Showing papers on "Recursive least squares filter published in 2012"

$L_1$ -Regularized STAP Algorithms With a Generalized Sidelobe Canceler Architecture for Airborne Radar

Abstract: In this paper, we propose novel l1-regularized space-time adaptive processing (STAP) algorithms with a generalized sidelobe canceler architecture for airborne radar applications. The proposed methods suppose that a number of samples at the output of the blocking process are not needed for sidelobe canceling, which leads to the sparsity of the STAP filter weight vector. The core idea is to impose a sparse regularization (l1-norm type) to the minimum variance criterion. By solving this optimization problem, an l1-regularized recursive least squares (l1-based RLS) adaptive algorithm is developed. We also discuss the SINR steady-state performance and the penalty parameter setting of the proposed algorithm. To adaptively set the penalty parameter, two switched schemes are proposed for l1-based RLS algorithms. The computational complexity analysis shows that the proposed algorithms have the same complexity level as the conventional RLS algorithm (O((NM)2)), where NM is the filter weight vector length), but a significantly lower complexity level than the loaded sample covariance matrix inversion algorithm (O((NM)3)) and the compressive sensing STAP algorithm (O((NsNd)3), where N8Nd >; NM is the angle-Doppler plane size). The simulation results show that the proposed STAP algorithms converge rapidly and provide a SINR improvement using a small number of snapshots.

Distributed Recursive Least-Squares: Stability and Performance Analysis

Abstract: The recursive least-squares (RLS) algorithm has well-documented merits for reducing complexity and storage requirements, when it comes to online estimation of stationary signals as well as for tracking slowly-varying nonstationary processes. In this paper, a distributed recursive least-squares (D-RLS) algorithm is developed for cooperative estimation using ad hoc wireless sensor networks. Distributed iterations are obtained by minimizing a separable reformulation of the exponentially-weighted least-squares cost, using the alternating-minimization algorithm. Sensors carry out reduced-complexity tasks locally, and exchange messages with one-hop neighbors to consent on the network-wide estimates adaptively. A steady-state mean-square error (MSE) performance analysis of D-RLS is conducted, by studying a stochastically-driven `averaged' system that approximates the D-RLS dynamics asymptotically in time. For sensor observations that are linearly related to the time-invariant parameter vector sought, the simplifying independence setting assumptions facilitate deriving accurate closed-form expressions for the MSE steady-state values. The problems of mean- and MSE-sense stability of D-RLS are also investigated, and easily-checkable sufficient conditions are derived under which a steady-state is attained. Without resorting to diminishing step-sizes which compromise the tracking ability of D-RLS, stability ensures that per sensor estimates hover inside a ball of finite radius centered at the true parameter vector, with high-probability, even when inter-sensor communication links are noisy. Interestingly, computer simulations demonstrate that the theoretical findings are accurate also in the pragmatic settings whereby sensors acquire temporally-correlated data.

Adaptive Widely Linear Reduced-Rank Interference Suppression Based on the Multistage Wiener Filter

Abstract: We propose a widely linear multistage Wiener filter (WL-MSWF) receiver to suppress inter-/intra-symbol interference, multiuser interference, and narrowband interference in a high data rate direct-sequence ultra wideband (DS-UWB) system. The proposed WL receiver fully exploits the second-order statistics of the received signal, yielding a smaller Minimum Mean Square Error (MMSE) than the linear receiver. The WL-MSWF receiver mainly consists of a low-rank transformation and an adaptive reduced-rank after. The rank-reduction is achieved via a transformation matrix. Based on the linear MSWF concept, two constructions of this rank-reduction matrix, namely total WL (TWL) and quasi WL (QWL), are proposed. We develop stochastic gradient (SG) and recursive least squares (RLS) adaptive versions of the proposed TWL/QWL-MSWF and theoretically analyze their convergence behavior. The comparison of the proposed TWL/QWL-MSWF and the existing algorithms is carried out in terms of the computational complexity and the resulting MMSE performance. Extensive simulation results show that the proposed TWL/QWL-MSWF schemes outperform the existing schemes in both convergence and steady-state performance under various conditions.

Variable Projection for Nonlinear Least Squares Problems

Abstract: The variable projection algorithm of Golub and Pereyra (SIAM J. Numer. Anal. 10:413---432, 1973) has proven to be quite valuable in the solution of nonlinear least squares problems in which a substantial number of the parameters are linear. Its advantages are efficiency and, more importantly, a better likelihood of finding a global minimizer rather than a local one. The purpose of our work is to provide a more robust implementation of this algorithm, include constraints on the parameters, more clearly identify key ingredients so that improvements can be made, compute the Jacobian matrix more accurately, and make future implementations in other languages easy.

Parameter Identification of an Induction Machine at Standstill Using the Vector Constructing Method

Abstract: The squirrel-cage induction machine (IM) has been widely employed in microgrid. Accurate electrical parameters are necessary for the field-oriented control of the IM to achieve excellent performance. In this paper, a new offline identification scheme is presented based on the vector constructing method. The IM parameters are estimated using the recursive least squares (RLS) algorithm, which is applied to the continuous-time model of the IM at standstill. A single-phase ac test is used to make the machine standstill. The main feature of the proposed scheme is that the stator voltage, stator current and their derivatives, which are normally needed for the RLS algorithm, are constructed by the vector constructing method. The constructing rules are elaborated, which indicate that the phase shift and the amplitude ratio between the fundamental components of the voltage and the current have to be unchanged. This feature can avoid the analog or digital differentiators and greatly increase the noise immunity. Furthermore, the digital low-pass filter is not required for the proposed scheme, which can reduce the complexity of the identification scheme. Simulation and experimental results have been presented to demonstrate the validity and the feasibility of the proposed scheme.

Active Online System Identification of Switch Mode DC–DC Power Converter Based on Efficient Recursive DCD-IIR Adaptive Filter

Abstract: This paper introduces a novel technique for online system identification. Specific attention is given to the parameter estimation of dc-dc switched-mode power converters; however, the proposed method can be applied to many alternative applications where efficient and accurate parameter estimation is required. The proposed technique is computationally efficient, based on a dichotomous coordinate descent algorithm, and uses an infinite impulse response adaptive filter as the plant model. The system identification technique reduces the computational complexity of existing recursive least squares algorithms. Importantly, the proposed method is also able to identify the parameters quickly and accurately, thus offering an efficient hardware solution that is well suited to real-time applications. Simulation analysis and validation based on experimental data obtained from a prototype synchronous dc-dc buck converter is presented. Results clearly demonstrate that the estimated parameters of the dc-dc converter are a very close match to those of the experimental system. The approach can be directly embedded into adaptive and self-tuning digital controllers to improve the control performance of a wide range of industrial and commercial applications.

Real-Time Identification of Hunt–Crossley Dynamic Models of Contact Environments

Abstract: Real-time estimates of environment dynamics play an important role in the design of controllers for stable interaction between robotic manipulators and unknown environments. The Hunt-Crossley (HC) dynamic contact model has been shown to be more consistent with the physics of contact, compared with the classical linear models, such as Kelvin-Voigt (KV). This paper experimentally evaluates the author's previously proposed single-stage identification method for real-time parameter estimation of HC nonlinear dynamic models. Experiments are performed on various dynamically distinct objects, including an elastic rubber ball, a piece of sponge, a polyvinyl chloride (PVC) phantom, and a PVC phantom with a hard inclusion. A set of mild conditions for guaranteed unbiased estimation of the proposed method is discussed and experimentally evaluated. Furthermore, this paper rigorously evaluates the performance of the proposed single-stage method and compares it with those of a double-stage method for the HC model and a recursive least squares method for the KV model and its variations in terms of convergence rate, the sensitivity to parameter initialization, and the sensitivity to the changes in environment dynamic properties.

Recursive Predictor-Based Subspace Identification With Application to the Real-Time Closed-Loop Tracking of Flutter

Abstract: A novel recursive predictor-based subspace identification method is presented to identify linear time-invariant systems with multi inputs and multi outputs. The method is implemented in real-time and is able to operate in open loop or closed loop. The recursive identification is performed via the subsequent solution of only three linear problems, which are solved using recursive least squares. The recursive implementation of the method is not only able to identify linear time-invariant models from measured data, but can also be used to track slowly time-varying dynamics if adaptive filters are used. The computational complexity is reduced by exploiting the structure in the data equations and by using array algorithms to solve the main linear problem. This results in a fast recursive predictor-based subspace identification method suited for real-time implementation. The real-time implementation and the ability to work with multi-input and multi-output systems operating in closed loop makes this approach suitable for online estimation of unstable dynamics. The ability to do so is demonstrated by the detection of flutter on an experimental 2-D-airfoil system.

On the BIBO Stability Condition of Adaptive Recursive FLANN Filters With Application to Nonlinear Active Noise Control

Abstract: In this paper, a bounded-input bounded-output (BIBO) stability condition for the recursive functional link artificial neural network (FLANN) filter, based on trigonometric expansions, is derived. This filter is considered as a member of the class of causal shift-invariant recursive nonlinear filters whose output depends linearly on the filter coefficients. As for all recursive filters, its stability should be granted or, at least, tested. The relevant conclusion we derive from the stability condition is that the recursive FLANN filter is not affected by instabilities whenever the recursive linear part of the filter is stable. This fact is in contrast with the case of recursive polynomial filters where, in general, specific limitations on the input range are required. The recursive FLANN filter is then studied in the framework of a feedforward scheme for nonlinear active noise control. The novelty of our study is due to the simultaneous consideration of a nonlinear secondary path and an acoustical feedback between the loudspeaker and the reference microphone. An output error nonlinearly Filtered-U normalized LMS adaptation algorithm, derived for the elements of the above-mentioned class of nonlinear filters, is then applied to the recursive FLANN filter. Computer simulations show that the recursive FLANN filter, in contrast to other filters, is able to simultaneously deal with the acoustical feedback and the nonlinearity in the secondary path.

Automatic removal of ocular artefacts using adaptive filtering and independent component analysis for electroencephalogram data

Abstract: A new method for eye movement artefacts removal based on independent component analysis (ICA) and recursive least squares (RLS) is presented. The proposed algorithm combines the effective ICA capacity of separating artefacts from brain waves, together with the online interference cancellation achieved by adaptive filtering. Eye blink, saccades, eyes opening and closing produce changes of potentials at frontal areas. For this reason, the method uses as a reference the electrodes closest to the eyes Fp1, Fp2, F7 and F8, which register vertical and horizontal eye movements in the electroencephalogram (EEG) caused by these activities as an alternative of using extra dedicated electrooculogram (EOG) electrodes, which could not always be available and could be subject to larger variability. Both reference signals and EEG components are first projected into ICA domain and then the interference is estimated using the RLS algorithm. The component related to EOG artefact is automatically eliminated using channel localisations. Results from experimental data demonstrate that this approach is suitable for eliminating artefacts caused by eye movements, and the principles of this method can be extended to certain other artefacts as well, whenever a correlated reference signal is available.

Performance analysis of the auxiliary model-based least-squares identification algorithm for one-step state-delay systems

Abstract: Based on the input–output representation of one-step state-delay systems, we use the auxiliary model-based recursive least-squares algorithm to estimate the parameters of the systems and study the convergence of the proposed algorithm by using the stochastic process theory. A simulation example is provided.

Localized, Adaptive Recursive Partial Least Squares Regression for Dynamic System Modeling

Abstract: A localized and adaptive recursive partial least squares algorithm (LARPLS), based on the local learning framework, is presented in this paper. The algorithm is used to address, among other issues in the recursive partial least-squares (RPLS) regression algorithm, the “forgetting factor” and sensitivity of variable scaling. Two levels of local adaptation, namely, (1) local model adaptation and (2) local time regions adaptation, and three adaptive strategies, (a) means and variances adaptation, (b) adaptive forgetting factor, and (c) adaptive extraction of local time regions, are provided using the LARPLS algorithm. Compared to RPLS, the LARPLS model is proven to be more adaptive in the face of process change, maintaining superior predictive performance, as demonstrated in the modeling of three different types of processes.

Errata: Recursive least-squares source tracking using one acoustic vector sensor

Abstract: An acoustic vector-sensor (a.k.a. vector-hydrophone) is composed of three acoustic velocity-sensors, plus a collocated pressure-sensor, all collocated in space. The velocity-sensors are identical, but orthogonally oriented, each measuring a different Cartesian component of the three-dimensional particle-velocity field. This acoustic vector-sensor offers an azimuth-elevation response that is invariant with respect to the source's center frequency or bandwidth. This acoustic vector-sensor is adopted here for recursive least-squares (RLS) adaptation, to track a single mobile source, in the absence of any multipath fading and any directional interference. A formula is derived to preset the RLS forgetting factor, based on the prior knowledge of only the incident signal power, the incident source's spatial random walk variance, and the additive noise power. The work presented here further advances a multiple-forgetting-factor (MFF) version of the RLS adaptive tracking algorithm, that requires no prior knowledge of these aforementioned source statistics or noise statistics. Monte Carlo simulations demonstrate the tracking performance and computational load of the proposed algorithms.

BFO optimized RLS algorithm for power system harmonics estimation

Abstract: In this paper a new estimation approach combining both Recursive Least Square (RLS) and Bacterial Foraging Optimization (BFO) is developed for accurate estimation of harmonics in distorted power system signals. The proposed RLS-BFO hybrid technique has been employed for estimating the fundamental as well as harmonic components present in power system voltage/current waveforms. The basic foraging strategy is made adaptive by using RLS that sequentially updates the unknown parameters of the signal. Simulation and experimental studies are included justifying the improvement in performance of this new estimation algorithm.

Real-time estimation of tyre-road friction peak with optimal linear parameterisation

Abstract: Spurred by the problem of identifying, in real-time, the adhesion levels between the tyre and the road, a practical, linear parameterisation (LP) model is proposed to represent the tyre friction. Towards that aim, results from the theory of function approximation, together with optimisation techniques, are explored to approximate the non-linear Burckhardt model with a new LP representation. It is shown that, compared with other approximations described in the literature, the proposed LP model is more efficient, that is, it requires a smaller number of parameters, and provides better approximation capabilities. Next, a modified version of the recursive least squares, subject to a set of equality constraints on parameters, is employed to identify the LP in real time. The inclusion of these constraints, arising from the parametric relationships present when the tyre is in free-rolling mode, reduces the variance of the parametric estimation and improves the convergence of the identification algorithm, particularly in situations with low tyre slips. The simulation results obtained with the full-vehicle CarSim model under different road adhesion conditions demonstrate the effectiveness of the proposed LP and the robustness of the friction peak estimation method. Furthermore, the experimental tests, performed with an electric vehicle under low-grip roads, provide further validation of the accuracy and potential of the estimation technique.

Adaptive Learning of Smoothing Functions: Application to Electricity Load Forecasting

Abstract: This paper proposes an efficient online learning algorithm to track the smoothing functions of Additive Models. The key idea is to combine the linear representation of Additive Models with a Recursive Least Squares (RLS) filter. In order to quickly track changes in the model and put more weight on recent data, the RLS filter uses a forgetting factor which exponentially weights down observations by the order of their arrival. The tracking behaviour is further enhanced by using an adaptive forgetting factor which is updated based on the gradient of the a priori errors. Using results from Lyapunov stability theory, upper bounds for the learning rate are analyzed. The proposed algorithm is applied to 5 years of electricity load data provided by the French utility company Electricite de France (EDF). Compared to state-of-the-art methods, it achieves a superior performance in terms of model tracking and prediction accuracy.

Greedy Sparse RLS

Abstract: Starting from the orthogonal (greedy) least squares method, we build an adaptive algorithm for finding online sparse solutions to linear systems. The algorithm belongs to the exponentially windowed recursive least squares (RLS) family and maintains a partial orthogonal factorization with pivoting of the system matrix. For complexity reasons, the permutations that bring the relevant columns into the first positions are restrained mainly to interchanges between neighbors at each time moment. The storage scheme allows the computation of the exact factorization, implicitly working on indefinitely long vectors. The sparsity level of the solution, i.e., the number of nonzero elements, is estimated using information theoretic criteria, in particular Bayesian information criterion (BIC) and predictive least squares. We present simulations showing that, for identifying sparse time-varying FIR channels, our algorithm is consistently better than previous sparse RLS methods based on the -norm regularization of the RLS criterion. We also use our sparse greedy RLS algorithm for computing linear predictions in a lossless audio coding scheme and obtain better compression than MPEG4 ALS using an RLS-LMS cascade.

A Flexible DG Interface Based on a New RLS Algorithm for Power Quality Improvement

Abstract: Distributed generation (DG) exists in distribution systems and is installed by either the utility or the customers. This paper proposes a novel utilization of the existing DG interface to not only control the active power flow, but also to mitigate unbalance, harmonics and voltage flicker, and manage the reactive power of the system. The proposed flexible distributed generation (FDG) is similar in functionality to FACTS, but works at the distribution level. Moreover, a novel recursive least square (RLS) structure is presented. The new structure is applied to multi-output (MO) systems for parameter tracking/estimation, and is called MO-RLS. It is dedicated to symmetrical components estimation. An innovative processing unit-based RLS is investigated to deal with unbalance, harmonics, and reactive power compensation. In addition, this paper portrays a technique for flicker mitigation based on the RLS algorithm for instantaneous tracking of the measured voltage envelope. One advantage of the proposed control system is its insensitivity to parameter variation, a necessity for distribution system applications. Simulations of the suggested FDG based control algorithm are conducted to evaluate the performance of the proposed system.

PETRELS: Subspace estimation and tracking from partial observations

Abstract: We consider the problem of reconstructing a data stream from a small subset of its entries, where the data stream is assumed to lie in a low-dimensional linear subspace, possibly corrupted by noise. It is also important to track the change of underlying subspace for many applications. This problem can be viewed as a sequential low-rank matrix completion problem in which the subspace is learned in an online fashion. The proposed algorithm, called Parallel Estimation and Tracking by REcursive Least Squares (PETRELS), identifies the underlying low-dimensional subspace via a recursive procedure for each row of the subspace matrix in parallel, and then reconstructs the missing entries via least-squares estimation if required. PETRELS outperforms previous approaches by discounting observations in order to capture long-term behavior of the data stream and be able to adapt to it. Numerical examples are provided for direction-of-arrival estimation and matrix completion, comparing PETRELS with state of the art batch algorithms.

Estimation of the forgetting factor in kernel recursive least squares

Abstract: In a recent work we proposed a kernel recursive least-squares tracker (KRLS-T) algorithm that is capable of tracking in non-stationary environments, thanks to a forgetting mechanism built on a Bayesian framework. In order to guarantee optimal performance its parameters need to be determined, specifically its kernel parameters, regularization and, most importantly in non-stationary environments, its forgetting factor. This is a common difficulty in adaptive filtering techniques and in signal processing algorithms in general. In this paper we demonstrate the equivalence between KRLS-T's recursive tracking solution and Gaussian process (GP) regression with a specific class of spatio-temporal covariance. This result allows to use standard hyperparameter estimation techniques from the Gaussian process framework to determine the parameters of the KRLS-T algorithm. Most notably, it allows to estimate the optimal forgetting factor in a principled manner. We include results on different benchmark data sets that offer interesting new insights.