Conventional Recursive Least Squares Algorithm Research Articles

Efficient enhanced Recursive Least Square algorithm adaptive filtering scheme for artifacts removal in ECG signals

This paper proposes an improved Recursive Least Square (RLS) algorithm to address the limitations of the conventional RLS algorithm, which suffers from poor performance when dealing with non-stationary noise. The proposed algorithm, along with various algorithms, have been designed using Xilinx System Generator (XSG). These algorithms have been tested to denoise ECG signals that have been corrupted with four types of real noise obtained from the MIT-BIH dataset. The improved algorithm utilizes a systolic architecture that enables faster processing and better noise reduction capabilities. The experimental results demonstrate that the proposed algorithm with and without systolic architecture outperforms the conventional RLS algorithm and other state-of-the-art algorithms in terms of signal-to-noise ratio (SNR), mean squared error (MSE), and convergence speed.

Recursive least-squares algorithm based on a third-order tensor decomposition for low-rank system identification

A recently developed third-order tensor (TOT) decomposition-based method has proved to be working very well in linear system identification problems that target the estimation of long length impulse responses. This technique exploits the decomposition of the impulse response based on the nearest Kronecker product and low-rank approximations, but it also owns a specific advantage. Its main feature is related to the way of handling the rank of a third-order tensor, which is controlled in terms of the rank of a matrix and, as a result, is limited to small values. In this paper, we further develop a recursive least-squares (RLS) algorithm based on the TOT decomposition technique. The resulting solution combines the estimates provided by three shorter adaptive filters, thus gaining in terms of both performance and complexity. The three component filters are updated in parallel, which represents an important practical advantage, in terms of the modularity of implementation. Also, as compared to the conventional RLS algorithm, a significant reduction of the computational complexity can be achieved for the common setup of the decomposition parameters. Besides, since the length of the adaptive filter highly influences the main performance criteria (e.g., convergence, tracking, and accuracy), the proposed RLS version based on the TOT decomposition outperforms both the conventional algorithm and a previously developed RLS-based solution that involves a second-order decomposition. These performance gains mainly reflect in a faster tracking capability and a better accuracy of the estimate (i.e., lower misalignment). Simulations performed in the framework of echo cancellation support the performance features of the proposed tensorial RLS-based algorithm.

A compact neuromorphic architecture with dynamic multiplexing to efficiently compute a nearest Kronecker product decomposition based RLS-NLMS algorithm for active noise control headphones

Recently, embedded applications in resource-constrained electronic appliances are increasingly being used for noise reduction. Specifically, modern headphones are used to mitigate the environmental noise effects using advanced active noise control (ANC) systems. Despite achieving great performance, there is still a great challenge to develop compact ANC headphones since these devices contain a limited area. In addition, there are more challenges linked to improvement of the convergence rate, tracking, and complexity of the adaptive algorithm which is used in these devices to efficiently reduce the environmental noise. Specifically, the convergence properties can be improved by using the cutting-edge advanced adaptive algorithms along with the nearest Kronecker product (NKP) decomposition. In this work, we present a new neuromorphic architecture to efficiently compute an improved variant of the Kronecker product recursive least-squares (RLS). To achieve this architecture, we present three contributions; (1) we made a combination between the filtered-X RLS algorithm and normalized least mean squares (NLMS) algorithm to decrease the computational complexity by reducing the number of arithmetic operations required to efficiently compute the filter coefficients. Therefore, the proposed method requires fewer operations when compared with conventional RLS and RLS-NKP algorithms, respectively; (2) we use the spiking neural P (SN P) systems along with their advanced variants, such as rules on the synapses, colored spikes and dendritic delays to design two compact parallel arithmetic circuits (adder and divisor). In this way, the proposed method can be computed at high processing speeds and expending low area; (3) we propose a new digital neuromorphic architecture to be applied in active noise cancellation in headphones. Specifically, we propose a new adaptive unit core, which contains the proposed parallel neural arithmetic circuits, to perform dual filter operations, i.e, the proposed unit is capable of simulating two adaptive algorithms by using the same core. To achieve this we use the dynamic multiplexing technique. Therefore, our proposal exhibits low area consumption. As a consequence, the implementation of the proposed method can be easily integrated into resource-constrained ANC headphones.

Recursive least-squares algorithm for a characteristic model with coloured noise by means of the data filtering technique

This work investigates the identification problems for a characteristic model with autoregressive moving average noise, and the sum of all coefficients of the model is equal to one. A recursive least-squares (RLS) algorithm using the data filtering technique is derived for the model. The basic idea is to use a linear filter to filter the input–output data, to decompose a characteristic model into a system model and a noise model, but the sum of all coefficients remains equalling to one. Moreover, the traditional RLS algorithm is also presented and compared with the proposed algorithm in terms of computational complexity and effectiveness. Finally, three numerical examples show that the proposed algorithm outperforms the conventional RLS algorithm.

Parameter identification of a lithium‐ion battery based on the improved recursive least square algorithm

Accurate parameter identification of a lithium-ion battery is a critical basis in the battery management systems. Based on the analysis of the second-order RC equivalent circuit model, the parameter identification process using the recursive least squares (RLS) algorithm is discussed firstly. The reason for the RLS algorithm affecting the accuracy and rapidity of model parameter identification is pointed out. And an improved RLS algorithm is proposed, an inner loop with the estimated parameter vector updated multiple times is inserted into the conventional RLS algorithm, so that the identification results are improved. The test platform of a single lithium-ion battery is built. The experimental results show that the improved RLS algorithm has better tracking ability, smaller prediction error and has a moderate computational burden compared with the conventional RLS algorithm and a variable forgetting factor RLS algorithm.

A Recursive Least-Squares Algorithm for the Identification of Trilinear Forms

High-dimensional system identification problems can be efficiently addressed based on tensor decompositions and modelling. In this paper, we design a recursive least-squares (RLS) algorithm tailored for the identification of trilinear forms, namely RLS-TF. In our framework, the trilinear form is related to the decomposition of a third-order tensor (of rank one). The proposed RLS-TF algorithm acts on the individual components of the global impulse response, thus being efficient in terms of both performance and complexity. Simulation results indicate that the proposed solution outperforms the conventional RLS algorithm (which handles only the global impulse response), but also the previously developed trilinear counterparts based on the least-mean- squares algorithm.

A New Local Polynomial Modeling Based Variable Forgetting Factor and Variable Regularized PAST Algorithm for Subspace Tracking

This paper proposes a new local polynomial modeling based variable forgetting factor (VFF) and variable regularized (VR) projection approximation subspace tracking (PAST) algorithm, which is based on a novel VR-VFF recursive least squares (RLS) algorithm with multiple outputs. The subspace to be estimated is modeled as a local polynomial model so that a new locally optimal forgetting factor (LOFF) can be obtained by minimizing the resulting mean square deviation of the RLS algorithm after using the projection approximation. An $l_2$ -regularization term is also incorporated to the LOFF-PAST algorithm to reduce the estimation variance of the subspace during signal fading. The proposed LOFF-VR-PAST algorithm can be implemented by the conventional RLS algorithm as well as the numerically more stable QR decomposition. Applications of the proposed algorithms to subspace-based direction-of-arrival estimation under stationary and nonstationary environments are presented to validate their effectiveness. Simulation results show that the proposed algorithms offer improved performance over the conventional PAST algorithm and a comparable performance to the Kalman filter with variable measurement subspace tracking algorithm, which requires a considerably higher arithmetic complexity. The new LOFF-VR-RLS algorithm may also be applicable to other RLS problems involving multiple outputs.

Enhanced RLS in Smart Antennas for Long Range Communication Networks

The utilisation of smart antenna (SA) techniques in future wireless and cellular networks is expected to have an impact on the efficient use of the spectrum and the optimization of service quality. This is because SAs can enhance the maximization of output power of the signal in desired directions amongst a whole lot of functions. Despite these benefits of SAs, long range communications still face unsolved challenges such as signal fading. Therefore, this paper focuses on enhancing the recursive least squares (RLS) in SA design for long range communication networks. The conventional RLS algorithm does not need any matrix inversion computations because the inverse correlation matrix is determined directly. Therefore, the RLS saves computational power. Hence, we have enhanced the RLS algorithm by introducing a constant m to the gain factor in order to yield an improved gain vector. Results from our simulations show that the enhanced RLS reduces mean square error (MSE), smoothens filter output and improves signal-to-noise ratio (SNR). These benefits further result in the antenna’s gain improvement leading to an increased range and directivity of the smart antenna over a long range communication networks.

A Combined DMI–RLS Algorithm in Adaptive Processing Antenna System

Smart antenna systems are rapidly emerging as one of the key technologies that can enhance overall wireless communications system performance. The purpose of this paper is to develop a novel adaptive beamforming system from two adaptive algorithms that are known in the literature as spatial filters. Our adaptive beamforming algorithm is a combination of the direct matrix inversion (DMI) and the recursive least square (RLS). This combination is called DMI–RLS and is used to calculate iteratively the optimum weights of smart antenna array and to ensure a possible faster convergence. Simulation data used for a uniform linear array antenna as an application verifies the accuracy of the analytical results. The performance of the DMI–RLS algorithm is also compared with the conventional RLS algorithm ones. From the simulation results, we noticed that, in the main, the performances of the DMI–RLS algorithm are sturdier than those of the conventional RLS algorithm.

Recursive identification of time-varying systems: Self-tuning and matrix RLS algorithms

In this paper, a new parallel adaptive self-tuning recursive least squares (RLS) algorithm for time-varying system identification is first developed. Regularization of the estimation covariance matrix is included to mitigate the effect of non-persisting excitation. The desirable forgetting factor can be self-tuning estimated in both non-regularization and regularization cases. We then propose a new matrix forgetting factor RLS algorithm as an extension of the conventional RLS algorithm and derive the optimal matrix forgetting factor under some reasonable assumptions. Simulations are given which demonstrate that the performance of the proposed self-tuning and matrix RLS algorithms compare favorably with two improved RLS algorithms recently proposed in the literature.

A New State-Regularized QRRLS Algorithm With a Variable Forgetting Factor

This brief proposes a new state-regularized (SR) and QR-decomposition-based (QRD) recursive least squares (RLS) adaptive filtering algorithm with a variable forgetting factor (VFF). It employs the estimated coefficients as prior information to minimize the exponentially weighted observation error, which leads to reduced variance over a conventional RLS algorithm and reduced bias over an L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -regularized RLS algorithm. To improve the tracking performance, a new measure of convergence status is introduced in controlling the forgetting factor. Consequently, the resultant SR-VFF-RLS algorithm stabilizes the update and adaptively selects the number of measurements by means of the VFF. Improved tracking performance, steady-state mean-square error, and robustness to power-varying inputs over conventional RLS algorithms can be achieved. Furthermore, the proposed algorithm can be implemented using QRD, which leads to a lower roundoff error and more efficient hardware realization than the direct implementation. The effectiveness of the proposed algorithm is demonstrated by computer simulations.

Adaptive Forgetting Factor Subarray RLS Beamforming for Multipath Environments

This letter presents an efficient adaptive beamformer to deal with the multipath environments created by signal source scatterings. To improve the performance possible with the fixed forgetting factor, the regular adaptive forgetting factor algorithm is derived and applied to the subarray recursive least squares (RLS) beamforming. Simulations confirm that the proposed scheme has better performance than not only the conventional RLS algorithm but also the subarray RLS and adaptive forgetting factor RLS algorithms.

A Recursive Least M-Estimate Algorithm for Robust Adaptive Filtering in Impulsive Noise: Fast Algorithm and Convergence Performance Analysis

This paper studies the problem of robust adaptive filtering in impulsive noise environment using a recursive least M-estimate algorithm (RLM). The RLM algorithm minimizes a robust M-estimator-based cost function instead of the conventional mean square error function (MSE). Previous work has showed that the RLM algorithm offers improved robustness to impulses over conventional recursive least squares (RLS) algorithm. In this paper, the mean and mean square convergence behaviors of the RLM algorithm under the contaminated Gaussian impulsive noise model is analyzed. A lattice structure-based fast RLM algorithm, called the Huber Prior Error Feedback-Least Squares Lattice (H-PEF-LSL) algorithm is derived. Part of the H-PEF-LSL algorithm was presented in ICASSP 2001. It has an order O(N) arithmetic complexity, where N is the length of the adaptive filter, and can be viewed as a fast implementation of the RLM algorithm based on the modified Huber M-estimate function and the conventional PEF-LSL adaptive filtering algorithm. Simulation results show that the transversal RLM and the H-PEF-LSL algorithms have better performance than the conventional RLS and other RLS-like robust adaptive algorithms tested when the desired and input signals are corrupted by impulsive noise. Furthermore, the theoretical and simulation results on the convergence behaviors agree very well with each other.

Modified recursive least squares (RLS) algorithm for neural networks using piecewise linear function

The recursive least squares (RLS) learning algorithm for multilayer feedforward neural networks uses a sigmoid nonlinearity at node outputs. It is shown that by using a piecewise linear function at node outputs, the algorithm becomes faster. The modified algorithm improves computational efficiency and by preserving matrix symmetry it is possible to avoid explosive divergence, which is normally seen in the conventional RLS algorithm due to the finite precision effects. Also the use of this piecewise linear function avoids the approximation, which is otherwise necessary in the derivation of the conventional algorithm with sigmoid nonlinearity. Simulation results on the XOR problem, 4–2–4 encoder and function approximation problem indicate that the modified algorithm reduces the occurrence of local minima and improves the convergence speed compared to the conventional RLS algorithm. A nonlinear system identification and control problem is considered to demonstrate the application of the algorithm to complex problems.

A nonlinear recursive least squares algorithm for crosstalk‐resistant noise canceler

AbstractIn this paper, a method of updating filter coefficients is proposed in which the RLS (Recursive Least Squares) algorithm is applied to a noise canceler with a filter for crosstalk removal. The RLS algorithm has an advantage over the Least Mean Square algorithm by virtue of better convergence. When the filter coefficients are updated including the filter for crosstalk removal, the error signal becomes nonlinear in terms of filter coefficients. Hence, a nonlinear RLS algorithm is derived in which such nonlinearity is taken into account. It is shown that the convergence is further improved in comparison with the conventional RLS algorithm. Finally, a method is proposed to reduce the noise contained in the transmitted voice signals of telephone by means of the present noise canceler and its effectiveness is evaluated. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(5): 36–44, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10039

Noncoherent adaptive channel identification algorithms for noncoherent sequence estimation

In this letter, two novel noncoherent adaptive algorithms for channel identification are introduced. The proposed noncoherent least-mean-square (LMS) and noncoherent recursive least squares (RLS) algorithms can be combined easily with noncoherent sequence estimation (NSE) for M-ary differential phase-shift keying signals transmitted over intersymbol interference (ISI) channels. It is shown that the resulting adaptive noncoherent receivers are very robust against carrier phase variations. For zero frequency offset, the convergence speed and the steady-state error of the noncoherent adaptive algorithms are similar to those of conventional LMS and RLS algorithms. However, the conventional algorithms diverge even for relatively small frequency offsets, whereas the proposed noncoherent algorithms converge for relatively large frequency offsets. Simulations confirm the good performance of NSE combined with noncoherent adaptive channel estimation in time-variant (fading) ISI channels.

Robust M-estimate adaptive filtering

An M-estimate adaptive filter for robust adaptive filtering in impulse noise is proposed. Instead of using the conventional least-square cost function, a new cost function based on an M-estimator is used to suppress the effect of impulse noise on the filter weights. The resulting optimal weight vector is governed by an M-estimate normal equation. A recursive least M-estimate (RLM) adaptive algorithm and a robust threshold estimation method are derived for solving this equation. The mean convergence performance of the proposed algorithm is also analysed using the modified Huber function (a simple but good approximation to the Hampel's three-parts-redescending M-estimate function) and the contaminated gaussian noise model. Simulation results show that the proposed RLM algorithm has better performance than other recursive least squares (RLS) like algorithms under either contaminated gaussian or alpha-stable noise environment. The initial convergence, steady-state error, robustness to system change and computational complexity are also found to be comparable to the conventional RLS algorithm under gaussian noise alone.

Blind adaptive multiuser detection for asynchronous dual-rate DS/CDMA systems

In this paper, the authors consider an asynchronous direct-sequence code division multiple access (DS/CDMA) system wherein users are allowed to transmit their symbols at one out of two available data rates. Three possible access schemes are considered, namely, the variable spreading length (VSL), the variable chip rate (VCR), and the variable chip rate with frequency shift (VCRFS) formats. Their performance is compared for the case that a linear one-shot multiuser receiver is employed. It is also shown that detection of the users transmitting at the higher rate requires a periodically time-varying processing of the observables. Moreover, the problem of blind adaptive receiver implementation is studied, and a cyclic blind recursive-least-squares (RLS) algorithm is provided which is capable of converging to the periodically time-varying high-rate users detection structure. Numerical results show that the proposed receivers are near-far resistant, and that the VCRFS access technique achieves the best performance. Finally as to the adaptive blind receiver implementation, computer simulations have revealed that the cyclic RLS algorithm for blind adaptive high-rate users demodulation outperforms the conventional RLS algorithm in most cases of primary importance.

Simultaneous suppression of multiaccess and narrow-band interference in asynchronous CDMA networks

This paper handles the simultaneous suppression of narrow-band and multiaccess interference in asynchronous CDMA networks. We consider both linear one-shot detection and block-detection, showing that, in both cases, the presence of an external narrow-band interferer generally results in the need for time-varying processing. As to the linear one-shot detectors, we derive both a zero-forcing and a minimum mean square error detector, showing that they are members of an only family, wherein the optimization criterion is the constrained minimization of a suitably defined output interference energy. We also present a comparative performance assessment between the various detection strategies, studying the impact of both the optimization criterion and other system parameters, such as the oversampling ratio and the length of the observation window. We also handle the problem of blind and adaptive detection. At first we show that the linear one-shot receivers are readily amenable to a blind implementation, upon off-line estimation of the covariance matrix of the observables. Next, we consider the problem of an adaptive implementation of a periodically time-varying minimum mean square error receiver, introducing and assessing a new cyclic recursive least squares (RLS) algorithm: we show that, unlike the conventional RLS algorithms, the new algorithm is capable of tracking the periodically time-varying variation of the receiver structure, induced by the presence of a data-like narrow-band interferer.

Numerically stable RLS algorithms for time‐varying signals

One reason that recursive least-squares (RLS) algorithms are not used as widely as LMS algorithms is an instability problem resulting from finite precision errors in the calculations; leaky LMS algorithms that are numerically stable have been proposed in the LMS literature. In this paper, we offer a new RLS criterion that includes a strong parameter energy factor. Experiments show that adaptive algorithms that meet this criterion are numerically more stable than conventional RLS algorithms. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 82(4): 26–37, 1999