Recursive Least-squares Algorithm Research Articles

Applicability of adaptive noise cancellation to fetal heart rate detection using photoplethysmography

In this paper, an approach based on adaptive noise cancellation (ANC) is evaluated for extraction of the fetal heart rate using photoplethysmographic signals from the maternal abdomen. A simple optical model is proposed in which the maternal and fetal blood pulsations result in emulated signals where the lower SNR limit (fetal to maternal) is - 25 dB . It is shown that a recursive least-squares algorithm is capable of extracting the peaks of the fetal PPG from these signals, for typical values of maternal and fetal tissues.

Nonlinear System Identification using a New Sliding-Window Kernel RLS Algorithm

In this paper we discuss in detail a recently proposed kernel-based version of the recursive least-squares (RLS) algorithm for fast adaptive nonlinear filtering. Unlike other previous approaches, the studied method combines a sliding-window approach (to fix the dimensions of the kernel matrix) with conventional ridge regression (to improve generalization). The resulting kernel RLS algorithm is applied to several nonlinear system identification problems. Experiments show that the proposed algorithm is able to operate in a time-varying environment and to adjust to abrupt changes in either the linear filter or the nonlinearity.

Performance analysis of a RLS-based MLP-DFE in time-invariant and time-varying channels

In this work, a recently derived recursive least-square (RLS) algorithm to train multi layer perceptron (MLP) is used in an MLP-based decision feedback equalizer (DFE) instead of the back propagation (BP) algorithm. Its performance is investigated and compared to those of MLP-DFE based on the BP algorithm and the simple DFE based on the least-mean square (LMS) algorithm. The results show improved performance obtained by the new structure in both time-invariant and time-varying channels. As will be detailed in this work, the newly proposed structure is a compromise between complexity and performance.

Diurnal Changes of Heart Rate and Sympathovagal Activity for Temporal Patterns of Transient Ischemic Episodes in 24-Hour Electrocardiograms

We test the hypothesis that different temporal patterns of transient ST segment changes compatible with ischemia (ischemic episodes) are a result of different physiologic mechanisms responsible for ischemia. We tested the hypothesis using records of the Long-Term ST Database. Each record was divided into three intervals of records: morning, day, and night intervals; and was inserted into one of three sets according to the temporal pattern of ischemia: salvo, periodic, and sporadic pattern. We derived time- and frequency-domain parameters of the heart rate time series in selected intervals in the neighborhood of ischemic episodes. We used the adaptive autoregressive method with a recursive least-square algorithm for consistent spectral tracking of heart rate time series and to study frequency-domain sympathovagal behavior during ischemia. The results support the hypothesis that there are at least two distinct populations, which differ according to mechanisms and temporal patterns of ischemia.

Fast RLS Fourier analyzers capable of accommodating frequency mismatch

Adaptive Fourier analyzers are used to estimate the discrete Fourier coefficients (DFC) of sine and cosine terms of noisy sinusoidal signals whose frequencies are usually assumed known a prior. The recursive least squares (RLS) Fourier analyzer provides excellent performance, but is computationally very intensive. In this paper, we first present four fast RLS (FRLS) algorithms based on the inherent characteristics of the DFC estimation problem. These FRLS algorithms show approximately the same performance and indicate estimation capabilities that are quite similar to those of the RLS, while requiring considerably less computational cost. Second, the performance of the proposed FRLS algorithms is analyzed in detail. Difference equations governing their dynamics as well as closed-form expressions for their steady-state mean square errors (MSE) are derived and compared with those of the LMS Fourier analyzer. Third, the RLS and four FRLS algorithms are modified by incorporating an adaptive scheme, to alleviate the influence of undesirable frequency mismatch (FM) on their performance. Extensive simulations as well as application to real noise signals are provided to demonstrate the relative performance capabilities of the RLS and four FRLS algorithms, the validity of analytical findings, and ability of the modified RLS and FRLS algorithms to mitigate the influence of the FM.

Multichannel fast QRD-RLS adaptive filtering: Block-channel and sequential-channel algorithms based on updating backward prediction errors

Fast QR decomposition recursive least-squares (FQRD-RLS) algorithms are well known for their fast convergence and reduced computational complexity. A considerable research effort has been devoted to the investigation of single-channel versions of the FQRD-RLS algorithms, while the multichannel counterparts have not received the same attention. The goal of this paper is to broaden the study of the efficient and low complexity family of multichannel RLS adaptive filters, and to offer new algorithm options. We present a generalized approach for block-type multichannel FQRD-RLS (MC-FQRD-RLS) algorithms that includes both cases of equal and multiple order. We also introduce new versions for block-channel and sequential-channel processing, details of their derivations, and a comparison in terms of computational complexity. The proposed algorithms are based on the updating of backward a priori and a posteriori error vectors, which are known to be numerically robust.

Recursive Least Squares with Linear Constraints

Recursive Least Squares (RLS) algorithms have wide-spread applications in many areas, such as real-time signal processing, control and communications. This paper shows that the unique solutions to linear-equality constrained and the unconstrained LS problems, respectively, always have exactly the same recursive form. Their only difference lies in the initial values. Based on this, a recursive algorithm for the linear-inequality constrained LS problem is developed. It is shown that these RLS solutions converge to the true parameter that satisfies the constraints as the data size increases. A simple and easily implementable initialization of the RLS algorithm is proposed. Its convergence to the exact LS solution and the true parameter is shown. The RLS algorithm, in a theoretically equivalent form by a simple modification, is shown to be robust in that the constraints are always guaranteed to be satisfied no matter how large the numerical errors are. Numerical examples are provided to demonstrate the validity of the above results.

Adaptive Sample Position Control System for Electrostatic Levitation Furnace

The Electrostatic Levitation Furnace (ELF) is one of the experiment facilities for materials science which is expected to be used on the International Space Station (ISS) in future. A unique feature of ELF is to levitate a sample inside the furnace by means of Coulomb's force throughout the fusion/solidification experiments. To realize this condition under the disturbances of the ISS environment we designed three customized control logics. Incidentally, when those logics were tested in a rocket experiment in 1998, the sample material showed an unexpectedly shaky motion during the experiment. The cause of this phenomenon was explained by analysis that the control force diminished when the sample temperature was high and the heating lasers were lit. Actually, the electrical charge of the sample significantly decreases when it is heated to a certain degree and is irradiated by the lasers. Hence, we redesigned the control software by adopting the Recursive Least-Squares Algorithm (RLSA), which identifies the amount of a sample's electrical charge in real-time. As a result, several numerical simulations have proved that the sample motion is well controlled with this adaptive control software even if the electrical charge changes significantly. Consequently, we concluded that this adaptive control technique is widely applicable to the systems whose parameters are changeable during operations.

Estimation of the Projection Operator in a Multiresolution Multisensor Data Fusion Scheme

Zhang presented a new multiresolution multisensor data fusion scheme for dynamic systems to be observed by multisensors of different resolutions. State space projection equation is introduced to associate the states of a system at each resolution with others. A discrete model of the system is built by using Haar wavelet or general compactly supported wavelet as a linear projection operator to approximate the state space projection. In fact, different wavelet corresponds to different sensor structure. For the multiresolution multisensor system with unknown sensor structure, the projection operator should be estimated online. Up to now, this problem has never been investigated. In this brief, the projection operator is estimated by using least-square estimation algorithm and recursive least-square estimation algorithm. The research on projection operator estimation lays a foundation for the popularization and application of the multiresolution multisensor system estimation algorithm in the real system

Recursive total instrumental-variable algorithm for solving over-determined normal equations and its applications

The well-known recursive least-squares (RLS) algorithms are directly dependent on the recursive estimation method for inversion of the auto-correlation matrix based on the matrix inverse lemma. On the basis of recursive estimation of the augmented cross-correlation matrix and the well-known power iteration, this paper establishes a recursive total instrumental-variable (RTIV) algorithm for tracking the total least-squares (TLS) solution of the normal equations in the over-determined instrumental-variable methods. Under the condition that the recursive estimation of the augmented cross-correlation matrix is asymptotically convergent, we show that the weight vector in the RTIV algorithm converges to the direction parallel to the singular vector associated with the smallest singular value of the augmented cross-correlation matrix. When the algorithm is applied in a parameter estimation problem, the converging weight vector corresponds to the TLS solution of the over-determined normal equations. Since the estimated parameters are optimal in the TLS sense, in the case where noise exists in both the input and output of the system or with the short sampling data, its noise rejection capability is superior to that of least-squares-based algorithms. The applicability and performance of the RTIV algorithm are demonstrated by computer simulations for adaptive IIR filtering and harmonic retrieval.

In situ measurement of wafer temperature using two sensors with different dynamical properties

As more and more features are packed onto smaller silicon chips, there is a need to optimize wafer fabrication process conditions to the fullest. Closed-loop control is one approach for meeting the rising need for more stringent control over the absolute and spatial temperature of wafers undergoing the post-exposure bake (PEB) process. For an automatic control loop to be implemented successfully, the feedback signals must be accurate and reliable. However, in situ temperature measurement systems based on either contact or non-contact sensors cannot achieve the required accuracy. Another challenge is to measure the wafer temperature without disrupting the manufacturing process. In this paper, a non-intrusive method that uses the readings from two contact sensors and the recursive least-squares algorithm to estimate the sensor model is described. When the sensor model is identified, the inverse model method is applied to achieve fast and accurate temperature measurements. Experimental results demonstrate that the algorithm is able to provide accurate real-time temperature measurement, which may be used as the feedback signal to achieve closed-loop control.

Robust extended multidelay filter and double-talk detector for acoustic echo cancellation

We propose an integrated acoustic echo cancellation solution based on a novel class of efficient and robust adaptive algorithms in the frequency domain, the extended multidelay filter (EMDF). The approach is tailored to very long adaptive filters and highly auto-correlated input signals as they arise in wideband full-duplex audio applications. The EMDF algorithm allows an attractive tradeoff between the well-known multidelay filter and the recursive least-squares algorithm. It exhibits fast convergence, superior tracking capabilities of the signal statistics, and very low delay. The low computational complexity of the conventional frequency-domain adaptive algorithms can be maintained thanks to efficient fast realizations. We also show how this approach can be combined efficiently with a suitable double-talk detector (DTD). We consider a corresponding extension of a recently proposed DTD based on a normalized cross-correlation vector whose performance was shown to be superior compared to other DTDs based on the cross-correlation coefficient. Since the resulting DTD also has an EMDF structure it is easy to implement, and the fast realization also carries over to the DTD scheme. Moreover, as the robustness issue during double talk is particularly crucial for fast-converging algorithms, we apply the concept of robust statistics into our extended frequency-domain approach. Due to the robust generalization of the cost function leading to a so-called M-estimator, the algorithms become inherently less sensitive to outliers, i.e., short bursts that may be caused by inevitable detection failures of a DTD. The proposed structure is also well suited for an efficient generalization to the multichannel case

Channel Identification with Linear Time-Varying Channel Model for Pilot Channel Aided DS/CDMA Systems

A new channel identification algorithm using both pilot and traffic channels is proposed. It is based on the linear modelling for the fading channel and takes the form of a modified recursive least-squares (RLS) algorithm. Its existence is also analyzed. It will be shown through computer simulation that the proposed algorithm is robust to the variation of the channel fade rate in a mean square error (MSE) sense.

A research of UWB rake receiver based on novel RLS adaptive algorithm

A modified RAKE receiver based on novel Recursive Least Squares (RLS) adaptive algorithm is proposed. The receiver uses L-fingered correlators, which are composed of RLS adaptive filters, to enhance the performance of multipath receiving. It can also track the amplitude of the received signal to form a real-time amplitude estimation which is correlated with the power of excess delay bin. The simulation results based on the IEEE UltraWide Band (UWB) channel models (CM1 to CM4) show that the novel RLS algorithm can alter the attenuation estimation with the finger’s power delay profile, and RAKE receiver with few fingers can be employed to get high performance.

Bias compensation based recursive least-squares identification algorithm for MISO systems

For multi-input single-output output-error systems, the least-squares (LS) estimates are biased. In order to obtain the unbiased estimates, we present a recursive LS identification algorithm based on a bias compensation technique. The basic idea is to eliminate the estimation bias by adding a correction term in the LS estimates, and further to derive a bias compensation based recursive LS algorithm. Finally, we test the proposed algorithms by simulation and show their effectiveness.

A floating-point FPGA-based self-tuning regulator

Recursive-least-square (RLS) algorithm is widely used in many areas with real-time implementation using digital signal processors. In this paper, the authors present a pure hardware implementation of a self-tuning regulator (STR) that uses a real-time RLS algorithm as the parameter estimator. The STR contains a controller design circuit and a controller circuit. Due to RLS computation-precision and dynamic-range requirements, the hardware implementation uses a floating-point format. The floating-point processing elements presented in this paper use parameterized design, where the number of exponents and mantissa bits can be changed as the data range and the accuracy of a specific application require. The strategies for overcoming the covariance matrix asymmetrical problem during the hardware computation and the covariance matrix resetting is introduced when the system is poorly exciting are presented. The design was verified with real-time experiments using a new testbed. The experiment results are presented.

RLS channel estimation with adaptive forgetting factor in space-time coded MIMO-OFDM systems

Considering that channel estimation plays a crucial role in coherent detection, this paper addresses a method of Recursive-least-squares (RLS) channel estimation with adaptive forgetting factor in wireless space-time coded multiple-input and multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. Because there are three different forgetting factor scenarios including adaptive, two-step and conventional ones applied to RLS channel estimation, this paper describes the principle of RLS channel estimation and analyzes the impact of different forgetting factor scenarios on the performances of RLS channel estimation. Simulation results proved that the RLS algorithm with adaptive forgetting factor (RLS-A) outperformed that with two-step forgetting factor (RLS-T) or with conventional forgetting factor (RLS-C) in both estimation accuracy and robustness over the multiple-input multiple-output (MIMO) channel, i.e., a wide-sense stationary uncorrelated scattering (WSSUS) and frequency-selective slowly fading channel. Hence, we can employ the RLS-A method by adjusting forgetting factor adaptively to track and estimate channel state parameters successfully in space-time coded MIMO-OFDM systems.

The study of structural system dynamic problems by recursive estimation method

This paper presents the recursion-relation algorithm to determine the input forces of beam structures and the individual node displacement. The system state equations of the beam structures are based on the average acceleration method, and a dynamic beam matrix equation is constructed by using the finite element method. Implementation of this method involves handling various systems' parameters such as the measurement noise, the modeling error, and the external disturbance. The Kalman filter is used to predict the applied forces and adjusted at each time step according to the measured dynamic response data of structures. The estimator employs a recursive least-squares algorithm to compute the magnitudes of the impulsive loads. The accuracy of the present method is demonstrated by the numerical simulations for loads applied along the axis of a beam on different time frames.

A novel phase-noise compensation scheme for communication receivers

A novel phase-noise (PHN) compensation method is proposed in this paper. The proposed approach uses the information provided by an additional signal path that is added with modest hardware overhead to better estimate the PHN. In this signal path, the oscillator output is self-downconverted to the baseband by mixing itself with a delayed and conjugated replica, so as to provide PHN information that is free from data modulation. A joint prediction and smoothing Wiener filter can then be employed to obtain the minimum mean-squared error estimate of the PHN. There are generally two types of PHN models commonly used in the literature: stationary PHN and Wiener PHN. Both types of PHN are considered in this paper. Adaptive schemes are also presented using the least-mean square algorithm and recursive least-square algorithm. Simulations of a 64-quadrature amplitude modulation receiver confirm the analysis results of the PHN estimation performance, and show that the proposed method can improve the receiver performance significantly over the conventional schemes.

Adaptive nonlinear PCA algorithms for blind source separation without prewhitening

Blind source separation (BSS) aims at recovering statistically independent source signals from their linear mixtures without knowing the mixing coefficients. Besides independent component analysis, nonlinear principal component analysis (NPCA) is shown to be another useful tool for solving this problem, but it requires that the measured data be prewhitened. By taking into account the autocorrelation matrix of the measured data, we present in this paper a modified NPCA criterion, and develop a least-mean-square (LMS) algorithm and a recursive least-squares algorithm. They can perform the online BSS using directly the unwhitened observations. Since a natural gradient learning is applied and the prewhitening process is removed, the proposed algorithms work more efficiently than the existing NPCA algorithms, as verified by computer simulations on man-made sources as well as practical speech signals.