Gradient-based variable forgetting factor RLS algorithm in time-varying environments

In this paper, a new control mechanism for the variable forgetting factor (VFF) of the recursive least square (RLS) adaptive algorithm is presented. The control algorithm is basically a gradient-based method of which the gradient is derived from an improved mean square error analysis of RLS. The new...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 53; no. 8; pp. 3141 - 3150
Main Authors: Shu-Hung Leung, So, C.F.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.08.2005
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Adaptive algorithm
Algorithm design and analysis
Algorithms
Analytical models
Applied sciences
Control algorithms
Control theory
Detection, estimation, filtering, equalization, prediction
Dynamics
Equations
Error analysis
Errors
Exact sciences and technology
Information, signal and communications theory
Least squares methods
Mathematical analysis
Mathematical models
Mean square error analysis
Mean square error methods
Mean square errors
Mean square values
Resonance light scattering
RLS
Signal and communications theory
Signal, noise
Steady-state
Studies
Telecommunications and information theory
time-varying
Transient analysis
variable forgetting factor
Target tracking
Adaptive algorithm
Forgetting factor
Correlation matrix
Theoretical study
Unsteady state
Recursive algorithm
Steady state
Time variation
Mean square error
Simulation
variable forgetting factor
Correlation analysis
Least squares method
Recursive method
RLS
Mean square error analysis
time-varying
Fast algorithm
Gradient method
Signal to noise ratio
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Summary:In this paper, a new control mechanism for the variable forgetting factor (VFF) of the recursive least square (RLS) adaptive algorithm is presented. The control algorithm is basically a gradient-based method of which the gradient is derived from an improved mean square error analysis of RLS. The new mean square error analysis exploits the correlation of the inverse of the correlation matrix with itself that yields improved theoretical results, especially in the transient and steady-state mean square error. It is shown that the theoretical analysis is close to simulation results for different forgetting factors and different model orders. The analysis yields a dynamic equation of mean square error that can be used to derive a dynamic equation of the gradient of mean square error to control the forgetting factor. The dynamic equation can produce a positive gradient when the error is large and a negative gradient when the error is in the steady state. Compared with other variable forgetting factor algorithms, the new control algorithm gives fast tracking and small mean square model error for different signal-to-noise ratios (SNRs).
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2005.851110