Model Order Estimation Research Articles

A Variable Regularized Recursive Subspace Model Identification Algorithm With Extended Instrumental Variable and Variable Forgetting Factor

This paper proposes a new smoothly clipped absolute deviation (SCAD) regularized recursive subspace model identification algorithm with square root(SR) extended instrumental variable (EIV) and locally optimal variable forgetting factor (LOFF). The proposed algorithm is based on a new local polynomial modeling (LPM)-based variable FF EIV projection approximation subspace tracking (PAST) and multivariate recursive least squares algorithms for estimating respectively the subspace of the extended observability matrix, and the input matrix and feedthrough matrix. The SREIV-PAST algorithm offers improved resilience to additive noise over the PAST algorithm and it is implemented using the more stable square-root form. The asymptotic mean square error of the corresponding LPM-based model is derived and minimized at each time instant to obtain the proposed LOFF for improving the convergence speed and steady state error. A recursive bi-iteration singular value decomposition (SVD) algorithm is also proposed for recursive computation of the pseudo-inverse of the state transition matrix and its eigenvalues. This facilitates online estimation of its model order using classical model selection criteria. Moreover, a new criterion based on the percentage of explained variance is also proposed with improved performance. The SCAD regularization is proposed for automatic model selection of the input and feedthrough matrices, as it is asymptotically unbiased. Efficient techniques for incorporating SCAD and estimating other required quantities are also developed. The proposed algorithms are evaluated using computer simulations under stationary and nonstationary environments and a real dataset on wing flutter data. Results show that the proposed algorithms offer improved convergence speed and steady state performance over the conventional algorithms and it also provides an online estimate of the system model order.

Frequency-Hopped Signal Source Identification in Frequency-Selective Channels

Blind source separation of frequency-hopped signals is a challenging problem for cases involving multipath exhibiting temporal and angular spread. A novel solution is proposed that exploits polarization-frequency correlation to separate signals, enabling association of hopped signal in these adverse conditions. Performance depends upon signal-to-noise ratios and channel-induced signal feature differences. The method has the advantage of not requiring model order estimation of multipath. The efficacy of the approach is demonstrated in experiments and numerical analyses.

An algorithm for discovery and determination of exponentially decaying components in nuclear magnetic resonance relaxometry data.

In many branches of physics, the time evolution of various quantities measured in systems passing from excited to equilibrium states, while theoretically very complex, can be in practice well approximated by a sum of exponential decays. Multiexponential relaxometry data analysis is about determining the number of exponential components and their corresponding amplitudes and decay rates, starting from noisy recorded time series, under the assumption of the discreteness of the number of components present. A technique for decomposing a signal modelled as a sum of exponential decays into its components is introduced, consisting of a modified version of the algorithm minimum description length (MDL)+matrix pencil, originally proposed by Lin et al. for the analysis of nuclear magnetic resonance spectroscopy data. The procedure starts by denoising the discrete time-domain signal, and then a number of different decimations are applied, each being followed by an MDL+matrix pencil detection-estimation step, and finally, a postprocessing of the intermediate outcomes is done. The comprised model order estimator eliminates the need of providing prior estimates of the number of components present.

Model order estimation methods for low frequency oscillations in power systems

Estimation of low frequency oscillation modes is important for taking remedial actions to ensure the small signal stability of the power system. This paper proposes three approaches to estimate the model order of low frequency oscillations using ringdown data from Phasor Measurement Units. The first approach uses a sequential cumulative sum test on the eigenvalues of the autocorrelation matrix of the signal data to estimate the model order. The second approach estimates the model order based on the eigenvalue contribution in the trace of the autocorrelation matrix. The third algorithm uses sum of squares of the eigenvalues to estimate the model order. All the methods are compared to ascertain their efficacy in estimating the model. The algorithms are tested on oscillation data obtained for WSCC 9 bus system simulated on RTDS and the field data from a generating station in India.

Simultaneous Model Order and Parameter Estimation (SMOPE) based on Random Asynchronous Particle Swarm Optimization


 
 
 
 Simultaneous model order and parameter estimation (SMOPE) is a metaheuristic based system identification method. SMOPE was introduced using particle swarm optimization (PSO). There are several iteration strategies for PSO. The original work on SMOPE is based on synchronous PSO (S-PSO). However, in some works PSO using other iteration strategy is found to give better results. In this work, based on six system identification problems random asynchronous (RA-PSO) based SMOPE is found to have slight advantage over S-PSO.
 
 
 

MUSIC-Like Algorithm for Source Localization in Electrical Impedance Tomography

In electrical impedance tomography (EIT), the noise amplified solution caused during matrix inversion can be avoided with nonparametric spectral-based estimation when the conductivity variation is bounded and spatially sparse. Among many spectral-based algorithms used in direction-of-arrival estimation, an algorithm called multiple signal classification (MUSIC) is one of the most well-known algorithms that has super resolution performance. However, its dependence on the model-order estimation can lead to performance degradation, especially for quasi-static environment, such as EIT application, and this is due to source location changes and conductivity variation. In this paper, the relationship between source position, conductivity variation, ill-conditioned array manifold, and eigenvalues of the covariance matrix are explored. An algorithm called MUSIC-like, which has high resolution performance comparable to MUSIC, is then proposed for EIT application. It is formulated under the beamforming framework and, therefore, does not require an estimation of model order from the covariance matrix. Simulation results show that the proposed method is capable of obtaining high resolution performance under various noise levels. An 8-electrode EIT system prototype was built using the proposed method, and experimental results confirm the high resolution performance capability of the proposed method.

Efficient and Accurate Detection and Frequency Estimation of Multiple Sinusoids

The method for detection of complex sinusoids in additive white Gaussian noise and estimation of their frequencies is proposed. It contains two stages: 1) sinusoid detection (model order estimation) and coarse frequency estimation, and 2) fine frequency estimation. The proposed method operates in the frequency domain, i.e., it uses the discrete Fourier transform (DFT) as the main tool. Sinusoid detection is performed so that a fixed probability of false alarm is provided (Neymann–Pearson criterion). For both coarse and fine frequency estimations, the three-point periodogram maximization approach is used. Simulations are carried out for variable signal-to-noise ratio, variable frequency displacement between the sinusoids and variable offset from the frequency grid. The proposed method meets the Cramer-Rao lower bound in frequency estimation and practically does not depend on the frequency displacement except for very small displacement values. In terms of model order estimation accuracy, it outperforms the state-of-the-art approaches. The most expensive operation in the method is the calculation of the DFT. Therefore, in terms of calculation complexity, the proposed method is on par with the most efficient algorithms for multiple frequency estimations.

Structural Deterioration Detection Using Enhanced Autoregressive Residuals

This paper presents a study on detecting structural deterioration in existing buildings using ambient vibration measurements. Deterioration is a slow and progressive process which reduces the structural performance, including load-bearing capacity. Each building has unique vibration characteristics which change in time due to deterioration and damage. However, the changes due to deterioration are generally subtler than the changes due to damage. Examples of deterioration include subtle loss of steel-concrete bond strength, slight corrosion of reinforcement and onset of internal cracks in structural members. Whereas damage can be defined as major sudden structural changes, such as major external cracks of concrete covers. Herein, a deterioration detection method which uses structural health monitoring (SHM) data is proposed to address the deterioration assessment problem. The proposed novel vibration-based deterioration identification method is a parametric-based approach, incorporated with a nonparametric statistical test, to capture changes in the dynamic characteristics of structures. First, autoregressive (AR) time-series models are fitted to the vibration response time histories at different sensor locations. A sensitive deterioration feature is proposed for detecting deterioration by applying statistical hypotheses of two-sample [Formula: see text]-test on the model residuals, based on which a function of the resulting [Formula: see text]-values is calculated. A novel AR model order estimation procedure is proposed to enhance the sensitivity of the method. The performance of the proposed method is demonstrated through comprehensive simulations of deterioration at single and multiple locations in finite element models (FEM) of 3- and 20-storey reinforced concrete (RC) frames. The method shows a promising sensitivity to detect small levels of structural deterioration prior to damage, even in the presence of noise.

Frequency, Damping, and Flutter Prediction from Aircraft Flight Data Using Autoregressive Model

Demonstration of flutter stability over the design envelope and identification of a safe flight envelope is a prerequisite for operational clearance of any new aircraft design. Generally, in all the flight flutter-testing programs, frequency and modal damping ratios are estimated at each flight-test point, and the trend of variation of frequency and damping is established. Frequencies and damping value estimations have to be as accurate as possible to define the aircraft flutter margin at each test point. In this study, stability parameters are estimated directly from the flight flutter-test time response data using an autoregressive (AR) model, which in turn is used to estimate the frequency and damping. In this paper, the focus is on determining an optimized AR model to ensure the accuracy of the model so that the estimation of stability parameters as well as frequency and damping parameters will be more accurate. Toward that, model order estimation techniques such as Akaike’s information criteria and final prediction error were used to predict the model order efficiently. Studies have been presented for different data lengths to prove the capability of this method to produce an accurate spectral estimate even with short data records. This will enable a quick evaluation of spectral estimate and flutter stability parameter using the same AR model, facilitating a quick flight envelope expansion.

Multistatic passive detection with parametric modeling of the IO waveform

This paper examines the target detection problem for a passive multistatic radar employing illuminators of opportunity (IOs), where the receivers are contaminated by non-negligible noise and direct-path interference (DPI). A parametric approach is proposed by modeling the unknown signal transmitted from the IO as an auto-regressive (AR) process whose temporal correlation is jointly estimated and exploited for passive detection. The proposed solution is developed based on the generalized likelihood ratio test principle, which involves non-linear estimation that is solved by using the expectation-maximization (EM) algorithm. We also discuss the initialization of the EM algorithm and the joint adaptive model order estimation for the AR process without using any training signal. In addition, we extend several conventional passive detectors, which were introduced by assuming no DPI is present, to provide them with an ability to handle the DPI problem. A clairvoyant matched filtering (MF) detector is derived as well assuming the knowledge of the IO waveform. Extensive simulation results are presented, using simulated waveforms whose temporal correlation can be easily controlled, as well as practical IO waveforms transmitted by frequency modulation (FM) radio. The results show that the proposed EM-based passive detector outperforms conventional passive detectors due to the exploitation of the waveform correlation.

A Multitarget Active Backscattering 2-D Positioning System With Superresolution Time Series Post-Processing Technique

An active backscattering 2-D positioning system is studied and demonstrated in this paper. The hardware is based on an investigated principle of switched injection phase locking for wireless ranging. A new post-processing technique and a system modeling for multitarget time-of-arrival (TOA) and direction-of-arrival (DOA) estimations are proposed and studied. The technique features a joint singular value decomposition-based ESPRIT algorithm and a matrix diagonalization technique using Moore–Penrose pseudoinverse for model order estimation as well as the TOA/DOA extraction. They make use of the shift invariant property of a backscattered signal in the time-domain. The accuracy and resolution are studied and are shown to be superior to those of the conventional frequency-domain technique using a fast Fourier transform (FFT). Moreover, the proposed algorithms take full advantage of the chirp bandwidth and allow all the targets to operate at the same modulation frequency and arbitrary carrier frequency. These merits avoid a commonly exercised compromise of the FFT method among the resolution, target quantity, signal-to-noise ratio, and other critical specifications. The system is simulated, and the demonstrator is constructed for experimental verifications in both indoor and outdoor environments, with a bandwidth of 600 MHz centered at 5.6 GHz.

Group-sparse regression using the covariance fitting criterion

In this work, we present a novel formulation for efficient estimation of group-sparse regression problems. By relaxing a covariance fitting criteria commonly used in array signal processing, we derive a generalization of the recent SPICE method for grouped variables. Such a formulation circumvents cumbersome model order estimation, while being inherently hyperparameter-free. We derive an implementation which iteratively decomposes into a series of convex optimization problems, each being solvable in closed-form. Furthermore, we show the connection between the proposed estimator and the class of LASSO-type estimators, where a dictionary-dependent regularization level is inherently set by the covariance fitting criteria. We also show how the proposed estimator may be used to form group-sparse estimates for sparse groups, as well as validating its robustness against coherency in the dictionary, i.e., the case of overlapping dictionary groups. Numerical results show preferable estimation performance, on par with a group-LASSO bestowed with oracle regularization, and well exceeding comparable greedy estimation methods.

Adaptive design of experiments for model order estimation in subspace identification

The first step in subspace methods for identification of multivariable systems is the estimation of the order of the model to be identified. Model order estimation is especially difficult for ill-conditioned systems. In previous work we showed heuristically that appropriately designed experiments with rotated PRBS inputs greatly facilitate model order estimation, hence overall model accuracy. However, design of such experiments depends on the very system to be identified. To overcome that difficulty, in this paper we propose an adaptive design of experiments. The proposed approach follows rigorous justification of the need for rotated PRBS inputs, and is tested through computer simulations on two case studies involving a high-purity distillation column and a fluidized catalytic cracking unit. Comparisons of the approach to open- and closed-loop alternatives are presented, and suggestions for further development are made.

Variational Bayesian Inference of Line Spectra

In this paper, we address the fundamental problem of line spectral estimation in a Bayesian framework. We target model order and parameter estimation via variational inference in a probabilistic model in which the frequencies are continuous-valued, i.e., not restricted to a grid; and the coefficients are governed by a Bernoulli-Gaussian prior model turning model order selection into binary sequence detection. Unlike earlier works which retain only point estimates of the frequencies, we undertake a more complete Bayesian treatment by estimating the posterior probability density functions (pdfs) of the frequencies and computing expectations over them. Thus, we additionally capture and operate with the uncertainty of the frequency estimates. Aiming to maximize the model evidence, variational optimization provides analytic approximations of the posterior pdfs and also gives estimates of the additional parameters. We propose an accurate representation of the pdfs of the frequencies by mixtures of von Mises pdfs, which yields closed-form expectations. We define the algorithm VALSE in which the estimates of the pdfs and parameters are iteratively updated. VALSE is a gridless, convergent method, does not require parameter tuning, can easily include prior knowledge about the frequencies and provides approximate posterior pdfs based on which the uncertainty in line spectral estimation can be quantified. Simulation results show that accounting for the uncertainty of frequency estimates, rather than computing just point estimates, significantly improves the performance. The performance of VALSE is superior to that of state-of-the-art methods and closely approaches the Cram\'er-Rao bound computed for the true model order.

Combining Antenna Array Elements by Using ICA Method for Remote Sensing of Sources

This letter deals with the problem of determining the number of RF sources faced by wireless communication systems. In presence of several sources, it is unavoidable to have signal superposition, loss of tracking, and degrading (ambiguous) estimation. Moreover, the well-known subspace-based methods for tracking and estimating sources require prior knowledge of the number of sources. It is shown here that the independent component analysis (ICA) method can be used not only to determine the number of sources, but also to increase the number of sensors (measures) by combining the array elements. The results also show that narrowband sources having a very small frequency difference $(\mathbf{\Delta F} = \mathbf{0.41}\%)$ are detected. The ICA ability of blind sources separation makes it suitable to determine the number of unknown sources, which is crucial in subspace-based techniques. For instance, the ICA can be used as preprocessing model order estimation in direction of arrival algorithms for smart antenna systems.

Short‐term wind speed forecasting using wavelet transformation and AdaBoosting neural networks in Yunnan wind farm

Wind speed presents a potential seasonal pattern revealed by the self-similarity in wavelet periodogram with various scales. The corresponding seasonal pattern will promote the improvement of the short-term wind speed forecasting accuracy. In this study, a novel method for short-term wind speed forecasting using wavelet transformation (WT) and AdaBoost technique is proposed to analyse the wind speeds distribution features and promote the model configuration. Power spectrum and seasonal pattern analysis using the WT are presented to investigate the wind speeds feature distribution based on the scalogram percentage of energy distribution in different seasons. This procedure contributes to perfecting the investigation of wind speed seasonal pattern characteristics over time and promotes the sample division by computing the statistics measurement based on the estimated frequencies interval. The model order estimation based on the information criteria is processed to reflect the systems dynamical sustainability between the current outputs and historical data. Finally, the experiments based on the real data from Yunnan wind farm are given to verify the effectiveness of the proposed approach.

Estimating the order of sinusoidal models using the adaptively penalized likelihood approach: Large sample consistency properties

Recently, the paper [2] introduced a method for model order estimation based on penalizing adaptively the likelihood (PAL). In this paper, we use the PAL based order estimation method for a nonlinear sinusoidal model and study its asymptotic statistical properties. We prove that the estimator of the model order using the PAL rule is consistent. Simulation examples are presented to illustrate the performance of the PAL method for small sample sizes and to compare it with that of three information criterion-based methods.

WBI Suppression for SAR Using Iterative Adaptive Method

Under the condition of wideband interference (WBI) with the characteristics of good time–frequency concentration but high nonstationarity, the limited time width of the window function in short-time Fourier transform (STFT) causes limited instantaneous frequency resolution and leads to great performance degradation of the conventional WBI suppression algorithm based on time–frequency filtering (TFF) method. A novel WBI suppression method using iterative adaptive approach (IAA) and orthogonal subspace projection (OSP) method is proposed for synthetic aperture radar (SAR). Dispensing with parametric search and model order estimation, the proposed method improves the instantaneous frequency resolution in STFT by means of the IAA method and filters the WBI based on the OSP method, meanwhile, obtains time–frequency distribution (TFD) with 2-D high resolution and no cross-terms. Both the simulation and experimental results are provided to illustrate the performance of the proposed method.

Reduced-Complexity Super-Resolution DOA Estimation with Unknown Number of Sources

When the number of sources is inaccurately estimated, it is well-known that the conventional subspace-based super-resolution direction-of-arrival (DOA) estimation techniques provide inconsistent spatial spectrum, and hence the DOA estimates. In this work, we present a novel technique which provides resolution capability comparable with that of the super-resolution techniques. While the working principle of the proposed technique is similar to that of the minimum-norm algorithm, the algorithm is insensitive to the estimated model-order. Simulation studies show that the proposed technique is advantageous over the use of subspace-based techniques with the number of sources estimated by well-known model order estimation techniques.

An Effective Dynamic Current Phasor Estimator for Synchrophasor Measurements

Accurate voltage and current phasor measurements are required to be provided by phasor measurement units placed at various buses in the system. This paper presents an effective method for estimation of alternating current signal fundamental phasor under dynamic conditions. The model-order estimation of the current signal has been carried out to separate the signal space and the noise space in the signal correlation matrix. The Vandermonde matrix of the total least square estimation of signal parameters via rotational invariance techniques method is extended to second-order Taylor's series approximation to estimate the dynamic phasor of the current signal. The suggested technique for the phasor estimation has been tested on simultaneous multimode amplitude and phase oscillations with decaying dc offset and noninteger harmonics, in the presence of noise and also for a fault scenario in New England 39-bus system. This paper also provides a few suggestions for a few possible amendments in the IEEE synchrophasor standard.