Circuits, Systems, and Signal Processing

, Volume 32, Issue 1, pp 223–232 | Cite as

Numeric Variable Forgetting Factor RLS Algorithm for Second-Order Volterra Filtering



Nonlinear adaptive filtering techniques for system identification (based on the Volterra model) are widely used for the identification of nonlinearities in many applications. In this correspondence, the improved tracking capability of a numeric variable forgetting factor recursive least squares (NVFF-RLS) algorithm is presented for first-order and second-order time-varying Volterra systems under a nonstationary environment. The nonlinear system tracking problem is converted into a state estimation problem of the time-variant system. The time-varying Volterra kernels are governed by the first-order Gauss–Markov stochastic difference equation, upon which the state-space representation of this system is built. In comparison to the conventional fixed forgetting factor recursive least squares algorithm, the NVFF-RLS algorithm provides better channel estimation as well as channel tracking performance in terms of the minimum mean square error (MMSE) for first-order and second-order Volterra systems. The NVFF-RLS algorithm is adapted to the time-varying signals by using the updating prediction error criterion, which accounts for the nonstationarity of the signal. The demonstrated simulation results manifest that the proposed method has good adaptability in the time-varying environment, and it also reduces the computational complexity.


Gauss–Markov model RLS algorithm Volterra filter NVFF-RLS Volterra filter Minimum mean square error Polynomial filters 



The authors are thankful to Mr. Ankur Gupta, Software Engineer, TATA Consultancy Services, India for his fruitful suggestions and motivational technical discussions regarding adaptive polynomial filtering and its applications.


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Electronics and Communication EngineeringThapar UniversityPatialaIndia
  2. 2.Department of Electronics and Communication EngineeringR.I.E.T.FaridabadIndia

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