Name
Title | ||
|---|---|---|
A Class of Adaptive Algorithms Based on Entropy Estimation Achieving CRLB for Linear Non-Gaussian Filtering |
Abstract | ||
|---|---|---|
Adaptive filtering has been extensively studied under the assumption that the noise is Gaussian. The most commonly used least-mean-square-error (LMSE) filter is optimal when the noise is Gaussian. However, in many practical applications, the noise can be modeled more accurately using a non-Gaussian distribution. In this correspondence, we consider non-Gaussian distributions for the noise model and show that the filter of using entropy bound minimization (EBM) leads to significant performance gain compared to the LMSE filter. The least mean p-norm (LMP) filter using the $\\alpha$-stable distribution to model noise is shown to be the maximum-likelihood solution when using the generalized Gaussian distribution (GGD) to model noise. The GGD model for noise allows us to compute the Cramér–Rao lower bound (CRLB) for the error in estimating the weights. Simulations show that both the EBM and LMP filters achieve the CRLB as the sample size increases. The EBM filter is shown to be less committed with respect to unseen data yielding generally superior performance in online learning when compared to LMP. We also show that, when the noise comes from impulsive $\\alpha$ -stable distributions, both the EBM and LMP filters provide better performance than LMSE. In addition, the EBM filter offers the advantage that it does not assume a certain parametric model for the noise, and by proper selection of the measuring functions, it can be adapted to a wide range of noise distributions. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1109/TSP.2011.2182345 | IEEE Transactions on Signal Processing |
Keywords | Field | DocType |
impulsive α -stable distribution,cramér–rao bounds,lmse filter,maximum-likelihood solution,maximum likelihood estimation,adaptive signal processing,noise modeling,least mean p-norm filter,linear nongaussian filtering,adaptive algorithm,entropy bound minimization,adaptive filtering,cramér-rao lower bound,generalized gaussian distribution,crlb,entropy estimation,α-stable distribution,weight estimation,non-gaussian noise,nongaussian distribution,entropy,gaussian noise,mean square error methods,least-mean-square-error filter,maximum likelihood,maximum likelihood estimate,least mean square,sample size,signal to noise ratio,computer model,cramer rao lower bound,least squares approximation,adaptive filter,gaussian distribution,shape,stable distribution,lower bound,parametric model,computational modeling | Value noise,Mathematical optimization,Signal-to-noise ratio,Filter (signal processing),Algorithm,Gaussian,Adaptive filter,Additive white Gaussian noise,Gaussian noise,Mathematics,Gradient noise | Journal |
Volume | Issue | ISSN |
60 | 4 | 1053-587X |
Citations | PageRank | References |
4 | 0.43 | 10 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hualiang Li | 1 | 148 | 10.69 |
| Xi-Lin Li | 2 | 547 | 34.85 |
| Matthew Anderson | 3 | 263 | 14.64 |
| Tülay Adali | 4 | 1690 | 126.40 |