Identification Of Impulse Responses Research Articles

A Fourth-Order Tensorial Wiener Filter Using the Conjugate Gradient Method

The recently developed iterative Wiener filter using a fourth-order tensorial (FOT) decomposition owns appealing performance in the identification of long length impulse responses. It relies on the nearest Kronecker product representation (with particular intrinsic symmetry features), together with low-rank approximations. Nevertheless, this new iterative filter requires matrix inversion operations when solving the Wiener–Hopf equations associated with the component filters. In this communication, we propose a computationally efficient version that relies on the conjugate gradient (CG) method for solving these sets of equations. The proposed solution involves a specific initialization of the component filters and sequential connections between the CG cycles. Different FOT-based decomposition setups are also analyzed from the point of view of the resulting parameter space. Experimental results obtained in the context of echo cancellation confirm the good behavior of the proposed approach and its superiority in comparison to the conventional Wiener filter and other decomposition-based versions.

Identification of Impulse Responses in Heat Transfer: Parameterization, Doses, Partial Time Moments

Convolutive models, linking a local or average temperature to a thermal excitation in transient regime are as good as analytical or numerical solutions of the heat equation and of its associated boundary conditions, provided that the corresponding equations are linear with coefficients that do not depend on time, but with possible dependence on the space dimensions. These convolutive models are based on an impulse response function which can be identified, using measurements of input and output signals, together with some kind of regularization because of the ill-posed character of this inverse problem. Here, another exploratory approach is tested. It is based i) on a parameterization of the three functions involved by projection onto a Dirac comb basis to get a vector/matrix form of the convolution model derived in terms of doses, ii) on an alternate model based on an exact analytical relationship between the time moments of these functions and iii) on the different ways to use this last model in an inversion procedure using the parsimony principle. This is applied to a heat transfer configuration of one-dimensional heat diffusion in a slab, where conclusions and perspectives are drawn for this type of dosal-moment model.

Heat transient processes identification of the elements of internal environment system

Introduction. The study of heat exchange transients in the climate system “Heater-Ventilator-Room”, when ventilator capacity varies step-wise, is presented. The construction of functional relations between inputs and outputs of the system is the object of special attention. This allows for a non-parametric identification of impulse responses in the system for simulation and control. Materials and methods. The climate system is represented by a combination of several different-type elements with step inputs and experimental data as outputs. Mathematical models of the elements are governed by Volterra integral equation of the 2nd kind. Solution of this equation is an ill-posed problem, and specifics of identification experiments do not allow applying computational methods of classical regularization algorithms. A non-parametric identification of impulse responses for the elements is performed by the authors’ stable algorithm with due regard for real technical systems specifics. The algorithm is founded on stable differentiation by smoothing cubic splines with optimal smoothing parameter estimation and special type boundary conditions. Results. Non-parametric identification algorithm is adapted for the investigated climate system. The inverse problems of impulse responses identification and the direct problems of heat flux reactions prediction are solved. A high convergence of theoretical and experimental data is shown. Conclusions. The behavior of the transients is predictable for the climate system under the particular operation mode. The algorithm proposed takes proper account of practical problems specifics. The results obtained suggest the efficiency of the algorithm for applied identification problems solutions in real complex technical systems.

Identification of Room Acoustic Impulse Responses via Kronecker Product Decompositions

The identification of room acoustic impulse responses represents a challenging problem in the framework of many important applications related to the acoustic environment, like echo cancellation, noise reduction, and microphone arrays, among others. In this context, the main issues are related to the long length of such impulse responses and their time-variant nature. These raise significant difficulties in terms of the convergence rate, computational complexity, and accuracy of the solution. Recently, a decomposition-based approach was developed for the identification of low-rank systems, which can also be applied (to some extent) for the identification of acoustic impulse responses. This approach exploits the nearest Kronecker product decomposition of the impulse response and solves a high-dimension system identification problem using a combination of low-dimension solutions (provided by shorter filters), thus gaining in terms of both performance and complexity. Nevertheless, it does not consider the intrinsic nature of the room acoustic impulse responses, which contain specific components (e.g., early reflections and late reverberation) that can be very different in nature. In this paper, we propose an improved decomposition-based method (via the Kronecker product) that takes into account these specific components and processes them separately, in order to better exploit their important low-rank features. Following this approach, an iterative Wiener filter is firstly developed, followed by a recursive least-squares (RLS) algorithm designed in the same framework. Both solutions outperform the conventional benchmarks, i.e., the conventional Wiener filter and the RLS algorithm, respectively. Moreover, they achieve superior performances as compared to the recently developed versions based on the nearest Kronecker product decomposition, also owning lower computational complexities than their previous counterparts. Simulations are performed in the framework of acoustic echo cancellation and the obtained results support the performance features of the proposed algorithms.

Correction to: A novel cost-effective sparsity-aware algorithm with Kalman-based gain for the identification of long acoustic impulse responses

Correction to: A novel cost-effective sparsity-aware algorithm with Kalman-based gain for the identification of long acoustic impulse responses

A novel cost-effective sparsity-aware algorithm with Kalman-based gain for the identification of long acoustic impulse responses

In this paper, a new robust sparsity (or sparseness)-aware adaptive filtering algorithm is proposed for the purpose of system identification and acoustic echo cancelation. It is named the improved proportionate fast normalized least mean square (IPFNLMS) algorithm. This latter has been derived by an effective integration of the update control matrix of the improved proportionate NLMS (IPNLMS) algorithm to the Kalman-based adaptation gain of the fast-NLMS (FNLMS) algorithm. Simulations were carried out both in synthetic and real long acoustic impulse responses at different sparseness levels with stationary and non-stationary inputs, followed by a verification with real experiment data. Results have shown interesting improvements for the proposed algorithm with respect to its ancestors in terms of convergence speed, steady-state performance, tracking capability and robustness against system sparsity variation.

Measurement and Adaptive Identification of Nonstationary Acoustic Impulse Responses

In this work, we present a method of measurement of nonstationary acoustic impulse responses identified by the fast version of the Recursive Least Squares algorithm (FRLS), using professional acoustic equipment. This measurement bench realized in a deaf room presents several tests of capability of adaptive algorithm to tracking the nonstationarities of true system to be identified. The tests of tracking capability obtained are stronger compared to what is encountered in real life and can be used in several applications.

Recursive Least-Squares Algorithms for the Identification of Low-Rank Systems

The recursive least-squares (RLS) adaptive filter is an appealing choice in many system identification problems. The main reason behind its popularity is its fast convergence rate. However, this algorithm is computationally very complex, which may make it useless for the identification of long length impulse responses, like in echo cancellation. Computationally efficient versions of the RLS algorithm, like those based on the dichotomous coordinate descent (DCD) iterations or QR decomposition techniques, reduce the complexity, but still have to face the challenges related to long length adaptive filters (e.g., convergence/tracking capabilities). In this paper, we focus on a different approach to improve the efficiency of the RLS algorithm. The basic idea is to exploit the impulse response decomposition based on the nearest Kronecker product and low-rank approximation. In other words, a high-dimension system identification problem is reformulated in terms of low-dimension problems, which are combined together. This approach was recently addressed in terms of the Wiener filter, showing appealing features for the identification of low-rank systems, like real-world echo paths. In this paper, besides the development of the RLS algorithm based on this approach, we also propose a variable regularized version of this algorithm (using the DCD method to reduce the complexity), with improved robustness to double-talk. Simulations are performed in the context of echo cancellation and the results indicate the good performance of these algorithms.

Linear System Identification Based on a Kronecker Product Decomposition

Linear system identification is a key problem in many important applications, among which echo cancelation is a very challenging one. Due to the long length impulse responses (i.e., echo paths) to be identified, there is always room (and needs) to improve the performance of the echo cancelers, especially in terms of complexity, convergence rate, robustness, and accuracy. In this paper, we propose a new way to address the system identification problem (from the echo cancelation perspective), by exploiting an optimal approximation of the impulse response based on the nearest Kronecker product decomposition. Also, we make a first step toward this direction, by developing an iterative Wiener filter based on this approach. As compared to the conventional Wiener filter, the proposed solution is much more attractive since its gain is twofold. First, the matrices to be inverted (or, preferably, linear systems to be solved) are smaller as compared to the conventional approach. Second, as a consequence, the iterative Wiener filter leads to a good estimate of the impulse response, even when a small amount of data is available for the estimation of the statistics. Simulation results support the theoretical findings and indicate the good results of the proposed approach, for the identification of different network and acoustic impulse responses.

Transient and steady-state MSE analysis of the IMPNLMS algorithm

Several techniques have been proposed in the literature to accelerate the convergence of adaptive algorithms for the identification of sparse impulse responses (i.e., with energy concentrated in a few coefficients). Among these techniques, the improved μ-law proportionate normalized least mean squares (IMPNLMS) algorithm is one of the most effective. This paper presents an accurate transient analysis of this algorithm and derives an estimate of its steady-state MSE, without requiring the assumption of white Gaussian input signals.

THE PRICE PUZZLE AND VAR IDENTIFICATION

In structural VARs, unexpected monetary tightening often leads to the price puzzle, a counterintuitive increase in inflation in the impulse response function. The identification of impulse responses requires at least a minimal set of structural assumptions, and models exhibiting the price puzzle typically use standard assumptions focusing mainly on relationships among contemporaneous disturbances. This note uses a well-established stylized fact, the long lags of monetary policy, to motivate a simple additional identifying assumption. The assumption eliminates a single term in one equation of the reduced form, and with it the price puzzle.

Identification of sparse impulse responses – design and implementation using the partial Haar block wavelet transform

This paper proposes an implementation for identifying sparse impulse responses. The new scheme follows the approach in which the location of the channel response peak is estimated in the wavelet domain. A short time-domain adaptive filter is then located about the estimated peak to identify the sparse response. The primary purpose of this paper is to present an efficient design of such a system. The use of a new block wavelet transform results in up to 70% less computational complexity and improved peak detection, as compared to previous solutions. A new robust time-domain adaptive filtering location and update scheme is also proposed that significantly reduces the occurrence of jitter problems and leads to improved residual mean-square error performance. The behavior of the transform-domain adaptive filter is analyzed, the Wiener solution is determined, and an accurate analytical model is obtained for the mean-square deviation of the adaptive coefficients. Monte Carlo simulations show excellent echo cancellation performance for typical ITU-T echo channels.

Mean-square error and stability analysis of a subband structure for the rapid identification of sparse impulse responses

In a context of supervised adaptive filtering, the sparsity of the impulse response to be identified can be employed to accelerate the convergence rate of the algorithm. This idea was first explored by the so-called proportionate NLMS (PNLMS) algorithm, where the adaptation step-sizes are made larger for the coefficients with larger magnitudes. Whereas fast initial adaptation convergence rate is obtained with the PNLMS algorithm for white-noise input, slow convergence is observed for colored input signals. The combination of the PNLMS approach and a subband structure results in an algorithm with better convergence rate for sparse systems and colored input signals. In this paper, the steady-state mean-square error (MSE) and the maximum value of the step-size @b that allows convergence of the subband PNLMS-type algorithm are analyzed. Theoretical results are confirmed by simulations.

Sufficiently Informative Excitation for Estimation of Linear Responses Due to Sparse Scattering

In this paper, we are concerned with the identification of linear systems' impulse responses modeled as deterministic multipath channels. In the class of channels we study, we consider the effect of delays, Doppler shifts, and different angles of arrival and departure for each signal path. We explore the efficacy of techniques based on sparse signal recovery, which typically define a basis constructed using a finite quantization grid over the parameter space, and approximate the impulse response as a sparse linear combination over such basis. Our goal is to provide guidelines on the design of pilot sequences that are sufficiently informative (SI), i.e., those inputs that guarantee identifiability of system impulse responses that fit in the sparse model. Inputs that are SI provide minimal requirements for uniquely identifying the system response. However, a smaller class of inputs leads to good mean squared estimation error in the presence of noise and modeling errors, due to the finite precision of the parameter space quantization. To single out the class of robust designs, we provide a new metric, called localized coherence, in lieu of the so called mutual coherence, as a measure for ranking SI designs in terms of robustness to noise and to modeling errors.

Sparse Adaptive Filters for Echo Cancellation

Abstract Adaptive filters with a large number of coefficients are usually involved in both network and acoustic echo cancellation. Consequently, it is important to improve the convergence rate and tracking of the conventional algorithms used for these applications. This can be achieved by exploiting the sparseness character of the echo paths. Identification of sparse impulse responses was addressed mainly in the last decade with the development of the so-called ``proportionate''-type algorithms. The goal of this book is to present the most important sparse adaptive filters developed for echo cancellation. Besides a comprehensive review of the basic proportionate-type algorithms, we also present some of the latest developments in the field and propose some new solutions for further performance improvement, e.g., variable step-size versions and novel proportionate-type affine projection algorithms. An experimental study is also provided in order to compare many sparse adaptive filters in different echo canc...

Identification of Experimental Unsteady Aerodynamic ImpulseResponses

The identification of experimental unsteady aerodynamic impulse responses using the Oscillating Turntable (OTT) at NASA Langley's Transonic Dynamics Tunnel (TDT) is described. Results are presented for two configurations: a Rigid Semispan Model (RSM) and a rectangular wing with a supercritical airfoil section. Both models were used to acquire unsteady pressure data due to pitching oscillations on the OTT. A deconvolution scheme involving a step input in pitch and the resultant step response in pressure, for several pressure transducers, is used to identify the pressure impulse responses. The identified impulse responses are then used to predict the pressure response due to pitching oscillations at several frequencies. Comparisons with the experimental data are presented.

Improvement of the convergence speed and the tracking ability of the fast Newton type adaptive filtering (FNTF) algorithm

In this paper, five new versions of the fast Newton type adaptive filtering (FNTF) algorithm are presented. A brief preliminary presentation of these algorithms was given in Djendi et al. [Comparative study of new version of the Newton type adaptive filtering algorithm, in: Proceedings of the IEEE ICASSP 2004, Montreal, Canada, May 2004, pp. 677–680]. The first algorithm is based on a simple modification of the filtering part, by introducing a scalar accelerator parameter. The second algorithm is based on the use of the temporal subdivision technique to update the local filter coefficients. The third algorithm is a modification of the second one, by the use of the final filtering errors to update the filter coefficients. The fourth and the fifth algorithms are based, respectively, on the combination of features from the first algorithm with features of the second and third algorithms. These new algorithms are proposed to improve the convergence speed of the original version of the FNTF algorithm for the identification of acoustic impulse responses, and also to improve the tracking ability when the systems vary in time. A comparative study of each algorithm with the original version of the FNTF algorithm is also presented.

Identification of Nonlinear Aeroelastic Systems Based on the Volterra Theory: Progress and Opportunities

The identification of nonlinear aeroelastic systems based on the Volterra theory of nonlinear systems is presented. Recent applications of the theory to problems in computational and experimental aeroelasticity are reviewed. Computational results include the development of computationally efficient reduced-order models (ROMs) using an Euler/Navier–Stokes flow solver and the analytical derivation of Volterra kernels for a nonlinear aeroelastic system. Experimental results include the identification of aerodynamic impulse responses, the application of higher-order spectra (HOS) to wind-tunnel flutter data, and the identification of nonlinear aeroelastic phenomena from flight flutter test data of the active aeroelastic wing (AAW) aircraft.

Structural Analysis of Cointegrating VARs

This survey uses a number of recent developments in the analysis of cointegrating Vector Autoregressions (VARs) to examine their links to the older structural modelling traditions using Autoregressive Distributed Lag (ARDL), and Simultaneous Equations Models (SEMs). In particular, it emphasizes the importance of using judgement and economic theory to supplement the statistical information. After a brief historical review it sets out the statistical framework, discusses the identification of impulse responses using the Generalized Impulse Response functions, reviews the analysis of cointegrating VARs and highlights the large number of choices applied workers have to make in determining a specification. In particular, it considers the problem of specification of intercepts and trends and the size of the VAR in more detail, and examines the advantages of the use of exogenous variables in cointegration analysis. The issues are illustrated with a small U.S. Macroeconomic model.

Estimating the effects of monetary shocks: An evaluation of different approaches

This paper compares several methods for estimating the effects of monetary innovations on key macroeconomic variables and, subsequently, clarifies issues related to the use of instrumental variables in the identification of structural impulse responses. In particular, we make explicit the property that a measure of monetary policy must satisfy in order to identify the effects of monetary shocks. Within our framework we find that none of the currently popular methods of identifying the effects of monetary shocks are supported by the data. We also indicate how current approaches can be combined to provide unbiased estimates of the effects of monetary disturbances.