Showing papers on "Recursive least squares filter published in 2009"

Adaptive Reduced-Rank Processing Based on Joint and Iterative Interpolation, Decimation, and Filtering

Abstract: We present an adaptive reduced-rank signal processing technique for performing dimensionality reduction in general adaptive filtering problems. The proposed method is based on the concept of joint and iterative interpolation, decimation and filtering. We describe an iterative least squares (LS) procedure to jointly optimize the interpolation, decimation and filtering tasks for reduced-rank adaptive filtering. In order to design the decimation unit, we present the optimal decimation scheme and also propose low-complexity decimation structures. We then develop low-complexity least-mean squares (LMS) and recursive least squares (RLS) algorithms for the proposed scheme along with automatic rank and branch adaptation techniques. An analysis of the convergence properties and issues of the proposed algorithms is carried out and the key features of the optimization problem such as the existence of multiple solutions are discussed. We consider the application of the proposed algorithms to interference suppression in code-division multiple-access (CDMA) systems. Simulations results show that the proposed algorithms outperform the best known reduced-rank schemes with lower complexity.

Distributed Recursive Least-Squares for Consensus-Based In-Network Adaptive Estimation

Abstract: Recursive least-squares (RLS) schemes are of paramount importance for reducing complexity and memory requirements in estimating stationary signals as well as for tracking nonstationary processes, especially when the state and/or data model are not available and fast convergence rates are at a premium. To this end, a fully distributed (D-) RLS algorithm is developed for use by wireless sensor networks (WSNs) whereby sensors exchange messages with one-hop neighbors to consent on the network-wide estimates adaptively. The WSNs considered here do not necessarily possess a Hamiltonian cycle, while the inter-sensor links are challenged by communication noise. The novel algorithm is obtained after judiciously reformulating the exponentially-weighted least-squares cost into a separable form, which is then optimized via the alternating-direction method of multipliers. If powerful error control codes are utilized and communication noise is not an issue, D-RLS is modified to reduce communication overhead when compared to existing noise-unaware alternatives. Numerical simulations demonstrate that D-RLS can outperform existing approaches in terms of estimation performance and noise resilience, while it has the potential of performing efficient tracking.

f-x adaptive seismic-trace interpolation

Abstract: We use exponentially weighted recursive least squares to estimate adaptive prediction filters for frequency-space (f-x) seismic interpolation. Adaptive prediction filters can model signals where the dominant wavenumbers vary in space. This concept leads to an f-x interpolation method that does not require windowing strategies for optimal results. In other words, adaptive prediction filters can be used to interpolate waveforms that have spatially variant dips. The interpolation method’s performance depends on two parameters: filter length and forgetting factor. We pay particular attention to selection of the forgetting factor because it controls the algorithm’s adaptability to changes in local dip. Finally, we use synthetic- and real-data examples to illustrate the performance of the proposed adaptive f-x interpolation method.

An auxiliary model based on a recursive least-squares parameter estimation algorithm for non-uniformly sampled multirate systems

Abstract: The lifted state-space models for a class of multirate systems non-uniformly sampled from their continuous-time systems are derived, and the corresponding input-output relationship is obtai...

Widely-linear recursive least-squares algorithm for adaptive beamforming

Abstract: Adaptive beamforming algorithms typically rely on a complex linear model between the sensor measurements and the desired signal output that does not enable the best performance from the data in some situations. In this paper, we present an extension of the well-known recursive least-squares algorithm for adaptive filters to widely-linear complex-valued signal and system modeling. The widely-linear RLS algorithm exploits a structured covariance matrix update that maintains information about the non-circularity of the input data to solve the widely-linear least-squares task at each snapshot. In addition, the WL-RLS algorithm can easily be switched between conventional and widely-linear complex modeling as needed. Application of the method to adaptive beamforming of mixed BPSK and QPSK signal transmissions shows that the system can extract all of the transmitted signal outputs in certain overloaded scenarios, and it performs up to 3dB better than the conventional RLS beamformer when the array is not overloaded.

Design and Application of Stable Predictive Controller Using Recurrent Wavelet Neural Networks

Abstract: This paper presents a design methodology for stable predictive control of nonlinear discrete-time systems via recurrent wavelet neural networks (RWNNs). This type of controller has its simplicity in parallelism to conventional generalized predictive control design and efficiency to deal with complex nonlinear dynamics. A mathematical model using RWNN is constructed, and a learning algorithm adopting a recursive least squares is employed to identify the unknown parameters in the consequent part of the RWNN. The proposed control law is derived based on the minimization of a modified predictive performance criterion. Two theorems are presented for the conditions of the stability analysis and steady-state performance of the closed-loop systems. Numerical simulations reveal that the proposed control gives satisfactory tracking and disturbance rejection performances. Experimental results for position control of a positioning mechanism show the efficacy of the proposed method with setpoint changes.

Robust Underwater Telemetry With Adaptive Turbo Multiband Equalization

Abstract: In this paper, a multicarrier modulation scheme is presented for acoustic communication at low signal-to-noise ratios (SNRs). User bits are put through a rate 1/3 turbo encoder and interleaved with periodic training bits. A maximal-length sequence is prefixed for signal detection and equalizer convergence, and the resulting bit stream is simultaneously modulated onto multiple phase-shift keyed carriers. Since each subband carries the same symbol sequence, the baseband ensemble is amenable to multichannel equalization. An adaptive multiband equalizer is thus constructed for joint equalization and despreading of the frequency bands. Iterative equalization using soft information from the turbo decoder further enhances the receiver performance. A reduction in complexity is achieved by equipping the subbands with separate recursive least squares tap updates, yet guided by a common error signal. The proposed algorithms are tested on acoustic data from the Baltic Sea, using eight subbands of 460 Hz each, at an effective data rate of 75 b/s. Robust receiver operation is demonstrated at overall receive SNRs down to - 12 dB in three different channels, which corresponds to an SNR per bit Eb/N 0=+ 5 dB.

Space-Time Adaptive MMSE Multiuser Decision Feedback Detectors With Multiple-Feedback Interference Cancellation for CDMA Systems

Abstract: In this paper, we propose a novel space-time minimum mean square error (MMSE) decision feedback (DF) detection scheme for direct-sequence code-division multiple access (DS-CDMA) systems with multiple receive antennas, which employs multiple-parallel-feedback (MPF) branches for interference cancellation. The proposed space-time receiver is then further combined with cascaded DF stages to mitigate the deleterious effects of error propagation for uncoded schemes. To adjust the parameters of the receiver, we also present modified adaptive stochastic gradient (SG) and recursive least squares (RLS) algorithms that automatically switch to the best-available interference cancellation feedback branch and jointly estimate the feedforward and feedback filters. The performance of the system with beamforming and diversity configurations is also considered. Simulation results for an uplink scenario with uncoded systems show that the proposed space-time MPF-DF detector outperforms existing schemes such as linear, parallel DF (P-DF), and successive DF (S-DF) receivers in terms of bit error rate (BER) and achieves a substantial capacity increase in terms of the number of users, compared with the existing schemes. We also derive the expressions for MMSE achieved by the analyzed DF structures, including the novel scheme, with imperfect and perfect feedback and expressions of signal-to-interference-plus-noise ratio (SINR) for the beamforming and diversity configurations with linear receivers.

Modeling hysteresis in piezoelectric actuators using NARMAX models

Abstract: This paper presents a non-linear moving average model with exogenous inputs (NMAX) and a non-linear auto-regressive moving average model with exogenous inputs (NARMAX) respectively to model static and dynamic hysteresis inherent in piezoelectric actuators. The modeling approach is based on the expanded input space that transforms the multi-valued mapping of hysteresis into a one-to-one mapping. In the expanded input space, a simple hysteretic operator is proposed to be used as one of the coordinates to specify the moving feature of hysteresis. Both the modified Akaike's information criterion (MAIC) and the recursive least squares (RLS) algorithm are employed to estimate the appropriate orders and coefficients of the models. The advantage of the proposed approach is in the systematic design procedure which can on-line update the model parameters so as to accommodate to the change of operation environment compared with the classical Preisach model. Moreover, the obtained model is non-linear in variables but linear in parameters so that it can avoid the problem of sticking in local minima which the neural network based models usually have. The results of the experiments have shown that the proposed models can accurately describe static and dynamic behavior of hysteresis in piezoelectric actuators.

The residual based interactive least squares algorithms and simulation studies

Abstract: This paper presents a two-stage least squares based iterative algorithm, a residual based interactive least squares algorithm and a residual based recursive least squares algorithm for identifying controlled autoregressive moving average (C-ARMA) models. The simulation studies indicate that the proposed algorithms can effectively estimate the parameters of the C-ARMA models.

Adaptive Predistortion With Direct Learning Based on Piecewise Linear Approximation of Amplifier Nonlinearity

Abstract: We propose an efficient Wiener model for a power amplifier (PA) and develop a direct learning predistorter (PD) based on the model. The Wiener model is formed by a linear filter and a memoryless nonlinearity in which AM/AM and AM/PM characteristics are approximated as piecewise linear and piecewise constant functions, respectively. A two-step identification scheme, wherein the linear portion is estimated first and the nonlinear portion is then identified, is developed. The PD is modeled by a polynomial and its coefficients are directly updated using a recursive least squares (RLS) algorithm. To avoid implementing the inverse of the PA's linear portion, the cost function for the RLS algorithm is defined as the sum of differences between the output of the PA's linear portion and the inverse of the PA's nonlinear portion. The proposed direct learning scheme, which is referred to as the piecewise RLS (PWRLS) algorithm, is simpler to implement, yet exhibits comparable performance, as compared with existing direct learning schemes.

Error estimates for the regularization of least squares problems

Abstract: The a posteriori estimate of the errors in the numerical solution of ill-conditioned linear systems with contaminated data is a complicated problem. Several estimates of the norm of the error have been recently introduced and analyzed, under the assumption that the matrix is square and nonsingular. In this paper we study the same problem in the case of a rectangular and, in general, rank-deficient matrix. As a result, a class of error estimates previously introduced by the authors (Brezinski et al., Numer Algorithms, in press, 2008) are extended to the least squares solution of consistent and inconsistent linear systems. Their application to various direct and iterative regularization methods are also discussed, and the numerical effectiveness of these error estimates is pointed out by the results of an extensive experimentation.

Adaptive dereverberation of speech signals with speaker-position change detection

Abstract: This paper proposes a method for adaptive speech dereverberation and speaker-position change detection, which have not previously been addressed. Signal transmission channels in rooms are modeled as auto-regressive systems in individual frequency bands. The proposed method adaptively estimates the regression coefficients of this model, which are called room regression coefficients (RRCs). The proposed method has two distinguishing features: (1) The method is based on the weighted recursive least squares algorithm, which enables an efficient RRC-estimate update as well as a fast convergence rate; (2) The method detects changes in speaker position and so can quickly catch up with the sudden channel changes that such position changes cause. Detection is realized by finding time frames where the power of dereverberated speech is anomalously amplified. Experimental results showed that the proposed method attained convergence in 5 seconds and successfully detected changes in speaker position.

The stability analysis of the adaptive fading extended Kalman filter using the innovation covariance

Abstract: The well-known conventional Kalman filter gives the optimal solution but to do so, it requires an accurate system model and exact stochastic information. However, in a number of practical situations, the system model and the stochastic information are incomplete. The Kalman filter with incomplete information may be degraded or even diverged. To solve this problem, a new adaptive fading filter using a forgetting factor has recently been proposed by Kim and co-authors. This paper analyzes the stability of the adaptive fading extended Kalman filter (AFEKF), which is a nonlinear filter form of the adaptive fading filter. The stability analysis of the AFEKF is based on the analysis result of Reif and co-authors for the EKF. From the analysis results, this paper shows the upper bounded condition of the error covariance for the filter stability and the bounded value of the estimation error. Keywords: Adaptive Kalman filter, forgetting factor, nonlinear filter, stability analysis.

Sequential Studies of Beamforming Algorithms for Smart Antenna Systems

Abstract: 3 Abstract: Smart antenna is the most efficient leading innovation for maximum capacity and improved quality and coverage. A systematic comparison of the performance of different Adaptive Algorithms for beamforming for Smart Antenna System has been extensively studied in this research work. Simulation results revealed that training sequence algorithms like Recursive Least Squares (RLS) and Least Mean Squares (LMS) are best for beamforming (to form main lobes) towards desired user but they have limitations towards interference rejection. While Constant Modulus Algorithm (CMA) has satisfactory response towards beamforming and it gives better outcome for interference rejection, but Bit Error Rate (BER) is maximum in case of single antenna element in CMA. It is verified that convergence rate of RLS is faster than LMS so RLS is proved the best choice. The effect of changing step size for LMS algorithm has also been studied.

A Fast Robust Recursive Least-Squares Algorithm

Abstract: We present a fast robust recursive least-squares (FRRLS) algorithm based on a recently introduced new framework for designing robust adaptive filters. The algorithm is the result of minimizing a cost function subject to a time-dependent constraint on the norm of the filter update. Although the characteristics of the exact solution to this problem are known, there is no closed-form solution in general. However, the approximate solution we propose is very close to the optimal one. We also present some theoretical results regarding the asymptotic behavior of the algorithm. The FRRLS is then tested in different environments for system identification and acoustic echo cancellation applications.

A least squares formulation for a class of generalized eigenvalue problems in machine learning

Abstract: Many machine learning algorithms can be formulated as a generalized eigenvalue problem. One major limitation of such formulation is that the generalized eigenvalue problem is computationally expensive to solve especially for large-scale problems. In this paper, we show that under a mild condition, a class of generalized eigenvalue problems in machine learning can be formulated as a least squares problem. This class of problems include classical techniques such as Canonical Correlation Analysis (CCA), Partial Least Squares (PLS), and Linear Discriminant Analysis (LDA), as well as Hypergraph Spectral Learning (HSL). As a result, various regularization techniques can be readily incorporated into the formulation to improve model sparsity and generalization ability. In addition, the least squares formulation leads to efficient and scalable implementations based on the iterative conjugate gradient type algorithms. We report experimental results that confirm the established equivalence relationship. Results also demonstrate the efficiency and effectiveness of the equivalent least squares formulations on large-scale problems.

On-line identification and control of pneumatic servo drives via a mixed-reality environment

Abstract: This paper presents a method to identify and control electro-pneumatic servo drives in a real-time environment. Acquiring the system’s transfer function accurately can be difficult for nonlinear systems. This causes a great difficulty in servo-pneumatic system modeling and control. In order to avoid the complexity associated with nonlinear system modeling, a mixed-reality environment (MRE) is employed to identify the transfer function of the system using a recursive least squares (RLS) algorithm based on the auto-regressive moving-average (ARMA) model. On-line system identification can be conducted effectively and efficiently using the proposed method. The advantages of the proposed method include high accuracy in the identified system, low cost, and time reduction in tuning the controller parameters. Furthermore, the proposed method allows for on-line system control using different control schemes. The results obtained from the on-line experimental measured data are used to determine a discrete transfer function of the system. The best performance results are obtained using a fourth-order model with one-step prediction.

Performance study of adaptive filtering algorithms for noise cancellation of ECG signal

Abstract: Removal of noises from ECG (Electrocardiogram) signal is a classical problem. Moreover, nullifying AC and DC noises using the two adaptive algorithms-the LMS and the RLS from the ECG is a new study in biomedical science. In this paper, the four types of AC and DC noises have been implemented according to their basic properties. After that, these noises have been mixed with ECG signal and nullify these noises using the LMS and the RLS algorithms. At the end of this paper, a performance study has been done between these algorithms based on their parameters and also discussed the effect of filter length and the corresponding correlation coefficient. Results indicate that the DC bias noises cannot be handled by the LMS filtering whereas the RLS can handle both types of noises. Also, it is true for both algorithms that the filter length is proportional to MSE (Mean Square Error) rate and it takes more time to converge for both algorithms. Furthermore, most of the cases the RLS has achieved best effective noise cancellation performance although its convergence time is slightly high. But eventually its error has always dipped down below that of the LMS algorithm.

Automatic removal of ocular artifacts from EEG data using adaptive filtering and Independent Component Analysis

Abstract: A method to eliminate eye movement artifacts based on Independent Component Analysis (ICA) and Recursive Least Squares (RLS) is presented. The proposed algorithm combines the effective ICA capacity of separating artifacts from brain waves, together with the online interference cancellation achieved by adaptive filtering. The method uses separate electrodes localized close to the eyes (Fp1, Fp2, F7 and F8), that register vertical and horizontal eye movements, to extract a reference signal. Each reference input is first projected into ICA domain and then the interference is estimated using the RLS algorithm. This interference estimation is subtracted from the EEG components in the ICA domain. Results from experimental data demonstrate that this approach is suitable for eliminating artifacts caused by eye movements, and the principles of this method can be extended to certain other sources of artifacts as well. The method is easy to implement, stable, and presents a low computational cost.

Fast online impedance estimation for robot control

Abstract: In this paper a fast online estimation method of impedance parameters is proposed based on the forgetting factor recursive least squares identification method. The performance of the proposed method is accessed by simulation and robotic experiments. Comparing with existing methods, the proposed method shows fast tracking performance to parameter changes while achieving robustness to noise. The algorithm has been implemented to online robot control and can be generalized to meet other needs.

On-line parameter estimation of PMSM in open loop and closed loop

Abstract: The paper discusses the multi-models approach for on-line parameter estimation of permanent magnet synchronous motor (PMSM) The study is focused on a PMSM with non sinusoidal electromotive force (emf) in open loop and closed loop conditions The electrical parameters of 2-phases models in Extended Park frame are estimated by using the recursive least squares algorithm (RLS)

Recursive least-squares adaptive channel estimation for spatial modulation systems

Abstract: In this paper, a recursive least-squares (RLS) adaptive channel estimation scheme is applied for spatial modulation (SM) system over a block fading multiple-input-multiple-output (MIMO) channel. The performance of spatial modulation with channel estimation is compared to vertical Bell Labs layered space-time (V-BLAST) and maximum ratio combining (MRC) transmission schemes for different pilot rates and a fixed 3-b/s/Hz spectral efficiency. Computer simulations carried out demonstrate the superiority of SM over V-BLAST and MRC schemes. In addition, the results in this study show that SM is more robust against channel estimation errors than the other MIMO schemes.

Identification and adaptation of linear look-up table parameters using an efficient recursive least-squares technique.

Abstract: Linear look-up tables are widely used to approximate and characterize complex nonlinear functional relationships between system input and output. However, both the initial calibration and subsequent real-time adaptation of these tables can be time consuming and prone to error as a result of the large number of table parameters typically required to map the system and the uncertainties and noise in the experimental data on which the calibration is based. In this paper, a new method is presented for identifying or adapting the look-up table parameters using a recursive least-squares based approach. The new method differs from standard recursive least squares algorithms because it exploits the structure of the look-up table equations in order to perform the identification process in a way that is highly computationally and memory efficient. The technique can therefore be implemented within the constraints of typical embedded applications. In the present study, the technique is applied to the identification of the volumetric efficiency look-up table commonly used in gasoline engine fueling strategies. The technique is demonstrated on a Ford 2.0L I4 Duratec engine using time-delayed feedback from a sensor in the exhaust manifold in order to adapt the table parameters online.

On properties of the widely linear MSE filter and its LMS implementation

Abstract: Widely linear filters have been receiving much attention lately and have been proposed for many signal processing applications where the traditional circularity assumptions on the complex data do not hold. In this paper, we study the properties of the mean-square-error (MSE) widely linear filter and its least mean squares (LMS) adaptive implementation. We show that in certain cases, widely linear filter does not provide any additional advantage compared to the linear filter even with highly noncircular data. On the other hand, we show examples of cases where it can lead to important performance gains even when the input is circular. We also show that its performance can slow down significantly with highly noncircular inputs when it is implemented using an LMS type gradient descent algorithm thus making recursive least squares type adaptive implementations more desirable for an adaptive widely linear filter.