Recursive Geman–McClure Estimator for Implementing Second-Order Volterra Filter

In this paper, we investigate the convergence performance of a sparsified kernel least mean square (KLMS) algorithm in which the input is added into the dictionary only when the prediction error in amplitude is larger than a preset threshold. Under certain conditions, we derive an approximate value of the steady-state excess mean square error (EMSE). Simulation results confirm the theoretical predictions and provide some interesting findings, showing that the sparsification can not only be used to constrain the network size (hence reduce the computational burden) but also be used to improve the steady-state performance in some cases.

Improved proportionate-type sparse adaptive filtering under maximum correntropy criterion in impulsive noise environments

Robust Bounding Ellipsoidal Adaptive Constrained least-squares algorithm and its performance analysis

A novel methodology to bound the steady-state mean square performance of the diffusion complex least mean square (D-CLMS) and the diffusion widely linear (augmented) CLMS (D-ACLMS) algorithm is proposed. This is achieved by exploiting the almost identical nature of the steady-state filter weights at all nodes. The proposed approach allows for the consideration of the second-order terms in the recursion for the weight error covariance matrix, without compromising the mathematical tractability of the problem. The closed form expressions for the mean square deviation (MSD) and excess mean square error (EMSE) for both the D-CLMS and D-ACLMS allow for the performance of the algorithms to be quantified as a function of the noncircularity of the input data.

The transform domain normalized least mean squares (TDNLMS) algorithm is an efficient adaptive algorithm, which offers fast convergence speed with a reasonably low arithmetic complexity. However, its convergence speed is usually limited by the fixed step-size so as to achieve a low desired misadjustment. In this paper a new switch-mode noise-constrained TDNLMS (SNC-TDNLMS) algorithm is proposed. It employs a maximum step-size mode in initial convergence and a noise-constrained mode afterwards to improve the convergence speed and steady-state performance. The mean and mean square convergence behaviors of the proposed algorithm are studied to characterize its convergence condition and steady-state excess mean square error (EMSE). Based on the theoretical results, an automatic threshold selection scheme for mode switching is developed. Computer simulations are conducted to show the effectiveness of the proposed algorithm and verify the theoretical results.

This paper proposes a new regularized transform domain normalized LMS (R-TDNLMS) algorithm and studies its mean and mean square convergence performances. The proposed algorithm extends the conventional TDNLMS algorithm by imposing a regularization term on the filter coefficients to reduce the variance of estimators due to the lacking of excitation in a certain frequency band or in the presence of modeling errors. Difference equations describing the mean and mean square convergence behaviors of this algorithm are derived so as to characterize its convergence condition and steady-state excess mean square error (MSE). It shows that regularization can help to reduce the MSE by trading slight bias for variance. Based on this analysis, a new formula to select the regularization parameter for white Gaussian inputs is proposed, which leads to a new variable regularized TDNLMS (VR-TDNLMS) algorithm. Computer simulations are conducted to examine the improved convergence performance, steady-state MSE and robustness to power-varying inputs of the proposed algorithm and verify the effectiveness of the theoretical analysis. Furthermore, the application of the proposed VR-TDNLMS algorithm to the design and implementation of acoustic system identification and active noise control (ANC) systems show that they considerably outperforms traditional TDNLMS algorithms at low excitation or in the presence of modeling errors. Moreover, the theoretical analysis provides simple design formulas for achieving a given excess MSE (EMSE) and step-size bound for stable operation.

In recent years, the hyperbolic family of adaptive algorithms have been widely used to combat impulsive noise. The novel exponential hyperbolic sine adaptive filters (EHSAF) and the normalized exponential hyperbolic sine adaptive filter (NEHSAF) suitable for impulsive noise environments are proposed in this brief. The cost function is based on the exponential hyperbolic sine-based error function. The stability condition based on the learning rate and the steady-state analysis are investigated too. Additionally, a variable scheme for the scaling parameter is proposed to remove the tradeoff between convergence speed and steady-state excess mean square error (EMSE). The computational complexity is presented too. The simulation results in the context of unknown system identification and echo cancellation application have been performed to prove the performance improvement of the proposed algorithms.

We study the excess mean square error (EMSE) above the minimum mean square error (MMSE) in large linear systems where the posterior mean estimator (PME) is evaluated with a postulated prior that differs from the true prior of the input signal. We focus on large linear systems where the measurements are acquired via an independent and identically distributed random matrix, and are corrupted by additive white Gaussian noise (AWGN). The relationship between the EMSE in large linear systems and EMSE in scalar channels is derived, and closed form approximations are provided. Our analysis is based on the decoupling principle, which links scalar channels to large linear system analyses. Numerical examples demonstrate that our closed form approximations are accurate.

Analysis and simulations to compare the standard least mean square (LMS) algorithm to the noncanonical LMS (NCLMS) algorithm are presented. The NCLMS algorithm is implemented using a variant of the standard FIR, called the non-canonical FIR (NCFIR). Simulation results are given which show a reduced excess mean square error (EMSE) level and an improved performance in an impulsive noise environment for the NCLMS over the conventional LMS algorithm.

This paper is concerned with the development and analysis of a nonlinear predictor for a non-Gaussian process using a zero-memory nonlinearity (ZMNL) followed by a second order Volterra filter (SVF). The processor exploits partial statistical information such as marginal probability density function (PDF) and the covariance structure. The ZMNL transforms the process into a Gaussian process. The SVF can be implemented as a parallel combination of linear and quadratic filters. Another equivalent structure is to carry out a linear prediction in the transformed Gaussian domain and pass the linear predicted samples through a second order polynomial.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Robust augmented space recursive least-constrained-squares algorithms

Objectives: To enhance the quality of Cardiac Signal for perfect diagnosis by the doctor. Methods/Statistical Analysis: We are introducing some adaptive filter structures for Cardiac Signal (CS) enhancement for the extraction of high resolution cardiac signals and these structures were based on the Proportionate Normalized Least Mean Square (PNLMS) algorithm. The main advantage of PNLMS over the conventional techniques is extraction of sparse coefficients, suitably weighing them and fast convergence. These ANCs are tested using MIT-BIH database to compare the performance. Findings: We consider Signal to Noise Ratio (SNR), Excess Mean Square Error (EMSE), Misadjustment (MSD), convergence curves and residual error plots as performance measures. Among the ANCs tested, PMNSRLMA based ANC is found to be better with reference to the considered performance measures and computational complexity. The average SNRI achieved by this ANC is 18.8856dBs for PLI elimination, 8.7580dBs for BW elimination, 8.5106dBs for MA elimination and 8.5012dBs for EM elimination. From the above results it is clear that in practical biotelemetry applications to minimize the computational complexity of the noise canceller we combine PNLMS with signature algorithms. Again, to reduce the complexity in the denominator of the normalized recursion, we use maximum normalized version of PNLMS. Finally, these variations result in seven algorithms in addition to PNLMS. Based on these algorithms, we develop various Adaptive Noise Cancellers (ANCs) to eliminate artifacts present in the CS and to present best quality signal to the doctor for diagnosis. Application/ Improvement: The standard of Cardiac Signal can be enhanced by improving data acquisition methods.

This paper introduces an adaptive noise canceller (ANC) using a proposed variable step size least mean-square (LMS) algorithm. The step size varies between two hard limits based on a predetermined nonlinear decreasing function of signal to noise ratio (SNR) estimated at every iteration of the algorithm. The performance of the proposed algorithm is studied for different power levels of both stationary and nonstationary Gaussian noise added to the original speech. Compared with other several variable step size algorithms, computer simulations show performance superiority of the proposed algorithm in decreasing excess mean square error (EMSE) in both stationary and nonstationary noise environments. Simulations of the proposed method also show substantial improvements in decreasing misadjustment and reverberation.

Adaptive RSOV filter using the FELMS algorithm for nonlinear active noise control systems

Performance analysis of the deficient length augmented CLMS algorithm for second order noncircular complex signals