Sensor Position Errors Research Articles

TDOA/FDOA based target tracking with imperfect position and velocity data of distributed moving sensors

This paper addresses the target tracking problem using time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measured by moving sensor network whose position and velocity are noise contaminated. It is a known fact that the existing approaches to this problem still have two unsolved technical issues; the unsatisfactory convergence behavior of the tracking filter mainly caused by severe nonlinearity of the problem itself and the tracking performance degradation due to the sensor position and velocity errors. In order to resolve these matters radically, the given target tracking problem is formulated as the robust state estimation problem of the linear system with stochastic uncertainties in its measurement matrix and solved by using the robust Kalman filter theory. The proposed scheme enables us to overcome the inherent limitations of the conventional nonlinear filters for its linear filter structure. It can also prevent the performance degradation due to imperfect sensor position and velocity information. Through the simulations, the effectiveness and reliable target tracking performance of the proposed method are demonstrated.

Map assisted PDR/Wi-Fi fusion for indoor positioning using smartphone

In this paper we present a map-assisted pedestrian navigation system for smartphone user which combines map information, IMU-based Pedestrian Dead Reckoning (PDR) and Wi-Fi localization using fingerprinting method. PDR (Pedestrian Dead Reckoning) using smartphone consist with step detection, step length estimation and heading estimation. However, these algorithms have errors caused by various reasons such as step length error at uncertain user, magnetic disturbance in indoor situation and unstable position of smartphone. To increase accuracy of the PDR, Wi-Fi fusion or map matching method has been proposed. However, previous methods could not solve fault matching or creating map in hall area. Especially in hall, pedestrian could make various trajectories that accurate map structures are required. For solving the structure of map database in hall problem and accurate link selection, we propose a Virtual Link (VL) algorithm with a Virtual Track (VT). Furthermore, an Extended Kalman Filter (EKF) is used for estimating pedestrian position and IMU sensor errors. With map information, step length estimation error, heading error at pedestrian dead reckoning and some IMU sensor errors are estimated. Real world experiments are conducted at building, and it shows less than 3m of CEP (Circular Error Probability) after 200m walk.

Semidefinite Programming Methods for Alleviating Sensor Position Error in TDOA Localization

This paper develops a unified solution for time-difference-of-arrival (TDOA) localization in the presence of sensor position errors. This technique starts with maximum likelihood estimation (MLE), which is known to be nonconvex. A semidefinite programming technique to effectively transform the MLE problem into a convex optimization is proposed, together with a unified solution for four scenarios: 1) without a calibration emitter; 2) with a single calibration emitter, whose position is subject to measurement errors; 3) with a single calibration emitter, whose position is perfectly known; and 4) with a single calibration emitter, whose position is completely unknown. The results are finally extended to the case of multiple calibration emitters, whose positions are also subject to errors. Similar to the existing schemes that are known to have good performances, the proposed solution also reaches the Cramer–Rao lower bound when sensor position errors and TDOA measurement noise are sufficiently small. However, as TDOA measurement noise or sensor position errors increase, comparison with the existing state-of-the-art methods for each scenario shows that the proposed solution performs significantly better.

Angle Estimation and Self-calibration Method for Bistatic MIMO Radar with Transmit and Receive Array Errors

The mutual coupling, gain-phase error and sensor position error of the transmit and receive arrays would significantly degrade the performance of high-resolution direction of departure and direction of arrival estimation algorithms. By applying two well-calibrated instrumental sensors in both transmit and receive arrays, a novel angle estimation and self-calibration method, which considers the combined influences of the above three array errors, is proposed for bistatic MIMO radar. We show that the integrated array errors can be translated to angularly dependent gain-phase error. Then, a reduced dimensional method is used to estimate the angles and the angularly dependent gain-phase error coefficients. Based on the estimated angularly dependent gain-phase error coefficients, the nonlinear least squares optimization model for the three array errors are established and a quasi-Newton optimization method is applied to estimate the mutual coupling matrix, gain-phase error and sensors position errors of the transmit and receive arrays, respectively. Our simulation results corroborate our analysis.

Disturbance Rejection with Distributed Acceleration Sensing for Small Unmanned Aircraft Systems

Rapid sensing of body motions is critical to stabilizing a flight vehicle in the presence of exogenous disturbances as well as providing high-performance tracking of desired control commands. This bandwidth requirement becomes more stringent as vehicle scale decreases. Many flying insects employ distributed networks of acceleration-sensitive sensors to provide information about body egomotion to rapidly detect forces and torques. In this work, a method for rapid sensing of force and torque using a distributed array of accelerometers, arbitrarily placed and rigidly affixed to a vehicle airframe, was developed. Simulations of the sensor array were performed to quantify the effects of sensor noise, sensor position error, and sensor number on acceleration state estimates. A hardware implementation of this distributed sensor array was designed and integrated into the avionics of a small quadrotor vehicle. The response of the array to induced acceleration stimuli was characterized. A linear state estimation matrix was derived from the calibration to directly estimate the total forces and torques exerted on the airframe. A force-adaptive control law utilizing the force and torque estimates provided by the sensor network was implemented to improve tracking of reference states while rejecting exogenous force and torque disturbances. Successful rejection of disturbances in the form of internal actuator variation and external wind gusts was demonstrated on the quadrotor vehicle in flight.

An Improved Algebraic Solution for TDOA Localization With Sensor Position Errors

This letter proposes an improved version of the popular two-stage weighted least squares (TSWLS) algorithm for source localization using time difference of arrival (TDOA) measurements in the presence of sensor position errors. The new technique remains to be closed-form and approximately efficient as TSWLS. But it exhibits lower estimation bias and better robustness to increased noise over TSWLS via using a new Stage-2 processing, where the localization error of its Stage-1 is estimated and subtracted from the Stage-1 output to generate the final source position estimate. Simulations corroborate the theoretical developments.

An Asymptotically Efficient Estimator in Closed-Form for 3-D AOA Localization Using a Sensor Network

Locating a signal source using angles of arrival (AOAs) in a wireless sensor network is attractive because it does not require synchronization of the distributed receivers as in the time-based localization. A challenge for AOA positioning is that the solution tends to have a large amount of bias compared with the maximum-likelihood estimator when using the computationally attractive pseudolinear formulation. AOA localization has been well studied for the 2-D situation, and relatively few developments are for the more practical 3-D scenario. This paper proposes a closed-form solution for 3-D localization using AOAs that can handle the presence of sensor position errors, achieves asymptotically the CRLB performance, and maintains a bias level close to the maximum-likelihood estimator. Theoretical analysis and simulation studies corroborate the performance of the proposed estimator.

Smooth estimation of human foot motion for zero-velocity-update-aided inertial pedestrian navigation system

Purpose – The purpose of this paper is to develop an online smoothing zero-velocity-update (ZUPT) method that helps achieve smooth estimation of human foot motion for the ZUPT-aided inertial pedestrian navigation system. Design/methodology/approach – The smoothing ZUPT is based on a Rauch–Tung–Striebel (RTS) smoother, using a six-state Kalman filter (KF) as the forward filter. The KF acts as an indirect filter, which allows the sensor measurement error and position error to be excluded from the error state vector, so as to reduce the modeling error and computational cost. A threshold-based strategy is exploited to verify the detected ZUPT periods, with the threshold parameter determined by a clustering algorithm. A quantitative index is proposed to give a smoothness estimate of the position data. Findings – Experimental results show that the proposed method can improve the smoothness, robustness, efficiency and accuracy of pedestrian navigation. Research limitations/implications – Because of the chosen smoothing algorithm, a delay no longer than one gait cycle is introduced. Therefore, the proposed method is suitable for applications with soft real-time constraints. Practical implications – The paper includes implications for the smooth estimation of most types of pedal locomotion that are achieved by legged motion, by using a sole foot-mounted commercial-grade inertial sensor. Originality/value – This paper helps realize smooth transitions between swing and stance phases, helps enable continuous correction of navigation errors during the whole gait cycle, helps achieve robust detection of gait phases and, more importantly, requires lower computational cost.

Effects of Sensor Position Errors on Farfield/Nearfield Wideband Beamformers for Microphone Arrays

It is well known that the presence of sensor position errors may lead to failure of farfield/nearfield wideband beamformers for microphone arrays. Therefore, many efforts have been made to design wideband beamformers for microphone arrays robust against sensor position errors in recent years. This paper presents the findings obtained on the study and analysis of the effects of sensor position errors to the performance of farfield/nearfield wideband beamformers for microphone arrays. Several useful properties have been derived through the conduct of a comprehensive statistical analysis, including the bias and variance analysis of array response, to provide in-depth insights into the robustness characteristics of farfield and nearfield wideband beamformers in the presence of sensor position errors. The analysis does not assume any specific array geometry and is thus applicable to arrays with arbitrary geometries. Numerical examples obtained via Monte Carlo simulations are presented to verify the proposed theoretical analysis. This paper is helpful to better understand the effects of sensor position errors on wideband beamformers and useful in microphone array design.

Array shape calibration using long-term ambient noise records

When using an acoustic array to determine the bearing of a source, errors in the sensor positions severely reduce the accuracy of any bearing measurements. This issue is particularly problematic for three sensor arrays, designed to work in two dimensions, because of the lack of redundancy built into the array. This paper presents a method for correcting errors in sensor positions. It is mathematically straightforward to determine the bearing of a far-field impulsive signal by determining the time difference of arrival between sensors by cross-correlation. These time delays can also be used to estimate the sound speed in the vicinity of the array. In an isotropic acoustic medium, the local sound speed is expected to be independent of the source bearing. If the sensor positions used to determine the sound speed and bearing are incorrect, the resulting sound speed measurements will be bearing-dependent. Using an analytically derived function, the correct array shape (with only translational and rotational ambiguity) can be backed out from the directional sound speed distribution. This method will be demonstrated using long-term ambient noise records from the Comprehensive Nuclear-Test Ban Treaty Organization’s (CTBTO) hydrophone arrays.

LiDAR Strip Adjustment Using Multifeatures Matched With Aerial Images

Airborne light detecting and ranging (LiDAR) systems have been widely used for the fast acquisition of dense topographic data. Regrettably, coordinate errors always exist in LiDAR-acquired points. The errors are attributable to several sources, such as laser ranging errors, sensor mounting errors, and position and orientation system (POS) systematic errors, among others. LiDAR strip adjustment (LSA) is the solution to eliminating the errors, but most state-of-the-art LSA methods neglect the influence from POS systematic errors by assuming that the POS is precise enough. Unfortunately, many of the LiDAR systems used in China are equipped with a low-precision POS due to cost considerations. Subsequently, POS systematic errors should be also considered in the LSA. This paper presents an aerotriangulation-aided LSA (AT-aided LSA) method whose major task is eliminating position and angular errors of the laser scanner caused by boresight angular errors and POS systematic errors. The aerial images, which cover the same area with LiDAR strips, are aerotriangulated and serve as the reference data for LSA. Two types of conjugate features are adopted as control elements (i.e., the conjugate points matched between the LiDAR intensity images and the aerial images and the conjugate corner features matched between LiDAR point clouds and aerial images). Experiments using the AT-aided LSA method are conducted using a real data set, and a comparison with the three-dimensional similarity transformation (TDST) LSA method is also performed. Experimental results support the feasibility of the proposed AT-aided LSA method and its superiority over the TDST LSA method.

Linearly constrained minimum variance spatial filtering for localization of conductivity changes in electrical impedance tomography.

We localize dynamic electrical conductivity changes and reconstruct their time evolution introducing the spatial filtering technique to electrical impedance tomography (EIT). More precisely, we use the unit-noise-gain constrained variation of the distortionless-response linearly constrained minimum variance spatial filter. We address the effects of interference and the use of zero gain constraints. The approach is successfully tested in simulated and real tank phantoms. We compute the position error and resolution to compare the localization performance of the proposed method with the one-step Gauss-Newton reconstruction with Laplacian prior. We also study the effects of sensor position errors. Our results show that EIT spatial filtering is useful for localizing conductivity changes of relatively small size and for estimating their time-courses. Some potential dynamic EIT applications such as acute ischemic stroke detection and neuronal activity localization may benefit from the higher resolution of spatial filters as compared to conventional tomographic reconstruction algorithms.

Performance and suitability assessment of a real-time 3D electromagnetic needle tracking system for interstitial brachytherapy.

PurposeAccurate insertion and overall needle positioning are key requirements for effective brachytherapy treatments. This work aims at demonstrating the accuracy performance and the suitability of the Aurora® V1 Planar Field Generator (PFG) electromagnetic tracking system (EMTS) for real-time treatment assistance in interstitial brachytherapy procedures.Material and methodsThe system's performance was characterized in two distinct studies. First, in an environment free of EM disturbance, the boundaries of the detection volume of the EMTS were characterized and a tracking error analysis was performed. Secondly, a distortion analysis was conducted as a means of assessing the tracking accuracy performance of the system in the presence of potential EM disturbance generated by the proximity of standard brachytherapy components.ResultsThe tracking accuracy experiments showed that positional errors were typically 2 ± 1 mm in a zone restricted to the first 30 cm of the detection volume. However, at the edges of the detection volume, sensor position errors of up to 16 mm were recorded. On the other hand, orientation errors remained low at ± 2° for most of the measurements. The EM distortion analysis showed that the presence of typical brachytherapy components in vicinity of the EMTS had little influence on tracking accuracy. Position errors of less than 1 mm were recorded with all components except with a metallic arm support, which induced a mean absolute error of approximately 1.4 mm when located 10 cm away from the needle sensor.ConclusionsThe Aurora® V1 PFG EMTS possesses a great potential for real-time treatment assistance in general interstitial brachytherapy. In view of our experimental results, we however recommend that the needle axis remains as parallel as possible to the generator surface during treatment and that the tracking zone be restricted to the first 30 cm from the generator surface.

TOA-based joint synchronization and source localization with random errors in sensor positions and sensor clock biases

This paper considers the problem of joint synchronization and source localization using time of arrival (TOA) when the known sensor positions and sensor clock biases are subject to random errors. We derive the Cramér–Rao lower bound (CRLB) of the source position and the source clock bias, and quantify the amount of estimation performance degradation due to sensor position errors and sensor clock bias errors. A mean square error (MSE) analysis is conducted and it shows that ignoring the errors in the known sensor positions and sensor clock biases would lead to an estimation accuracy worse than the CRLB. This paper then proceeds to develop a new joint synchronization and source localization algorithm. The new method takes into consideration the presence of sensor position errors and sensor clock bias errors, and has the advantage of being a closed-form solution. Theoretical performance analysis proves that the proposed algorithm can attain the CRLB accuracy under small noise condition. Computer simulations are used to corroborate the theoretical derivations and demonstrate the good performance of the newly developed algorithm.

A Study on the Effects of Sensor Position Error and the Placement of Calibration Emitter for Source Localization

Modern applications use mobile or randomly deployed sensors whose positions are not precise when locating a signal source. An estimator would require statistical knowledge of the sensor position errors to reach the optimum localization performance. Further accuracy improvement necessitates a calibration emitter whose position is known exactly to correct the sensor positions. Under Gaussian error model, this paper shows that when the covariance matrices of the sensor position errors and the measurement noise satisfy certain relation, taking the sensor position errors into account is not necessary and a simpler estimator that pretends the sensor position uncertainties are absent is sufficient to reach the optimum performance. The performance gain from a calibration emitter depends on where it is placed. We derive the optimum calibration position by improving the Fisher information matrix of the source location estimate. The optimum position is of theoretical interest and may not be practical. A suboptimum criterion for realistic calibration emitter placement is then proposed. We shall use TOA, TDOA, and AOA localizations to illustrate the derived results. Simulations support very much the theoretical developments and performance analysis.

Bias analysis of maximum likelihood target location estimator

This paper investigates the bias of the maximum likelihood target location estimate resulting from the Gaussian data measurement noise and sensor position errors. The bias components from them are interrelated, except when they are independent and identically distributed. The bias behaviors of time of arrival, time difference of arrival, and angle of arrival positionings are contrasted, and geometric conditions under which the location bias becomes zero are elaborated.We illustrate the developed results for bias compensation in improving the performance of target tracking.

Joint source localisation and sensor refinement using time differences of arrival and frequency differences of arrival

The accuracy of sources locations and velocities estimate is very sensitive to the accurate knowledge of sensor locations and velocities. In the presence of sensor position and velocity errors, this study considers the problem of simultaneously locating multiple disjoint sources and refining erroneous sensor positions and velocities using time differences of arrival and frequency differences of arrival. The previous work by Sun and Ho to solve this problem provided an efficient estimator for multiple disjoint sources, but it cannot provide optimum accuracy for the sensor positions and sensor velocities. In many practical applications, it is necessary and helpful to refine sensor locations and velocities while localising multiple sources. The proposed method improves the previous method so that both the source and the sensor position and velocity estimates can achieve the Cramér–Rao lower bound accuracy very well over small noise region. The theoretical derivation is corroborated by simulations.

Regularization using Monte Carlo simulation to make optimal beamformers robust to system perturbations.

Design of optimal beamformers that withstand system perturbations such as channel mismatch, sensor position error, and pointing error has been a key issue in real-world applications of arrays. This paper aims to characterize the array performance in relation to the random perturbations from a statistical perspective. In the synthesis stage, directivity index and front-to-back ratio are employed as the performance measures for beamformer optimization. Filter coefficients of the arrays are determined using the least-squares and convex optimization approaches using the preceding performance measures. Next, Monte Carlo sampling are conducted to simulate the stochastic system perturbations following either uniform distribution or normal distribution. Statistics including the sample mean, maximum, minimum, and the maximum likelihood (ML) of the preceding performance measures are calculated. Three regularization criteria based on max-mean, max-min, and max-ML of performance measures are proposed for choosing regularization parameters used in beamformer optimization. The max-mean criterion was found most useful to determine either a simple constant or a frequency-dependent regularization parameter. To validate the proposed methods, experiments of beam patterns and automatic speech recognition test were conducted for directional and diffuse noise suppression problems, where optimal beamformers designed with the regularization parameter selected by the preceding procedures were utilized.

Identifiability Analysis for Array Shape Self-Calibration Based on Hybrid Cramér-Rao Bound

In array shape self-calibration where the sensor position errors and source locations are both unknown, the identifiability of the unknowns is a fundamental problem. Previously, using an approximate hybrid Cramer-Rao bound (HCRB), it was found that under the assumption of small random errors, a nominally linear array is impossible to self-calibrate, but a nominally non-linear array is possible to self-calibrate with three noncollinear far-field sources. In this letter, both small and large random errors are considered, thus the crucial small-error approximation has to be dropped. An accurate HCRB is then derived using fully the prior information about the errors. The accurate HCRB proves that if it is tight, a perturbed nominally linear array is possible to self-calibrate. The larger the sensor position errors, the easier the self-calibration. This is important because of the wide application of linear array. Moreover, two noncollinear far-field sources are sufficient to self-calibrate an array of arbitrary nominal shape.

A Calibration Method for High Precision Vision Measurement System

In order to realize precision measurement for the computer vision measurement system, a system comprehensive calibration method based on straight line imaging characteristics is proposed. The method uses parallel straight line edges of general 00 level gauge groups to comprehensively calibrate the measurement system. It establishes the calibration function that describes the corresponding relationship between the imaging point location and space point position, and then determines the coefficient of the calibration function according to the linear characteristic of gauge block measurement surface edges imaging. This method is simple to operate and is easy to realize and has good versatility. It can comprehensively correct all kinds of system errors such as the optical distortion, the perspective error, the sensor position error and location error of edge detection algorithm. Repeated measurement experiments for the gauges show that the precision of the measurement system can reach by means of this calibration method.