Uncorrelated Noise Field Research Articles

Determining the probability of correct resolution of the left–right ambiguity in towed array sonar

When a towed sonar array is straight, it has the difficulty that it cannot distinguish a contact on the left from one at the same angle on the right. When the array isnotstraight and its shape known, we calculate the probability that the left–right ambiguity is resolved correctly, using the Neyman–Pearson hypothesis testing framework, assuming a delay-sum beamformer, a single-frequency contact, and Gaussian noise. We also initially consider the noise field to be uncorrelated and show that the evaluation of the probability of correct resolution reduces to evaluating a one-dimensional integral. We find, as expected, that the probability increases, as the signal-to-noise ratio and the lateral deviation of the array from straight increase. For demonstration purposes, we also evaluate the probability of correct resolution for two representative shapes the array might assume in practice. Finally, we consider a more realistic, correlated noise field and we show that the initial assumption of an uncorrelated noise field provides a good approximation when the lateral deviation of the array is sufficiently large.

The impact of correlated noise on galaxy shape estimation for weak lensing

The robust estimation of the tiny distortions (shears) of galaxy shapes caused by weak gravitational lensing in the presence of much larger shape distortions due to the point-spread function (PSF) has been widely investigated. One major problem is that most galaxy shape measurement methods are subject to bias due to pixel noise in the images ("noise bias"). Noise bias is usually characterized using uncorrelated noise fields; however, real images typically have low-level noise correlations due to galaxies below the detection threshold, and some types of image processing can induce further noise correlations. We investigate the effective detection significance and its impact on noise bias in the presence of correlated noise for one method of galaxy shape estimation. For a fixed noise variance, the biases in galaxy shape estimates can differ substantially for uncorrelated versus correlated noise. However, use of an estimate of detection significance that accounts for the noise correlations can almost entirely remove these differences, leading to consistent values of noise bias as a function of detection significance for correlated and uncorrelated noise. We confirm the robustness of this finding to properties of the galaxy, the PSF, and the noise field, and quantify the impact of anisotropy in the noise correlations. Our results highlight the importance of understanding the pixel noise model and its impact on detection significances when correcting for noise bias on weak lensing.

Effects of Stochastic Ice Strength Perturbation on Arctic Finite Element Sea Ice Modeling

Abstract The ice strength parameter P* is a key parameter in dynamic/thermodynamic sea ice models that cannot be measured directly. Stochastically perturbing P* in the Finite Element Sea Ice–Ocean Model (FESOM) of the Alfred Wegener Institute aims at investigating the effect of uncertainty pertaining to this parameterization. Three different approaches using symmetric perturbations have been applied: 1) reassignment of uncorrelated noise fields to perturb P* at every grid point, 2) a Markov chain time correlation, and 3) a Markov chain time correlation with some spatial correlation between nodes. Despite symmetric perturbations, results show an increase of Arctic sea ice volume and a decrease of Arctic sea ice area for all three approaches. In particular, the introduction of spatial correlation leads to a substantial increase in sea ice volume and mean thickness. The strongest response can be seen for multiyear ice north of the Greenland coast. An ensemble of eight perturbed simulations generates a spread in the multiyear ice comparable to the interannual variability of the model. Results cannot be reproduced by a simple constant global modification of P*.

Coherence effects on the detection performance of quadratic array processors, with applications to large-array matched-field beamforming

The effect of coherence on the detection performance of quadratic array processors is examined using an exponential-power-law model for the signal wave-front correlation in an uncorrelated noise field. Detection performance is quantified by the small-signal deflection criterion, which is first reviewed in the general setting of quadratic detectors, and then applied to matched-field and optimal quadratic beamformers. It is shown that the detection performance of matched-field beamforming is substantially degraded for large arrays and typical coherence lengths. The optimal quadratic processor reduces this coherence loss, however, at a cost of greatly increased processor complexity. Several suboptimal beamformers with reduced computational load are also developed, and their detection performance is compared to that of the matched-field and optimal beamformers. One suboptimal processor, the subarray beamformer, has proved outstanding for this application in three respects: It can realize within 1 dB of optimal performance, is robust over a class of correlation functions, and entails a computational burden no greater than full-array matched-field beamforming.

Noise and array configuration considerations for matched‐field processing in phone and mode space

The conditions under which mode space matched‐field processing offers performance gains relative to phone space matched‐field processing are investigated. Particular emphasis is placed on determining the effects of spatially correlated versus spatially uncorrelated noise fields and choice of array configuration on signal detection. Varying amounts of homogeneous white noise and spatially correlated noise as calculated by a normal mode noise model were combined with the field due to a submerged source to produce simulated phone space covariance matrices for a range of array configuration parameters. A phone‐to‐mode spacing mapping was then used to obtain the corresponding cross‐amplitude correlation matrices. The results of both conventional and MLM processing were analyzed and the trade‐off between the number of phones and percent of the water column spand was investigated.

Gain of a linear array for spatially dependent signal coherence

The coherent or conventional gain of a linear array in an uncorrelated noise field is presented for various models of signal coherence decay with increasing sensor separation. For the case of linear decay, the coherent array gain is shown to approach a maximum of DL/s as the array length increases; where DL, the linear decay length, is defined as the vanishing point of the signal coherence and s is the adjacent sensor separation having some minimum value commensurate with the assumption of uncorrelated noise. For exponential decay of signal coherence a good approximation to the maximum coherent array gain is shown to be 2 DE/s for DE 〉〉s, where DE is the exponential decay length. However, for both linear and exponential decay it is shown that additional gain is achievable beyond the coherent gain limit using incoherent processing. Also a closed form expression is derived for the coherent gain of an array for Gaussian phase fluctuations which are correlated in a linear fashion. Subject Classification: [43]60.20, [43]60.30.

Bayes optimum array detection of targets of known location

This paper presents a Bayes optimum approach to detecting a target of known location by processing the outputs of an array of sensors. Beamforming is not postulated a priori. The complex exponential Fourier series is used to represent the deterministic signals and random processes. Using Bayes decision theory, important existing results and new results are unified and presented in a single mathematical framework. Optimum receiver structures and performance are derived for detecting a known signal source in a Gaussian noise field. They are also derived for detecting a signal source which generates an uncertain waveform in either a spatially uncorrelated noise field or a noise field with spatial correlation due to a farfield noise source. Important new results concerning factorization of optimum array receivers are presented for detecting signal sources of known location which generate either known or uncertain waveforms. A technique for applying existing scalar results to array problems is presented for several cases. Detection performance results, in terms of the receiver operating characteristics (ROC), which are characterized in some cases by the detectability index, are presented for a number of situations.

Partial Recovery of Loss of Array Gain due to Quantization in Digital Beamformers by Post Filtering

By assuming a sinusoidal wave embedded in Gaussian noise as array input signal, the output autocorrelation function of a digital beamformer can be expressed as the sum of infinite series Rsxs, Rnxn, and Rsxn, involving signal and its harmonics, ascending powers of noise cross-correlation functions, and “quantizer functions” of various orders [H. S. C. Wang, J. Acoust. Soc. Am. 53, 929 (1973)]. It is demonstrated that the effect of bandpass filtering of post-beamforming signal can be rigorously analyzed, without transforming to the frequency domain, by applying certain factors attributed first to Davenport [W. B. Davenport, Jr., J. Appl. Phys. 24, 702 (1953)] to the successive terms of the series Rnxk and Rsxn-In the special case of DIMUS processor, the series of quantizer functions reduce exactly to Davenport's confluent hyper-geometric series for his “bandpass rooter” with n → ∞. For a 12-channel beamformer, the array gain improvement or partial recovering of quantizing (clipping) loss by post filtering in correlated and uncorrelated noise fields at different values of input SNR is numerically evaluated and displayed.

Target Detection Using Echo-to-Echo Cross Covariance

Traditional signal-processing techniques such as replica correlation and narrow-band filtering are ineffective for noise rejection when one uses a wide-band source in an active sonar system. Some signal processors such as cross-covariance and integrated-square-law detectors, however, can take advantage of the available high time-bandwidth products for noise rejection. Output statistics for such devices are well known for the case of identical signals in uncorrelated noise fields. But this is an optimistic case for sonar applications where the signals are consecutive target echoes that will decorrelate with target aspect and multipath changes, and where the noises may be fairly stable and, therefore, correlated reverberation. Output statistics were developed, which included the effects of signal and noise correlation. Detection thresholds were then calculated from the output statistics.

Signal-To-Noise Ratio for Arrays in an Uncorrelated Noise Field

Signal-To-Noise Ratio for Arrays in an Uncorrelated Noise Field