Recursive Least-squares Schemes Research Articles

Analysis of robust recursive least squares: Convergence and tracking

Outliers and impulsive noise are inevitable factors in recursive least squares (RLS). Developing robust RLS is vital in practical applications such as system identification in which outliers in the desired signals may severely divert the solutions. Almost all suggested robust RLS schemes have been designed for the impulsive noise and Gaussian environments. Recently, employing the Maximum Correntropy Criterion (MCC), the RGMCC (Recursive General MCC) algorithm has been given which yields more exact results for system identification problem in non-Gaussian environments. Here, we develop a new Robust RLS (R2LS) scheme based on the MCC. In contrast to RGMCC, the structure of our model, although being complex, makes it possible to conduct convergence and performance analysis in both the stationary and non-stationary environments. Especially, the model is capable to reasonably predict and track the signals when the original signal is contaminated by non-Gaussian noise. To establish convergence and performance, we apply a half-quadratic optimization algorithm in the multiplicative form to successively convert our model to a quadratic problem which can be effectively solved by the classical tools. Numerical experiments are done on real and synthetic datasets; they show that the proposed algorithm outperforms the conventional RLS as well as some of its recent extensions.

Fractional-order algorithms for tracking Rayleigh fading channels

This paper presents the tracking behavior of fractional-order (FO) variants of the normalized least mean square (NLMS) algorithm in a nonstationary environment modeled as time-varying Rayleigh fading sequence. The celebrated recursive least squares (RLS) or its variant extended RLS (E-RLS) algorithms fail in such situations although they exhibit faster convergence but with the undesired feature of higher computational complexity. The FO algorithms are based on the Riemann–Liouville differintegral operator which is used in the gradient calculation; such schemes provide two step sizes and an FO to control the rate of convergence. In evaluation, we consider a high-speed mobile environment with a Rayleigh channel which results in different Doppler frequency shifts depending upon the transmission frequency, relative velocity of the transmitter and receiver. The proposed algorithms are compared with the NLMS, RLS and E-RLS schemes, and numerical experiments show the superiority of the FO variants over these schemes in terms of stability and model accuracy in the steady state. A hybrid scheme is also shown where the weights of an FO variant are initially trained with RLS and then performs self-adaptation; the FO scheme is confirmed to have better performance than all traditional counterparts.

New Decentralized Positioning Schemes for Wireless Sensor Networks Based on Recursive Least-Squares Optimization

This letter presents a recursive least-squares (RLS) optimization process to solve the positioning problem for wireless sensor networks, where a recursive-in-time cost function is first defined and then an iterative decentralized algorithm is derived. It is shown that the RLS scheme is equivalent to the incremental subgradient method with an appropriate variable step size for each iteration. With this, we further replace each gradient value by its "sign" to form a reduced-complexity RLS (RCRLS) scheme. Simulation results show that RCRLS has some performance degradation as compared to RLS, but both of them outperform previous related methods.

Partitioned online sequential extreme learning machine for large ordered system modeling

In this paper, we propose an algorithm entitled “partitioned OS-ELM” (POS-ELM) that partitions a large data matrix into small matrices, applies an RLS (Recursive Least Square) scheme in each of the small sub-matrices and assembles the whole estimation vector by the concatenation of the sub-vectors from the RLS outputs of the sub-matrices. Consequently, the algorithm is less complex than the conventional OS-ELM and maintains an almost compatible estimation performance.

Parallel interference cancellation for carrier frequency offset in OFDM assisted with recursive least squares algorithm

Parallel interference cancellation (PIC) assisted with recursive least squares (RLS) algorithm is proposed to cancel the interference due to the carrier frequency offset (CFO) in orthogonal frequency division multiplexing (OFDM) system. The proposed algorithm is composed of two stages, which are RLS scheme and PIC scheme. RLS scheme is selected to compensate the frequency offset in the time domain in the first stage, and the interference induced by residual frequency offset is canceled by the PIC scheme in the frequency domain in the second stage. The result of bit error rate (BER) shows that its performance is robust for cancellation as comparison criteria, even though the frequency offset is 0.45. The 16QAM constellation is also simulated to observe the improvements from the proposed suppression schemes.

Efficient global motion estimation algorithm using recursive least squares

Global motion estimation plays an important role in video compensation and video analysis. We present an efficient method to estimate global motion parameters. First, a feature point selection scheme that exploits the symmetry properties of camera motion is developed. Then, we use parametric motion models to characterize global motion and a recursive least-squares scheme to accelerate the computation of parameter estimation. In the proposed method, the motion vectors in the background area are selected to estimate the parameters of motion models, which improves estimate reliability. Simulation results show that the proposed method gives better performance than the previous methods in terms of the computational efficiency and the estimate accuracy.

Blind adaptive multiuser detection based on affine projection algorithm

In this letter, we introduce a novel blind multiuser detector based on the affine projection algorithm (APA) for direct-sequence code-division multiple-access (DS-CDMA) systems. Computational complexities of least mean-squares (LMS), recursive least squares (RLS), Kalman, and APA-based blind multiuser detection algorithms are compared. The proposed technique has similar convergence and tracking properties as the RLS algorithm with much reduced computational cost. Simulation results are presented to compare our APA-based algorithm with the blind LMS, RLS, and Kalman schemes.

Recursive least squares with forgetting for online estimation of vehicle mass and road grade: theory and experiments

Good estimates of vehicle mass and road grade are important in automation of heavy duty vehicles, vehicle following manoeuvres or traditional powertrain control schemes. Recursive least square (RLS) with multiple forgetting factors accounts for different rates of change for different parameters and thus, enables simultaneous estimation of the time-varying grade and the piece-wise constant mass. An ad hoc modification of the update law for the gain in the RLS scheme is proposed and used in simulation and experiments. We demonstrate that the proposed scheme estimates mass within 5% of its actual value and tracks grade with good accuracy provided that inputs are persistently exciting. The experimental setups, signals, their source and their accuracy are discussed. Issues like lack of persistent excitations in certain parts of the run or difficulties of parameter tracking during gear shift are explained and suggestions to bypass these problems are made.

A revisit to block and recursive least squares for parameter estimation

In this paper, the classical least squares (LS) and recursive least squares (RLS) for parameter estimation have been re-examined in the light of the present day computing capabilities. It has been demonstrated that for linear time-invariant systems, the performance of blockwise least squares (BLS) is always superior to that of RLS. In the context of parameter estimation for dynamic systems, the current computational capability of personal computers are more than adequate for BLS. However, for time-varying systems with abrupt parameter changes, standard blockwise LS may no longer be suitable due to its inefficiency in discarding “old” data. To deal with this limitation, a novel sliding window blockwise least squares approach with automatically adjustable window length triggered by a change detection scheme is proposed. Two types of sliding windows, rectangular and exponential, have been investigated. The performance of the proposed algorithm has been illustrated by comparing with the standard RLS and an exponentially weighted RLS (EWRLS) using two examples. The simulation results have conclusively shown that: (1) BLS has better performance than RLS; (2) the proposed variable-length sliding window blockwise least squares (VLSWBLS) algorithm can outperform RLS with forgetting factors; (3) the scheme has both good tracking ability for abrupt parameter changes and can ensure the high accuracy of parameter estimate at the steady-state; and (4) the computational burden of VLSWBLS is completely manageable with the current computer technology. Even though the idea presented here is straightforward, it has significant implications to virtually all areas of application where RLS schemes are used.

Evolutionary adaptive active vibration control

This paper presents an investigation into the development of an adaptive active control mechanism for vibration suppression using genetic algorithms (GAs). GAs are used to estimate the adaptive controller characteristics, where the controller is designed on the basis of optimal vibration suppression using the plant model. This is realized by minimizing the prediction error of the actual plant output and the model output. A MATLAB GA toolbox is used to identify the controller parameters. A comparative performance of the conventional recursive least-squares (RLS) scheme and the GA is presented. The active vibration control system is implemented with both the GA and the RLS schemes, and its performance assessed in the suppression of vibration along a flexible beam structure in each case.

Recursive autoregressive spectral maps for ocular pathology detection

This article presents a new approach to the problem of obtaining topological maps for tissue characterization, based on spectral parameters extracted from radio frequency (RF) backscattered ultrasonic signals. The spectral parameter we deal with is the power spectral density centroid, since it is an efficient indicator of the tissue microstructure characteristics as far as the particle dimensions are concerned. The spectral analysis of RF ultrasonic echoes is performed using a recursive least-squares scheme with a variable forgetting factor, based on low-order autoregressive models. The proposed technique is particularly tailored to the differentiation of ocular pathologies; moreover, it is capable of tracking the spatial highvarying signal characteristics. The proposed approach was tested on simulated signals and on a gel suspension of calibrated latex spheres; finally, it was applied to signals scattered by in vitro eye specimens, giving satisfactory results in terms of frequency resolution and computational efficiency. The reduced computational burden allows an on-line implementation of the procedure. Topological spectral maps, combined with the conventional B-mode display, may offer a complete and integrated diagnostic tool, able to locally characterize the investigated tissue region in terms of amplitude and frequency shift of the corresponding echoes.

A D-step predictor in lattice and ladder form

We use the orthogonalizing property of the two-multiplier linear prediction lattice filter to construct a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</tex> -step ahead predictor in lattice form. The predictor generates <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</tex> -step forward and backward residuals in a recursive way and possesses most of the interesting properties of the basic one-step prediction lattice filter. An exact solution is presented first assuming a stationary observation process, using orthogonal projections in Hilbert space. Two adaptive implementations are also proposed for the case where the statistics of the signal process are unknown or time varying: a gradient method and a recursive least-squares scheme. Finally, we show how to construct an adaptive <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</tex> -step ahead predictor by adding a ladder part to the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</tex> -step lattice structure.