Sensor Position Errors Research Articles

Array calibration of angularly dependent gain and phase uncertainties with carry-on instrumental sensors

Array calibration with angularly dependent gain and phase uncertainties has long been a difficult problem. Although many array calibration methods have been reported extensively in the literature, they almost all assumed an angularly independent model for array uncertainties. Few calibration methods have been developed for the angularly dependent array uncertainties. A novel and efficient auto-calibration method for angularly dependent gain and phase uncertainties is proposed in this paper, which is called ISM (Instrumental Sensors Method). With the help of a few well-calibrated instrumental sensors, the ISM is able to achieve favorable and unambiguous direction-of-arrivals (DOAs) estimate and the corresponding angularly dependent gain and phase estimate simultaneously, even in the case of multiple non-disjoint sources. Since the mutual coupling and sensor position errors can all be described as angularly dependent gain/phase uncertainties, the ISM proposed still works in the presence of a combination of all these array perturbations. The ISM can be applied to arbitrary array geometries including linear arrays. The ISM is computationally efficient and requires only one-dimensional search, with no high-dimensional nonlinear search and convergence burden involved. Besides, no small error assumption is made, which is always an essential prerequisite for many existing array calibration techniques. The estimation performance of the ISM is analyzed theoretically and simulation results are provided to demonstrate the effectiveness and behavior of the proposed ISM.

Prediction of the magnetic field beyond a rectangular array of sensors

A mathematical method is developed for the reconstruction of the magnetic field of a source with sensors arranged in a rectangular array on a plane. A prolate spheroidal shell encloses the source. The magnetic field of the source is expressed in prolate spheroidal coordinates and the prolate spheroidal expansion coefficients are determined by the application of the derived selective functions to the x component of the measured magnetic field. In a simulation with 192 sensors, the magnetic field is accurately reconstructed for sample sources in the presence of sensor noise, sensor position, and orientation error. The reconstruction error is the least for sources with significant dipolar component.

Robust direction‐of‐arrival estimation against array sensor errors using Hopfield neural network

AbstractWhen direction‐of‐arrival estimation methods based on eigenvalue expansion such as MUSIC and ESPRIT are applied to an ideal sensor array, high resolution can be attained. However, if there exist array sensor errors due to sensor position errors and degradation of the phase shifters, significant errors may arise in the estimation results. Also, in order to obtain sufficient estimation accuracy, a relatively high signal‐to‐noise ratio is required in the array input. In this paper, the Hopfield neural network is employed for direction‐of‐arrival estimation and a direction‐of‐arrival estimation method that is robust to array errors by virtue of using training signals is proposed. By means of computer simulation, the method is compared with that of MUSIC and its effectiveness is verified. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(6): 19–28, 2003; Pub‐lished online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10062

Array self-calibration with large sensor position errors

Self-calibration algorithms estimate both source directions of arrival (DOAs) and perturbed array response vector parameters, such as sensor locations. Calibration errors are usually assumed to be small and a first order approximation to the perturbed array response vector is often used to simplify the estimation procedure. In this paper, we develop a more robust procedure that does not rely on the small error assumption. It has better performance for large estimation errors, and when used to initialize the Weiss and Friedlander MUSIC-based iterative technique, we see significant improvement over existing techniques for both small and large errors.

3D ultrasound measurement of large organ volume

Freehand 3D ultrasound is particularly appropriate for the measurement of organ volumes. For small organs, which can be fully examined with a single sweep of the ultrasound probe, the results are known to be much more accurate than those using conventional 2D ultrasound. However, large or complex shaped organs are difficult to quantify in this manner because multiple sweeps are required to cover the entire organ. Typically, there are significant registration errors between the various sweeps, which generate artifacts in an interpolated voxel array, making segmentation of the organ very difficult. This paper describes how sequential freehand 3D ultrasound, which does not employ an interpolated voxel array, can be used to measure the volume of large organs. Partial organ cross-sections can be segmented in the original B-scans, and then combined, without the need for image-based registration, to give the organ volume. The inherent accuracy (not including position sensor and segmentation errors) is demonstrated in simulation to be within ±2%. The in vivo precision of the complete system is demonstrated (by repeated observations of a human liver) to be ±5%.

Array calibration methods for sensor position and pointing errors

In order to make an antenna array more robust to array uncertainties, this paper extends the gain/phase calibration technique proposed by Ng, Er, and Kot to the problems of bearing estimation and adaptive beamforming involving sensor position error and signal pointing error, respectively. The basic idea of this technique is that the true array steering vector is approximated in terms of the nominal one by applying the first-order Taylor series expansion, and then using the null spectrum characteristics of the MUSIC algorithm; the steering vector error containing the information on the array error can be obtained by solving a set of constrained minimization formulations. For sensor position error, a calibration signal is used to impinge upon an array at two different angles. As for pointing error, we impose the orthogonal property between the transformed steering vectors of the signal and jammers on the calibration method. © 2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 26: 132–137, 2000.

Optimal array element localization

Advanced array processing methods require accurate knowledge of the location of individual elements in a sensor array. Array element localization (AEL) methods are typically based on inverting acoustic travel-time measurements from a series of controlled sources at well-known positions to the sensors to be localized. An important issue in AEL is designing the configuration of source positions: a well-designed configuration can produce substantially better sensor localization than a poor configuration. In this paper, the effects of the source configuration and of errors in the data, source positions, and ocean sound speed are quantified using a sensor-position error measure based on the a posteriori uncertainty of a general formulation of the AEL inverse problem. Optimal AEL source configurations are determined by minimizing this error measure with respect to the source positions using an efficient hybrid optimization algorithm. This approach is highly flexible, and can be applied to any sensor configuration and combination of errors; it is also straightforward to apply constraints to the source positions, or to include the effects of data errors that vary with range. The ability to determine optimal source configurations as a function of the number of sources and of the errors in the data, source positions, and sound speed allows the effects of each of these factors to be examined quantitatively in a consistent manner. A modeling study considering these factors can guide in the design of AEL systems to meet specific objectives for sensor localization.

Imposing pattern nulls on broadband array responses

This paper considers the problem of altering a quiescent design for an array of omni-directional sensors so that the altered design rejects a far-field broadband signal from a given direction. This problem occurs where microphone arrays are to be used to acquire speech signals for telecommunication and interferring signals must be rejected. Three main results are presented in this paper. First, conditions for imposing an exact broadband null upon any given quiescent array response are derived. Second, an analysis of the sensitivity of exact nulling array responses to sensor position error is presented. Third, frequency domain formulations for broadband nulls are obtained and it is shown that these are less restrictive than the exact null conditions which are imposed in the time domain. A Lagrange multiplier approach is used to impose the null conditions upon a quiescent array response to minimize the square error between the quiescent and nulled responses. A design example is given.

Optimal array element localization

Measuring ocean acoustic fields at an array of sensors allows the application of advanced signal processing methods such as beamforming and matched-field processing. However, these methods require accurate knowledge of the positions of individual sensors. Typically, an acoustic survey is required to localize the sensors, a procedure referred to as array element localization (AEL). AEL generally consists of measuring the traveltimes of acoustic signals transmitted from a series of known positions to the sensors to be localized. These traveltime data can then be inverted for estimates of the sensor locations using a linearized inversion algorithm. An important issue in AEL is designing the configuration of acoustic source positions: a well-designed source configuration can produce substantially better AEL results than a poor configuration. In this paper, a procedure is developed to determine optimal AEL source locations for arrays of any configuration. This procedure minimizes the condition number of the Jacobian matrix of partial derivatives on which the linearized inversion is based. Minimizing the condition number in effect minimizes the magnification of data (traveltime) errors into model (sensor position) errors in the inversion. Monte Carlo simulations verify that optimal AEL source configurations can lead to significant improvements in sensor localization.

Two-dimensional angle-of-arrival estimation for uniform planar arrays with sensor position errors

The one-dimensional bearing estimation problem of linearly periodic arrays with sensor position errors has been tackled by the Toeplitz approximation method (TAM), iterative TAM, modified TAM, and iterative MTAM without calibrating the sensor positions. This paper extends these methods to the two-dimensional situation using a uniform planar array with sensor position errors to estimate the 2-D angle-of-arrivals (AOAs), azimuth and elevation angles of the emitting sources. Based on the block Toeplitz property and eigenstructure of the ideal covariance matrix observed by the unperturbed array, we extend the methods to alleviate the effect caused by the random perturbations in sensor position. The Music algorithm incorporating a 2-D AOA searching is applied for bearing estimation. Further, the 1-D processing approach presented earlier for solving the 2-D AOA estimation problem can also be applied to reduce the computational burden of 2-D AOA searching.

Improving performance for matched field processing with a minimum variance beamformer

Matched field processing (MFP) employing reduced minimum variance beamforming (RMVB) has been described in the literature as being robust to signal phase errors for vertical line arrays in modal noise. These techniques are extended to horizontal line arrays and evaluated for both horizontal and vertical arrays. The evaluation of RMVB is also more general in that it is extended to white and modal noise fields in the presence of phase or amplitude errors. Two phase error models were employed, one corresponding to constant sensor-position errors the other to short-term fluctuations of mode phase during the covariance matrix estimation. For minimum variance beamforming (MVB), in the presence of both types of random phase errors, array gain, peak-to-sidelobe ratios, and peak-to-background ratios all decreased in a modal noise field. Performance was far less sensitive to phase errors in spatially white noise than in modal noise. MVB was modified by reducing the number of eigenvectors employed in the matching. For the modified forms performance was improved over that of MVB with an attendant reduction in the number of computations. The equispaced horizontal arrays consistently outperformed and were more robust than the equispaced vertical arrays. Similar results were obtained with amplitude errors that were constant during the estimation.

Bearing estimation without calibration for randomly perturbed arrays

The bearing estimation problem of linearly periodic arrays with the presence of sensor position errors is discussed. Conventional approaches for solving this problem generally consist of two steps: calibrating sensor locations and then performing bearing estimation based on the calibrated sensor locations. Approaches to carrying out bearing estimation based on the Toeplitz and eigenstructure reconstruction of the covariance matrix without the need for calibration are proposed. The Toeplitz approximation method (TAM) and a modification of it (MTAM) are used to reconstruct a matrix with Toeplitz structure. To further enhance the capabilities of the TAM and MTAM, an iterative algorithm incorporating with the TAM (ITAM) and the MTAM (IMTAM) is proposed to iteratively reconstruct both the Toeplitz and the desired eigenstructure from the observed covariance matrix. Computer simulations show that the MTAM is more effective than the TAM. Moreover, the iterative methods are superior to the noniterative ones at the price of computations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Mesoscale ocean eddy measurements by multibeam altimetry

A multibeam microwave radar altimeter concept is numerically simulated to evaluate its capability to remotely sense mesoscale oceanographic features and eddies in particular. The study tests the sensitivity of the sensor to variations of systematic and environmental parameters, including sensor attitude angle, sensor position, and system errors. A novel concept of computing eddy vorticity from the multibeam data is explored. Application of this concept to the detection of simulated ocean eddies in the presence of tracker noise gives excellent results; the technique is shown to be simple and accurate. The minimum size of the eddy detectable by the multibeam altimeter is presented for a given performance characteristic of the radar.