Robust Spectral Estimation Research Articles

Fully Integrated Optical Spectrometer in Visible and Near-IR in CMOS.

Optical spectrometry in the visible and near-infrared range has a wide range of applications in healthcare, sensing, imaging, and diagnostics. This paper presents the first fully integrated optical spectrometer in standard bulk CMOS process without custom fabrication, postprocessing, or any external optical passive structure such as lenses, gratings, collimators, or mirrors. The architecture exploits metal interconnect layers available in CMOS processes with subwavelength feature sizes to guide, manipulate, control, diffract light, integrated photodetector, and read-out circuitry to detect dispersed light, and then back-end signal processing for robust spectral estimation. The chip, realized in bulk 65-nm low power-CMOS process, measures 0.64 mm 0.56 mm in active area, and achieves 1.4nm in peak detection accuracy for continuous wave excitations between 500 and 830nm. This paper demonstrates the ability to use these metal-optic nanostructures to miniaturize complex optical instrumentation into a new class of optics-free CMOS-based systems-on-chip in the visible and near-IR for various sensing and imaging applications.

Robust noise power spectral density estimation for binaural speech enhancement in time-varying diffuse noise field

In speech enhancement, noise power spectral density (PSD) estimation plays a key role in determining appropriate de-nosing gains. In this paper, we propose a robust noise PSD estimator for binaural speech enhancement in time-varying noise environments. First, it is shown that the noise PSD can be numerically obtained using an eigenvalue of the input covariance matrix. A simplified estimator is then derived through an approximation process, so that the noise PSD is expressed as a combination of the second eigenvalue of the input covariance matrix, the noise coherence, and the interaural phase difference (IPD) of the input signal. Later, to enhance the accuracy of the noise PSD estimate in time-varying noise environments, an eigenvalue compensation scheme is presented, in which two eigenvalues obtained in noise-dominant regions are combined using a weighting parameter based on the speech presence probability (SPP). Compared with the previous prediction filter-based approach, the proposed method requires neither causality delays nor explicit estimation of the prediction errors. Finally, the proposed noise PSD estimator is applied to a binaural speech enhancement system, and its performance is evaluated through computer simulations. The simulation results show that the proposed noise PSD estimator yields accurate noise PSD regardless of the direction of the target speech signal. Therefore, slightly better performance in quality and intelligibility can be obtained than that with conventional algorithms.

On Robust Estimation of Power Spectra

Let us consider the problem of robust spectral density estimation. Conventional methods to obtain estimates of spectral density function are not robust in the presence of outlying observations. We present different methods to robustly estimate the spectral density function that are insensitive against outliers. The proposed methods are applied to simulated and real data and the results are compared. As a special practical application we focus on the frequency-domain analysis of short-term heart rate variability measurements of diabetes patients.

Robust fine acquisition algorithm for GPS receiver with limited resources

The signal acquisition stage of a GPS receiver detects GPS satellites in view and provides coarse estimate of the GPS signal Doppler frequency shift and code delay for use by the tracking loops. The accuracy of the signal acquisition has a direct influence on the tracking performance. The implementation of a GPS signal acquisition algorithm requires compromising between acquisition frequency resolution improvement and reduction in acquisition time. A robust fine acquisition method is proposed to acquire the carrier frequency accurately after the completion of the coarse acquisition of the GPS signals. The proposed method uses Gram-Schmidt orthogonalization to provide robust spectral estimation of satellite Doppler frequency with less computational time. The proposed method starts after the coarse acquisition has been accomplished. The C/A code phase is striped off from the carrier signal. Then, sinusoidal candidate functions are generated at each of the frequencies range of interest, which is typically set around the estimated Doppler shift acquired from the coarse acquisition stage. Finally, an orthogonal search algorithm is utilized to detect the carrier frequency accurately. The performance of the proposed method is evaluated against of the computational load and the effects of the noise. Its performance was also compared to the state-of-the-art FFT and zero-padding FFT-based fine acquisition algorithms. The simulation and experimental results show that the proposed method outperforms existing methods and has sufficient acquisition accuracy for its application in the real world.

New Robust Estimators of Correlation and Weighted Basis Pursuit

The autocorrelation function is a commonly used tool in statistical time series analysis. In this paper we examine the robustness of two estimators of correlation based on memoryless nonlinear functions of the observations, the Median-of-Ratios Estimator (MRE) and the Phase-Phase Correlator (PPC), which are applicable to complex-valued Gaussian random processes. We show that they are robust to impulsive noise from a bias perspective at the expense of statistical efficiency at the Gaussian distribution. Additionally, we develop iterative versions of these estimators named the IMRE and IPPC, realizing an improved bias performance over their non-iterative counterparts and the well-known robust Schweppe-type Generalized M-estimator utilizing a Huber cost function (SHGM). We use robust Mahalanobis distances generated by the IMRE and IPPC to improve the performance of impulsive noise suppression through the use of weighted basis pursuit methods. These estimation and data-cleaning techniques are applied to both synthetic and actual collected data using an Ettus Research USRP to perform robust spectral estimation on signals from the digital television band in the presence of additive impulsive noise. Finally, the analysis reveals that if the time series is highly correlated and the contamination rate is low, the MRE outperforms the PPC estimator from a variance and bias perspective. However, the PPC is the estimator of choice when the correlation is lower and is better suited to time critical applications due to lower computation costs.

Robust, Non-Gaussian Wideband Spectrum Sensing in Cognitive Radios

In this paper, we propose detectors (both parametric and robust) for wideband spectrum sensing in cognitive radios (CR's). The proposed detectors are able to detect spectral activity over a wide frequency range, while assuming little knowledge about the signals of interest. The parametric detector is based on a locally optimal (LO) Neyman-Pearson (NP) test and assumes a known non-Gaussian noise distribution. The corresponding decision statistic of the LO NP detector is expressed in frequency domain, allowing to identify the active channels within the wide frequency band of interest. On the other hand, for situations in which the noise distribution is only approximately known, we propose a robust signal detector that is immune to deviations of the noise model from a certain nominal distribution. The proposed wideband robust detector is based on a robust spectral estimator and is formulated as a non-linear regression. This regression problem can be solved using a fixed-point iteration algorithm at a quadratic computational complexity, in contrast with the Newton's method which would have cubic complexity order. The simulation results show that the proposed detectors can achieve better detection performance in the presence of non-Gaussian noise, compared to existing detectors under the same conditions.

Robust spectral estimation for speed of sound with phase shift correction applied online in yeast fermentation processes

Ultrasound techniques are well suited to provide real‐time characterization of bioprocesses in non‐invasive, non‐contact, and non‐destructive low‐power consumption measurements. In this paper, a spectral analysis method was proposed to estimate time of flight (TOF) between the propagated echoes, and its corresponding speed of sound (USV). Instantaneous power spectrum distribution was used for accurate detection of echo start times, and phase shift distribution for correcting the involved phase shifts. The method was validated by reference USV for pure water at 9–30.8°C, presenting a maximum error of 0.22%, which is less than that produced by the crosscorrelation method. Sensitivity analyses indicated a precision of 6.4 × 10−3% over 50 repeated experiments, and 0.11% over two different configurations. The method was competently implemented online in a yeast fermentation process, and the calculated USV was combined with temperature and nine signal features in an artificial neural network. The network was designed by back propagation algorithm to estimate the instantaneous density of the fermentation mixture, producing a maximum error of 0.95%.

Robust Spectral Analysis

In this paper I introduce quantile spectral densities that summarize the cyclical behavior of time series across their whole distribution by analyzing periodicities in quantile crossings. This approach can capture systematic changes in the impact of cycles on the distribution of a time series and allows robust spectral estimation and inference in situations where the dependence structure is not accurately captured by the auto-covariance function. I study the statistical properties of quantile spectral estimators in a large class of nonlinear time series models and discuss inference both at fixed and across all frequencies. Monte Carlo experiments illustrate the advantages of quantile spectral analysis over classical methods when standard assumptions are violated.

Robust detection of periodic time series measured from biological systems

BackgroundPeriodic phenomena are widespread in biology. The problem of finding periodicity in biological time series can be viewed as a multiple hypothesis testing of the spectral content of a given time series. The exact noise characteristics are unknown in many bioinformatics applications. Furthermore, the observed time series can exhibit other non-idealities, such as outliers, short length and distortion from the original wave form. Hence, the computational methods should preferably be robust against such anomalies in the data.ResultsWe propose a general-purpose robust testing procedure for finding periodic sequences in multiple time series data. The proposed method is based on a robust spectral estimator which is incorporated into the hypothesis testing framework using a so-called g-statistic together with correction for multiple testing. This results in a robust testing procedure which is insensitive to heavy contamination of outliers, missing-values, short time series, nonlinear distortions, and is completely insensitive to any monotone nonlinear distortions. The performance of the methods is evaluated by performing extensive simulations. In addition, we compare the proposed method with another recent statistical signal detection estimator that uses Fisher's test, based on the Gaussian noise assumption. The results demonstrate that the proposed robust method provides remarkably better robustness properties. Moreover, the performance of the proposed method is preferable also in the standard Gaussian case. We validate the performance of the proposed method on real data on which the method performs very favorably.ConclusionAs the time series measured from biological systems are usually short and prone to contain different kinds of non-idealities, we are very optimistic about the multitude of possible applications for our proposed robust statistical periodicity detection method.AvailabilityThe presented methods have been implemented in Matlab and in R. Codes are available on request. Supplementary material is available at: .

State-space spectral estimation of characteristic electromagnetic responses in wideband data

This letter utilizes a robust spectral estimation method, based on state-space control theory, to coherently process wideband frequency domain field data of any object and extract specific modal (or characteristic) responses associated with wave propagation along the object. The estimation problem is formulated in terms of well-known range processing used in radar imaging. Thus, the data is modeled in terms of complex sinusoids, whose amplitude is scaled by the decay constants of the modes and whose phase yields the range associated with scattering centers pertinent to modal propagation. Unlike other approaches that require the system poles to be inside the unit circle, the complex poles yielding the decay constants in the proposed approach can be located anywhere in the z-plane, and can vary with frequency, in order to capture the dynamic wideband behavior of the scattering mechanism. The method is illustrated by application to mode extraction for a cylindrically stratified dielectric scatterer.

Nonlinear functionals of the periodogram

A central limit theorem is stated for a wide class of triangular arrays of nonlinear functionals of the periodogram of a stationary linear sequence. Those functionals may be singular and not‐bounded. The proof of this result is based on Bartlett decomposition and an existing counterpart result for the periodogram of an independent and identically distributed sequence, here taken to be the driving noise. The main contribution of this paper is to prove the asymptotic negligibility of the remainder term from Bartlett decomposition, feasible under short dependence assumption. As it is highlighted by applications (to estimation of nonlinear functionals of the spectral density, robust spectral estimation, local polynomial approximation and log‐periodogram regression), this extends may results until then tied to Gaussian assumption.

Super resolution SAR imaging via parametric spectral estimation methods

Super resolution synthetic aperture radar (SAR) image formation via sophisticated parametric spectral estimation algorithms is considered. Parametric spectral estimation methods are devised based on parametric data models and are used to estimate the model parameters. Since SAR images rather than model parameters are often used in SAR applications, we use the parameter estimates obtained with the parametric methods to simulate data matrices of large dimensions and then use the fast Fourier transform (FFT) methods on them to generate SAR images with super resolution. Experimental examples using the MSTAR and Environmental Research Institute of Michigan (ERIM) data illustrate that robust spectral estimation algorithms can generate SAR images of higher resolution than the conventional FFT methods and enhance the dominant target features.

Robust recursive time series modeling based on an AR model excited by a t-distribution process

In this correspondence, a new robust recursive spectral estimation based on an AR model is proposed. The optimal coefficients are selected by assuming that the excitation signal has a t-distribution t(/spl alpha/) with /spl alpha/ degrees of freedom. With /spl alpha/=/spl infin/, we get the RLS method. Simulation results show that the obtained estimates using the proposed method with small /spl alpha/ are more efficient, and the standard deviation (SD) of the estimation results is smaller and more accurate than that with large /spl alpha/. The proposed estimator with small /spl alpha/ is also more efficient and more accurate than the recursive method based on Huber's M estimate. Two approaches are used, i.e., the infinite memory and the exponentially weighted approaches.

Quantitative NMR signal analysis by an iterative quadratic maximum likelihood method

The iterative quadratic maximum likelihood (IQML) method is a robust spectral estimation algorithm that can be applied to yield accurate quantification of NMR data. This method only requires a few iterations (normally less than 5) of quadratic minimization and is demonstrated to be a much more accurate and much less biassed estimator than a linear prediction and singular value decomposition (LPSVD) based method.

A robust spectral estimation by modeling an estimated autocovariance with an ARMA model

The development, analysis, simulation results, and comparison of techniques for estimating spectral peaks of stationary signals in environments with low signal-to-noise ratio are discussed. Unlike traditional parametric methods, the proposed method estimates parameters of a model which best approximates the estimated autocovariance lag rather than the received signal. This technique is studied and evaluated in three different respects: using a performance index in the spectral domain, suppression of the moving-average (MA) portion and in terms of effective signal-to-noise ratio. This estimation technique demonstrates outstanding robustness and resolution for estimating both spectral peaks and amplitudes of multiple sinusoids embedded in white Gaussian noise, compared to traditional methods. When used in conjunction with Cadzow's autoregressive moving-average (ARMA) method using singular value decomposition (SVD), the technique extracts frequencies and amplitudes of existing sinusoids down to -17 dB while the ARMA method alone achieves only -10 dB on average.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A New ARMA Spectral Estimator

Abstract In this article a new autoregressive moving average (ARMA) spectral estimator is introduced, which does not require estimation of the moving average parameters. The estimator makes use of Burg (or Marple) estimates in the purely autoregressive model to initialize the autoregressive coefficients in the mixed model. The coefficients are estimated using an algorithm of Tsay and Tiao, which is computationally reasonably fast. Several examples are given that include ARMA and non-ARMA data. These examples demonstrate that prefiltering the data is usually a good idea. A method for dynamically determining the proper filter is described in some detail. Having demonstrated the utility of an ARMA model for modeling the spectrum and having determined a dynamic prefiltering method and a reasonably efficient method of estimating the AR coefficients, a new robust ARMA spectral estimator is obtained as follows: 1. Prefilter the data, , with , where is the dynamically determined prefilter. 2. Model the filtered d...