Showing papers on "Recursive least squares filter published in 2003"

Optimal training design for MIMO OFDM systems in mobile wireless channels

Abstract: This paper describes a least squares (LS) channel estimation scheme for multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems based on pilot tones. We first compute the mean square error (MSE) of the LS channel estimate. We then derive optimal pilot sequences and optimal placement of the pilot tones with respect to this MSE. It is shown that the optimal pilot sequences are equipowered, equispaced, and phase shift orthogonal. To reduce the training overhead, an LS channel estimation scheme over multiple OFDM symbols is also discussed. Moreover, to enhance channel estimation, a recursive LS (RLS) algorithm is proposed, for which we derive the optimal forgetting or tracking factor. This factor is found to be a function of both the noise variance and the channel Doppler spread. Through simulations, it is shown that the optimal pilot sequences derived in this paper outperform both the orthogonal and random pilot sequences. It is also shown that a considerable gain in signal-to-noise ratio (SNR) can be obtained by using the RLS algorithm, especially in slowly time-varying channels.

Recursive identification of Hammerstein systems with discontinuous nonlinearities containing dead-zones

Abstract: This note deals with the recursive parameter identification of Hammerstein systems with discontinuous nonlinearities, i.e., two-segment piecewise-linear with dead-zones and preloads. A special form of the Hammerstein model with this type of nonlinearity is incorporated into the recursive least squares identification scheme supplemented with the estimation of model internal variables. The proposed method is illustrated by examples.

Method and apparatus for generalized recursive least-squares process for battery state of charge and state of health

Abstract: A method for determining a voltage based or current based state of charge (SOC) and state of health (SOH) of a battery system is provided. The method includes: providing a model of the battery system including an equivalent circuit having both low frequency and high frequency elements; establishing a plurality of functional relationships comprising relationship of the equivalent circuit with SOC; reducing at least part of the plurality of functional relationships into a set of time segmented recursive functional relationships, wherein a state at a first time t can be modeled by a functional presentation of a state at a second time t−Δt that occurred before the first time t; and computing a set of data points based upon the set of time segmented recursive functional relationships using a matrix for operation in matrix algebra.

A robust time-varying identification algorithm using basis functions.

Abstract: We extend a recently developed time invariant (TIV) model order search criterion named the optimal parameter search algorithm (OPS) for identification of time varying (TV) autoregressive (AR) and autoregressive moving average (ARMA) models. Using the TV algorithm is facilitated by the fact that expanding each TV coefficient onto a finite set of basis sequences permits TV parameters to become TIV. Taking advantage of this TIV feature of expansion parameters exploits the features of the OPS, which has been shown to provide accurate model order selection as well as extraction of only the significant model terms. Another advantage of the new algorithm is its ability to discriminate insignificant basis sequences thereby reducing the number of expansion parameters to be estimated. Due to these features, the resulting algorithm can accurately estimate TV AR or ARMA models and determine their orders. Indeed, comparison via computer simulations of AR models between the proposed method and one of the well-known iterative methods, recursive least squares, shows the greater capability of the new method to track TV parameters. Furthermore, application of the new method to experimentally obtained renal blood flow signals shows that the new method provides higher-resolution time-varying spectral capability than does the short-time Fourier transform (STFT), concomitant with fewer spurious frequency peaks than obtained with the STFT spectrogram. © 2003 Biomedical Engineering Society. PAC2003: 8710+e, 8719Uv, 8780Tq

A multidimensional filter algorithm for nonlinear equations and nonlinear least squares

Abstract: We introduce a new algorithm for the solution of systems of nonlinear equations and nonlinear least-squares problems that attempts to combine the efficiency of filter techniques and the robustness of trust-region methods. The algorithm is shown, under reasonable assumptions, to globally converge to zeros of the system, or to first-order stationary points of the Euclidean norm of its residual. Preliminary numerical experience is presented that shows substantial gains in efficiency over the traditional monotone trust-region approach.

Fast computation of coefficients for a variable delay decision feedback equalizer

Abstract: Optimal Decision Feedback Equalizer (DFE) coefficients are determined from a channel estimate by casting the DFE coefficient problem as a standard recursive least squares (RLS) problem and solving the RLS problem. In one embodiment, a fast recursive method, e.g., fast transversal filter (FTF) technique, is used to compute the Kalman gain of the RLS problem, which is then directly used to compute MIMO Feed Forward Equalizer (FFE) coefficients. The FBE coefficients are computed by convolving the FFE coefficients with the channel impulse response. Complexity of a conventional FTF algorithm may be reduced to one third of its original complexity by selecting a DFE delay to force the FTF algorithm to use a lower triangular matrix. The length of the DFE may be selected to minimize the tap energy in the FBE coefficients or to ensure that the tap energy in the FBE coefficients meets a threshold.

Recursive least squares adaptive noise cancellation filtering for heart sound reduction in lung sounds recordings

Abstract: It is rarely possible to obtain recordings of lung sounds that are 100% free of contaminating sounds from non-respiratory sources, such as the heart. Depending on pulmonary airflow, sensor location, and individual physiology, heart sounds may obscure lung sounds in both time and frequency domains, and thus pose a challenge for development of semi-automated diagnostic techniques. In this study, recursive least squares (RLS) adaptive noise cancellation (ANC) filtering has been applied for heart sounds reduction, using lung sounds data recorded from anterior-right chest locations of six healthy male and female subjects, aged 10-26 years, under three standardized flow conditions: 7.5 (low), 15 (medium) and 22.5 mL/s/kg (high). The reference input for the RLS-ANC filter was derived from a modified band pass filtered version of the original signal. The comparison between the power spectral density (PSD) of original lung sound segments, including, and void of, heart sounds, and the PSD of RLS-ANC filtered sounds, has been used to gauge the effectiveness of the filtering. This comparison was done in four frequency bands within 20 to 300 Hz for each subject. The results show that RLS-ANC filtering is a promising technique for heart sound reduction in lung sounds signals.

On the equivalence of RLS implementations of LCMV and GSC processors

Abstract: This letter compares the transients of the constrained recursive least squares (CRLS) algorithm with the generalized sidelobe canceler (GSC) employing the recursive least squares (RLS) algorithm. We prove that the two adaptive implementations are equivalent everywhere regardless of the blocking matrix chosen. This guarantees that algorithm tuning is not affected by the blocking matrix. This result differs from the more restrictive case for transient equivalence of the constrained least mean-square (CLMS) algorithm and the GSC employing the least mean square (LMS) algorithm, for in this case the blocking matrix needs to be unitary.

Identification of positive real models in subspace identification by using regularization

Abstract: In time-domain subspace methods for identifying linear-time invariant dynamical systems, the model matrices are typically estimated from least squares, based on estimated Kalman filter state sequences and the observed outputs and/or inputs. It is well known that for an infinite amount of data, this least squares estimate of the system matrices is unbiased, when the system order is correctly estimated. However, for a finite amount of data, the obtained model may not be positive real, in which case the algorithm is not able to identify a valid stochastic model. In this note, positive realness is imposed by adding a regularization term to a least squares cost function in the subspace identification algorithm. The regularization term is the trace of a matrix which involves the dynamic system matrix and the output matrix.

Evaluation of the Suitability of Different Chiller Performance Models for On-Line Training Applied to Automated Fault Detection and Diagnosis (RP-1139)

Abstract: This paper presents the research results of comparing the suitability of four different chiller performance models to be used for on-line automated fault detection and diagnosis (FDD) of vapor-compression chillers. The models were limited to steady-state performance and included (a) black-box multivariate polynomial (MP) models; (b) artificial neural network (ANN) models, specifically radial basis function (RBF) and multilayer perceptron (MLP); (c) the generic physical component (PC) model approach; and (d) the lumped physical Gordon-Ng (GN) model. All models except for (b) are linear in the parameters. A review of the engineering literature identified the three following on-line training schemes as suitable for evaluation: ordinary recursive least squares (ORLS) under incremental window scheme, sliding window scheme, and weighted recursive least squares (WRLS) scheme, where more weight is given to newer data. The evaluation was done based on five months of data from a 220 ton field-operated chiller from ...

A new algorithm for array pattern synthesis using the recursive least squares method

Abstract: This letter presents a new array pattern synthesis algorithm using the recursive least squares method. This new algorithm designs a minimax array pattern without an ad hoc weighting function, and without solving a matrix inverse at each iteration. Numerical examples are presented to illustrate this new algorithm.

Design of a parameterizable silicon intellectual property core for QR-based RLS filtering

Abstract: The availability of an intellectual property core for recursive least squares (RLS) filtering could enable the RLS algorithm to replace the least mean squares algorithm in a wide range of applications. The goal of this study is to develop a parameterizable generic architecture for RLS filtering in the form of a hardware description language (HDL) description, which can be used to generate highly efficient silicon layout. The key issue is to develop a family of circuit architectures that are 100% efficient and locally connected. This paper presents a generic mapping for RLS filtering and circuit architectures that can be mapped to a range of application requirements. It outlines the transition from array to architecture covering detailed design issues such as timing and control generation. The result is a family of QR designs, which are parameterized in terms of architecture size, wordlength, performance, and arithmetic processor timing.

Lossless compression of digital audio using cascaded RLS-LMS prediction

Abstract: This paper proposes a cascaded RLS-LMS predictor for lossless audio coding. In this proposed predictor, a high-order LMS predictor is employed to model the ample tonal and harmonic components of the audio signal for optimal prediction gain performance. To solve the slow convergence problem of the LMS algorithm with colored inputs, a low-order RLS predictor is cascaded prior to the LMS predictor to remove the spectral tilt of the audio signal. This cascaded RLS-LMS structure effectively mitigates the slow convergence problem of the LMS algorithm and provides superior prediction gain performance compared with the conventional LMS predictor, resulting in a better overall compression performance.

Combined RLS-LMS initialization for per tone equalizers in DMT-receivers

Abstract: In discrete multitone receivers, the classical equalizer structure consists of a (real) time domain equalizer (TEQ) combined with complex one-tap frequency domain equalizers. An alternative receiver is based on a per tone equalization (PTEQ), which optimizes the signal-to-noise ratio (SNR) on each tone separately and, hence, the total bitrate. In this paper, a new initialization scheme for the PTEQ is introduced, based on a combination of least mean squares (LMS) and recursive least squares (RLS) adaptive filtering. It is shown that the proposed method has only slightly slower convergence than full square-root RLS (SR-RLS) while complexity as well as memory cost are reduced considerably. Hence, in terms of complexity and convergence speed, the proposed algorithm is in between LMS and RLS.

Recursive adaptive algorithms for fast and rapidly time-varying systems

Abstract: In this paper, some new schemes are developed to improve the tracking performance for fast and rapidly time-varying systems. A generalized recursive least-squares (RLS) algorithm called the trend RLS (T-RLS) algorithm is derived which takes into account the effect of local and global trend variations of system parameters. A bank of adaptive filters implemented with T-RLS algorithms are then used for tracking an arbitrarily fast varying system without knowing a priori the changing rates of system parameters. The optimal tracking performance is attained by Bayesian a posteriori combination of the multiple filter outputs, and the optimal number of parallel filters needed is determined by extended Akaike's Information Criterion and Minimum Description Length information criteria. An RLS algorithm with modification of the system estimation covariance matrix is employed to track a time-varying system with rare but abrupt (jump) changes. A new online wavelet detector is designed for accurately identifying the changing locations and the branches of changing parameters. The optimal increments of the covariance matrix at the detected changing locations are also estimated. Thus, for a general time-varying system, the proposed methods can optimally track its slowly, fast and rapidly changing components simultaneously.

Kalman filter based method and apparatus for linear equalization of CDMA downlink channels

Abstract: Disclosed is a minimum mean square error (MMSE) equalizer and method for single-user detection of a signal received from a downlink code-division multiple access CDMA channel. The equalizer includes a Kalman filter having an input coupled to the received signal for generating a best linear unbiased estimate of a transmitted chip sequence for a single user. A reduced computational complexity Kalman filter embodiment is also disclosed that only periodically updates a Kalman filter prediction error covariance matrix P(k|k−1), a Kalman filter filtering error covariance matrix P(k|k) and the Kalman gain K(k).

RLS-based initialization for per-tone equalizers in DMT receivers

Abstract: Per-tone equalization has recently been proposed as an alternative receiver structure for discrete multitone-based systems improving upon the well-known structure based on time-domain equalization. Fast initialization of all the equalizer coefficients has been identified as an open problem. In this letter, a recursive initialization scheme based on recursive least squares with inverse updating is presented for the per-tone equalizers. Simulation results show convergence with an acceptably small number of training symbols. Complexity calculations are made for per-tone equalization and for the case where tones are grouped. It is demonstrated with an example that in the latter case, initialization complexity becomes sufficiently low and comparable to complexity during data transmission.

Towards a Unified Theory of GPS Ambiguity Resolution

Abstract: In this invited contribution a brief review will be presented of the integer estimation theory as developed by the author over the last decade and which started with the introduction of the LAMBDA method in 1993. The review discusses three different, but closely related classes of ambiguity estimators. They are the integer estimators, the integer aperture estimators and the integer equivariant estimators. Integer estimators are integer aperture estimators and integer aperture estimators are integer equivariant estimators. The reverse is not necessarily true however. Thus of the three types of estimators the integer estimators are the most restrictive. Their pull-in regions are translational invariant, disjunct and they cover the ambiguity space completely. Well-known examples are integer rounding, integer bootstrapping and integer least-squares. A less restrictive class of estimators is the class of integer aperture estimators. Their pull-in regions only obey two of the three conditions. They are still translational invariant and disjunct, but they do not need to cover the ambiguity space completely. As a consequence the integer aperture estimators are of a hybrid nature having either integer or non-integer outcomes. Examples of integer aperture estimators are the ratio-testimator and the differencetestimator. The class of integer equivariant estimators is the less restrictive of the three classes. These estimators only obey one of the three conditions, namely the condition of being translational invariant. As a consequence the outcomes of integer equivariant estimators are always realvalued. For each of the three classes of estimators we also present the optimal estimator. Although the Gaussian case is usually assumed, the results are presented for an arbitrary probability density function of the float solution. The optimal integer estimator in the Gaussian case is the integer least-squares estimator. The optimality criterion used is that of maximizing the probability of correct integer estimation, the so-called success rate. The optimal integer aperture estimator in the Gaussian case is the one which only returns the integer least-squares solution when the integer least-squares residual resides in the optimal aperture pull-in region. This region is governed by the probability density function of the float solution and by the probability density function of the integer least-squares residual. The aperture of the pull-in region is governed by a userdefined aperture parameter. The optimality criterion used is that of maximizing the probability of correct integer estimation given a fixed, user-defined, probability of incorrect integer estimation. The optimal integer aperture estimator becomes identical to the optimal integer estimator in case the success rate and the fail rate sum up to one. The best integer equivariant estimator is an infinite weighted sum of all integers. The weights are determined as ratios of the probability density function of the float solution with its train of integer shifted copies. The optimality criterion used is that of minimizing the mean squared error. The best integer equivariant estimator therefore always outperforms the float solution in terms of precision.

Experimental nonlinear identification of a two mass system

Abstract: The paper presents nonlinear modeling and on-line identification of a two mass mechanical system driven by a DC motor together with real-time experiments made. The paper also describes how to obtain a simpler identification routine for the nonlinear systems. Linear and nonlinear models for the system are obtained for identification purposes and the major nonlinearities in the system such as the Coulomb friction and the dead-zone are investigated and integrated in the nonlinear model. Hammerstein nonlinear system approach is used for the identification of the nonlinear system model. On-line identification of the linear and nonlinear system models is performed using the Recursive Least Squares (RLS) method. Results of the real-time experiments are graphically and numerically presented, and advantages of the nonlinear identification approach are definitely revealed.

Acoustic echo cancellation using multiple sub-filters

Abstract: We present the modeling of the acoustic echo path based on the process segmentation approach. A new algorithm is proposed using the concept of decomposing the long adaptive filter into low order multiple sub-filters. Simulation results show that the decomposed LMS adaptive algorithm significantly improves the convergence rate while keeping the steady state error almost the same as that of the original long adaptive filter.

Separate-variable adaptive combination of LMS adaptive filters for plant identification

Abstract: The Least Mean Square (LMS) algorithm has become a very popular algorithm for adaptive filtering due to its robustness and simplicity An adaptive convex combination of one fast a one slow LMS filters has been previously proposed for plant identification, as a way to break the speed vs precision compromise inherent to LMS filters In this paper, an improved version of this combination method is presented Instead of using a global mixing parameter, the new algorithm uses a different combination parameter for each weight of the adaptive filter, what gives some advantage when identifying varying plants where some of the coefficients remain unaltered, or when the input process is colored Some simulation examples show the validity of this approach when compared with the one-parameter combination scheme and with a different multi-step approach

Methods, apparatus and computer program products for adaptively controlling a system by combining recursive system identification with generalized predictive control

Abstract: Methods, apparatus and computer program products combine recursive least squares system identification operations and generalized predictive control operations to yield recursive generalized predictive control (RGPC) operations that can simultaneously achieve robust performance and robust stability characteristics. These RGPC operations can be applied in real-time without prior system (plant) information for control design because the operations for system identification are performed continuously. Moreover, the RGPC operations can be applied in the presence of changing operating environments because the control design is updated adaptively.