Time-varying spatial spectrum estimation using a maneuverable sonar array

This paper addresses the problem of field directionality mapping (FDM) or spatial spectrum estimation in dynamic environments with a maneuverable towed acoustic array. Array processing algorithms for towed arrays are typically designed assuming the array is straight, and are thus degraded during tow-ship maneuvers. In this paper, maneuvering the array is treated as a feature allowing for left and right disambiguation as well as improved resolution toward endfire. The Cramér-Rao lower bound is used to motivate the improvement in source localization which can be theoretically achieved by exploiting array maneuverability. Two methods for estimating time-varying field directionality with a maneuvering array are presented: (1) Maximum likelihood (ML) estimation solved using the expectation maximization algorithm and (2) a non-negative least squares (NNLS) approach. The NNLS method is designed to compute the field directionality from beamformed power outputs, while the ML algorithm uses raw sensor data. A multi-source simulation is used to illustrate both the proposed algorithms' ability to suppress ambiguous towed array backlobes and resolve closely spaced interferers near endfire which pose challenges for conventional beamforming approaches especially during array maneuvers. Receiver operating characteristics are presented to evaluate the algorithms' detection performance versus signal-to-noise ratio. The results indicate that both FDM algorithms offer the potential to provide superior detection performance when compared to conventional beamforming with a maneuverable array.

The most prominent subspace decomposition methods for spatial spectrum estimation include multiple signal classification algorithm (MUSIC) as well as estimation signal parameter via rotational invariance technique (ESPRIT). However, the drawbacks of MUSIC is that estimating the number of source signals are constraint by the following two aspects: array aperture and a large number of sampling data. After carefully investigating the theory of compressive sensing (CS), this paper constructs the model for spatial spectrum estimation on the basis of the sparsity of source signals in the angle spectrum. According to the principle of CS, spatial signals can be sampled with much less sensors, which leads to small sampling data. Furthermore, the source signals can be reconstructed accurately by some recovery algorithms. The approaches are compared with MUSIC and three numerical simulation experiments are programmed with MATLAB. The reconstruction results are found to be approximately to the original signals. The most attractive merits of our proposed method not only reduces the number of elements which are needed for sampling as well as decreases the amount of sampling data, but also the source signals can be reconstructed in terms of their amplitude and bearing simultaneously.

The present algorithms on 2-D temporal-spatial spectrum estimation are deteriorated when the number of signals become close to the dimension of the array. The expenses of the hardware and the software have to be increased to alleviate this degradation. In this paper, a kind of new signal model and approach for 2-D temporal-spatial spectrum estimation is proposed. Through the temporal projection, the maximal number of the signals this method can deal with is much more than present algorithms. Simulation results are presented to demonstrate the performance of the proposed algorithm

A novel single-channel direction finding (DF) method with spatial spectrum estimation is proposed based on 1 bit time-modulated array (TMA). Its performance is analyzed from theoretical derivation to numerical simulations and compared with other existing DF methods. The proposed DF method is implemented as follows. First, the received sideband signals from the 1 bit modulated single-channel signal are deduced, followed by the detailed analysis of the received noise distribution. Second, the harmonic recovery (HR) method with the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{2} $ </tex-math></inline-formula> -norm approximation is utilized to recover the original array signals. Finally, conventional spatial spectrum estimation methods are easily applied for high-accuracy DF. Meanwhile, The DF accuracy of the proposed 1 bit method is analyzed under the Gaussian noise model, and its Cramér–Rao lower bounds (CRLBs) are deduced for the first time and compared with conventional arrays and other DF TMA systems. Numerical simulations are provided to show that the proposed 1 bit TMA system and HR method can achieve better accuracy performance over the existing TMA systems when the circuit noise is predominant in the received noises. An <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S$ </tex-math></inline-formula> -band 1 bit TMA system is fabricated and implemented to experimentally verify the feasibility of the proposed method under circumstances of a single incident source and two coherent sources.

A planar array spatial spectrum estimator has been developed from an extension to a-MUSIC (1995), for discriminating between two closely spaced sources over a wide range of signal correlations. For two closely spaced and/or correlated signals, the second eigenvector in the signal subspace is not observable since the signal covariance matrix tends to be singular. Thus standard MUSIC methods only find one source which is a power weighted centroid of these signals. The /spl delta/-MUSIC spatial spectrum estimator derives an estimate of the second source eigenvector by applying a spatial derivative operator to the covariance matrix. A new signal subspace is formed by a projection operator which combines the first eigenvector and the second eigenvector estimate. The /spl delta/-MUSIC algorithm has been tested, modified and compared to the MUSIC algorithm using a point source simulation for both a linear and a planar array at various levels of correlation for two sources. The algorithm is also tested with simulated data from a Terrain Scattered Interference Source. The algorithm is found to be relatively insensitive to correlation and can separate targets to better than one-half the angular separation of MUSIC.

In this letter, a novel direction-finding method with spatial spectrum estimation is proposed and verified, based on the time-modulated linear array (TMLA) and a single radio-frequency channel. Its principle is as follows. The TMLA receives and periodically modulates the incident signal. After the power combiner, the modulated signal is down-converted to the intermediate frequency and sampled in the single-channel receiver. In the digital domain, the array manifold vector can be calculated from the Fourier coefficients and the harmonic characteristic matrix related to modulation sequences, and thus, the autocorrelation matrix can be estimated. Afterward, the multiple signal classification algorithm is applied to estimate the incident angle, and the spatial smoothing method is exploited to deal with the direction finding of coherent sources. The proposed method has a simple structure and low computational complexity. Numeric simulations and corresponding experiments have been conducted to verify its effectiveness.

Array signal processing is one of the most important branches of signal processing. In the field of array signal processing, many methods suffer from the condition that has multiple non-ideal factors to get the DOA estimation. This paper proposes a method to obtain a high accuracy robust DOA estimation against sensor coupling and coherent signals in Gaussian colored noise. By adding auxiliary sensors, the proposed method firstly decouples the signal steering vector from the mutual coupling matrix, weakening the sensors’ mutual coupling effect. Then, the proposed method reconstructs the received signals’ covariance matrix to reduce the correlation of the coherent signals, avoiding the influence of coherent signals on the spatial spectrum estimation. And then the proposed method uses power inversion to avoid the influence of Gaussian colored noise on the subsequent spatial spectrum estimation such as correlated fake peaks, and finally achieves the accurate estimation of the target radiation source wave arrival directions under non-ideal environment. Numerical simulations verify the effectiveness of the proposed method.KeywordsDOASensor couplingAuxiliary sensorCoherent signalGaussian colored noisePower inversion

For non-invasive imaging of cardiac electrical activity using magnetocardiogram (MCG) data measured on human body surface, a key problem that needs to be solved is to enhance the spatial resolution of reconstructing distributed current source dipole moment strength in MCG imaging. In this paper, a beamforming method of suppressing spatial filter output noise-power gain (SONG) is proposed based on the minimum variance beamforming (MVB). The purpose is to improve the resolution of the distributed source dipole moment strength reconstruction, i.e., the ability to resolve the source for distributed current source spatial spectrum estimation, in order to enhance the resolution of the cardiac electrical activity magnetic imaging. The method offers a new spatial filter weight matrix by using a low-trace positively-semidefinite matrix that will affect the spatial filter output power, on the premise that the influence of noise spatial spectrum of spatial filter on the estimation of current source spatial spectrum has been constrained by the noise spatial spectrum intensity normalization. The positively-semidefinite matrix is specially constructed to satisfy the condition that the eigenvalue is not greater than 1 and the trace of the matrix is lower than its order, so that it can be used to constrain the spatial filter output noise-power gain for improving the robustness to noise of the source spatial spectrum estimation. In addition, a classical model of the horizontally layered conductor is used as the heart-torso model to calculate the lead-field matrix that needs to be used in source spatial spectrum estimation. The results obtained in this study are as follows. For validating the proposed method, a theoretical analysis and simulation tests of the current source reconstruction are performed, where the SONG and MVB methods are compared and a parameter of the signal-to-noise ratio is considered according to the realistic MCG data. In this paper we also give the cardiac electrical activity imaging of 36-channel cardiac magnetic field data of single-cycle from two healthy people, where a heart profile from the magnetic resonance imaging is used as a reference and adjusted to the MCG measurement system. The results show that the SONG method has ability to better resolve the current source and can observe the significant electrophysiological characteristics such as the strong electrical activity in the ventricles of the healthy people at the time of Rpeak. In summary, our proposed method can improve the visual effect of the cardiac electrical activity imaging, when the signal-to-noise ratio of the single-cycle cardiac magnetic signal is not lower than 10 dB. Therefore, this method of measuring the non-invasively imaging cardiac electrical activity is a promising one and helpful for relevant medical research and applications.

This letter addresses the challenges of electromagnetic (EM) vortex radar imaging related to resolution and prior knowledge, proposing an innovative high‐resolution imaging algorithm in range and azimuth dimensions. Traditional imaging methods, such as the fast Fourier transform (FFT) and spatial spectrum estimation, are hindered by the imaging quality and the requirement for precise estimation of subspace dimension. To address these, this study proposes a novel 2‐dimensional imaging method integrating gain modulation with low‐rank modified multiple signal classification (MUSIC) theory. By employing single‐rank eigen decomposition, the proposed method eliminates dependence on prior information while optimising computational complexity. The proper gain modulation further enhances the multi‐target imaging capabilities. In contrast to FFT and sparse imaging techniques, simulation results and quantitative analyses validated the superior resolution and robustness of the method in complex target scenarios, advancing the EM vortex radar for target observation applications.

At present, polarimetric SAR interferometry has been a new technology of measuring terrain parameters. Among the known methods of extracting interferometric phase, some methods developed from spatial spectrum estimation, such as MUSIC or TLS-ESPRIT algorithm, are being perfected. But using these methods we can not get higher phase precision due to few observation data with the SAR signals. An interferometric phase estimation method based on unitary ESPRIT can improve estimation precision by using the plural observation data and its conjugated data. In this paper, the algorithm is proposed and described in detail. Using SIR-C/X-SAR L band data, its effectiveness is tested

Partial discharge is an important symbol of insulation defects. Partial discharge detection system based on UHF antenna array can realize partial discharge location in air-insulated substation. Using spatial spectrum estimation can reduce the antenna array and achieve high-precision positioning with smaller array size. This paper discusses the direction finding accuracy of different antenna arrays with the help of Cram&#x00E9;r-Rao lower bound. Through theoretical derivation and numerical calculation, the influence of array structure on direction finding performance is studied, which provides guidance for optimizing antenna array. The results show that in order to achieve high direction finding accuracy, the offset B in the analytical expression of array factor q should be as large as possible, and the amplitude A and initial phase $\gamma$ should be selected reasonably according to the application requirements. The farther a single burst deviates from the original equilibrium position, the more drastic the change of the Cram&#x00E9;r-Rao lower bound with the variable azimuth angle, and the worse the comprehensive direction finding performance.

With the improvement of people's health awareness, the state increases the construction of public sport facilities, which complicates the allocation and management of resources. The existing spatial spectrum estimation method cannot eliminate the relevant interference data, resulting in duplicate data in the results of resource allocation and management, reducing the accuracy of resource allocation and management. In order to optimize the allocation and management of public sport facilities resources, this study proposes a spatial spectrum estimation method, which is used to deeply tap the potential information in public sport facilities resources and optimize the allocation and management. First, analyze the resources of public sport facilities and put forward the feature vector of allocation and management optimization. Then, use the spatial spectrum estimation method to learn the test samples, get the optimal threshold and weight, and build the resource allocation and management model of public sport facilities. Finally, the accuracy of spatial spectrum estimation method is 98% and the variation range is (0, 10), which is better than the accuracy of the original algorithm is 80% and the variation range is (0, 20). Moreover, change of the spatial spectrum estimation method is smoother, and the correlation between various analyses is better. In unit time, the amount of configuration and management data of spatial spectrum estimation method is higher than that of existing algorithms, which indirectly indicate that the configuration and management time of the spatial spectrum estimation method is short. At the same time, unstructured data account for a large proportion of the data tested this time. Therefore, the accuracy and variation range of the spatial spectrum estimation method is good, which is suitable for the construction of public sport facilities and realizes the optimization of resource allocation and management.

Accurate and consistent information on the area and production of field crops is vital for national and state planning and ensuring food security in India. Satellite-based remote sensing offers a suitable and cost-effective technique for regional- and national-scale crop monitoring. The use of remote sensing data for crop yield estimation has been demonstrated using a semi-physical approach with reasonable success. Assimilating remote sensing data with the DSSAT model and spectral indices-based regression analysis are promising methods for spatially estimating rice crop yields. Rice area and yield in the Cauvery delta zone of Tamil Nadu, India was estimated during samba (August–January) season in the years 2020–2021 using Sentinel 1A Synthetic Aperture Radar satellite data with three different spatial yield estimation methods, namely a spectral indices-based regression analysis, semi-physical approach, and integrating remote products with DSSAT crop growth model. A rice area map was generated for the study area using a rule-based classifier approach utilizing parameterization with a classification accuracy of 94.5% and a kappa score of 0.89. The total classified rice area in Cauvery Delta Region was 379,767 ha, and the Start of Season (SoS) maps for samba season revealed that the major planting period for rice was between 22 September and 9 November in 2020. The study also aimed to identify promising spatial yield estimation techniques for optimal rice yield prediction over large areas. Regression models resulted in rice yields of 3234 to 3905 kg ha−1 with a mean of 3654 kg ha−1. The net primary product was computed using the periodical PAR, fAPAR, Wstress, Tstress, and maximum radiation use efficiency in a semi-physical approach. The resultant rice yields ranged between 2652 and 3438 kg ha−1 with the mean of 3076 kg ha−1. During the integration of remote sensing products with crop growth models, LAI values were extracted from dB images and utilized to simulate rice yields in the range of 3684 to 4012 kg ha−1 with the mean of 3855 kg ha−1. When compared to the semi-physical approach, both integrating remote sensing products with the DSSAT crop growth model and spectral indices-based regression analysis had R2 greater than 0.80, NRMSE of less than 10%, and agreement of more than 90%, indicating that these two approaches could be used for spatial rice yield estimation.

The term hidden semi-Markov model (HSMM) refers to a large class of stochastic models developed to address some of the shortcomings of hidden Markov models (HMMs). As with HMMs, the underlying sequence of states of a process is modelled as a discrete Markov chain. Unlike HMMs, each state in an HSMM can emit a variable length sequence of observations, with many ways to model duration and observation densities. Parameter estimation in HSMMs is typically done using EM or Viterbi (dynamic programming) algorithms. These algorithms require batch processing of large amounts of data, and so are not useful for online learning. To address this issue, we present here a recursive maximum-likelihood estimation (RMLE) algorithm for online estimation of HSMM parameters, based on a similar method developed for HMMs

We address a new approach to solving radar imaging problems stated and treated as uncertain ill-conditioned inverse problems of nonparametric spatial power spectrum estimation via processing the finite number of independent observations of the degraded array data signals (one realization of the trajectory signal in the case of SAR). The idea is to adapt a statistically optimal minimum risk nonparametric power spectrum estimation approach to the radar imaging scenarios with model-level and system-level uncertainties. The proposed incorporation of the worst-case performance optimization-adapted robust regularization aggregated with the descriptive experiment design paradigm into the minimum risk nonparametric estimation strategy leads to a new unified doubly regularized minimum risk approach for robust adaptive high-resolution reconstructive imaging in the uncertain remote sensing scenarios.