS for Consensus-Based In-Network Adaptive Processing , 2009, IEEE Transactions on Signal Processing.

[9]  Reza Olfati-Saber,et al.  Distributed Kalman filtering for sensor networks , 2007, 2007 46th IEEE Conference on Decision and Control.

[10]  Ali H. Sayed,et al.  Adaptive Processing over Distributed Networks , 2007, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[11]  Ali H. Sayed,et al.  Diffusion LMS Strategies for Distributed Estimation , 2010, IEEE Transactions on Signal Processing.

[12]  Milos S. Stankovic,et al.  Decentralized Parameter Estimation by Consensus Based Stochastic Approximation , 2011, IEEE Trans. Autom. Control..

[13]  A. Nedić,et al.  Stochastic Incremental Gradient Descent for Estimation in Sensor Networks , 2007, 2007 Conference Record of the Forty-First Asilomar Conference on Signals, Systems and Computers.

[14]  Ali H. Sayed,et al.  Diffusion mechanisms for fixed-point distributed Kalman smoothing , 2008, 2008 16th European Signal Processing Conference.

[15]  Qiang Zhang,et al.  Distributed Parameter Estimation Over Unreliable Networks With Markovian Switching Topologies , 2012, IEEE Transactions on Automatic Control.

[16]  Stephen P. Boyd,et al.  A space-time diffusion scheme for peer-to-peer least-squares estimation , 2006, 2006 5th International Conference on Information Processing in Sensor Networks.

[17]  Ali H. Sayed,et al.  Incremental Adaptive Strategies Over Distributed Networks , 2007, IEEE Transactions on Signal Processing.

[18]  Sandip Roy,et al.  Kronecker products of defective matrices: Some spectral properties and their implications on observability , 2012, 2012 American Control Conference (ACC).

[19]  L. Ljung,et al.  Exponential stability of general tracking algorithms , 1995, IEEE Trans. Autom. Control..

[20]  Lennart Ljung,et al.  Performance analysis of general tracking algorithms , 1995 .

[21]  Stergios I. Roumeliotis,et al.  Consensus in Ad Hoc WSNs With Noisy Links—Part II: Distributed Estimation and Smoothing of Random Signals , 2008, IEEE Transactions on Signal Processing.