Showing papers in "IEEE Transactions on Signal Processing in 1990"
TL;DR: It is shown that the SR methods are statistically less efficient than MUSIC, at least for a sufficiently large number of snapshots, and an optimally-weighted SR method which may approach the MUSIC level of statistical performance for one direction parameter is introduced.
Abstract: The statistical performance of subspace rotation (SR) methods (such as the Toeplitz approximation method and a variant of ESPRIT) for direction estimation using arrays composed of matched sensor doublets is studied. The distributional properties of these methods are established, and a compact explicit formula for the covariance matrix of their estimation error is provided. Next, using this formula and a similar formula for MUSIC covariance matrix, it is shown that the SR methods are statistically less efficient than MUSIC, at least for a sufficiently large number of snapshots. The difference in statistical performance between the commonly used SR method and MUSIC may be substantial if the number of sensors in the array is large. An optimally weighted SR method which may approach the MUSIC level of statistical performance for one direction parameter (specified by the user) is introduced. >
132 citations
Journal Article•
TL;DR: A linear method and a modification to an existing linear method are proposed for consistent parameter estimation in measurement noise under the assumption that the system order is known and both recursive closed-form and batch least-squares versions of the parameter estimators are presented.
Abstract: The problem of estimating the parameters of a moving average model from the cumulant statistics of the noisy observations of the system output is discussed The system is driven by an independently identically distributed nonGaussian sequence that is not observed The noise is additive and may be colored and nonGaussian Following some existing linear parametric approaches to this problem, a linear method and a modification to an existing linear method are proposed for consistent parameter estimation in measurement noise under the assumption that the system order is known Both recursive closed-form and batch least-squares versions of the parameter estimators are presented The existing and the proposed linear methods utilize only a partial set of the relevant output statistics (this restriction being necessary to obtain a linear estimator), whereas there exist nonlinear method that exploit a much larger set of output statistics A simulation example where two existing linear methods and the two new methods are compared to two existing nonlinear methods is presented >
116 citations
TL;DR: The hyperbolic SVD accurately and efficiently finds the eigenstructure of any matrix that is expressed as the difference of two matrix outer products and applies in problems where the conventional SVD cannot be employed.
Abstract: A new generalization of the singular value decomposition (SVD), the hyperbolic SVD, is advanced, and its existence is established under mild restrictions. The hyperbolic SVD accurately and efficiently finds the eigenstructure of any matrix that is expressed as the difference of two matrix outer products. Signal processing applications where this task arises include the covariance differencing algorithm for bearing estimation in sensor arrays, sliding rectangular windowing, and array calibration. Two algorithms for effecting this decomposition are detailed. One is sequential and follows a similar pattern to the sequential bidiagonal based SVD algorithm. The other is for parallel implementation and mimics Hestenes' SVD algorithm (1958). Numerical examples demonstrate that like its conventional counterpart, the hyperbolic SVD exhibits superior numerical behavior relative to explicit formation and solution of the normal equations. Furthermore, the hyperbolic SVD applies in problems where the conventional SVD cannot be employed. >
65 citations
TL;DR: Re-parametrization of an existing linear method, and a modification to it, are discussed, and results show a distinct improvement in the numerical conditioning of both, the reparametrized algorithm and its modification, for the noisefree case.
Abstract: The problem of estimating the parameters of a moving average model from the cumulant statistics of the noisy observations of the system output is considered. The system is driven by an i.i.d. (independent and identically distributed) non-Gaussian sequence that is not observed. The noise is additive and may be colored and non-Gaussian. Re-parametrization of an existing linear method, and a modification to it, are discussed. Simulation results show a distinct improvement in the numerical conditioning of both, the reparametrized algorithm and its modification, for the noisefree case. For the case of i.i.d. noise, the reparametrized algorithm shows a marked degradation in performance whereas its modification degrades far more gracefully. >
57 citations
TL;DR: It is demonstrated that, when the noise additive sources are spatially correlated Gaussian with unknown cross-spectral matrix (CSM), the cross-bispectrum method provides better bearing estimates that the stochastic maximum likelihood method with known CSM.
Abstract: A new array processing method is presented for bearing estimation based on the cross bispectrum of the array output data. The method is based on the asymptotic distribution of cross-bispectrum estimates and uses maximum likelihood theory. It is demonstrated that, when the noise additive sources are spatially correlated Gaussian with unknown cross-spectral matrix (CSM), the cross-bispectrum method provides better bearing estimates than the stochastic maximum likelihood method with known CSM. Analytical studies and simulations are given to document the performance of the new method. >
45 citations
TL;DR: A maximum likelihood (ML) direction-of-arrival (DOA) estimation algorithm which is robust against outliers and distributional uncertainties in the Gaussian noise and capable of handling coherent signals as well as single snapshot cases.
Abstract: Presents a maximum likelihood (ML) direction-of-arrival (DOA) estimation algorithm which is robust against outliers and distributional uncertainties in the Gaussian noise. The algorithm performs much better than the Gaussian ML algorithm when the underlying noise distribution deviates from the assumed Gaussian while still performing almost as well in the pure Gaussian noise. As with the Gaussian ML estimation, it is capable of handling coherent signals as well as single snapshot cases. The authors analyze the performance of the new algorithm using the variance expression derived from influence function (IF), and then present a resolution test procedure for determining whether a given DOA estimation algorithm can resolve two dominant sources with very close DOAs for a given confidence level. Using the test, one can also check the presence of the reflected path having its DOA exactly the negative of the direct path DOA. >
24 citations
TL;DR: A new method is presented for optimal model order selection for autoregressive bispectrum estimation and simulation results are reviewed which demonstrate the method's performance for the case of quadratically coupled sinusoids embedded in white Gaussian noise.
Abstract: A novel method is presented for optimal model order selection for autoregressive (AR) bispectrum estimation. The method depends solely on the data and requires no a priori information about the process. The method selects the model order that maximizes the cross correlation between the direct (fast Fourier transform-based) bispectrum estimate and the autoregressive bispectrum estimate. Simulation results are reviewed which demonstrate the method's performance for the case of quadratically coupled sinusoids embedded in white Gaussian noise. >
9 citations
TL;DR: The authors develop fast algorithms for multichannel autoregressive moving average (ARMA) model identification that use only scalar operations and are well suited for parallel implementation.
Abstract: The authors develop fast algorithms for multichannel autoregressive moving average (ARMA) model identification that use only scalar operations. The given multivariate (vector) ARMA process is mapped (one-to-one) to an equivalent univariate (scalar), periodic ARMA process. The scalar ARMA parameters are identified and then the inverse mapping is used to identify the multivariate model. The univariate AR parameters are estimated by deriving a set of modified Yule-Walker type equations and then developing a Trench-Zohar type algorithm to solve them. The algorithm, besides employing computation of scalar quantities only, is well suited for parallel implementation with the processors connected in a ring-like manner, the number of processors being the same as the number of channels. The identification of the MA part (scalar) of the model needs estimates of the input samples. The MA estimation algorithm, using least squares techniques, also employs scalar computation only and is equally well suited for parallel implementation. >
6 citations