Array Errors Research Articles

Self-Calibration Method of Sensors Array Errors Based on Rotation Measurement

Array calibration is the premise of successful array signal processing. The active calibration needs to know the direction of arrival (DOA) of calibration source signals accurately; otherwise, the performance will deteriorate. Although the conventional self-calibration does not need accurate DOA of calibration sources, it may suffer from falling into the local extremum since there are too many parameters to be estimated. Thus, we propose a novel self-calibration method based on the rotation measurement. The rotation measurement is that the array receives signals from a fixed source with different array rotation angles. The proposed method jointly estimates array errors and DOAs of the sources by an alternative minimization (AM) algorithm. Through the derivation of a suitable initial value in the AM algorithm, we could improve the robustness and reduce the computational complexity. The proposed method can achieve as high calibration accuracy as the active method even if there is an error in the source DOA information and can apply to arbitrary planar arrays. Both simulation and field experiment results demonstrate the effectiveness of the proposed method.

Sparsity-Based Joint Array Calibration and Ambiguity Resolving for Forward-Looking Multi-Channel SAR Imagery

Forward-looking multi-channel synthetic aperture radar (FLMC-SAR) can realize two-dimension image formation in monostatic mode. This system must face the problem of left–right Doppler ambiguity. In the traditional methods, the spatial degrees of freedom of the FLMC-SAR system is expected to achieve Doppler ambiguity resolving by beamforming approaches. However, the influence of array error on beamforming cannot be ignored. In practice, the array error will lead to the mismatch of the space–time characteristic, which will reduce the performance of the Doppler ambiguity resolving method based on beamforming. This paper proposes a sparsity-based joint array calibration and ambiguity resolving method to enhance the robustness of FLMC-SAR imagery. For the FLMC-SAR system, the space–time characteristic of targets is first analyzed, based on which the observation model of FLMC-SAR Doppler ambiguity combined with array error is derived. Then, the Doppler ambiguity resolving and array error estimation are transformed into a sparse recovery problem. A modified quasi-Newton method is proposed to realize the array error estimation and Doppler ambiguity resolving of all targets in the local area. Finally, the results of the simulation and the real-data experiments verify that the proposed method can achieve FLMC-SAR Doppler ambiguity resolving and imaging.

Automatic Sensor Array Calibration and Coregistration for On-Scalp MEG

Accurate MEG localization of neural electrical activity requires registration between the MEG sensors and MRI. To reduce the geometric error of the sensor array and realize automatic registration, an array geometry calibration algorithm based on prior knowledge is proposed, which automatically completes the position and orientation calibration of OPM-MEG array with the reference of the design model of MEG helmet. Full-process automatic co-registration based on optical scanning is realized. A position error of 0.23 ± 0.12mm and orientation error of 0.34 ± 0.14° are obtained in the calibration results of 85 sensors on-scalp MEG system. The proposed array geometric calibration algorithm is used to quantify the deviation between the manufactured array and the theoretical array for the first time. The results show a mean position deviation of 0.57mm and an angle deviation of 0.68° in the manufactured array, with the maximum position deviation of 1.45 mm and the maximum orientation deviation of 2.13°. It is indicated that the replacement of the manufactured array by the theoretical array in previous research may introduce significant errors in the MEG source localization results.

End-to-End Moving Target Indication for Airborne Radar Using Deep Learning

Moving target indication (MTI) based on space–time adaptive processing (STAP) has been widely used in airborne radar due to its ability for clutter suppression performance. However, the existing MTI methods suffer from the problems of insufficient training samples and low detection probability in a non-homogeneous clutter environment. To address these issues, this paper proposes a novel deep learning framework to improve target indication capability. First, combined with the problems of target indication caused by the non-homogeneous clutter, the clutter-plus-target training dataset was modeled by simulation, where various non-ideal factors, such as aircraft crabbing, array errors and internal clutter motion (ICM), were considered. The dataset considers various realistic situations, making the proposed method more robust. Then, a five-layer two-dimensional convolutional neural network (D2CNN) was designed and applied to learn the clutter and target characteristics distribution. The proposed D2CNN can predict the target with a high resolution to implement an end-to-end moving target indication (ETE-MTI) with a higher detection accuracy. In this D2CNN, the input was obtained by the clutter-plus-target angle-Doppler spectrum with a low-resolution estimated only by a few samples. The label was given by the target angle-Doppler spectrum with a high-resolution obtained by the target’s exact angle and Doppler. Thirdly, the proposed method used a few samples to improve the target indication and detection probability, which solved the problem of insufficient samples in the non-homogeneous clutter environments. To elaborate, the proposed method directly implements ETE-MTI without the support of the conventional STAP algorithm to suppress the clutter. The results verify the validity and the robustness of the proposed ETE-MTI with a few samples in the non-homogeneous and low signal-to-clutter ratio (SCR) environments.

Deblurring of Sound Source Orientation Recognition Based on Deep Neural Network.

Underwater target detection and identification technology are currently two of the most important research directions in the information disciplines. Traditionally, underwater target detection technology has struggled to meet the needs of current engineering. However, due to the large manifold error of the underwater sonar array and the complexity of ensuring long-term signal stability, traditional high-resolution array signal processing methods are not ideal for practical underwater applications. In conventional beamforming methods, when the signal-to-noise ratio is lower than −43.05 dB, the general direction can only be vaguely identified in the general direction. To address the above challenges, this paper proposes a beamforming method based on a deep neural network. Through preprocessing, the space-time domain of the target sound signal is converted into two-dimensional data in the angle-time domain. Subsequently, we trained the network with enough sample datasets. Finally, high-resolution recognition and prediction of two-dimensional images are realized. The results of the test dataset in this paper demonstrate the effectiveness of the proposed method, with a minimum signal-to-noise ratio of −48 dB.

Analysis of the influence of simultaneous phase-shifting shearing interference polarizer

The aspheric surface testing system based on the shearing interference principle is used to better analyze how the installation and fabrication errors of linear polarizer affects the precision of the aspheric surface. The effects of the angle error of the linear polarizer and the phase-shifting error of the wave plate on the reconstruction of the aspheric surface are studied. Constructing the model of the Jones matrix with the error term system, the reconstruction surface and residual after the corresponding error system are obtained using the four-step phase-shifting and differential Zernike method. The polarizer array of an angle of θ was varied from ( θ − 1 deg ) to ( θ + 2 deg ) every 0.2 deg, and the changes of the fitting surface and the residual surface were simulated. The phase-shifting error of the simulated one-fourth wave plate was <λ / 300. Then, the change of the fitting surface and residual surface when these two errors exist at the same time were simulated. The simulation results show that the influence of the phase-shifting error of the wave plate on the fitting surface is much greater than the angle error of the polarizer array. When assembling the interference system, the phase-shifting error of the wave plate should be <λ / 300 when the light transmission angle error of the polarizer array is between −0.2 deg and 0.2 deg, which will ensure the testing precision of the aspheric surface testing system.

WCA-Based Low-PSLL and Wide-Nulling Beampattern Synthesis for Radar Applications

There are many unavoidable array errors in practical scenarios, which would drastically increase the sidelobe level (SLL) and distort the performance of radar systems accordingly. In this paper, an effective beampattern synthesis approach is proposed to realize a low peak sidelobe level (PSLL) and wide-nulling in the presence of array errors, thus improving the consequent performance of the radar. In particular, the covariance matrix of the sidelobe region (CMSR) is incorporated into the optimization. Considering the randomness of array errors, the statistical mean method is adopted to obtain a more accurate calculation of the CMSR in the presence of array errors based on a Monte Carlo trial. To efficiently and effectively solve the optimization problem, an advanced metaheuristic algorithm, i.e., the water cycle algorithm (WCA), is adopted when seeking the corresponding optimal weight vectors. Numerical results are provided and discussed to demonstrate the effectiveness of the proposed approach including the results based on a wideband linearly spaced magneto-electric (ME) dipole array.

Online Gain-Phase Self-Calibration Method of MIMO Array Based on Statistical Characteristics of Target Angle Distribution

As a hot research topic, the gain-phase error self-calibration in MIMO radar systems has been investigated for many years. In this paper, we proposed a novel array error self-calibration method, termed online errors self-calibration based on feature learning (OES-FL). This method regards the statistical characteristics of the detected targets’ DOA as a prior knowledge and does not require the calibrated antenna subarray or external reference source to correct the array disturbances in real time. First, we analyse the monostatic MIMO signal model suffering gain-phase error. Then, we exploit the statistical characteristics of DOA of many targets for correcting gain-phase error of antenna array. Next, the gain-phase error estimation scheme based on LMS and the DOA deviation estimation method based on LSTM are proposed, respectively. Using real-life radar data collected at the integrated transportation hubs to generate simulation data, the proposed approach is shown to be effective in correcting gain-phase errors and, therefore, provides a promising model for online error self-calibration in monostatic MIMO radars.

Ultraprecision tool-servo cutting of pure nickel for fabricating micro/nanostructure arrays

The fabrication of micro/nanostructure arrays on nickel or nickel alloy surfaces is still a challenge because of the high hardness and low thermal conductivity. Motivated by this, this study proposed the ultraprecision tool-servo cutting process to fabricate micro/nanostructure arrays on the nickel surfaces. Experimental results showed the micro-lens array and sawtooth-shaped nanostructure array were successfully fabricated on pure nickel surfaces. The fabrication error of the micro-lens array is<1.2%, demonstrating the high fabrication accuracy of the proposed cutting process. Furthermore, the sawtooth-shaped nanostructure array triggers the generation of different structural colors. The cyan, blue, yellow, and green with high chromaticity and high brightness were clearly observed on the pure nickel surface. The fabrication time of the sawtooth-shaped nanostructure array is 45 mins, demonstrating the high fabrication efficiency of the proposed cutting process. This study provides a flexible and highly efficient fabrication method to generate micro/nanostructure arrays, which could extend the application fields of nickel and its alloy to optics.

A robust sparsity‐based tri‐iterative space‐time adaptive processing method for airborne radar

To enhance the system performance of airborne radar in a limited-sample environment, a robust sparsity-based tri-iterative space-time adaptive processing (RSBTI-STAP) method is proposed here. First, the proposed RSBTI-STAP method constructs the clutter dictionary matrix by exploiting the a priori knowledge of radar platform. Next, the clutter representation coefficient, array error and weighted vectors are iteratively updated until convergence so as to obtain the estimated values of these three parameters. Finally, combined with the estimated clutter representation coefficient and array error vectors, the STAP weight vector is calculated for the purpose of clutter suppression. The proposed method can be robust to the array amplitude/phase error and can be free of the hyperparameters. Additionally, it does not need the training samples and has the global convergent properties. Numerical experiments based on the simulated data demonstrate the effectiveness of the proposed RSBTI-STAP method.

An improved method of impact point positioning at sea based on Beidou and dual cross-array

Ocean acoustics is an important research topic in ocean engineering. Among them, the location of the impact point at sea is an important method to evaluate the firing accuracy of naval guns. Most of the traditional methods for locating the impact point at sea use the optical positioning principle, which is expensive and has a high false alarm rate. It is easy to be affected by natural conditions, such as marine visibility. Based on this, this paper proposes an improved location method of the impact point at sea based on the Beidou differential and acoustic array, which improves positioning accuracy greatly. First, through the simulation analysis of single array positioning error, this paper gives the basis of the positioning method, then deduces the positioning principle of this method in detail, and simulates and analyzes the positioning error of the double array. Finally, the simulation experiment of the voice signal is carried out to verify the positioning performance of the dual cross-array. The results show that the direction finding of the dual cross-array is very accurate, and the ranging error is relatively large. Among the five positioning points selected in this paper, the maximum relative direction-finding error is 0.33%, and the maximum relative ranging error is only about 1%, which is much better than the ranging performance of a single array. It has certain engineering application values and provides a certain reference for the design of the impact point positioning scheme at sea.

Tensor coaxial calibration of magnetic sensor array

In order to effectively solve the influence of the magnetic sensor array error caused by axial inconsistency on the measurement accuracy, an array composed of four fluxgate sensors is built by using the Euler rotation matrix, and the consistency correction is carried out. Firstly, aiming at the non orthogonal, scale factor, zero bias and other error factors of the sensor itself, a 9-PARAMETER correction coefficient matrix is constructed to compensate the non orthogonal magnetic field measurement of the sensor, and the ideal orthogonal three component magnetic field measurement value is obtained. On the above-mentioned basis, the reference sensor in the magnetometry array is selected, and the roll, pitch and azimuth of the sensor to be calibrated are transformed to establish the Euler rotation matrix, and the model for 9-PARAMETER consistency correction is constructed. The reference sensor and the sensor to be calibrated are placed on the magnetic gradiometer for experimental verification. The experimental results show that the root mean square error of magnetic field measurement is within 10 nT after the sensor measurement error compensation correction, and the angle error of each axis measurement is within 0.01åfter the consistency correction (4.22 nT). It shows that the magnetic field measurement values of different measuring points in the sensor array can be well projected on the coordinate axis of the reference sensor after correction, and the magnetic field information of the measuring points can be correctly projected, which has high reliability.

FEM simulation based adaptive sensors array error compensation method for impact monitoring on stiffened composite structures

To eliminate the sensor array based impact localization bias on stiffened composite structures, a finite element method (FEM) simulation based adaptive sensors array errors compensation method for impact monitoring is introduced. Firstly, detailed analysis and comparison discussion about Lamb wave propagation errors between the simple and stiffened plate are provided using FEM simulation, and the gain-phase errors obtained are structured as a array error matrix. Secondly, array error matrix is substituted into the steering vector of standard two-dimensional Multiple Signal Classification (2D-MUSIC) algorithm to compensate the stiffener effect. And then initial estimates of impact could be estimated by the compensated 2D-MUSIC algorithm. Finally substituting these initial estimates, the cost function is minimized by adaptive iterative to calculate the reasonable location of the impact source. The experiments on a carbon fiber composite stiffened plate demonstrate the validity and effectiveness of the proposed method.

A 12-Bit, 100 MS/s SAR ADC Based on a Bridge Capacitor Array with Redundancy and Non-Linearity Calibration in 28 nm CMOS

This paper presents a 12-bit, 100 MS/s successive approximation register (SAR) analog-to-digital converter (ADC) based on a bridge capacitor array with redundancy and non-linearity calibration. The differential non-linearity calibration method was proposed to compensate for the linearity, which is degraded by the parasitic capacitance of the bridge capacitor. To reduce the power dissipation and alleviate the settling error of the DAC capacitor array, a hybrid redundant scheme was proposed. A low-power, high-performance SAR ADC was implemented based on the proposed techniques. This SAR ADC prototype was implemented in 28 nm CMOS technology. Measurement results showed that the proposed SAR ADC could achieve a (signal-to-noise distortion ratio) SNDR of 61.46 dB and 58.82 dB at low and Nyquist input frequencies, respectively, resulting in figure of merits (FOMs) of 8.69 fJ/conversion and 11.8 fJ/conversion step, respectively. The SAR ADC core occupied an active area 0.0227 mm2.

Design and analysis of monolithic integrated MEMS vector hydrophone micro-array

Based on the high sensitivity and miniaturization advantages of MEMS vector hydrophone, we proposed and designed a monolithic integrated micro-array vector hydrophone composed of multiple sensor units. The theoretical model shows that the micro-array can improve the structural sensitivity and output signal-to-noise ratio while eliminating the problem of port and starboard ambiguity. Meanwhile, the micro-array structure clearly reduces the installation error of conventional vector array and improve the directional accuracy. Taking 5-element micro-array as an example, the resonance frequency in wet mode reaches 956 Hz that meets the requirement of test frequency band. Through theoretical and computational analysis, the sensitivity of micro-array is increased 14 dB and the SNR is increased 3.1 dB compared with that of the single vector hydrophone. The standing-wave tube experiment verified the directional effect of vector micro-array. The research of vector hydrophone micro-array is helpful to the application of underwater acoustic engineering.

BA-Based Low-PSLL Beampattern Synthesis in the Presence of Array Errors

In practical scenarios, there are always array errors, which would increase the sidelobe level (SLL) of the array and distort the performance of the electronic devices consequently. Nevertheless, most of the reported works do not take these unavoidable errors into consideration when implementing array beampattern synthesis. To remedy this problem, a low sidelobe beampattern synthesis approach is proposed in the presence of array errors based on the bat algorithm (BA). In particular, the covariance matrix of the sidelobe region in the presence of array errors is incorporated into the optimization problem. Generally, there are many factors that would contribute to array errors in practical scenarios. Therefore, to reduce the influence of the uncertainty characteristic of the errors on the low-SLL beampattern synthesis, the statistical mean method is utilized to obtain a robust calculation of the covariance matrix in the presence of array errors. Theoretical analysis using signal processing technique and electromagnetic simulation using Ansoft HFSS workbench are combined to testify the effectiveness of the proposed approach. Numerical results show that peak SLLs (PSLLs) of around −22dB and −20dB can be respectively achieved in the above two simulation situations with the obtained weight vectors.

Dynamic Zero Current Method to Reduce Measurement Error in Low Value Resistive Sensor Arrays for Low Power Wearable Electronics

Dynamic Zero Current Method to Reduce Measurement Error in Low Value Resistive Sensor Arrays for Low Power Wearable Electronics

The Statistics of Superdirective Beam Patterns

Superdirective arrays have been extensively studied because of their considerable potential accompanied, unfortunately, by a high sensitivity to random errors that affect the responses and positions of array elements. However, the statistics of their actual beam pattern (BP) has never been systematically investigated. This paper shows that the Rician probability density function (PDF), sometimes adopted to study the impact of errors in conventional arrays, is a valid approximation for superdirective BP statistics only where some mathematical terms are negligible. The paper also shows that this is the case for all linear end-fire arrays considered. A similar study is proposed concerning the correlation between BP lobes, showing that for the superdirective arrays considered the lobes, especially non-adjacent ones, are almost independent. Furthermore, knowledge of the PDF of the actual BP allows one to define quantile BP functions, whose probability of being exceeded, at any point, is fixed. Combining the lobes&#x2019; independence with quantile BP functions, an empirical equation for the probability that the entire actual BP will not exceed a quantile function over an interval larger than a given size is obtained. This new knowledge and these tools make it possible to devise new methods to design robust superdirective arrays via optimization goals with clearer and more relevant statistical meaning.

Detection of Strain Magnitude and Direction Based on an RFID Sensor Array

Radio frequency identification (RFID) antenna sensors have become one of the most interesting areas of passive strain sensing owing to the advantages of battery-less and wireless interrogation. However, existing RFID methods could mainly detect strain magnitude with its direction along the length or width of the radiant element. To meet the practical purpose of strain detection, a magnitude and direction detection method based on an RFID sensor array is proposed. First, a single strain sensor, i.e., a short stub feed patch antenna, is designed. Specifically, taking resonant frequency shift (RFS) as the feature of strain amplitude, the sensor has different sensitivities in the electrical length direction and width direction. Then, based on this characteristic, a sensor array consisting of four sensors with a mutual angle of 45&#x00B0; is proposed to achieve the quantitative detection of strain magnitude and direction. Finally, the feasibility of the proposed method is validated by simulations and experiments. Experimental results show that the sensitivities of the single strain sensor in the longitude direction and transverse direction are &#x2212;873.91 and 57.28 Hz/<inline-formula> <tex-math notation="LaTeX">$\mu \varepsilon $ </tex-math></inline-formula>, respectively. The strain magnitude detection accuracy of the proposed sensor array is within 10&#x0025; except for individual abnormal values, and the direction detection error of the sensor array is within 3&#x00B0;.

A Two-Stage STAP Method Based on Fine Doppler Localization and Sparse Bayesian Learning in the Presence of Arbitrary Array Errors.

In the presence of unknown array errors, sparse recovery based space-time adaptive processing (SR-STAP) methods usually directly use the ideal spatial steering vectors without array errors to construct the space-time dictionary; thus, the steering vector mismatch between the dictionary and clutter data will cause a severe performance degradation of SR-STAP methods. To solve this problem, in this paper, we propose a two-stage SR-STAP method for suppressing nonhomogeneous clutter in the presence of arbitrary array errors. In the first stage, utilizing the spatial-temporal coupling property of the ground clutter, a set of spatial steering vectors with array errors are well estimated by fine Doppler localization. In the second stage, firstly, in order to solve the model mismatch problem caused by array errors, we directly use these spatial steering vectors obtained in the first stage to construct the space-time dictionary, and then, the constructed dictionary and multiple measurement vectors sparse Bayesian learning (MSBL) algorithm are combined for space-time adaptive processing (STAP). The proposed SR-STAP method can exhibit superior clutter suppression performance and target detection performance in the presence of arbitrary array errors. Simulation results validate the effectiveness of the proposed method.