White Noise Constraint Research Articles

Robust matched field processing for array tilt and environmental mismatch

Adaptive matched field processing with the minimum variance beamformer provides excellent sidelobe suppression for source localization, but suffers from sensitivity to mismatch between the modeled and true acoustic field (i.e., environmental mismatch). To increase tolerance to the mismatch while retaining satisfactory sidelobe control, robust algorithms such as the white noise constraint (WNC) can be employed. The WNC alone, however, is not sufficient when the mismatch results from an unknown array tilt (i.e., geometric mismatch). This study introduces an adaptive matched field beamformer that is tolerant to both array tilt and environmental mismatch. By modeling the pressure fields corresponding to a set of assumed tilt angles, we impose multiple constraints that, when applied to the beamformer, increase robustness to the array tilt. Simulations and data results are presented to demonstrate localization and tracking of a surface ship (200–500 Hz) using a 16-element, 56-m long, tilted vertical array in approximately 100-m deep shallow water.

Performance limitation of networked control systems with networked delay and two-channel noises constraints

ABSTRACTThe performance limitation of networked control systems (NCSs) with networked delay and two-channel noises constraints are studied in this paper. The networked parameters mainly consider the networked delay in the forward channel and white Gaussian noise constraint existing in forward channel and feedback channel. The tracking performance limitation expression is achieved by using the spectral decomposition technique and selecting the optimal one-parameter structure. The obtained result shows that the tracking performance limitation of NCSs is related to the position of the non-minimum phase zeroes, the position of the unstable poles, networked delay, two-channel noises and input signal. We can also know that the networked delay and white Gaussian noise have influence on the tracking performance limitation of NCSs. Finally, a simulation example is given to demonstrate effectiveness of the theoretical results.

Multi-frequency sparse Bayesian learning for matched field processing in non-stationary noise

Using simulations and data, we localize a quiet source in the presence of an interferer. The SWellEx-96 Event S59 consists of a submerged source towed along an isobath over a 65 min duration with an interferer traversing the source track. This range independent, multi-frequency scenario includes mismatch, non-stationary noise, and operational uncertainty. Mismatch is defined as a misalignment between the actual source field observed at the array and the modeled replica vector. The noise process changes likely with time. This is modelled as a heteroscedastic Gaussian process, meaning that the noise variance is non-stationary across snapshots. Sparse Bayesian learning (SBL) has been applied previously to the matched field processing application [Gemba et al, J. Acoust. Soc. Am., 141:3411-3420, 2017]. Results demonstrate that SBL exhibits desirable robustness properties and improved localization performance when compared to the white noise constraint and Bartlett processors.

Multi-frequency sparse Bayesian learning for robust matched field processing.

The multi-snapshot, multi-frequency sparse Bayesian learning (SBL) processor is derived and its performance compared to the Bartlett, minimum variance distortionless response, and white noise constraint processors for the matched field processing application. The two-source model and data scenario of interest includes realistic mismatch implemented in the form of array tilt and data snapshots not exactly corresponding to the range-depth grid of the replica vectors. Results demonstrate that SBL behaves similar to an adaptive processor when localizing a weaker source in the presence of a stronger source, is robust to mismatch, and exhibits improved localization performance when compared to the other processors. Unlike the basis or matching pursuit methods, SBL automatically determines sparsity and its solution can be interpreted as an ambiguity surface. Because of its computational efficiency and performance, SBL is practical for applications requiring adaptive and robust processing.

Adaptive and compressive matched field processing.

Matched field processing is a generalized beamforming method that matches received array data to a dictionary of replica vectors in order to locate one or more sources. Its solution set is sparse since there are considerably fewer sources than replicas. Using compressive sensing (CS) implemented using basis pursuit, the matched field problem is reformulated as an underdetermined, convex optimization problem. CS estimates the unknown source amplitudes using the replica dictionary to best explain the data, subject to a row-sparsity constraint. This constraint selects the best matching replicas within the dictionary when using multiple observations and/or frequencies. For a single source, theory and simulations show that the performance of CS and the Bartlett processor are equivalent for any number of snapshots. Contrary to most adaptive processors, CS also can accommodate coherent sources. For a single and multiple incoherent sources, simulations indicate that CS offers modest localization performance improvement over the adaptive white noise constraint processor. SWellEx-96 experiment data results show comparable performance for both processors when localizing a weaker source in the presence of a stronger source. Moreover, CS often displays less ambiguity, demonstrating it is robust to data-replica mismatch.

Multiple snapshot and multiple frequency compressive matched field processing

Matched field processing is a generalized beamforming method which matches received array data to a dictionary of replica vectors to locate and track a source. Its solution set generally is sparse since there are considerably fewer sources than replicas. The problem is also underdetermined since the number of sensors are less than the number of unique depth-range cells. Using compressive sensing (CS), the traditional spatial matched-filter problem is reformulated as a convex optimization problem subject to a row-sparsity constraint (RSC). The RSC selects the best match among the replica dictionary when using multiple snapshots. It is found that CS performance is equivalent to the Bartlett processor when comparing the sparse solution to the ambiguity surface’s peak for any number of snapshots in a single frequency—single source scenario. Results also indicate that CS performs similarly to the adaptive white noise constraint processor in a multiple source scenario. The RSC can further be exploited to select a common depth-range cell from snapshots corresponding to multiple frequencies to improve the source tracking in the presence of data-replica mismatch. Results are demonstrated using both simulated and SWellEx-96 experiment data.

Single and multiple snapshot compressive matched field processing

Matched field processing is a generalized beamforming method which matches received array data to a dictionary of replicas to locate and track a source. The solution set generally is sparse since there are considerably fewer sources than replicas. This underdetermined problem can be solved with sparse processing (SP) which potentially is attractive for several reasons. The traditional spatial matched-filter problem is reformulated as a convex optimization problem subject to a sparsity constraint. For example, an elastic net seems to be an appropriate penalty in order to find the best match among a correlated group of replicas. Another advantage is that SP does not require inversion of the sample covariance matrix and therefore can outperform conventional high-resolution processors in snapshot deficient scenarios (i.e., fast moving sources). A third potential advantage is that SP can achieve super-resolution at high SNR and discriminate between closely spaced sources. Here, we demonstrate the performance of single and multi-snapshot SP to track a towed source using the SWellEx-96 data set. Results are benchmarked using the Bartlett and the white noise constraint processors. We further discuss the processing of multiple frequencies in order to improve the source tracking.

Reweighted sparse source-location acoustic mapping in shallow water

Various applications for monitoring and surveillance in littoral waters rely on passive sonar for localizing acoustic sources in shallow-water environments. Although adaptive matched-field processing (MFP) has been successfully used for localization, its performance is degraded when localizing multiple sources at low signal-to-noise ratios (SNRs) and in the presence of model mismatch. Robust MFP using, e.g., the white-noise constraint offers an alternative to cope with the mismatch issue but remains ineffective in the multisource and low SNR setup. This work capitalizes on sparsity for constructing a source location map for shallow water environments. Sparsity naturally arises since only locations corresponding to acoustic sources are expected to appear in the map (nonzero entries), while the remaining map locations are empty (zero entries). A high-resolution map is constructed via a two-step approach that capitalizes on a model for the acoustic propagation environment while being robust to model mismatch. During the first step the robust map is obtained by solving a regularized least-squares (LS) problem. Then, the map coefficients are used to devise a modified criterion with a weighted regularizer yielding a lower-ambiguity map, facilitating detection of quiet sources in the presence of loud interferers.

Application of acoustic noise and self-potential localization techniques to a buried hydrothermal vent (Waimangu Old Geyser site, New Zealand)

A seismo-acoustic and self-potential survey has been performed in the hydrothermal area of the old Waimangu Geyser (New Zealand), which was violently erupting a century ago. Nowadays, no surface activity is visible there. We set-up an array of 16 geophones and recorded a high and steady acoustic ambient noise. We applied the matched field processing (MFP) approach to the acoustic data to locate the sources responsible for the ambient noise. The white noise constraint processor reveals the presence of a unique and well-focused acoustic source at a depth of 1.5 m below the seismic array. For this very shallow source, the application of MFP enabled the determination of both the source location and the dispersion curve of seismic velocity. The study was completed by self-potential (SP) measurements on several profiles around the acoustic noise source, which displayed a large positive anomaly above it. The results of the SP inversion gave an electric streaming current density source very close to the acoustic one. Both sources likely belong to a shallow hydrothermal structure interpreted as a small convective cell of boiling water beneath an impermeable layer. The joint application of these methods is a promising technique to recognize hydrothermal structures and to study their dynamics.

Broadband high frequency matched-field processing.

Adaptive matched-field processing (MFP) is extremely sensitive to environmental uncertainties. While conventional and adaptive techniques may work for low-frequency signals in well-studied environments, the localization performance usually degrades rapidly as frequency increases, such that MFP in the 3.5 kHz regime, in shallow water environments, is typically problematic. A broadband coherent method [IEEE J. Ocean. Eng. 21, 384–392], combined with white noise constraint and principal component techniques, is implemented to construct robust replicas from experimental data. Matched-field tomography is then used to better understand the origin of the frequency dependent MFP mismatch (uncertain bottom structure, sound speed fluctuations, or both), and the results are compared with simulations. Ultimately, we want to gain some insights into how to implement a robust matched-field processor for high-frequency scenarios without using experimental data to create replica vectors. In particular, we are seeking to understand the thresholds for adaptive processors as function of signal to noise ratio and frequency dependent environmental mismatch. [Work supported by ONR.]

Robust matched-field processing using a coherent broadband white noise constraint processor

Adaptive matched-field processing (MFP) is not only very sensitive to mismatch, but also requires the received sound levels to exceed a threshold signal-to-noise ratio. Furthermore, acoustic sources and interferers have to move slowly enough across resolution cells so that a full rank cross-spectral density matrix can be constructed. Coherent-broadband MFP takes advantage of the temporal complexity of the signal, and therefore offers an additional gain over narrow-band processing by augmenting the dimension of the data space. However, the sensitivity to mismatch is also increased in the process, since a single constraint is usually not enough to achieve robustness and the snapshot requirement becomes even more problematic. The white noise constraint method, typically used for narrow-band processing, is applied to a previously derived broadband processor to enhance its robustness to environmental mismatch and snapshot deficiency. The broadband white noise constraint theory is presented and validated through simulation and experimental data. The dynamic range bias obtained from the snapshot-deficient processing is shown to be consistent with that previously presented in the literature for a single frequency.

Coherent-broadband, white noise constraint, matched-field processing

Coherent-broadband matched-field processing takes advantage of the temporal complexity of the signal and, therefore, offers an increased gain over narrowband processing. However, the problem of mismatch is aggravated in adaptive versions such as the MVDR. One constraint is not enough to achieve robustness in such high-dimensional spaces. Some coherent algorithms also require a large number of snapshots, leading to ill-conditioned cross-spectral density matrices in the context of the required MVDR matrix inversions. The white noise constraint algorithm developed by Cox et al. [IEEE Trans. on Acoustics, Speech, and Sig. Proc. 35, 1365–1376 (1987)], and typically used for narrowband processing, is applied to some previously derived broadband processors to enhance their robustness. The broadband white noise constraint theory is presented and validated through simulation and experimental data. [Work supported by ONR.]

Higher frequency matched‐field processing

We study matched‐field processing (MFP) in the 3.5‐kHz shallow water regime at a range of 4 km for which MFP is typically problematic. Data are used to construct both the cross‐spectral‐density‐matrix (CSDM) and the weight vectors for the Bartlett, minimum variance distortionless response (MV), and white noise constraint (WNC) processors. There is sufficient data to construct the weight vectors as a function of time as measured around the CSDM construction time. While the MV processor degrades significantly over a few minutes, the WNC processor remains stable for 15 min or longer. We study these experimentally derived weight vectors to further understand the origin of the increased stability of the WNC over the MV and to gain further insight into how to construct a robust MFP processor. [Work supported by ONR.]

Null broadening with snapshot-deficient covariance matrices in passive sonar

Adaptive-array beamforming achieves high resolution and sidelobe suppression by producing sharp nulls in the adaptive beampattern. Large-aperture sonar arrays with many elements have small resolution cells; interferers may move through many resolution cells in the time required for accumulating a full-rank sample covariance matrix. This leads to processing. In this paper, the null-broadening technique originally developed for an ideal stationary problem is extended to the snapshot-deficient problem combined with white-noise constraint (WNC) adaptive processing. Null broadening allows the strong interferers to move through resolution cells and increases the number of degrees of freedom, thereby improving the detection of weak stationary signals.

Some approaches to robust, snapshot-deficient, adaptive processing

We typically assume that longer arrays and more sensors are always beneficial. However, one of the issues identified by the ONR Ocean Acoustic Observatory Panel was ‘‘snapshot-deficient adaptive processing’’ arising, for example, from the motion of strong interferers (e.g., ships) through the small resolution cells of large arrays. This paper discusses two different but related concepts to reject the moving interferers: (1) null broadening for individual nulling and (2) model-based projection for collective nulling. The plane wave null broadening approach is combined with the robust white noise constraint and extended to matched field processing. The model-based projection exploits the fact that most interferers are close to the surface while targets of interest are usually in the middle of the water column. The projection matrix is constructed from the most significant eigenvectors of a replica covariance matrix from many independent sources within a surface strip. Simulations and experimental data illustrate the techniques.

Improvement in matched field processing using the CLEAN algorithm.

Adaptive matched field processing such as the minimum variance distortionless processor (MV) provides excellent sidelobe (or ambiguity) suppression capability in source localization given a perfect knowledge of the ocean environment. Unfortunately, this processing is very sensitive to sources of mismatch and robust adaptive algorithms are then employed such as a white noise constraint (WNC) often at the expense of insufficient sidelobe control. The CLEAN algorithm was introduced in radio astronomy [Astron. Astrophys. Suppl. Ser. 15, 417-426 (1974)] to produce a high quality image of the sky by reducing sidelobe-induced artifacts. In this paper, the CLEAN concept is extended to matched field processing. Numerical simulations and experimental data demonstrate that matched field processing combined with the CLEAN algorithm can improve performance, especially when a weak source is masked by sidelobes from a much stronger source.

Null-broadening in a waveguide.

Null-broadening, introduced in plane wave beamforming, is extended to an ocean waveguide in the context of matched field processing. The method is based on the minimum variance processor with white noise constraint and the distribution of fictitious sources using the theory of waveguide invariants. The proposed method is demonstrated in simulation as well as with data collected during the SWellEx-96 experiment. As another application, it is shown that the width of a null can be controlled in an adaptive time reversal mirror with a source-receive array.

Robust adaptive nulling in matched field processing

Nulling out sources of interference is a major goal of adaptive array processing. For moving interferers, null-broadening is a useful technique to reduce the interference. A null-broadening approach has been recently developed for planewave beamforming [R. J. Mailloux, Electron. Lett. 31, 771–772 (1995)] [M. Zatman, ibid. 31, 2141–2142 (1995)] to cover the angular extent of the motion. One way to achieve this is to introduce the effects of dispersion into a covariance matrix, which is equivalent to averaging the covariance matrix over a finite bandwidth in frequency. In this study, the null-broadening approach is extended to the matched field processing (MFP) in an ocean waveguide, based on an MV processor with a white noise constraint. In particular, the null-broadening in range is accomplished through using waveguide invariant properties. Simulations as well as the SWELLEX-96 experimental data clearly demonstrate the null-broadening effect.