Least-squares Lattice Research Articles

A Harmonic Detection Method of UPQC Based on LSL Algorithm in Photovoltaic Microgrids

Photovoltaic microgrids have discontinuity and intermittency issues that affect the load current amplitude and frequency, and this leads to disturbances. The unified power quality conditioner (UPQC) combines a series active power filter (SAPF) and a parallel active power filter (PAPF), and therefore, it has the advantages of SAPF and PAPF to treat power quality problems. Considering detection precision and response speed, and to meet the fast speed and accuracy of PAPF harmonic detection, the algorithm principle of adaptation and least-squares lattice (LSL) is analyzed. A new harmonic detection method of three-phase circuit based on LSL adaptive algorithm is proposed. The two other harmonic detection methods between least mean square and instantaneous power theory based are compared using the Simulink simulation platform. The compensation effect of LSL is more stable and better than the two other methods. The experimental results also indicate that the new method based on LSL can accurately detect and compensate the harmonic component in photovoltaic microgrids in real time. Therefore, this harmonic detection method based on LSL can be used in the practical engineering applications, and it provides a new method for harmonic detection of UPQC PAPF.

Double-Talk Robust Multichannel Acoustic Echo Cancellation Using Least-Squares MIMO Adaptive Filtering: Transversal, Array, and Lattice Forms

In this paper, we address the problem of noise-robust multiple-input multiple-output (MIMO) adaptive filtering that is optimal in least-squares sense with application to multichannel acoustic echo cancellation. We formulate the problem as minimization of a multichannel least-squares cost function that incorporates near-end speech and noise statistics resulting in a novel noise-robust framework for MIMO adaptive filtering. Although the issue of numerical stability has been widely explored in the context of recursive least-squares (RLS) filtering, a rigorous mathematical treatment of the MIMO case in the context of numerically stable noise-robust multichannel echo cancellation remains absent. Guided by quantization-error modeling, we resolve the issue of numerical instability in our noise-robust scheme by utilizing transversal RLS filtering of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Type 2</i> . Thereafter, an explicit derivation of its inverse QR-decomposition (IQRD) counterpart based on Givens rotations is presented. We also derive computationally efficient lattice forms for our noise-robust RLS Type-2 and IQRD algorithms. It is highlighted that propagation of angle-normalized errors occurs <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">naturally</i> within the numerically stable least-squares lattice (LSL). Thus, our approach combines the four sought after attributes in a multichannel echo cancellation scheme, i.e., computational efficiency, numerical stability, fast convergence and tracking, and robustness against noise. We analyze our formulations using simulations in terms of convergence, re-convergence, robustness in the presence of double-talk, and numerical stability.

Recursive Least-Squares Lattice Algorithm Combined With Secondary-Path Innovation and Lattice-Order Decision Algorithms for Active Noise Control

This paper proposes a new active noise control (ANC) system based on a recursive least-squares lattice (RLSL) algorithm by designing secondary-path innovation (SPI) and lattice-order decision (LOD) algorithms. The SPI algorithm associated with the power spectral factorization of the secondary path is designed to apply the RLSL algorithm to the ANC system without the filtered-input structure. The SPI algorithm whitens the error microphone signals into the virtual error signals just ahead of the secondary path to construct the virtual desired signals corresponding to the outputs of the lattice filter. The LOD algorithm is designed to operate the ANC system without knowing the tap length of the optimal finite impulse response (FIR) filter. The decision algorithm using the initial and final estimation errors of the lattice filter estimates the tap length of the optimal FIR filter by increasing the lattice order one-by-one until the final estimation error reaches below a threshold value. Even in environments where the tap length of the optimal FIR filter is unknown, the proposed ANC system with low computational complexity shows almost the same performance as the ANC system based on a filtered-input recursive least squares algorithm.

Parallel Computation of Adaptive Filtering Algorithms on Multi-Core Systems

The performance of recent CPUs has been rapidly increasing with the help of parallel architectural supports, such as SIMD (Single Instruction Multiple Data) extensions and multi-core architecture. However, efficient use of such parallel supports for adaptive filtering is difficult due to feedback loops that induce the data dependency problem. In this paper, efficient parallel computation of adaptive filters is studied for multi-core architecture with SIMD arithmetic support. Control- and data-level parallel computation methods are considered, where the former finds parallelism in the evaluation of one output sample, while the latter processes multiple output samples at a time to increase the degree of parallelism. The control-level parallel approach frequently utilizes the pipelining technique to uncover the parallelism, whereas the data-level approach employs a parallel computation method for linear recurrence equations to resolve the dependency. Not only adaptive transversal LMS (Least Mean Square) but also gradient adaptive lattice (GAL) and QR-decomposition based least-square lattice (QRD-LSL) filters are implemented on a PC that employs both SIMD and multi-core architecture.

Echo cancellation in VoIP with improved least square lattice method

In this work, an approach to echo cancellation in VoIP network based on the packet-based echo cancellation model was employed. In addition, a comparative validation was performed and then analysed specifically in the state of echo canceller as adaptive filtering was done by using three algorithms: normalised least mean square (NLMS), recursive least square (RLS) and least square lattice (LSL). Communication environments with three different echo strength levels: 20%, 50% and 70% of far-end speech were simulated. The result shows that in terms of time computation, NLMS is the best, followed by LSL and RLS as the last. However, NLMS suffers from the measure of ERLE, as it falls to the third place, followed by LSL and RLS as the first. Then, taking them all into consideration, it could be concluded that LSL is the best among all for echo cancellation as verified in the experimental simulation.

FPGA implementation of adaptive segmentation for non-stationary biomedical signals

A novel field programmable gate array (FPGA) implementation of adaptive segmentation for non-stationary biomedical signals is presented. The design uses Simulink-to-FPGA methodology and has been successfully implemented onto Xilinx Virtex II Pro device. The implementation is based on the recursive least-squares lattice (RLSL) algorithm using double-precision floating-point arithmetic and is programmable for users providing data length, system order and threshold selection functions. The implemented RLSL design provides very good performance in obtaining accurate conversion factor values with a mean correlation above 99% and detecting segment boundaries with high accuracy for both synthesised and real-world biomedical signals.

Optimal Estimation of the Acceleration of a Car Under Performance Tests

In this paper, a recursive least-squares lattice (RLSL) adaptive filter was used to carry out the optimal estimation of the relevant signal coming from an accelerometer placed in car under performance tests. Here, the signal of interest is buried in a broadband noise background where we have little knowledge of the noise characteristics. In addition, due to the fact that the noise and the relevant information sometimes share the same or a very similar frequency spectrum, it is very difficult to cancel the noise that corrupts the relevant information without causing that information to deteriorate. The results of the experiment are satisfactory and, in order to compare classical filtering with optimal adaptive filtering, the signal coming from the accelerometer was also filtered by using a third-order lowpass digital Butterworth filter. The results of comparing the aforementioned filters show that the optimal adaptive filter is superior to the classical filter. Here, a significant improvement of 22.4 dB in the signal-to-noise ratio (SNR) at the RLSL adaptive filter output was achieved. However, the improvement in the SNR at the Butterworth filter output was 6.1 dB, which shows very clear that the optimal adaptive filter performs much better than the classical one

A reliable modeless mobile multi-sensor integration technique based on RLS-lattice

The last two decades have witnessed an increasing trend in integrating different navigation sensors for the overall purpose of overcoming the limitation of stand-alone systems. An example of this integration is the fusion of the global positioning system (GPS) and inertial navigation system (INS) for several navigation and positioning applications. Both systems have their unique features and shortcomings. Therefore, their integration offers a robust navigation solution. This paper introduces a novel multi-sensor system integration using a recursive least-squares lattice (RLSL) filter. The proposed system has a similar structure to the widely used KF. However, it has the major advantage of working without the need of either dynamic or stochastic models. Furthermore, no prior information about the covariance information of INS and GPS is required. The proposed RLSL filter parameters, similar to Kalman gain, are tuned recursively in the update mode utilizing the GPS velocity components. The RLSL, in turn, can filter out the high frequency noise associated with the INS. To test the capabilities of the proposed architecture, a field test was conducted in a land vehicle using a tactical grade INS system (the Honeywell HG1700) integrated with differential GPS measurements collected by a NovAtel OEM4 GPS receiver. The proposed system is examined during the availability of the GPS signal and with intentionally introduced GPS signal outages. The results indicate that the proposed RLSL system is robust in providing a reliable modeless INS/GPS integration module.

A new data extrapolation algorithm for high resolution ISAR imaging

A new data extrapolation algorithm for high resolution radar imaging is presented. The backscattered data are modeled as an autoregressive process where the prediction coefficients are computed using 1D least-square lattice filters. Unlike the well-known Burg or modified covariance methods, least square lattice modeling yields different prediction coefficients for forward and backward directions. The proposed method does not need to satisfy Levinson recursion, i.e. does not suffer from the limitations of the Burg method such as spectral splitting or bias in the locations of the scattering centers. Moreover, due to its lattice structure it does not need any matrix inversion like the modified covariance method. Results obtained for an experimental target are included to confirm the proposed algorithm.

Adaptive Peak Frequency Estimation Using a Database of PARCOR Coefficients

This paper presents an adaptive peak frequency estimation method using a database that stores PARCOR coefficients as key attributes and the corresponding peak frequencies as nonkey attributes. The least-square lattice algorithm is used to recursively estimate the PARCOR coefficients to adapt to changing circumstances. The nearest neighbor to the current PARCOR coefficient is retrieved from the database, and the corresponding peak frequency is regarded as the estimation. A simultaneous execution of database construction and peak estimation with database update is performed to accelerate the processing time and to improve the estimation accuracy.

The normalized least-squares order-recursive lattice smoother

This paper introduces a variance- and angle-normalized version of the least-squares order-recursive lattice (LSORL) smoother, say the normalized LSORL smoother, via a geometric approach. The normalized LSORL smoother has excellent round-off noise properties and inherits all the other advantages of the normalized LSORL as well. Simulation results show that the normalized LSORL smoother outperforms the existing LSORL and QRD-based least-squares lattice smoother algorithms when finite-precision arithmetic is used.

On-line powerspectra identification and whitening for the noise in interferometricgravitational wave detectors

The knowledge of the noise power spectral density of aninterferometric detector of gravitational waves isfundamental for detection algorithms and for the analysis ofthe data. In this paper we address both the problem ofidentifying the noise power spectral density ofinterferometric detectors by parametric techniques and theproblem of the whitening procedure of the sequence of data.We will concentrate the study on a power spectral densitylike that of the Italian-French detector VIRGO and we showthat with a reasonable number of parameters we succeed inmodelling a spectrum like the theoretical one of VIRGO,reproducing all of its features.We alsopropose the use of adaptive techniques to identify and towhiten the data of interferometric detectors on-line. Weanalyse the behaviour of the adaptive techniques in the fieldof stochastic gradient and in the least-squares filters. As aresult, we find that the least-squares lattice filter is thebest among those we have analysed. It succeedsoptimally infollowing all the peaks of the noise power spectrum, and oneof its outputs is the whitened part of the spectrum. Besides,the fast convergence of this algorithm, it lets us follow theslow non-stationarity of the noise. These procedures could beused to whiten the overall power spectrum or only some regionof it. The advantage of the techniques we propose is that theydo not require a priori knowledge of the noise powerspectrum to be analysed. Moreover, the adaptive techniqueslet us identify and remove the spectral line, withoutbuilding any physical model of the source that producedit.

A state-space approach to QRD-LSL interpolation and QRD-LSL smoothing

Sayed and Kailath (1994) demonstrated the feasibility of directly deriving many known adaptive filtering algorithms in square-root forms by a proper reformulation of the original adaptive problem into a state-space form. This work employs this state-space form to develop adaptive interpolation and smoothing algorithms. In particular, a systematic and concise derivation of the QR-decomposition least-squares lattice (QRD-LSL) interpolation and smoothing algorithms using correspondences between Kalman filtering and LSL adaptive filtering is given.

A New Approach to the Generalized Transfer Function and Its Application to Biomedical Signal Analysis

In this paper, we present a method for modeling an electrocardiogram (ECG) signal using time-varying parameters by considering that the signal is generated by a linear, time-varying (LTV) system with a stationary white noise input, and then by estimating the time-varying coefficients of the LTV system. In effect, since the ECG signal is considered to be non-stationary, this method is based on the Wold-Cramer representation of a non-stationary signal. The relationship between the generalized transfer function of an LTV system and the time-varying coefficients of the difference equation of a discrete-time system is not addressed clearly in the literature; in this paper, we propose a new approach to this problem and apply it for modeling a human ECG signal. We first derive a relationship between the system generalized transfer function and the time-varying parameters of the system. Then we develop an algorithm to solve for the system time-varying parameters from the time-frequency kernel of the system output using the time-varying autocorrelation function (TVACF) and by modifying the modified least-square (MLS) and Durbin's approximation algorithms. A comparison between the proposed algorithm and the recursive least-square (RLS) and RLS lattice (RLSL) algorithms is considered. Computer simulations illustrating the effectiveness of our algorithm are presented when the signal is embedded in noise.

A modified QRD for smoothing and a QRD-LSL smoothing algorithm

This paper introduces a modified QR-decomposition (QRD) that extends the method of QRD to a more general case to solve the least-squares lattice smoothing problems. We show that the conventional QRD is a special form of the modified QRD that occurs when no future data values are used. Within the framework of the modified QRD procedure, an order-recursive QRD based least-squares lattice (QRD-LSL) smoothing algorithm is formulated. The algorithm combines all the desirable features of the standard QRD-LSL filtering algorithm with a more accurate smoothing process. The results of some computer simulations of a channel equalizer are also presented.

Detection of zero-Doppler underwater signals

Four-channel real reverberation signals recorded in shallow water are appropriately combined with zero-Doppler synthetic signals, regarded as the contact signals, to evaluate the performance of a least-squares lattice filter when applied to the detection of zero-Doppler contacts buried in reverberation, for different levels of input signal-to-reverberation ratio.

Application of a Least Squares Lattice Algorithm to Active Noise Control for an Automobile

The purpose of this paper is to propose an alternative approach to active noise control (ANC) using the least squares lattice (LSL) algorithm. Typically, in ANC applications, the least-mean-square (LMS) algorithm has been used because of its simplicity. However, the LMS algorithm has the disadvantage of slow convergence speed in the case of broadband noise, such as the road noise present in the passenger compartment of automobiles traveling on rough road surfaces. In order to solve this problem, the LSL algorithm for ANC is considered. By computer simulation using actual car data, the LSL algorithm proves to be more effective than the LMS one.

STAR recursive least square lattice adaptive filters

The recursive least square lattice (LSL) algorithm based on the newly developed scaled tangent rotations (STAR) is derived. Similar to other recursive least square lattice algorithms for adaptive filtering, this algorithm requires only O(N) operations. This algorithm also preserves the desired properties of the STAR recursive least square (STAR-RLS) algorithm. Specifically, it can be pipelined at fine-grain level. To this end, a pipelined version of the STAR-LSL (referred to as PSTAR-LSL) is also developed. Computer simulations show that the performance of the STAR-LSL algorithm is as good as the QRD-LSL algorithm. The finite precision error properties of the STAR-LSL algorithm are also analyzed. The mean square error expressions show that the numerical error propagates from stage to stage in the lattice, and the numerical error of different quantities in the algorithm varies differently with /spl lambda/. This suggests that different word lengths need to be assigned to different variables in the algorithm for best performance. Finally, finite word length simulations are carried out to compare the performances of different topologies.

A state-space approach to adaptive RLS filtering

Adaptive filtering algorithms fall into four main groups: recursive least squares (RLS) algorithms and the corresponding fast versions; QR- and inverse QR-least squares algorithms; least squares lattice (LSL) and QR decomposition-based least squares lattice (QRD-LSL) algorithms; and gradient-based algorithms such as the least-mean square (LMS) algorithm. Our purpose in this article is to present yet another approach, for the sake of achieving two important goals. The first one is to show how several different variants of the recursive least-squares algorithm can be directly related to the widely studied Kalman filtering problem of estimation and control. Our second important goal is to present all the different versions of the RLS algorithm in computationally convenient square-root forms: a prearray of numbers has to be triangularized by a rotation, or a sequence of elementary rotations, in order to yield a postarray of numbers. The quantities needed to form the next prearray can then be read off from the entries of the postarray, and the procedure can be repeated; the explicit forms of the rotation matrices are not needed in most cases.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The Absorption Correction of Debye-Scherrer Diagrams

AbstractAn extension of the Nelson-Riley absorption correction of Debye-Scherrer diagrams is given. This enables the calculation of the shifts of the reflection angles if the absorption coefficient is known. Alternatively, these shifts can be found by including the corresponding coefficient in a least-squares lattice constant refinement.