Showing papers on "Recursive least squares filter published in 2005"
TL;DR: In this article, an ad hoc modification of the update law for the gain in the recursive least square (RLS) scheme is proposed and used in simulation and experiments, demonstrating that the proposed scheme estimates mass within 5% of its actual value and tracks grade with good accuracy.
Abstract: Good estimates of vehicle mass and road grade are important in automation of heavy duty vehicles, vehicle following manoeuvres or traditional powertrain control schemes. Recursive least square (RLS) with multiple forgetting factors accounts for different rates of change for different parameters and thus, enables simultaneous estimation of the time-varying grade and the piece-wise constant mass. An ad hoc modification of the update law for the gain in the RLS scheme is proposed and used in simulation and experiments. We demonstrate that the proposed scheme estimates mass within 5% of its actual value and tracks grade with good accuracy provided that inputs are persistently exciting. The experimental setups, signals, their source and their accuracy are discussed. Issues like lack of persistent excitations in certain parts of the run or difficulties of parameter tracking during gear shift are explained and suggestions to bypass these problems are made.
459 citations
TL;DR: For multivariable discrete-time systems described by transfer matrices, an HLSI algorithm and a hierarchical least squares iterative algorithm based on a hierarchical identification principle are developed and shown to have significant computational advantage over existing identification algorithms.
Abstract: For multivariable discrete-time systems described by transfer matrices, we develop a hierarchical least squares iterative (HLSI) algorithm and a hierarchical least squares (HLS) algorithm based on a hierarchical identification principle. We show that the parameter estimation error given by the HLSI algorithm converges to zero for the deterministic cases, and that the parameter estimates by the HLS algorithm consistently converge to the true parameters for the stochastic cases. The algorithms proposed have significant computational advantage over existing identification algorithms. Finally, we test the proposed algorithms on an example and show their effectiveness.
297 citations
TL;DR: A new control mechanism for the variable forgetting factor (VFF) of the recursive least square (RLS) adaptive algorithm is presented, which is basically a gradient-based method of which the gradient is derived from an improved mean square error analysis of RLS.
Abstract: In this paper, a new control mechanism for the variable forgetting factor (VFF) of the recursive least square (RLS) adaptive algorithm is presented. The control algorithm is basically a gradient-based method of which the gradient is derived from an improved mean square error analysis of RLS. The new mean square error analysis exploits the correlation of the inverse of the correlation matrix with itself that yields improved theoretical results, especially in the transient and steady-state mean square error. It is shown that the theoretical analysis is close to simulation results for different forgetting factors and different model orders. The analysis yields a dynamic equation of mean square error that can be used to derive a dynamic equation of the gradient of mean square error to control the forgetting factor. The dynamic equation can produce a positive gradient when the error is large and a negative gradient when the error is in the steady state. Compared with other variable forgetting factor algorithms, the new control algorithm gives fast tracking and small mean square model error for different signal-to-noise ratios (SNRs).
178 citations
01 Nov 2005
TL;DR: This paper presents a novel architecture for matrix inversion by generalizing the QR decomposition-based recursive least square (RLS) algorithm, and using Squared Givens rotations and a folded systolic array for FPGA implementation.
Abstract: This paper presents a novel architecture for matrix inversion by generalizing the QR decomposition-based recursive least square (RLS) algorithm. The use of Squared Givens rotations and a folded systolic array makes this architecture very suitable for FPGA implementation. Input is a 4 × 4 matrix of complex, floating point values. The matrix inversion design can achieve throughput of 0.13M updates per second on a state of the art Xilinx Virtex4 FPGA running at 115 MHz. Due to the modular partitioning and interfacing between multiple Boundary and Internal processing units, this architecture is easily extendable for other matrix sizes.
167 citations
TL;DR: A computationally efficient recursive least squares (RLS) type algorithm for jointly estimating the parameters of the channel and the receiver is developed in order to suppress multiaccess (MAI) and inter-symbol interference (ISI).
Abstract: A code-constrained constant modulus (CCM) design criterion for linear receivers is investigated for direct sequence code division multiple access (DS-CDMA) in multipath channels based on constrained optimization techniques. A computationally efficient recursive least squares (RLS) type algorithm for jointly estimating the parameters of the channel and the receiver is developed in order to suppress multiaccess (MAI) and inter-symbol interference (ISI). An analysis of the method examines its convergence properties and simulations under nonstationary environments show that the novel algorithms outperform existent techniques.
111 citations
21 Nov 2005
TL;DR: In this article, a novel online capacitance estimation method for a DC-link capacitance in a three-phase AC/DC/AC PWM converter is presented, where a controlled AC current with a lower frequency than the line frequency is injected into the input side, which then causes AC voltage ripples at the DC output side.
Abstract: A novel online capacitance estimation method for a DC-link capacitor in a three-phase AC/DC/AC PWM converter is prepared. At no load, a controlled AC current with a lower frequency than the line frequency is injected into the input side, which then causes AC voltage ripples at the DC output side. By extracting the AC voltage and current components on the DC output side using digital filters, the capacitance can then be calculated using the recursive least squares method. The proposed method can be simply implemented with only software and no additional hardware. Experimental results confirm that the estimation error is less than 0.26%.
107 citations
TL;DR: In this article, an adaptive control scheme is proposed to reduce force ripple effects impeding motion accuracy in Permanent Magnet Linear Motors (PMLMs) by using a Fast Fourier Transform (FFT) analysis.
100 citations
17 May 2005
TL;DR: In this article, an active noise cancellation technique for recovering wearable biosensor signals corrupted by bodily motion is presented, where a finger mounted photoplethysmograph (PPG) ring sensor with a collocated MEMS accelerometer is considered.
Abstract: This paper presents an active noise cancellation technique for recovering wearable biosensor signals corrupted by bodily motion. A finger mounted photoplethysmograph (PPG) ring sensor with a collocated MEMS accelerometer is considered. The system by which finger acceleration disturbs PPG output is identified and a means of modeling this relationship is prescribed using either FIR or Laguerre models. This means of modeling motivates the use of a recursive least squares active noise cancellation technique using the MEMS accelerometer reading as an input for a FIR or Laguerre model. The model parameters are identified and tuned in real time to minimize the power of the recovered PPG signal. Experiments show that the active noise cancellation method can recover pulse information from PPG signals corrupted with up to 2G of acceleration with 85% improvement in mean squared error.
87 citations
TL;DR: It is shown that the proposed adaptive technique is considerably simpler to implement than a V-BLAST processor with channel tracking, yet the performances are almost comparable.
Abstract: In an attempt to reduce the computational complexity of vertical Bell Labs layered space time (V-BLAST) processing with time-varying channels, an efficient adaptive receiver is developed based on the generalized decision feedback equalizer (GDFE) architecture. The proposed receiver updates the filter weight vectors and detection order using a recursive least squares (RLS)-based time- and order-update algorithm. The convergence of the algorithm is examined by analysis and simulation, and it is shown that the proposed adaptive technique is considerably simpler to implement than a V-BLAST processor with channel tracking, yet the performances are almost comparable.
80 citations
TL;DR: Dr. Bernard Widrow presents a personal view on the discovery of the least mean squares algorithm.
Abstract: Dr. Bernard Widrow presents a personal view on the discovery of the least mean squares algorithm.
72 citations
TL;DR: The proposed intelligent diagnostic system for rotating machinery is implemented on the platform of a floating point digital signal processor, where a photo switch and an accelerometer supply the shaft speed and acceleration signals, respectively.
28 Nov 2005
TL;DR: The proposed state-space model and fractional order difference equation are used in an identification procedure which produces very accurate results.
Abstract: The paper is devoted to the application of fractional calculus concepts to modeling, identification and control of discrete-time systems. Fractional difference equations (FAE) models are presented and their use in identification, state estimation and control context is discussed. The fractional difference state-space model is proposed for that purpose. For such a model stability conditions are given. A fractional Kalman filter (FKF) for this model is recalled. The proposed state-space model and fractional order difference equation are used in an identification procedure which produces very accurate results. Finally, the state-space model is used in closed-loop state feedback control form together with FKF as a state estimator. The latter is also given in an adaptive form together with FKF and a modification of recursive least squares (RLS) algorithm as a parameters identification procedure. All the algorithms presented were tested in simulations and the example results are given in the paper
TL;DR: A consistent LMS-type algorithm is proposed for the data least square estimation problem, based on the geometry of the mean squared error (MSE) function, rendering the step-size normalization and the heuristic filtered estimation of the noise variance, respectively, for fast convergence and robustness to stochastic noise.
Abstract: When the ordinary least squares method is applied to the parameter estimation problem with noisy data matrix, it is well-known that the estimates turn out to be biased. While this bias term can be somewhat reduced by the use of models of higher order, or by requiring a high signal-to-noise ratio (SNR), it can never be completely removed. Consistent estimates can be obtained by means of the instrumental variable method (IVM),or the total/data least squares method (TLS/DLS). In the adaptive setting for the such problem, a variety of least-mean-squares (LMS)-type algorithms have been researched rather than their recursive versions of IVM or TLS/DLS that cost considerable computations. Motivated by these observations, we propose a consistent LMS-type algorithm for the data least square estimation problem. This novel approach is based on the geometry of the mean squared error (MSE) function, rendering the step-size normalization and the heuristic filtered estimation of the noise variance, respectively, for fast convergence and robustness to stochastic noise. Monte Carlo simulations of a zero-forcing adaptive finite-impulse-response (FIR) channel equalizer demonstrate the efficacy of our algorithm.
TL;DR: In this article, a special form of the Hammerstein model, which is linear in parameters, is incorporated into the recursive least squares identification scheme supplemented with the estimation of model internal variables, enabling online estimation of the linear block parameters, the coefficients determining the partition of nonlinearity subdomains and the corresponding linear segment slopes.
Abstract: This brief deals with the recursive parameter identification of Hammerstein type nonlinear dynamic systems with time-varying piecewise-linear characteristics. A special form of the Hammerstein model, which is linear in parameters, is incorporated into the recursive least squares identification scheme supplemented with the estimation of model internal variables. This enables online estimation of the linear block parameters, the coefficients determining the partition of nonlinearity subdomains and the corresponding linear segment slopes. An illustrative example is included.
TL;DR: A simple recursive solution to passive tracking of maneuvering targets using time difference of arrival (TDOA) measurements is presented, and an iterative Gauss-Newton algorithm is developed for stationary target localization based on a constrained weighted least-squares criterion.
Book•
01 Jan 2005
TL;DR: In this article, the authors present a toolbox for FDSP tools for software applications with a focus on the FDSP toolbox and a discussion of the problems of software applications.
Abstract: 1. Signal Processing Motivation / Signals and Systems / Signal Sampling / Signal Reconstruction / Prefilters and Postfilters / Conversion Circuits / The FDSP Toolbox / Software Applications / Chapter Summary / Problems 2. Discrete-Time System Analysis Motivation / Z-Transform Pairs / Z-Transform Properties / Inverse Z-Transform / Transfer Functions / Signal Flow Graphs / The Impulse Response and Convolution / Stability / Frequency Response / Software Applications / Chapter Summary / Problems 3. The DFT and Spectral Analysis Motivation / The Discrete-Time Fourier Transform (DTFT). The Discrete Fourier Transform (DFT). DFT Properties. The Fast Fourier Transform (FFT). White Noise. Discrete-Time Frequency Response. Zero Padding. Power Density Spectrum Estimation. The Spectrogram. Software Applications. Chapter Summary. Problems. 4. Convolution and Correlation Motivation / Convolution / Fast Convolution / Cross-Correlation / Fast Correlation / Auto-Correlation / Extracting Periodic Signals from Noise / Software Applications / Chapter Summary / Problems 5. Filter Specifications and Structures Motivation. Filter Design Specifications. Linear-Phase Filters. Minimum-Phase and Allpass Filters. FIR Filter Realization Structures. IIR Filter Realization Structures. FIR Finite Word Length Effects. IIR Finite Word Length Effects. Software Applications. Chapter Summary. Problems. 6. FIR Filter Design Motivation / Windowing Method / Frequency Sampling Method / Least Squares Method / Optimal Equiripple Method / Differentiators and Hilbert Transformers / Software Applications / Chapter Summary / Problems 7. Multirate Signal Processing Motivation / Integer Decimators and Interpolators / Rational Sampling Rate Converters / Multirate Filter Realization Structures / Subband Processing / Oversampling ADC / Oversampling DAC / Software Applications / Chapter Summary / Problems 8. IIR Filter Design Motivation / Filter Design by Pole-Zero Placement / Filter Design Parameters / Classical Analog Filters / Bilinear Transformation Method / Frequency Transformations / Software Applications / Chapter Summary / Problems 9. Adaptive Signal Processing Motivation / Mean Square Error / The Least Mean Square (LMS) Method / Performance Analysis of the LMS Method / Modified LMS Methods / Adaptive FIR Filter Design / The Recursive Least Squares (RLS) Method / Active Noise Control / Nonlinear System Identification / Software Applications / Chapter Summary / Problems APPENDICES: 1. MATLAB Workspace / Variables and Initialization / Mathematical Operators / Input and Output / Branching and Loops / Built-In Functions / User-Defined Functions / GUIs 2. FDSP Toolbox Installation / Driver Module f_dsp / Chapter GUI Modules / FDSP Toolbox Functions 3. Transform Tables Fourier Series / Fourier Transform / Laplace Transform / Z-Transform / Discrete-Time Fourier Transform (DTFT), Discrete Fourier Transform (DFT) 4. Mathematical Identifies Complex Numbers / Euler"s Identity / Trigonometric Identities / Inequalities
Patent•
10 Nov 2005
TL;DR: In this paper, a recursive algorithm is provided for adaptive multi-parameter regression enhanced with forgetting factors unique to each regressed parameter, which can include lead acid batteries, nickel-metal hydride batteries, and lithium-ion batteries.
Abstract: A recursive algorithm is provided for adaptive multi-parameter regression enhanced with forgetting factors unique to each regressed parameter. Applications of this algorithm can include lead acid batteries, nickel-metal hydride batteries, and lithium-ion batteries, among others. A control algorithm is presented, having an arbitrary number of model parameters, each having its own time-weighting factor. A method to determine optimal values for the time-weighting factors is included, to give greater effect to recently obtained data for the determination of a system's state. A methodology of weighted recursive least squares is employed, wherein the time weighting corresponds to the exponential-forgetting formalism. The derived mathematical result does not involve matrix inversion, and the method is iterative, i.e. each parameter is regressed individually at every time step.
TL;DR: In this article, the authors consider recursive least squares (RLS) as an alternative for online estimation and run-to-run (RtR) control in semiconductor manufacturing.
Abstract: Run-to-run (RtR) control technology has received tremendous interest in semiconductor manufacturing. Exponentially weighted moving average (EWMA), double-EWMA, and internal model control (IMC) filters are recognized methods for online RtR estimation. In this paper, we consider recursive least squares (RLS) as an alternative for online estimation and RtR control. The relationship between EWMA-type and RLS-type estimates is analyzed and verified with simulations. Because measurement delay is almost inevitable in semiconductor manufacturing, we discuss and compare the performance of EWMA, RtR-IMC, and RLS controllers in handling measurement delay and measurement noise for processes with a deterministic drift. An ad hoc solution is proposed to handle measurement delay for processes with time-varying drifts. The results are illustrated through several simulations and a shallow trench isolation (STI) etch process as an industrial example.
TL;DR: An adaptive algorithm based on weighted recursive least squares is derived and implemented that is likely to play a critical role in optimal operation of hybrid electric vehicles and on-board diagnostics.
Abstract: An adaptive algorithm based on weighted recursive least squares is derived and implemented. The generality of the approach is underscored by the application of the algorithm to a 42 V lead acid and a high-voltage (375 V) nickel metal hydride battery system. The algorithm is fully recursive in that the only variables required for on-line regression are those of the previous time step and the current time step. A time-weighting technique often referred to as exponential forgetting is employed to damp exponentially the influence of older data on the regression analysis. The output from the adaptive algorithm is the battery state of charge (remaining energy), state of health (relative to the battery's nominal rating), and power capability. Such algorithms are likely to play a critical role in optimal operation of hybrid electric vehicles and on-board diagnostics. The behavior of the algorithm in terms of convergence, accuracy, and robustness is examined.
08 Sep 2005
TL;DR: This work presents a batch algorithm to extract all the canonical vectors through an iterative regression procedure, which at each iteration uses as desired output the mean of the outputs obtained in the previous iteration, and derives in a straightforward manner a recursive least squares algorithm for online CCA.
Abstract: Canonical Correlation Analysis (CCA) is a classical tool in statistical analysis that measures the linear relationship between two or several data sets. In [1] it was shown that CCA of M = 2 data sets can be reformulated as a pair of coupled least squares (LS) problems. Here, we generalize this idea to M > 2 data sets. First, we present a batch algorithm to extract all the canonical vectors through an iterative regression procedure, which at each iteration uses as desired output the mean of the outputs obtained in the previous iteration. Furthermore, this alternative formulation of CCA as M coupled regression problems allows us to derive in a straightforward manner a recursive least squares (RLS) algorithm for online CCA. The proposed batch and on-line algorithms are applied to blind equalization of single-input multiple-output (SIMO) channels. Some simulation results show that the CCA-based algorithms outperform other techniques based on second-order statistics for this particular application.
TL;DR: This paper presents an approach to the identification of time-varying, nonlinear pH processes based on the Wiener model structure that produces an on-line estimate of the titration curve, where the shape of this static nonlinearity changes as a result of changes in the weak-species concentration and/or composition of the process feed stream.
TL;DR: Recursion least squares and least mean squares subspace-based adaptive algorithms in order to identify the impulse response of the multipath channel and demonstrate the improved performance of these methods as compared with the already-existing techniques in the literature.
Abstract: The problem of blind adaptive channel estimation in code-division multiple access (CDMA) systems is considered. Motivated by the iterative power method, which is used in numerical analysis for estimating singular values and singular vectors, we develop recursive least squares (RLS) and least mean squares (LMS) subspace-based adaptive algorithms in order to identify the impulse response of the multipath channel. The schemes proposed in this paper use only the spreading code of the user of interest and the received data and are therefore blind. Both versions (RLS and LMS) exhibit rapid convergence combined with low computational complexity. With the help of simulations, we demonstrate the improved performance of our methods as compared with the already-existing techniques in the literature.
TL;DR: In this article, an affine structure with additional assumptions is considered, in particular, Toeplitz and Hankel structured, noise free and unstructured blocks are allowed simultaneously in the augmented data matrix, and an equivalent optimization problem is derived that has as decision variables only the estimated parameters.
TL;DR: In this paper, the procedure of parameters identification of DC motor model using a method of recursive least squares is described in order to identify the system an experimental measuring of signals was carried out at input - supply of voltage and output of the system for identification - motor angle speed.
Abstract: The procedure of parameters identification of DC motor model using a method of recursive least squares is described in this paper. To identify the system an experimental measuring of signals was carrying out at input - supply of voltage and output of the system for identification - motor angle speed. For the needs of the experiment, a system has been configured with a motor and an optical encoder whose output is connected with the counter input of acquisition card LCK-6013 which over a block connector CB-68LP makes a connection with a computer. The speed of the motor measured by optical encoder is compared with the speed of identified system in order to confirm the quality of the motor model’s parameters estimation.
TL;DR: Simulation results are shown, indicating that an alternative method, called the method of weighted least squares (WLS), outperforms the OLS method in terms of mean squared error.
TL;DR: This work considers a class of hybrid systems which is modeled by continuous-time linear systems with Markovian jumps in the parameters (LSMJP), and derives the best linear mean square estimator for such systems.
Abstract: We consider a class of hybrid systems which is modeled by continuous-time linear systems with Markovian jumps in the parameters (LSMJP). Our aim is to derive the best linear mean square estimator for such systems. The approach adopted here produces a filter which bears those desirable properties of the Kalman filter: A recursive scheme suitable for computer implementation which allows some offline computation that alleviates the computational burden. Apart from the intrinsic theoretical interest of the problem in its own right and the application-oriented motivation of getting more easily implementable filters, another compelling reason why the study here is pertinent has to do with the fact that the optimal nonlinear filter for our estimation problem is not computable via a finite computation (the filter is infinite dimensional). Our filter has dimension Nn, with n denoting the dimension of the state vector and N the number of states of the Markov chain.
03 Jul 2005
TL;DR: In this article, the authors proposed a robust adaptive beamforming by combining the attributes of the least mean square (LMS) algorithm and the sample matrix inversion (SMI) algorithm.
Abstract: The least mean squares (LMS) algorithm is a simple adaptive beamforming algorithm that is well suited for continuous transmission systems. The LMS algorithm converges slowly when compared with other complicated algorithms, such as recursive least squares (RLS) (Shubair, R.M. and Merri, A., 2005). On the other hand, the sample matrix inversion (SMI) algorithm has a fast convergence behavior. However, because its speedy convergence is achieved through the use of matrix inversion, the SMI algorithm is computationally intensive. Moreover, the SMI algorithm has a block adaptive approach for which it is required that the signal environment does not undergo significant change during the course of block acquisition. The paper develops an algorithm for robust adaptive beamforming by combining the attributes of the LMS algorithm and SMI algorithm. This new algorithm uses the LMS algorithm, which is simple to implement and not computationally intensive, but with SMI initialization in order to ensure fast convergence. Numerical results verify the improved convergence, accuracy, and computational efficiency of the combined LMS/SMI algorithm.
TL;DR: Two novel blind set-theoretic adaptive filtering algorithms for suppressing "Multiple Access Interference (MAI)," which is one of the central burdens in DS/CDMA systems, achieve much higher speed of convergence with rather better bit error rate performance than other blind methods.
Abstract: This paper presents two novel blind set-theoretic adaptive filtering algorithms for suppressing "Multiple Access Interference (MAI)," which is one of the central burdens in DS/CDMA systems. We naturally formulate the problem of MAI suppression as an asymptotic minimization of a sequence of cost functions under some linear constraint defined by the desired user's signature. The proposed algorithms embed the constraint into the direction of update, and thus the adaptive filter moves toward the optimal filter without stepping away from the constraint set. In addition, using parallel processors, the proposed algorithms attain excellent performance with linear computational complexity. Geometric interpretation clarifies an advantage of the proposed methods over existing methods. Simulation results demonstrate that the proposed algorithms achieve (i) much higher speed of convergence with rather better bit error rate performance than other blind methods and (ii) much higher speed of convergence than the non-blind NLMS algorithm (indeed, the speed of convergence of the proposed algorithms is comparable to the non-blind RLS algorithm).
TL;DR: The comparison between the state-space-based channel estimation algorithm and the FIR-based Recursive Least Squares algorithm shows the former is a more robust modeling approach than the latter.
TL;DR: In this article, the adaptive recursive least squares (RLS) filter was used to identify changes in structural stiffness for the ASCE benchmark structure health monitoring (SHM) problem.