Pisarenko's Method Research Articles

Toward Ant-Sized Moving Object Localization Using Deep Learning in FMCW Radar: A Pilot Study

We propose a deep learning-based approach to localizing a small moving object with a single millimeter-wave frequency-modulated continuous-wave (FMCW) radar. The main challenge that foils conventional localization techniques, such as 3-D fast Fourier transform (3-D-FFT), Pisarenko method, multiple signal classification (MUSIC), estimation of signal parameters via rotational invariance technique (ESPRIT), Capon’s method, and Burg’s method, is the low signal-to-noise ratio of the reflected signal from millimeter-sized objects. Our key idea is to combine useful but noisy features from classical transforms [e.g., fast Fourier transform (FFT)] with neural networks that can refine and interpret those features into range and angle estimates by training on a large dataset of examples. Importantly, our networks were designed to be translation-equivariant, which enables accurate predictions of unseen object locations and improves the range and azimuth root mean square error (RMSE) scores by 34%–46% and 41%–60%, respectively, over state-of-the-art approaches. This pilot study establishes a new baseline for small-object tracking using FMCW and can enable tracking of small animals, such as ants inside the colony for behavior studies. Our first FMCW-small-object dataset and the source code are publicly available on <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/shikuzen/RA-CNN</uri> .

An Improved Method for Parametric Spatial Spectrum Estimation in Internet of Things

When massive numbers of wireless IoT devices are being deployed, cognitive spectrum management is critical to satisfy the explosive broadband requirements of IoT applications. Heterogeneous the target of the spatial spectrum estimation which is part of array signal processing is to achieve the evaluation of space signal parameters and source location, which result in that the spatial spectrum estimation becomes the most basic content of the array signal processing. It needs a method by which the large dimensional array still has its consistency. Therefore, this paper studies an improved large dimensional array parameterized spatial spectrum estimation method based on Pisarenko method, named G‐Pisarenko method. Firstly, an improved estimator about the logarithm of the covariance matrix of a certain bilinear form is analyzed which is based on the theory of large dimension random matrix. We can find out a relatively better method, i.e., MW method. The method will become the primitive method for us to improve. Then, aimed at the relating covariance matrix in MW, we use an improved large dimensional array estimation method which can improve the logarithm of the covariance matrix estimation. Finally, we compare the improved method and the original method by simulation, and it can be seen the clear advantage of G‐Pisarenko method when the sample number and observed dimensions are in the same order of magnitude.

A modified version of the Pisarenko method to estimate the power spectral density of any asymptotically wide sense stationary vector process

The Pisarenko method estimates the power spectral density (PSD) of Gaussian wide sense stationary (WSS) 1-dimensional (scalar) processes when the PSD is Lipschitz. In this paper we modify the Pisarenko method to estimate the generating function of a sequence of block Toeplitz matrices from another sequence of matrices when both sequences are asymptotically equivalent. This modified version of the Pisarenko method allows us to estimate the PSD of any asymptotically WSS (AWSS) multidimensional (vector) process even if the process is not Gaussian and even if the PSD is continuous, but not Lipschitz.

Joint Detection and Localization of an Unknown Number of Sources Using the Algebraic Structure of the Noise Subspace

Source localization and spectral estimation are among the most fundamental problems in statistical and array signal processing. Methods which rely on the orthogonality of the signal and noise subspaces, such as Pisarenko's method, MUSIC, and root-MUSIC are some of the most widely used algorithms to solve these problems. As a common feature, these methods require both apriori knowledge of the number of sources, and an estimate of the noise subspace. Both requirements are complicating factors to the practical implementation of the algorithms, and when not satisfied exactly, can potentially lead to severe errors. In this paper, we propose a new localization criterion based on the algebraic structure of the noise subspace that is described for the first time to the best of our knowledge. Using this criterion and the relationship between the source localization problem and the problem of computing the greatest common divisor (GCD), or more practically approximate GCD, for polynomials, we propose two algorithms which adaptively learn the number of sources and estimate their locations. Simulation results show a significant improvement over root-MUSIC in challenging scenarios such as closely located sources, both in terms of detection of the number of sources and their localization over a broad and practical range of SNRs. Further, no performance sacrifice in simple scenarios is observed.

Seismotectonic Properties and Zonation of the Far-Eastern Eurasian Plate Around the Korean Peninsula

Regional seismotectonics provides crucial information for seismic hazard analysis, which is difficult to address with short-term earthquake records. The far-eastern Eurasian plate around the Korean Peninsula presents a stable intraplate environment with diffuse seismicity, of which responsible tectonics and active faults are difficult to identify. Combined analysis of instrumental and historical earthquake records is required for assessment of long-term seismicity properties. Seismotectonic provinces are identified from the spatial distribution of seismicity properties controlled by the medium properties and stress field. The boundaries of the seismotectonic provinces are defined considering the medium properties that can be inferred from geological, geophysical and tectonic features. The Gutenberg–Richter frequency–magnitude relationships and maximum magnitudes for the seismotectonic provinces are determined using instrumental and historical earthquake records. The validity of maximum magnitude estimation is tested with synthetic data. A parametric method, the Tate–Pisarenko method, produces more accurate estimates than non-parametric methods. A modified Tate–Pisarenko method is proposed for estimation of maximum magnitudes for incomplete short-term earthquake catalogs. The maximum magnitude of events for the whole region is approximately the same as the average of the maximum magnitudes of events for subdivided provinces, causing apparent variation in maximum magnitudes depending on the number of seismotectonic provinces. Consideration of a reasonable number of seismotectonic provinces may be needed for proper assessment of seismic hazard potentials is recommended. The combined analysis of historical and instrumental earthquake records suggests maximum magnitudes greater than 7 around the peninsula.

Frequency and Damping Estimation Methods - An Overview

Frequency and Damping Estimation Methods - An Overview This overview paper presents and compares different methods traditionally used for estimating damped sinusoid parameters. Firstly, direct nonlinear least squares fitting the signal model in the time and frequency domains are described. Next, possible applications of the Hilbert transform for signal demodulation are presented. Then, a wide range of autoregressive modelling methods, valid for damped sinusoids, are discussed, in which frequency and damping are estimated from calculated signal linear self-prediction coefficients. These methods aim at solving, directly or using least squares, a matrix linear equation in which signal or its autocorrelation function samples are used. The Prony, Steiglitz-McBride, Kumaresan-Tufts, Total Least Squares, Matrix Pencil, Yule-Walker and Pisarenko methods are taken into account. Finally, the interpolated discrete Fourier transform is presented with examples of Bertocco, Yoshida, and Agrež algorithms. The Matlab codes of all the discussed methods are given. The second part of the paper presents simulation results, compared with the Cramér-Rao lower bound and commented. All tested methods are compared with respect to their accuracy (systematic errors), noise robustness, required signal length, and computational complexity.

Modified Pisarenko Harmonic Decomposition for Single-Tone Frequency Estimation

In this correspondence, based on an alternative derivation of the Pisarenko harmonic decomposition (PHD) method, a new asymptotically unbiased estimator for the frequency of a single real tone in white noise is devised with the use of novel sample covariance expressions. Furthermore, extension to sample covariances with higher lags for performance enhancement is investigated while a simple and effective scheme is suggested to resolve the corresponding frequency ambiguity problem. The variance of the modified Pisarenko's method is also derived, which is then utilized to find the best estimate among all admissible solutions from various sets of sample covariances. Computer simulations are included to corroborate the theoretical development and to demonstrate that the proposed approach outperforms several existing low-complexity frequency estimators in terms of nearly uniform performance and estimation accuracy.

Improved Variant of Pisarenko Harmonic Decomposition for Single Sinusoidal Frequency Estimation

It is well known that Pisarenko's frequency estimate for a single real tone can be computed easily using the sample covariance with lags 1 and 2. In this Letter, we propose to use alternative covariance expressions, which are inspired from the modified covariance (MC) frequency estimator, in Pisarenko's algorithm. Computer simulations are included to corroborate the theoretical development of the variant and to demonstrate its superiority over the MC and Pisarenko's methods.

An efficient approach for computing non-Gaussian ARMA model coefficients using Pisarenko's method

This paper addresses the problem of estimating the coefficients of a general autoregressive moving average (ARMA) model from only third order cumulants (TOCs) of the noisy observations of the syste...

An efficient approach for computing non-Gaussian ARMA model coefficients using Pisarenko's method

This paper addresses the problem of estimating the coefficients of a general autoregressive moving average (ARMA) model from only third order cumulants (TOCs) of the noisy observations of the system output. The observed signal may be corrupted by additive coloured Gaussian noise. The system is driven by a zero-mean independent and identically distributed (i.i.d.) non-Gaussian sequence. The input is not observed. The unknown model coefficients are obtained using eigenvalue–eigenvector decomposition. The derivation of this procedure is an extension of Pisarenko harmonic autocorrelation-based (PHA) method to third order statistics. It will be shown that the desired ARMA coefficients vector corresponds to the eigenvector associated with the minimum eigenvalue of a data covariance matrix of TOCs. The proposed method is also compared with well-known algorithms as well as with the PHA method. Copyright © 2005 John Wiley & Sons, Ltd.

Employing Symmetry Constraints for Improved Frequency Estimation by Eigenanalysis Methods

The problem of extracting sinusoid signals from noisy observations made at equally spaced times is considered. Eigenanalysis methods, such as Pisarenko's method and the extended Prony method, find the eigenvector with minimum eigenvalue of a suitably chosen matrix and then obtain the complex sinusoids as the roots of the polynomial that has the components of the eigenvector as coefficients. For the sinusoids to be undamped, it is necessary that the roots lie on the unit circle and hence that the eigenvector be conjugate symmetric. It is shown how this symmetry constraint can be incorporated into eigenanalysis estimation methods in a routine way. The practical importance of the constraint is investigated by Cramer-Rao variance-bound calculations and by simulation. The following conclusions are made: (1) The symmetry constraint is straightforward to implement and reduces the amount of computation required. (2) The relative reduction in variance of the constrained over the unconstrained frequency estimators is arbitrarily large for frequencies close together or near a multiple of 4. There are also frequency values however, for which the symmetry constraint gives no reduction in variance at low noise-to-signal ratios. (3) The relative reduction in variance converges to 0 for large sample sizes. (4) The symmetry constraint increases the breakdown noise-to-signal ratios above which the various methods fail to give useful results.

Employing Symmetry Constraints for Improved Frequency Estimation by Eigenanalysis Methods

The problem of extracting sinusoid signals from noisy observations made at equally spaced times is considered. Eigenanalysis methods, such as Pisarenko's method and the extended Prony method, find the eigenvector with minimum eigenvalue of a suitably chosen matrix and then obtain the complex sinusoids as the roots of the polynomial that has the components of the eigenvector as coefficients. For the sinusoids to be undamped, it is necessary that the roots lie on the unit circle and hence that the eigenvector be conjugate symmetric. It is shown how this symmetry constraint can be incorporated into eigenanalysis estimation methods in a routine way. The practical importance of the constraint is investigated by Cramer-Rao variance-bound calculations and by simulation. The following conclusions are made: (1) The symmetry constraint is straightforward to implement and reduces the amount of computation required. (2) The relative reduction in variance of the constrained over the unconstrained frequency estimators is arbitrarily large for frequencies close together or near a multiple of 4. There are also frequency values however, for which the symmetry constraint gives no reduction in variance at low noise-to-signal ratios. (3) The relative reduction in variance converges to 0 for large sample sizes. (4) The symmetry constraint increases the breakdown noise-to-signal ratios above which the various methods fail to give useful results.

Tracking of time-varying frequency of sinusoidal signals

We propose to track time-varying frequencies of complex sinusoids in noise, by applying a new algorithm based on Pisarenko's method combined with Kamen's pole factorization. The algorithm is a sequential estimation of AR parameters followed by an adaptive root solving.

Modifications to Pisarenko Harmonic Retrieval Method to Cope with Rough Noise Channels Conditions

Pisarenko method is an important technique to estimate the sinusoidal signal frequencies in white noise. In this paper, we show that the assumption of fair white noise and its corresponding equal values diagonal covariance matrix can be perturbed in some noise environments. Therefore, the simple criterion form of Pisarenko is not suitable and other modified algorithms are to be proposed to alleviate this problem. These algorithms and their results are shown.

Constrained maximum likelihood estimators for superimposed exponential signals

Recently Kundu(1993a) has proposed a non-linear eigenvalue method for finding the maximum likelihood estimators (MLE) of the parameters of undamped exponential signals.It is known to perform better than the previously existing methods like FBLP of Tufts and Kumaresan or Pisarenko's method (Pisarenko;),in the sense of lower mean squared errors.The solution in general depends on the roots of a polynomial equation.It is observed that the coefficients of the polynomial exhibit a certain symmetry.Since it is known (Crowder; 1984) that the MLE with constraints is more efficient than the unconstrained MLE,modified maximum likelihood method.

Rectangular Pisarenko method applied to source localization

Most high-resolution (HR) direction-of-arrival (DOA) estimation schemes require the extraction of a low-dimensional subspace: a task that takes O(N/sup 3/) flops for an order S matrix. Different techniques have been recently proposed to reduce this computational load. For those working on blocks of data, the number of flops required is generally O(N/sup 2/P), where P, which is the dimension of the subspace (the number of sources), is often quite small as compared with N, which is the number of sensors. The method we propose is a HR technique that requires O(NP/sup 2/)+O(P/sup 3/) flops, i.e., that is linear in the number of sensors. The price to be paid for this drastic computational saving is a reduction in performance. Although the Cramer-Rao lower bound (CRLB) on the variance of the direction estimates is of the order T/sup -1/ N/sup -3/ (with T the number of snapshots), this variance is of order T/sup -1/ N/sup -2/ for the proposed procedure. The idea behind the method is to apply a Pisarenko method to a rectangular matrix extracted from the Toeplerized estimated covariance matrix, and it is this Toeplerization that allows preservation of the O(T/sup -1/ N/sup -2/) level of performance.

Computational analysis of rotational search methods for adaptive Pisarenko harmonic retrieval

The rotational search method (RSM), which reduces the computational burden of the Pisarenko method for identifying undamped sinusoids in additive noise, is discussed. A brief review of previous adaptive algorithms for implementing the method is presented. Two simulations are presented which show the inherent sensitivity of the RSM algorithm. The sensitivity is shown to depend upon the Rayleigh-Ritz eigenvector estimate and the value of the minimum eigenvalue estimate. The errors in their tracking result in a loss of search direction orthogonality to the estimated minimum eigenvector. A higher precision for the enforced search direction orthogonality which minimizes the added computation is proposed, resulting in the altered RSM (ARSM). >

Statistical analysis of Pisarenko type tone frequency estimator

Abstract In this paper we investigate a tone frequency estimation method based on the Pisarenko technique. The frequency estimate is obtained in terms of the first and second autocorrelation coefficients of the input samples, in the case of a single tone in white Gaussian noise. Statistical analysis of this frequency estimate has been carried out. New expressions related to the expected value and the variance of the estimate are derived. It is shown that the Pisarenko method breaks down for low signal to noise ratio (SNR) values and achieves the Cramer Rao Lower Bound (CRLB) for high SNR values and that the estimator is biased. The performance of this method is shown to be sensitive to the frequency of the sinusoid with best results being obtained for ω1 = π/4 and 3π/4.

On the total least squares linear prediction method for frequency estimation

The total least squares (TLS) linear prediction (LP) method recently presented by Rahman and Yu (1987) and the equivalent improved Pisarenko's (IP) method by Kumaresan (1986) are reviewed and generalized by the whitening approach. The resulting whitened-TLS-LP method yields higher estimation accuracy than the TLS-LP. This simulation was carried out in double precision FORTRAN-77 on VAX-8810. The IMSL routines were used to perform eigendecompositions, compute the polynomial roots, and to generate the pseudo-Gaussian random numbers.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Characterization of microstrip antennas using the TLM simulation associated with a Prony‐Pisarenko method

AbstractThe transmission‐line matrix (TLM) method enables simulation of interior electromagnetic field propagation problems. With the use of absorbent walls, we can simulate exterior problems such as the radiaition of a microstrip antenna. The input impedance is deduced from the standing wave observed in the feedline. The radiation pattern is determined from the field over a plane located in the immediate vicinity of the antenna, using the theory of radiating apertures. However, the CPU time and memory space involved are excessive. Since the radiating structure has several resonant frequencies, it is convenient to apply classical digital signal processing techniques such as finite impulse response filtering associated with a linear prediction method. The present paper focuses on a Prony–Pisarenko method to improve on the TLM method in terms of both computation time and precision of the frequency‐domain analysis of the results. In this case, overall CPU time is reduced by a factor of 2 to 3. The paper discusses the results obtained for radiation patterns. This represents a new field of application for the TLM method whose drawbacks are reduced by using appropriate signal processing methods.