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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| Veröffentlicht in: | IEEE transactions on signal processing Jg. 53; H. 8; S. 3141 - 3150 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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New York, NY
IEEE
01.08.2005
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 1053-587X, 1941-0476 |
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| Abstract | 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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| AbstractList | 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). 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. |
| Author | Shu-Hung Leung So, C.F. |
| Author_xml | – sequence: 1 surname: Shu-Hung Leung fullname: Shu-Hung Leung organization: Dept. of Electron. Eng., City Univ. of Hong Kong, China – sequence: 2 givenname: C.F. surname: So fullname: So, C.F. organization: Dept. of Electron. Eng., City Univ. of Hong Kong, China |
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| Keywords | 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 |
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| References | ref13 Farhang-Boroujeny (ref2) 1998 ref15 ref14 Gantmacher (ref17) 1977; I ref11 ref10 ref16 ref18 ref8 ref7 ref9 ref4 Urkowitz (ref19) 1983 ref3 ref6 Kailath (ref20) 1980 ref5 Leung (ref12) 2000; 147 Haykin (ref1) 1996 |
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| SubjectTerms | 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 |
| Title | Gradient-based variable forgetting factor RLS algorithm in time-varying environments |
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