Design of momentum LMS algorithm for control autoregressive autoregressive systems

This study presents a variant of least mean square (LMS) algorithm, i.e., momentum LMS (M-LMS), with faster convergence speed for measuring the system parameter of linear as well as nonlinear control autoregressive autoregressive (CARAR) models. The M-LMS effectively exploits the input/output data by utilizing the previous gradients information in update rule to avoid trapping in local minimum (MNM) and yields better convergence behavior than conventional LMS approach. The speedy convergence of M-LMS is achieved by increasing the proportion of previous gradients but at the cost of little compromise in final steady-state behavior. The correctness of the M-LMS is established by effective optimization of the linear as well as nonlinear CARAR model identification. The robustness of the scheme is verified through accurate measurement of CARAR systems parameters for various noise levels. The statistical analyses based on multiple independent trials through proximity measures in terms of fitness, mean squared error, and Nash Sutcliffe efficiency further validated the superior performance of M-LMS for identification of CARAR models.

In the present work, strength of momentum least mean square (MLMS) algorithm is exploited for nonlinear system identification problems represented with Hammerstein model. The MLMS algorithm uses the previous gradient information to estimate the current weights instead of using only current value of gradient; thus, it is faster in the convergence and less probable to trap in local minima. The perfection of the design scheme is certified through effective parameter estimation of nonlinear Hammerstein control autoregressive models. The robustness of the scheme is established by examining the performance for different levels of noise variance. The performance comparison through mean square error and Nash–Sutcliffe efficiency parameters, calculated for sufficiently large number of multiple runs, proves the intrinsic worth of MLMS algorithm in system identification.

Among all adaptive noise cancellers, Widrow and Hoff's least mean square (LMS) algorithm has probably become the most popular because of its robustness, good tacking properties and simplicity of implementation. An important limitation of LMS algorithm is that the selection of a certain value for the step size implies compromise between speed of convergence and steady-state misadjustment, The variable step size normalized least-mean-square (VSS- NLMS) algorithm is appropriate to solve the conflicting requirement of fast convergence and low misadjustment of the LMS algorithm. To reduce noise in the output signal of the ANC, a step size for coefficient update is controlled according to the signal-to-noise ratio (SNR). This paper investigates the performance of a noise canceller with DSP processor (TI TMS320C6713) using the LMS algorithm, normalized least-mean-square (NLMS) algorithm, and VSS-NLMS algorithm. Results show the proposed combination of hardware and VSS-NLMS algorithm has not only a faster convergence rate but also lower distortion when compared with the fixed step size LMS algorithm and NLMS algorithm in real-time environments.

The method of least mean square (LMS) is the commonly used algorithm in Adaptive filter due to its simplicity and robustness in implementation. In Active Noise Control application, a filtered reference signal is used prior to LMS algorithm to overcome the constraint on stability and convergence performance of the system due to the existence of the auxiliary path. This is known as Filtered-X LMS algorithm. In conventional Filtered-X LMS algorithm, each filter weight is updated once on every audio sample. This paper proposes the improved version of Filtered-X LMS algorithm with the use of multiple iteration of filter weight on every sample of audio signal. The proposed work uses field programmable gate arrays to realize real-time simulation on hardware for the noise signal of 500 Hz. Results from the real-time hardware simulations have shown much faster error convergence and better adaptation performance for different selections of learning constant μ, as compared with the conventional method.

We describe the application of a genetic algorithm (GA) to the problem of parameter optimization for an adaptive finite impulse response (FIR) filter combining genetic algorithm (GA) and least mean square (LMS) algorithm. For system identification problem, LMS algorithm computes the filter coefficients and GA search the optimal step-size adaptively. Because step-size influences on the stability and performance, so it is necessary to apply method that can control it. The simulation results of the GA were compared to the traditional LMS algorithm. We obtained that genetic algorithm was clearly superior (in accuracy) in most cases.

It is shown that two algorithms obtained by simplifying a Kalman filter considered for a second-order Markov model are H∞ suboptimal. Similar to least mean squares (LMS) and normalised LMS (NLMS) algorithms, these second order algorithms can be thought of as approximate solutions to stochastic or deterministic least squares minimisation. It is proved that second-order LMS and NLMS are exact solutions causing the maximum energy gain from the disturbances to the predicted and filtered errors to be less than one, respectively. These algorithms are implemented in two steps. Operation of the first step is like conventional LMS/NLMS algorithms and the second step consists of the estimation of the weight increment vector and prediction of weights for the next iteration. This step applies simple smoothing on the increment of the estimated weights to estimate the speed of the weights. Also they are cost-effective, robust and attractive for improving the tracking performance of smoothly time-varying models.

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.

Three adaptive multichannel L-filters based on marginal data ordering are proposed. They rely on well-known algorithms for the iterative minimization of the mean square error (MSE), namely, the least mean squares (LMS), the normalized LMS (NlMs), and the LMS- Newton (LMSN) algorithms. We treat both the unconstrained minimization of the MSE and the minimization of the MSE when structural constraints are imposed on the filter coefficients. The performance of the proposed adaptive multichannel L-filters is compared to that of other multivariate nonlinear filters in color image filtering. Adaptive multichannel linear filters and adaptive single-channel L-filters are considered as well. Performance comparisons are made in both RGB and U*V*W* color spaces. The proposed adaptive multichannel L-filters outperform the other candidates in noise suppression for color images corrupted by mixed impulsive and additive white contaminated Gaussian noise.

A novel method of the computation of the Discrete Fractional Cosine Transform (DFRCT) based on adaptive Least Mean Square (LMS) algorithm is proposed. The weight vectors are adjusted or adapted in accord with the least mean square error between the “desired response” and the reconstructed signal. It can be proved that the weight vector is in relation to the previous N-point DFRCT by choosing the iterative index properly. Theoretical analysis and simulation results show that the performance of the proposed algorithm is very close to that of Pei <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[2]</sup> , and also it is simple in computation.

In many system identification applications, the unknown system is characterized by time-varying parameters. Therefore, fast on-line identification is required in order to keep the system stable and improve the control performance. In this paper, we show that the dimensionality of system identification can be dramatically reduced if the unknown system is sparse, in the sense that its parameter set has a concise representation when expressed in a proper basis. In such cases, the system identification can be effectively carried out in a subspace of reduced dimension. Based on this theory, we further proposed two new least-mean-square (LMS) algorithms, namely, prominent system subspace LMS (PSS-LMS) and enhanced PSS-LMS (PSS-LMS+) to exploit this sparsity for fast system identification. Finally, we conducted experiments to compare the convergence performances of PSS-LMS, PSS-LMS+, and conventional LMS using numerical simulation, and the results confirm the superior performances of the proposed algorithms.

Adaptive signal processing sensor arrays, known also as smart antennas .The smart antenna adaptive algorithms achieve the best weight vector for beam forming by iterative means. The Least Mean Square (LMS) algorithm, is an adaptive algorithm .LMS incorporates an iterative procedure that makes successive corrections to the weight vector in the direction of the negative of the gradient vector which eventually leads to the minimum mean square error. Beam forming is directly determined by the two factors. The performance of the traditional LMS algorithm for different parameters is analysed in this paper. This algorithm can be applied to beam forming with the software Matlab. The result obtain can achieve faster convergence and lower steady state error. The algorithms can be simulated in MATLAB 7.10 version.

In this paper, we present a blind adaptive gradient (BAG) algorithm for code-aided suppression of multiple-access interference (MAI) and narrow-band interference (NBI) in direct-sequence/code-division multiple-access (DS/CDMA) systems. This BAG algorithm is based on the concept of accelerating the convergence of a stochastic gradient algorithm by averaging. This ingenious concept of averaging was invented by Polyak and Juditsky (1992)-this paper examines its application to blind multiuser detection and NBI suppression in DS/CDMA systems. We prove that BAG has identical convergence and tracking properties to recursive least squares (LMS) but has a computational cost similar to the least mean squares (LMS) algorithm-i.e., an order of magnitude lower computational cost than RLS. Simulations are used to compare our averaged gradient algorithm with the blind LMS and LMS schemes.

This work presents a new mixed (2,p-like)-norm penalized least mean squares (LMS) algorithm for block-sparse system identifications where the nonzero coefficients in the impulse response vector of unknown systems are structured in a single cluster or multiple clusters. The new algorithm divides the tap-weight vector into groups of equal-sized sub-vectors and then introduces a mixed $$l_{2,p\text {-like}}$$ -norm constraint on the filter tap-weight vector in addition to the original mean-square-error cost function. The parameter p in the $$l_{2,p\text {-like}}$$ -norm constraint takes any value between zero and two, thus improving the identification performance of the block-sparse systems. The effect of the parameter p and the group size on the performance of the proposed algorithm is studied, and general guidelines for choosing these two parameters are provided to facilitate practical use. The advantage of the proposed scheme is that no comparison operations are required while algebraic operations are of the same order as the block-sparse LMS algorithm. Numerical simulations show that the proposed $$(2,p\text {-like})$$ -norm penalized LMS algorithm outperforms the existing $$l_{2,0}$$ - and $$l_{2,1}$$ -norm-based block-sparsity-aware algorithms and single-norm penalized LMS strategies.

The celebrated least mean square (LMS) algorithm is the widely used system identification approach which can be easily implemented. With the assumption of no dependence among the tapped-delay input vectors, the mean square analysis of LMS algorithm based on independence theory is only an approximate description of its convergence behavior, especially when updated with a large step-size. In this paper, we propose a modified mean square error (MSE) update formula that exactly describes the convergence process of LMS for tapped-delay independent identical distributed (i.i.d.) input data. The qualitative analysis is presented to reveal the significance and rationality of the proposed formula. Moreover, the simulations in various conditions validate that, even with a large step-size used, the study curves produced by the proposed formula are much more accurate in predicting the convergence behavior, compared with that based on independence assumption.

Smart antenna systems are of great importance in wireless communication and radar applications. They effectively enhance the system capacity and reduce the co-channel interference. Smart antenna is an array antenna that uses adaptive beamforming algorithms to steer the main beam toward the desired signal direction and reject the interfering signals of the same frequency from other directions without moving the antenna. This is achieved by continuously updating the weights of each radiating element (antenna). An algorithm with low complexity, low computation costs, high speed convergence rates and better performance is usually preferred. This paper introduces a new performance investigation and comparison between five different beamforming algorithms: Least Mean Square (LMS), Normalized Least Mean Square (NLMS), Sample Matrix Inversion (SMI), Recursive Least Square (RLS) and Hybrid Least Mean Square / Sample Matrix Inversion (LMS/SMI). In this investigation, the number of array elements and the displacement among them are changed in each algorithm. Simulation experiments are carried out, and the results are compared to verify the effectiveness of this investigation. The performance of each algorithm is optimized and demonstrated using MATLAB software package.