Johann F. Böhme

Estimation of spectral parameters of correlated signals in wavefields

Abstract The statistical properties of a known method to estimate the spectral matrix of signals in a wavefield are investigated assuming the output of an array of sensors is observed. Because the wave parameters, for example bearings and ranges, of the sources are usually unknown, a suitable technique for estimating them separately is reported. Assuming the wave parameters, conditions for the identifiability of the signal spectral parameters are derived. Optimal properties of the estimate for the spectral matrix of signals are shown, for example, minimum variance unbiasedness for normally distributed data. A numerical experiment demonstrates some properties of the estimates of all parameters, for example, the estimates of signal spectral powers and bearings are significantly correlated for sources close together.

Matrix fitting approach to direction of arrival estimation with imperfect spatial coherence of wavefronts

The performance of high-resolution direction of arrival (DOA) estimation methods significantly degrades in several practical situations where the wavefronts have imperfect spatial coherence. The original solution to this problem was proposed by Paulraj and Kailath (1988), but their technique requires a priori knowledge of the matrix characterizing the loss of wavefront coherence along the array aperture. A novel solution to this problem is proposed, which does not require a priori knowledge of the spatial coherence matrix.

Estimation of source parameters by maximum likelihood and nonlinear regression

Statistical properties of certain parametric array processing methods are investigated. Asymptotic normality of Fourier-transformed sensor outputs for usual signal plus noise models is applied to define likelihood functions which have to be maximized for parameter estimation. In the first well known approach, the parameter structure is contained in the spectral density matrix of the outputs. The second likelihood function is conditional and results in a nonlinear regression problem. Since the likelihood equations are difficult to solve in general, properties of approximate solutions, for example Liggetts method, are of interest. Asymptotic distributions of the estimates and their approximations and results of some numerical experiments are discussed.

Time-frequency analysis of multiple resonances in combustion engine signals

Abstract This paper presents time–frequency analysis of multiple resonances in combustion chamber pressure signals and corresponding structure-born sound signals of the cylinder block of a combustion engine considering only one combustion cycle. Since the Wigner distribution proved itself as a good tool for these kinds of signals, the requirement which we imposed here was to produce a sum of the Wigner distributions of the signal components separately, but without cross-terms using only one signal realization. A distribution having this property can be achieved using the S-method. Based on this property of the method, we investigate a procedure to estimate the instantaneous frequencies that are functions of temperature within the combustion chamber and the energies of the components that are used for knock detection. The calculation delay is smaller than the duration of one combustion cycle. This can provide an efficient and accurate combustion control of spark-ignition car engines. The procedure is demonstrated on several simulated and experimental signals.

Robust L-estimation based forms of signal transforms and time-frequency representations

The L-estimation based signal transforms and time-frequency (TF) representations are introduced by considering the corresponding minimization problems in the Huber (1981, 1998) estimation theory. The standard signal transforms follow as the maximum likelihood solutions for the Gaussian additive noise environment. For signals corrupted by an impulse noise, the median-based transforms produce robust estimates of the non-noisy signal transforms. When the input noise is a mixture of Gaussian and impulse noise, the L-estimation-based signal transforms can outperform other estimates. In quadratic and higher order TF analysis, the resulting noise is inherently a mixture of the Gaussian input noise and an impulse noise component. In this case, the L-estimation-based signal representations can produce the best results. These transforms and TF representations give the standard and the median-based forms as special cases. A procedure for parameter selection in the L-estimation is proposed. The theory is illustrated and checked numerically.

Multidimensional rank reduction estimator for parametric MIMO channel models

A novel algebraic method for the simultaneous estimation of MIMO channel parameters from channel sounder measurements is developed. We consider a parametric multipath propagation model with discrete paths where each path is characterized by its complex path gain, its directions of arrival and departure, time delay, and Doppler shift. This problem is treated as a special case of the multidimensional harmonic retrieval problem. While the well-known ESPRIT-type algorithms exploit shift-invariance between specific partitions of the signal matrix, the rank reduction estimator (RARE) algorithm exploits their internal Vandermonde structure. A multidimensional extension of the RARE algorithm is developed, analyzed, and applied to measurement data recorded with the RUSK vector channel sounder in the 2 GHz band.

Adaptive beamforming algorithms with robustness against jammer motion

The performance of adaptive array algorithms is known to degrade in rapidly moving jammer environments. This degradation occurs due to the jammer motion that may bring the jammers out of the sharp notches of the adapted pattern. We develop the robust modifications of the sample matrix inversion (SMI) algorithm, loaded SMI (LSMI) algorithm, and eigenvector projection (EP) algorithm by means of artificial broadening of the null width in the jammer directions. For this purpose, data-dependent sidelobe derivative constraints that do not require any a priori information about the jammer directions are used.

Detection of the Number of Signals Using the Benjamini-Hochberg Procedure

This paper presents a novel approach to detect multiple signals embedded in noisy observations from a sensor array. We formulate the detection problem as a multiple hypothesis test. To control the global level of the multiple test, we apply the false discovery rate (FDR) criterion proposed by Benjamini and Hochberg. Compared to the classical familywise error rate (FWE) criterion, the FDR-controling procedure leads to a significant gain in power for large size problems. In addition, we apply the bootstrap technique to estimate the observed significance level required by the FDR-controling procedure. Simulations show that the FDR-controling procedure always provides higher probability of correct detection than the FWE-controling procedure. Furthermore, the reliability of the proposed test procedure is not affected by the gain in power of the test

Constrained Hung-Turner adaptive beam-forming algorithm with additional robustness to wideband and moving jammers

We present a new modification of the Hung-Turner (HT) adaptive beam-forming algorithm, providing additional robustness of a narrowband adaptive array in wideband and moving-jammer scenarios. The robustness is achieved by involving the derivative constraints toward the jammer directions in the conventional Hung-Turner (1983) algorithm. The important advantage of the constraints used is that they do not require any a priori information about jammer directions. The computer simulations with wideband and moving jammers show that the proposed algorithm provides the significant improvement of the adaptive array performance as compared with the conventional HT algorithm. At the same time, for a moderate order of derivative constraints, the new algorithm has a computational efficiency, comparable with the conventional HT algorithm.

On least squares methods for direction of arrival estimation in the presence of unknown noise fields

The direction-of-arrival estimation of signal wavefronts in the presence of unknown noise fields is investigated. Generalizations of known criteria for both conditional and nonconditional maximum-likelihood estimates are developed. Numerical calculations show that the usual Gauss-Newton iteration for conditional maximum-likelihood estimates cannot give good results. Therefore, a related, relatively simple two-step least-squares estimate is constructed. Results of numerical experiments are presented and indicate that the two-step estimate has approximately the same power as the least-squares estimate using the exact noise correlation structure.<<ETX>>