Optimal high-order Yule-Walker estimation of sinusoidal frequencies

The asymptotic properties of sinusoidal frequency estimators based on the high-order Yule-Walker (HOYW) equations were analyzed recently. The results of that analysis are used to propose two classes of frequency estimators; one class uses singular value decomposition, and the other uses a sparse matrix solution. Both classes entail two estimation steps: the first step generates initial estimates which are used to obtain an optimal weighting matrix, and the second step generates an optimally weighted estimate. Each two-step method produces asymptotically minimum variance estimates over all estimators of their class. The implementation of the proposed estimators is described in detail, and numerical examples are presented to evaluate their performance     

Performance analysis of forward-backward matched-filterbankspectral estimators

The problem of complex spectral estimation is of great interest in many applications. This paper studies the general class of the forward-backward matched-filterbank (MAFI) spectral estimators including the widely used Capon as well as the more recently introduced amplitude and phase estimation of a sinusoid (APES) methods. In particular, we show by means of a higher order expansion technique that the one-dimensional (1-D) Capon estimator underestimates the true spectrum, whereas the 1-D APES method is unbiased; we also show that the bias of the forward-backward Capon is half that of the forward-only Capon (to within a second-order approximation). Furthermore. We show that these results can be extended to the two-dimensional (2-D) Capon and APES estimators. Numerical examples are also presented to demonstrate quantitatively the properties of and the relation between these MAFI estimators     

Detection tests for array processing in unknown correlated noisefields

This paper introduces two eigenvalue-based rules for estimating the number of signals impinging on an array of sensors along with a spatially correlated noise field. The first rule, called S, is derived under the assumption that the noise spatial covariance is block diagonal or banded. The assumption underlying the second detection rule, named T, is that the temporal correlation of the noise has a shorter length than that of the signals. In both cases, a matrix is built from the array output data covariances, the smallest eigenvalue of which is equal to zero under the hypothesis that the source number is overestimated. The sample distribution of the aforementioned smallest eigenvalue is derived and used to formulate the detection rules S and T. Both these rules are computationally quite simple. Additionally, they can be used with a noncalibrated array. The paper includes numerical examples that lend empirical support to the theoretical findings and illustrate the kind of performance that can be achieved by using the S and T detection rules     

Polyurethane doped with low‐concentration erbium

Polyurethane (PU) with lactate structures in its conformation can be used as a biological and biodegradable polymer. Polyurethane lactate (PUL) was doped with small quantities of an erbium (Er³⁺) complex, which hindered the N?N group. 2,2′‐Dihydroxyazobenzene was used as a ligand for the Er³⁺ complex. PUL in the presence of the used Er³⁺ complex caused water from the complex to be replaced by the polar structures from the polymer. These structures acted as crystallization germs for the structuration of the PU matrix. As a consequence, both the mechanical and thermal properties of the polymer were improved. The sample with the highest mechanical properties contained only 0.064 μmol of Er³⁺ complex/g of sample. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 659–669, 2007     

Subspace-based estimation of time delays and Doppler shifts

This paper considers the problem of estimating the time delays and Doppler shifts of a known waveform received via several distinct paths by an array of antennas. The general maximum likelihood estimator is presented, and is shown to require a 2d-dimensional nonlinear minimization, where d is the number of received signal reflections. Two alternative solutions based on signal and noise subspace fitting are proposed, requiring only a d-dimensional minimization. In particular, we show how to decouple the required search into a two-step procedure, where the delays are estimated and the Dopplers solved for explicitly. Initial conditions for the time delay search can be obtained by applying generalizations of the MUSIC and ESPRIT algorithms, which are also outlined in the paper. Simulation examples are included to illustrate the algorithms' performance relative to the Cramer-Rao bound     

Decentralized array processing using the MODE algorithm

Centralized methods for source location using sensor arrays have computational and communication burdens that increase significantly with the number of sensors in the array. Therefore, these methods may not be usable in the applications involving very large arrays. In such applications, the data processing may need to be decentralized. This paper introduces two methods for decentralized array processing, based on the recently proposed MODE algorithm. For prescribed nonoverlapping subarrays, both methods are shown to be statistically optimal in the sense that asymptotically they provide the most accurate decentralized estimates of source location parameters. The problem of subarray selection to further optimize the estimation accuracy is only briefly addressed. The two methods are intended for different types of applications: the first should be preferred when there exist significant possibilities for local processing or for parallel computation in the central processor; otherwise the second method should be preferred. The accuracy of the two decentralized methods is compared to the centralized Cramér-Rao bound, both analytically and numerically, in order to provide indications about the loss of accuracy associated with decentralized processing.The work of P. Stoica was supported by a grant from the Royal Swedish Academy of Engineering Sciences and by the Swedish Research Council for Engineering Sciences under contract 91-676. The work of A. Nehorai was supported by the Air Force Office of Scientific Research under grant no. AFOSR-90-0164, and by the Office of Naval Research under grant no. N00014-91-J-1298.on leave at the Department of Applied Electronics, Chalmens University of Technology, 2-41296 Göthensberg, Sweeden.     

Cisoid parameter estimation in the colored noise case: asymptoticCramer-Rao bound, maximum likelihood, and nonlinear least-squares

The problem of estimating the parameters of complex-valued sinusoidal signals (cisoids, for short) from data corrupted by colored noise occurs in many signal processing applications. We present a simple formula for the asymptotic (large-sample) Cramer-Rao bound (CRB) matrix associated with this problem. The maximum likelihood method (MLM), which estimates both the signal and noise parameters, attains the performance corresponding to the asymptotic CRB, as the sample length increases. More interestingly, we show that a computationally much simpler nonlinear least-squares method (NLSM), which estimates the signal parameters only, achieves the same performance in large samples     

State-space and Yule-Walker approaches to pole estimation

The pole estimates provided by the state-space and Yule-Walker approaches are shown to coincide in the cases where the Hankel matrix of sample covariances used by both methods has full column rank.<>