Algorithms for deterministic balanced subspace identification

New algorithms for identification of a balanced state space representation are proposed. They are based on a procedure for the estimation of impulse response and sequential zero input responses directly from data. The proposed algorithms are more efficient than the existing alternatives that compute the whole Hankel matrix of Markov parameters. It is shown that the computations can be performed on Hankel matrices of the input–output data of various dimensions. By choosing wider matrices, we need persistency of excitation of smaller order. Moreover, this leads to computational savings and improved statistical accuracy when the data is noisy. Using a finite amount of input–output data, the existing algorithms compute finite time balanced representation and the identified models have a lower bound on the distance to an exact balanced representation. The proposed algorithm can approximate arbitrarily closely an exact balanced representation. Moreover, the finite time balancing parameter can be selected automatically by monitoring the decay of the impulse response. We show what is the optimal in terms of minimal identifiability condition partition of the data into “past” and “future”

Transfer function estimation using time-frequency analysis

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1998.Includes bibliographical references (p. 135-136).Given limited and noisy data, identifying the transfer function of a complex aerospace system may prove difficult. In order to obtain a clean transfer function estimate despite noisy data, a time-frequency analysis approach to system identification has been developed. The method is based on the observation that for a linear system, an input at a given frequency should result in a response at the same frequency, and a time localized frequency input should result in a response that is nearby in time to the input. Using these principles, the noise in the response can be separated from the physical dynamics. In addition, the impulse response of the system can be restricted to be causal and of limited duration, thereby reducing the number of degrees of freedom in the estimation problem. The estimation method consists of finding a rough estimate of the impulse response from the sampled input and output data. The impulse response estimate is then transformed to a two dimensional time-frequency mapping. The mapping provides a clear graphical method for distinguishing the noise from the system dynamics. The information believed to correspond to noise is discarded and a cleaner estimate of the impulse response is obtained from the remaining information. The new impulse response estimate is then used to obtain the transfer function estimate. The results indicate that the time-frequency transfer function estimation method can provide estimates that are often less noisy than those obtained from other methods such as the Empirical Transfer Function Estimate and Welch's Averaged Periodogram Method.by Corinne Rachel Ilvedson.S.M

Optimal orientation estimators for detection of cylindrical objects

International audienceThis paper introduces low level operators in the context of detecting cylindrical axis in 3 D images. Knowing the axis of a cylinder is particularly useful since cylinder location, length and curvature derive from this knowledge. This paper introduces a new gradient-based optimal operator dedicated to accurate estimation of the direction toward the axis. The operator relies on Finite Impulse Response filters. The approach is presented first in a 2-D context, thus providing optimal gradient masks for locating the center of circular objects. Then, a 3-D extension is provided, allowing the exact estimation of the orientation toward the axis of cylindrical objects when this axis coincides with one of the mask reference axes. Applied to more general cylinders and to noisy data, the operator still provides accurate estimation and outperforms classical gradient operators

Maximum Likelihood Estimation in Data-Driven Modeling and Control

Recently, various algorithms for data-driven simulation and control have been proposed based on the Willems' fundamental lemma. However, when collected data are noisy, these methods lead to ill-conditioned data-driven model structures. In this work, we present a maximum likelihood framework to obtain an optimal data-driven model, the signal matrix model, in the presence of output noise. Data compression and noise level estimation schemes are also proposed to apply the algorithm efficiently to large datasets and unknown noise level scenarios. Two approaches in system identification and receding horizon control are developed based on the derived optimal estimator. The first one identifies a finite impulse response model. This approach improves the least-squares estimator with less restrictive assumptions. The second one applies the signal matrix model as the predictor in predictive control. The control performance is shown to be better than existing data-driven predictive control algorithms, especially under high noise levels. Both approaches demonstrate that the derived estimator provides a promising framework to apply data-driven algorithms to noisy data

Kernel-based system identification from noisy and incomplete input-output data

In this contribution, we propose a kernel-based method for the identification of linear systems from noisy and incomplete input-output datasets. We model the impulse response of the system as a Gaussian process whose covariance matrix is given by the recently introduced stable spline kernel. We adopt an empirical Bayes approach to estimate the posterior distribution of the impulse response given the data. The noiseless and missing data samples, together with the kernel hyperparameters, are estimated maximizing the joint marginal likelihood of the input and output measurements. To compute the marginal-likelihood maximizer, we build a solution scheme based on the Expectation-Maximization method. Simulations on a benchmark dataset show the effectiveness of the method.Comment: 16 pages, submitted to IEEE Conference on Decision and Control 201

Blind MultiChannel Identification and Equalization for Dereverberation and Noise Reduction based on Convolutive Transfer Function

This paper addresses the problems of blind channel identification and multichannel equalization for speech dereverberation and noise reduction. The time-domain cross-relation method is not suitable for blind room impulse response identification, due to the near-common zeros of the long impulse responses. We extend the cross-relation method to the short-time Fourier transform (STFT) domain, in which the time-domain impulse responses are approximately represented by the convolutive transfer functions (CTFs) with much less coefficients. The CTFs suffer from the common zeros caused by the oversampled STFT. We propose to identify CTFs based on the STFT with the oversampled signals and the critical sampled CTFs, which is a good compromise between the frequency aliasing of the signals and the common zeros problem of CTFs. In addition, a normalization of the CTFs is proposed to remove the gain ambiguity across sub-bands. In the STFT domain, the identified CTFs is used for multichannel equalization, in which the sparsity of speech signals is exploited. We propose to perform inverse filtering by minimizing the $\ell_1$-norm of the source signal with the relaxed $\ell_2$-norm fitting error between the micophone signals and the convolution of the estimated source signal and the CTFs used as a constraint. This method is advantageous in that the noise can be reduced by relaxing the $\ell_2$-norm to a tolerance corresponding to the noise power, and the tolerance can be automatically set. The experiments confirm the efficiency of the proposed method even under conditions with high reverberation levels and intense noise.Comment: 13 pages, 5 figures, 5 table

Reverberation time estimation on the ACE corpus using the SDD method

Reverberation Time (T60) is an important measure for characterizing the properties of a room. The author's T60 estimation algorithm was previously tested on simulated data where the noise is artificially added to the speech after convolution with a impulse responses simulated using the image method. We test the algorithm on speech convolved with real recorded impulse responses and noise from the same rooms from the Acoustic Characterization of Environments (ACE) corpus and achieve results comparable results to those using simulated data.Comment: In Proceedings of the ACE Challenge Workshop - a satellite event of IEEE-WASPAA 2015 (arXiv:1510.00383