Adaptive filtering techniques have gained much popularity in the modeling of unknown system identification problem. These techniques can be classified as either iterative or direct. Iterative techniques include stochastic descent method and its improved versions in affine space. In this paper we present a comparative study of the least mean square (LMS) algorithm and some improved versions of LMS, more precisely the normalized LMS (NLMS), LMS-Newton, transform domain LMS (TDLMS) and affine projection algorithm (APA). The performance evaluation of these algorithms is carried out using adaptive system identification (ASI) model with random input signals, in which the unknown (measured) signal is assumed to be contaminated by output noise. Simulation results are recorded to compare the performance in terms of convergence speed, robustness, misalignment, and their sensitivity to the spectral properties of input signals. Main objective of this comparative study is to observe the effects of fast convergence rate of improved versions of LMS algorithms on their robustness and misalignment.
The FXLMS algorithm, used extensively in active noise control (ANC), exhibits frequency-dependent convergence behavior. This leads to degraded performance for time-varying tonal noise and noise with multiple stationary tones. Previous work by the authors proposed the eigenvalue equalization filtered-x least mean squares (EE-FXLMS) algorithm. For that algorithm, magnitude coefficients of the secondary path transfer function are modified to decrease variation in the eigenvalues of the filtered-x autocorrelation matrix, while preserving the phase, giving faster convergence and increasing overall attenuation. This paper revisits the EE-FXLMS algorithm, using a genetic algorithm to find magnitude coefficients that give the least variation in eigenvalues. This method overcomes some of the problems with implementing the EE-FXLMS algorithm arising from finite resolution of sampled systems. Experimental control results using the original secondary path model, and a modified secondary path model for both the previous implementation of EE-FXLMS and the genetic algorithm implementation are compared.
A number of applications in active noise control require the ability to control and track multiple frequencies. If a standard filtered-x algorithm is used, the system must be designed to be stable for the slowest converging frequency anticipated, thereby leading to reduced overall performance of the system. Previous work has focused on overcoming this through development of a method that equalizes the eigenvalues of the system over the operating frequency range, leading to more uniform performance. The current work has built on the previous work to extend the method for implementation in systems that control the acoustic energy density. Minimizing energy density has been shown to have favorable performance characteristics when used for controlling enclosed acoustic fields. Thus, combining the approach of equalizing the system eigenvalues with energy density control leads to a system that incorporates the advantages of both methods. The control approach is demonstrated through implementation in a mock helicopter cabin, to demonstrate the favorable convergence characteristics, along with the global control of the field.
Helicopter cabin noise is dominated by low-frequency tonal noise, making it an ideal candidate for active noise control. Previous work in active control of cabin noise suggests an energy density approach to be a good solution [B. Faber and S.D. Sommerfeldt, Global Control in a Mock Tractor Cabin Using Energy Density, Proc. ACTIVE 04, Sept. 2004.] Simulations for active noise control using energy density minimization have been made using recorded data from a Robinson R44 helicopter. Initial computer models show substantial noise reductions in excess of 6 dB at the error sensor are possible. Performance results for computer models and simulations in a mock cab for different control arrangements will be compared.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.