Surendra Prasad

A transform-based covariance differencing approach for some classes of parameter estimation problems

A method of parameter estimation is presented for a class of problems in which the desired signal is embedded in colored noise with unknown covariance. The proposed algorithm does not require multiple estimates of the signal covariance matrix; instead, it uses a priori knowledge of the structure of the noise covariance matrix to transform the array covariance matrix in a way that leaves its noise component unchanged while the signal component is transformed in some appropriate manner. The noise component is then eliminated by forming the difference of the original and transformed covariance differencing methods to be applied to a wider class of problems than was previously possible. This is illustrated by applying the algorithm to the problems of bearing estimation, resolution of overlapping echos, and transient response analysis. Simulation results demonstrate that the technique affords significant improvement in certain situations over conventional methods. >

A new approach for estimation of statistically matched wavelet

This paper presents a new approach for the estimation of wavelets that is matched to a given signal in the statistical sense. Based on this approach, a number of new methods to estimate statistically matched wavelets are proposed. The paper first proposes a new method for the estimation of statistically matched two-band compactly supported biorthogonal wavelet system. Second, a new method is proposed to estimate statistically matched semi-orthogonal two-band wavelet system that results in compactly supported or infinitely supported wavelet. Next, the proposed method of estimating two-band wavelet system is generalized to M-band wavelet system. Here, the key idea lies in the estimation of analysis wavelet filters from a given signal. This is similar to a sharpening filter used in image enhancement. The output of analysis highpass filter branch is viewed to be equivalent to an error in estimating the middle sample from the neighborhood. To minimize this error, a minimum mean square error (MMSE) criterion is employed. Since wavelet expansion acts like Karhunen-Loe/spl grave/ve-type expansion for generalized 1/f/sup /spl beta// processes, it is assumed that the given signal is a sample function of an mth-order fractional Brownian motion. Therefore, the autocorrelation structure of a generalized 1/f/sup /spl beta// process is used in the estimation of analysis filters using the MMSE criterion. We then present methods to design a finite impulse response/infinite impulse response (FIR/IIR) biorthogonal perfect reconstruction filterbank, leading to the estimation of a compactly supported/infinitely supported statistically matched wavelet. The proposed methods are very simple. Simulation results to validate the proposed theory are presented for different synthetic self-similar signals as well as music and speech clips. Estimated wavelets for different signals are compared with standard biorthogonal 9/7 and 5/3 wavelets for the application of compression and are shown to have better results.

Broadband DOA estimation using "Spatial-Only" modeling of array data

Most of the existing techniques for DOA estimation of broadband sources use both spatial and temporal modeling. This may lead to increased complexity besides a large algorithmic delay. We propose a technique that employs only spatial information in the form of a single spatial array covariance matrix. Assuming the source to have an ideal bandpass power spectral density, we formulate two subspace-based search functions for the estimation of the DOAs of broadband sources. One of these employs a multidimensional search in the parameter space, whereas the other requires a MUSIC like one-dimensional (1-D) search. The multidimensional cost function is shown to be consistent, yields performance close to the Cramer-Rao (CR) bound, and is insensitive to correlation between sources. Both the proposed methods are shown to be robust to deviations from the assumption of ideal bandpass power spectral density used in their formulation.

A new method of estimating wavelet with desired features from a given signal

This paper proposes a new method of estimating both biorthogonal compactly supported as well as semi-orthogonal infinitely/compactly supported wavelet from a given signal. The method is based on maximizing projection of the given signal onto successive scaling subspace. This results in minimization of energy of signal in the wavelet subspace. The idea used to estimate analysis wavelet filter is similar to a sharpening filter used in image enhancement. First, a new method is proposed that helps in the design of 2-band FIR biorthogonal perfect reconstruction filter bank from a given signal. This leads to the design of biorthogonal compactly supported wavelet. It is also shown that a wavelet with desired support as well as desired number of vanishing moments can be designed with the proposed method. Next, a method is proposed to design semi-orthogonal wavelets that are usually infinitely supported wavelets. Here, corresponding to FIR analysis filters, the resulting synthesis filters are IIR filters that satisfy the property of perfect reconstruction.

A modified likelihood function approach to DOA estimation in the presence of unknown spatially correlated Gaussian noise using a uniform linear array

The problem of modified ML estimation of DOAs of multiple source signals incident on a uniform linear array (ULA) in the presence of unknown spatially correlated Gaussian noise is addressed here. Unlike previous work, the proposed method does not impose any structural constraints or parameterization of the signal and noise covariances. It is shown that the characterization suggested here provides a very convenient framework for obtaining an intuitively appealing estimate of the unknown noise covariance matrix via a suitable projection of the observed covariance matrix onto a subspace that is orthogonal complement of the so-called signal subspace. This leads to a formulation of an expression for a so-called modified likelihood function, which can be maximized to obtain the unknown DOAs. For the case of an arbitrary array geometry, this function has explicit dependence on the unknown noise covariance matrix. This explicit dependence can be avoided for the special case of a uniform linear array by using a simple polynomial characterization of the latter. A simple approximate version of this function is then developed that can be maximized via the-well-known IQML algorithm or its variants. An exact estimate based on the maximization of the modified likelihood function is obtained by using nonlinear optimization techniques where the approximate estimates are used for initialization. The proposed estimator is shown to outperform the MAP estimator of Reilly et al. (1992). Extensive simulations have been carried out to show the validity of the proposed algorithm and to compare it with some previous solutions.

DOA estimation of wideband sources using a harmonic source model and uniform linear array

We consider the problem of estimation of the DOAs of multiple wideband sources incident on a uniform linear array (ULA) in the presence of spatially and temporally white Gaussian noise (WGN). The approach presented builds up on the IQML algorithm suggested by Bresler and Macovski (1986) for the case of narrowband DOA estimation. It is shown that the concept of an ARMA model for the observed data vector for the narrowband case can be generalized to model an appropriately stacked, space-time data vector obtained by combining the space-time samples. The coefficients of the corresponding 2-D predictor polynomial can be used to represent the null subspace of the wideband array steering matrix, and rooting of the polynomial at each frequency, separately, gives the DOA estimates. These separate estimates at multiple frequencies are combined into a single DOA estimate in a least squares sense. This leads to the formulation of an IQML like procedure for the spatial parameter estimation of wideband sources. Like its narrowband counterpart, the proposed approach is applicable to both noncoherent and coherent sources. The performance of the proposed method is studied via extensive computer simulations and by comparison with the Cramer-Rao bounds.

Robust adaptive beamforming for wide-band, moving, and coherent jammers via uniform linear arrays

The problem of providing robustness to the conventional narrow-band uniform linear array configuration so as to handle wide-band and moving jammers is addressed. This robustness is achieved via the use of derivative constraints in jammer directions. However, since the jammer directions are not known a priori, these constraints are incorporated with a maximum likelihood characterization of the so-called jammer subspace. This formulation does not need to assume the availability of signal-free observations, as stipulated in earlier work. Computer simulation results are presented, which show that the algorithms proposed here yield significantly better performance as compared to the previous algorithms of Gershman et al. (see ibid., vol.44, p.361-6, 1996, and IEEE Trans. Signal Processing, vol.45, p.1878-85, 1997) and Hung and Turner (1983) in a variety of situations required to handle wide-band, moving, and coherent jammers.

Direction-of-arrival estimation using rank revealing QR factorization

The authors describe a novel technique for direction-of-arrival estimation based on computing a permutation matrix E and a QR factorization RE=HB of the permuted covariance matrix R, such that a possible rank deficiency of R is revealed in the triangular factor B having a minimum norm lower right block. A subset of the columns of the orthogonal matrix, H, is shown to be orthogonal to the direction vectors of sources and hence can be used to estimate their bearings. The cost of this algorithm is only slightly more than that of one QR factorization, but is much lower than that of an eigen-decomposition. Simulation results are included to show that the proposed method performs nearly as well as MUSIC in terms of signal resolution, bias, and variance of the estimated bearings. >

On the index for array optimization and the discrete prolate spheroidal functions

A class of array optimization problems is considered in which we seek to optimize the array response in a specified angular sector. The optimization of array directivity is shown to be a special limiting case of these problems as the width of the specified angular sector approaches zero. The optimum array patterns are also shown to be related to the well-known prolate-spheroidal functions.

Brief paper: Recursive decision directed estimation of reflection coefficients for seismic data deconvolution

This paper concerns the problem of estimation of the location and intensity of reflections of a seismic wavelet. A recursive maximum a posteriori probability (MAP) algorithm is derived as an alternative to the maximum likelihood (ML) algorithm of Mendel and Kormylo. The MAP approach proposed here yields a suboptimal detector which is substantially different in details from the corresponding approximate ML detector of Mendel and Kormylo. Simulation studies are presented to show that the MAP detector performs as well as the ML detector and can yield comparable results with much less computational effort. A comparative study of both the MAP and ML detectors has been made via simulations which show some interesting differences in structure as well as performance.