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Showing papers on "Recursive least squares filter published in 2013"


Journal ArticleDOI
TL;DR: If proper weighting strategies are applied, the weighted linear least squares approach shows high performance characteristics in terms of accuracy/precision and may even be preferred over nonlinear estimation methods.

403 citations


Journal ArticleDOI
Feng Ding1
TL;DR: In this article, a coupled-least-squares (C-LS) parameter identification algorithm is introduced for the purpose of avoiding the matrix inversion in the multivariable recursive least squares (RLS) algorithm for estimating the parameters of the multiple linear regression models.
Abstract: This article studies identification problems of multiple linear regression models, which may be described a class of multi-input multi-output systems (i.e. multivariable systems). Based on the coupling identification concept, a novel coupled-least-squares (C-LS) parameter identification algorithm is introduced for the purpose of avoiding the matrix inversion in the multivariable recursive least-squares (RLS) algorithm for estimating the parameters of the multiple linear regression models. The analysis indicates that the C-LS algorithm does not involve the matrix inversion and requires less computationally efforts than the multivariable RLS algorithm, and that the parameter estimates given by the C-LS algorithm converge to their true values. Simulation results confirm the presented convergence theorems.

220 citations


Journal ArticleDOI
TL;DR: Novel methods for estimating sideslip angle and roll angle using real-time lateral tire force measurements, obtained from the multisensing hub units, for practical applications to vehicle control systems of in-wheel-motor-driven electric vehicles are proposed.
Abstract: Robust estimation of vehicle states (e.g., vehicle sideslip angle and roll angle) is essential for vehicle stability control applications such as yaw stability control and roll stability control. This paper proposes novel methods for estimating sideslip angle and roll angle using real-time lateral tire force measurements, obtained from the multisensing hub units, for practical applications to vehicle control systems of in-wheel-motor-driven electric vehicles. In vehicle sideslip estimation, a recursive least squares (RLS) algorithm with a forgetting factor is utilized based on a linear vehicle model and sensor measurements. In roll angle estimation, the Kalman filter is designed by integrating available sensor measurements and roll dynamics. The proposed estimation methods, RLS-based sideslip angle estimator, and the Kalman filter are evaluated through field tests on an experimental electric vehicle. The experimental results show that the proposed estimator can accurately estimate the vehicle sideslip angle and roll angle. It is experimentally confirmed that the estimation accuracy is improved by more than 50% comparing to conventional method's one (see rms error shown in Fig. 4). Moreover, the feasibility of practical applications of the lateral tire force sensors to vehicle state estimation is verified through various test results.

218 citations


Journal ArticleDOI
TL;DR: By incorporating a simple online vector quantization method, a recursive algorithm is derived to update the solution, namely the quantized kernel recursive least squares algorithm.
Abstract: In a recent paper, we developed a novel quantized kernel least mean square algorithm, in which the input space is quantized (partitioned into smaller regions) and the network size is upper bounded by the quantization codebook size (number of the regions). In this paper, we propose the quantized kernel least squares regression, and derive the optimal solution. By incorporating a simple online vector quantization method, we derive a recursive algorithm to update the solution, namely the quantized kernel recursive least squares algorithm. The good performance of the new algorithm is demonstrated by Monte Carlo simulations.

178 citations


Journal ArticleDOI
Feng Ding1
TL;DR: In this article, a two-stage least squares based iterative algorithm is proposed for identifying the system model parameters and the noise model parameters for stochastic systems described by CARARMA models.

171 citations


Journal ArticleDOI
Feng Ding1
TL;DR: An iterative least squares algorithm to estimate the parameters of output error systems is derived and the partitioned matrix inversion lemma is used to implement the proposed algorithm in order to enhance computational efficiencies.

149 citations


Journal ArticleDOI
TL;DR: The proposed algorithm, dubbed Parallel Estimation and Tracking by REcursive Least Squares (PETRELS), first identifies the underlying low-dimensional subspace, and then reconstructs the missing entries via least-squares estimation if required, comparing PETRELS with state of the art batch algorithms.
Abstract: Many real world datasets exhibit an embedding of low-dimensional structure in a high-dimensional manifold. Examples include images, videos and internet traffic data. It is of great significance to estimate and track the low-dimensional structure with small storage requirements and computational complexity when the data dimension is high. Therefore we consider the problem of reconstructing a data stream from a small subset of its entries, where the data is assumed to lie in a low-dimensional linear subspace, possibly corrupted by noise. We further consider tracking the change of the underlying subspace, which can be applied to applications such as video denoising, network monitoring and anomaly detection. Our setting can be viewed as a sequential low-rank matrix completion problem in which the subspace is learned in an online fashion. The proposed algorithm, dubbed Parallel Estimation and Tracking by REcursive Least Squares (PETRELS), first identifies the underlying low-dimensional subspace, and then reconstructs the missing entries via least-squares estimation if required. Subspace identification is performed via a recursive procedure for each row of the subspace matrix in parallel with discounting for previous observations. Numerical examples are provided for direction-of-arrival estimation and matrix completion, comparing PETRELS with state of the art batch algorithms.

148 citations


Journal ArticleDOI
TL;DR: A new CWLS estimator is proposed to separate the source coordinates and the additional variable to different sides of the linear equations where the latter is first solved via a quadratic equation.

99 citations


Journal ArticleDOI
Mooryong Choi1, Jiwon Oh1, Seibum B. Choi1
TL;DR: The parameters, including the tire-road friction coefficient, of the combined longitudinal and lateral brushed tire model are identified by linearized recursive least squares (LRLS) methods, which efficiently utilize measurements related to both vehicle lateral and longitudinal dynamics in real time.
Abstract: The tire-road friction coefficient is critical information for conventional vehicle safety control systems. Most previous studies on tire-road friction estimation have only considered either longitudinal or lateral vehicle dynamics, which tends to cause significant underestimation of the actual tire-road friction coefficient. In this paper, the parameters, including the tire-road friction coefficient, of the combined longitudinal and lateral brushed tire model are identified by linearized recursive least squares (LRLS) methods, which efficiently utilize measurements related to both vehicle lateral and longitudinal dynamics in real time. The simulation study indicates that by using the estimated vehicle states and the tire forces of the four wheels, the suggested algorithm not only quickly identifies the tire-road friction coefficient with great accuracy and robustness before tires reach their frictional limits but successfully estimates the two different tire-road friction coefficients of the two sides of a vehicle on a split- μ surface as well. The developed algorithm was verified through vehicle dynamics software Carsim and MATLAB/Simulink.

92 citations


Journal ArticleDOI
TL;DR: The Hammerstein model is transferred into two regression identification models, and a data filtering based recursive least squares method is presented to estimate the parameters of these two identification models.

86 citations


01 Jan 2013
TL;DR: This paper describes the comparison between adaptive filtering algorithms that is least meansquare (LMS), Normalized least mean square (NLMS), time varying least means square (TVLMS, Recursive least square (RLS), Fast Transversal Recursive less square (FTRLS) and implementation aspects of these algorithms, their computational complexity and Signal to Noise ratio are examined.
Abstract: This paper describes the comparison between adaptive filtering algorithms that is least mean square (LMS), Normalized least mean square (NLMS),Time varying least mean square (TVLMS), Recursive least square (RLS), Fast Transversal Recursive least square (FTRLS). Implementation aspects of these algorithms, their computational complexity and Signal to Noise ratio are examined. These algorithms use small input and output delay. Here, the adaptive behaviour of the algorithms is analyzed. Recently, adaptive filtering algorithms have a nice tradeoff between the complexity and the convergence speed. Three performance criteria are used in the study of these algorithms: the minimum mean square error, the algorithm execution time and the required filter order.

Journal ArticleDOI
TL;DR: The convergence analysis shows that the parameter estimates weakly converge to the true parameter across the network, yet the global activation behavior along the way tracks the set of correlated equilibria of the underlying activation control game.
Abstract: This paper presents a game-theoretic approach to node activation control in parameter estimation via diffusion least mean squares (LMS). Nodes cooperate by exchanging estimates over links characterized by the connectivity graph of the network. The energy-aware activation control is formulated as a noncooperative repeated game where nodes autonomously decide when to activate based on a utility function that captures the trade-off between individual node's contribution and energy expenditure. The diffusion LMS stochastic approximation is combined with a game-theoretic learning algorithm such that the overall energy-aware diffusion LMS has two timescales: the fast timescale corresponds to the game-theoretic activation mechanism, whereby nodes distributively learn their optimal activation strategies, whereas the slow timescale corresponds to the diffusion LMS. The convergence analysis shows that the parameter estimates weakly converge to the true parameter across the network, yet the global activation behavior along the way tracks the set of correlated equilibria of the underlying activation control game.

Journal ArticleDOI
TL;DR: This work shows that the wLMS algorithm is the most accurate algorithm and does not require parameter tuning, making it an ideal candidate for clinical implementation, and sees that the structure of a patient's respiratory motion trace has strong influence on the outcome of prediction.
Abstract: In robotic radiosurgery, it is necessary to compensate for systematic latencies arising from target tracking and mechanical constraints. This compensation is usually achieved by means of an algorithm which computes the future target position. In most scientific works on respiratory motion prediction, only one or two algorithms are evaluated on a limited amount of very short motion traces. The purpose of this work is to gain more insight into the real world capabilities of respiratory motion prediction methods by evaluating many algorithms on an unprecedented amount of data. We have evaluated six algorithms, the normalized least mean squares (nLMS), recursive least squares (RLS), multi-step linear methods (MULIN), wavelet-based multiscale autoregression (wLMS), extended Kalman filtering, and ?-support vector regression (SVRpred) methods, on an extensive database of 304 respiratory motion traces. The traces were collected during treatment with the CyberKnife (Accuray, Inc., Sunnyvale, CA, USA) and feature an average length of 71?min. Evaluation was done using a graphical prediction toolkit, which is available to the general public, as is the data we used. The experiments show that the nLMS algorithm?which is one of the algorithms currently used in the CyberKnife?is outperformed by all other methods. This is especially true in the case of the wLMS, the SVRpred, and the MULIN algorithms, which perform much better. The nLMS algorithm produces a relative root mean square (RMS) error of 75% or less (i.e., a reduction in error of 25% or more when compared to not doing prediction) in only 38% of the test cases, whereas the MULIN and SVRpred methods reach this level in more than 77%, the wLMS algorithm in more than 84% of the test cases. Our work shows that the wLMS algorithm is the most accurate algorithm and does not require parameter tuning, making it an ideal candidate for clinical implementation. Additionally, we have seen that the structure of a patient?s respiratory motion trace has strong influence on the outcome of prediction. Further work is needed to determine a priori the suitability of an individual?s respiratory behaviour to motion prediction.

Journal ArticleDOI
TL;DR: The proposed decoupled RLS (DRLS) technique is adapted for real-time estimation of phasors and harmonics and shows considerable improvement in terms of reducing the turnaround time on two different off-the-shelf research and development DSP platforms.
Abstract: This paper presents the mathematical basis to restructure the recursive-least-squares (RLS) technique for real-time implementations on digital signal processors (DSPs). The proposed decoupled RLS (DRLS) technique is adapted for real-time estimation of phasors and harmonics. The comparison between the proposed technique and the conventional RLS one shows considerable improvement in terms of reducing the turnaround time on two different off-the-shelf research and development DSP platforms. The DRLS technique also shows better computational efficiency than the adaptive linear combiner (ADALINE) and recursive discrete Fourier transform (RDFT) techniques in direct estimation of amplitude and phase angle when implemented on DSPs. The DRLS technique performance is also superior to that of the ADALINE and RDFT techniques under the presence of noise, subharmonics, and frequency variations. The performance of the proposed technique has been evaluated by simulations using MATLAB-Simulink and through real-time experiments. Selected results presented in this paper confirm the DSP turnaround time improvementand satisfactory performance of the proposed technique.

Journal ArticleDOI
TL;DR: An iterative least squares algorithm and a recursive least squares algorithms are developed for estimating the parameters of moving average systems and the simulation results validate that the proposed algorithms can work well.

Proceedings ArticleDOI
25 Jun 2013
TL;DR: It is shown that the deconvolution based estimation can decrease of the order of ten times the size of the training database, while still being able to achieve comparable root mean square errors in the distance estimation.
Abstract: In this paper, the problem of Received Signal Strength (RSS)-based WLAN positioning is newly formulated as a deconvolution problem and three deconvolution methods (namely Least Squares, Weighted Least Squares and Minimum Mean Square Error) are investigated with several RSS path loss models. The deconvolution approaches are compared with the fingerprinting approach in terms of performance and complexity. The main advantage of the deconvolution-based approaches versus the fingerprinting methods is the significant reduction in the size of the training database that need to be stored at the server side (and transferred to the mobile device) for the WLAN-based positioning. We will show that the deconvolution based estimation can decrease of the order of ten times the size of the training database, while still being able to achieve comparable root mean square errors in the distance estimation.

Journal ArticleDOI
TL;DR: A new algorithm, the so-called constrained adaptive robust integration Kalman filter (CARIKF) is presented, which implements adaptive integration upon the robust direct fusion solution and is superior to other algorithms and can significantly improve the precision and reliability of the integrated solution.
Abstract: Constraints can provide additional aids to a multi-sensor integrated navigation system and hence can increase accuracy of the solution and enhance reliability of the system. To integrate the constraints with the data from the sensors, the traditional integration Kalman filter (IKF) needs to be reconstructed. A new algorithm, the so-called constrained adaptive robust integration Kalman filter (CARIKF) is presented, which implements adaptive integration upon the robust direct fusion solution. In the algorithm the raw observations from all heterogeneous sensors are corrected by the pseudoobservations derived from state equality constraint. The posterior covariances of the corrected observations are subsequently estimated upon the robust maximum-likelihood-type estimation (M-estimation) theory. The fusion state and its covariance are solved for all sensors further in the least squares (LS) sense. The pseudoobservations are constructed according to the estimated state and its covariance. They are further combined with the dynamic model of the host platform in an adaptive Kalman filter (AKF), from which a reliable and accurate navigation solution can be then obtained. A state constraint model is proposed upon Newton's forward differential extrapolation numerical method. To demonstrate performance of the CARIKF algorithm, simulations have been conducted in different dynamic and observation scenarios. Several algorithms are compared to evaluate the validity and efficiency of the CARIKF. The results show that the CARIKF is superior to other algorithms and can significantly improve the precision and reliability of the integrated solution.

Journal ArticleDOI
TL;DR: A high-performance implementation scheme for a least mean square adaptive filter based on a new strategy based on the offset binary coding scheme has been proposed in order to update these LUTs from time to time.
Abstract: A high-performance implementation scheme for a least mean square adaptive filter is presented. The architecture is based on distributed arithmetic in which the partial products of filter coefficients are precomputed and stored in lookup tables (LUTs) and the filtering is done by shift-and-accumulate operations on these partial products. In the case of an adaptive filter, it is required that the filter coefficients be updated and, hence, these LUTs are to be recalculated. A new strategy based on the offset binary coding scheme has been proposed in order to update these LUTs from time to time. Simulation results show that the proposed scheme consumes very less chip area and operates at high throughput for large base unit size k ( = N/m) , where m is an integer and N is the number of filter coefficients. For example, a 128-tap finite-impulse-response adaptive filter with the proposed implementation produces 12 times more throughput (for k = 8) and consumes almost 26% less area when compared to the best of existing architectures.

Journal ArticleDOI
TL;DR: In this article, a fuzzy system based method for modeling both rate-independent and rate-dependent hysteresis in the piezoelectric actuator is proposed, where the antecedent structure of the fuzzy system is identified through uniform partition of its input variable.

Journal ArticleDOI
TL;DR: A methodology is described here allowing to estimate in advance the potential response of flexible end-consumers to price variations, subsequently embedded in an optimal price-signal generator.
Abstract: Household-based demand response is expected to play an increasing role in supporting the large scale integration of renewable energy generation in existing power systems and electricity markets. While the direct control of the consumption level of households is envisaged as a possibility, a credible alternative is that of indirect control based on price signals to be sent to these end-consumers. A methodology is described here allowing to estimate in advance the potential response of flexible end-consumers to price variations, subsequently embedded in an optimal price-signal generator. In contrast to some real-time pricing proposals in the literature, here prices are estimated and broadcast once a day for the following one, for households to optimally schedule their consumption. The price-response is modeled using stochastic finite impulse response (FIR) models. Parameters are estimated within a recursive least squares (RLS) framework using data measurable at the grid level, in an adaptive fashion. Optimal price signals are generated by embedding the FIR models within a chance-constrained optimization framework. The objective is to keep the price signal as unchanged as possible from the reference market price, whilst keeping consumption below a pre-defined acceptable level.

Journal ArticleDOI
TL;DR: Simulation results in system-identification and channel-equalization applications are presented which demonstrate that improved steady-state misalignment, tracking capability, and readaptation can be achieved relative to those in some state-of-the-art competing algorithms.
Abstract: Two new improved recursive least-squares adaptive-filtering algorithms, one with a variable forgetting factor and the other with a variable convergence factor are proposed. Optimal forgetting and convergence factors are obtained by minimizing the mean square of the noise-free a posteriori error signal. The determination of the optimal forgetting and convergence factors requires information about the noise-free a priori error which is obtained by solving a known L1-L2 minimization problem. Simulation results in system-identification and channel-equalization applications are presented which demonstrate that improved steady-state misalignment, tracking capability, and readaptation can be achieved relative to those in some state-of-the-art competing algorithms.

Journal ArticleDOI
Wei Li1, Deren Gong1, Meihong Liu1, Jian Chen1, Dengping Duan1 
TL;DR: In this article, an adaptive robust Kalman filter algorithm is derived to account for both process noise and measurement noise uncertainty, which is successfully implemented in relative navigation using global position system for spacecraft formation flying in low earth orbit, with real-orbit perturbations and non-Gaussian random measurement errors.
Abstract: An adaptive robust Kalman filter algorithm is derived to account for both process noise and measurement noise uncertainty. The adaptive algorithm estimates process noise covariance based on the recursive minimisation of the difference between residual covariance matrix given by the filter and that calculated from time-averaging of the residual sequence generated by the filter at each time step. A recursive algorithm is proposed based on both Massachusetts Institute of Technology (MIT) rule and typical non-linear extended Kalman filter equations for minimising the difference. The measurement update using a robust technique to minimise a criterion function originated from Huber filter. The proposed adaptive robust Kalman filter has been successfully implemented in relative navigation using global position system for spacecraft formation flying in low earth orbit, with real-orbit perturbations and non-Gaussian random measurement errors. The numerical simulation results indicate that the proposed adaptive robust filter can provide better relative navigation performance in terms of accuracy and robustness as compared with previous filter algorithms.

Journal ArticleDOI
TL;DR: An adaptive framework for building soft-sensors based on radial basis function (RBF) neural network models, which approximates the unknown system based on input-output data from it and can be successfully applied to model the two nonlinear systems.
Abstract: This work presents an adaptive framework for building soft-sensors based on radial basis function (RBF) neural network models. The adaptive fuzzy means algorithm is utilized in order to evolve an RBF network, which approximates the unknown system based on input–output data from it. The methodology gradually builds the RBF network model, based on two separate levels of adaptation: On the first level, the structure of the hidden layer is modified by adding or deleting RBF centers, while on the second level, the synaptic weights are adjusted with the recursive least squares with exponential forgetting algorithm. The proposed approach is tested on two different systems, namely a simulated nonlinear DC Motor and a real industrial reactor. The results show that the produced soft-sensors can be successfully applied to model the two nonlinear systems. A comparison with two different adaptive modeling techniques, namely a dynamic evolving neural-fuzzy inference system (DENFIS) and neural networks trained with online backpropagation, highlights the advantages of the proposed methodology.

Journal ArticleDOI
TL;DR: In this paper, the authors present a method of directly estimating the variance of each mode estimate in addition to estimating the frequency and damping of each modes in an online setting using a recursive maximum likelihood estimator.
Abstract: Accurate and near real-time estimates of electromechanical modes are of great importance since the modal damping is a key indicator of the stability of the power system. If the estimates of the electromechanical modes are to be useful, knowing the variability in the estimates is critically important. This paper presents a method of directly estimating the variance of each mode estimate in addition to estimating the frequency and damping of each mode in an online setting using a recursive maximum likelihood (RML) estimator. The variance estimates are achieved using two closed-form multidimensional Taylor series approximations, the details of which are fully derived here. The proposed method is validated using a Monte Carlo simulation with a low order model of the Western Electricity Coordinating Council (WECC) power system under both ambient and probing conditions, with multiple modes closely spaced in frequency, and is compared to the regularized robust recursive least squares (R3LS) method. It is also successfully applied to phasor measurement unit (PMU) data collected from the actual WECC system, also under both ambient and probing conditions.

Journal ArticleDOI
TL;DR: In this paper, the convergence properties of the least square parameter estimation algorithm for multivariable systems that can be parameterized into a class of multivariate linear regression models were investigated.

Journal Article
TL;DR: In these notes, least squares is illustrated by applying it to several basic problems in signal processing, e.g. singular value decomposition, or the pseudo-inverse.
Abstract: Ivan Selesnick March 7, 2013 NYU-Poly These notes address (approximate) solutions to linear equations by least squares. We deal with the ‘easy’ case wherein the system matrix is full rank. If the system matrix is rank deficient, then other methods are needed, e.g., QR decomposition, singular value decomposition, or the pseudo-inverse, [2, 3]. In these notes, least squares is illustrated by applying it to several basic problems in signal processing:

Proceedings ArticleDOI
26 May 2013
TL;DR: In this article, an adaptive distributed technique that is suitable for node-specific parameter estimation in an adaptive network where each node is interested in a set of parameters of local interest as well as the set of network global parameters is introduced.
Abstract: We introduce an adaptive distributed technique that is suitable for node-specific parameter estimation in an adaptive network where each node is interested in a set of parameters of local interest as well as a set of network global parameters. The estimation of each set of parameters of local interest is undertaken by a local Least Mean Squares (LMS) algorithm at each node. At the same time and coupled with the previous local estimation processes, an incremental mode of cooperation is implemented at all nodes in order to perform an LMS algorithm which estimates the parameters of global interest. In the steady state, the new distributed technique converges to the MMSE solution of a centralized processor that is able to process all the observations. To illustrate the effectiveness of the proposed technique we provide simulation results in the context of cooperative spectrum sensing in cognitive radio networks.

Journal ArticleDOI
TL;DR: In this paper, a new method is proposed to calibrate three-axis magnetometers using differential evolution (DE) algorithm, which can avoid the troublesome procedure to select suitable initial parameters, thus it can improve the calibration performance of 3D magnetometers.

Journal ArticleDOI
TL;DR: Simulations for a number of scenarios of interest with a DS-CDMA system show that the proposed algorithms outperform previously reported techniques with a smaller number of parameter updates and a reduced risk of overbounding or underbounding.
Abstract: This work presents blind constrained constant modulus (CCM) adaptive algorithms based on the set-membership filtering (SMF) concept and incorporates dynamic bounds for interference suppression applications. We develop stochastic gradient and recursive least squares type algorithms based on the CCM design criterion in accordance with the specifications of the SMF concept. We also propose a blind framework that includes channel and amplitude estimators that take into account parameter estimation dependency, multiple access interference (MAI) and inter-symbol interference (ISI) to address the important issue of bound specification in multiuser communications. A convergence and tracking analysis of the proposed algorithms is carried out along with the development of analytical expressions to predict their performance. Simulations for a number of scenarios of interest with a DS-CDMA system show that the proposed algorithms outperform previously reported techniques with a smaller number of parameter updates and a reduced risk of overbounding or underbounding.

Journal ArticleDOI
TL;DR: In this paper, the authors proposed a two-step identification method for estimating the four parameters of a nonlinear model of a position-controlled servomechanism, which eliminates the effect of constant disturbances affecting the servomechms and filters out the high-frequency measurement noise.
Abstract: This study proposes a two-step identification method for estimating the four parameters of a nonlinear model of a position-controlled servomechanism. In the first step, the proposed approach, called the algebraic recursive identification method (ARIM), uses a parametrization derived from the operational calculus currently employed in algebraic identification methods (AIM) recently proposed in the literature. The procedure for obtaining this parametrization eliminates the effect of constant disturbances affecting the servomechanism and filters out the high-frequency measurement noise. A recursive least squares algorithm uses the parametrization for estimating the linear part of the servomechanism model, and allows eliminating the singularity problems found in the AIM. The second step uses the parameters obtained in the first step for computing the Coulomb friction coefficient and the constant disturbance acting on the servomechanism. Experimental results on a laboratory prototype allow comparing the results obtained using the AIM and the ARIM.