Receiver Position Errors Research Articles

TDOA and FDOA Hybrid Positioning of Mobile Radiation Source with Receiver Position Errors

TDOA and FDOA Hybrid Positioning of Mobile Radiation Source with Receiver Position Errors

Instantaneous velocity determination and positioning using Doppler shift from a LEO constellation

To provide backup and supplementation for the Global Navigation Satellite System (GNSS), Doppler shift from Low Earth Orbit (LEO) satellites can be used as signals of opportunity to provide positioning, navigation, and timing service. In this contribution, we first investigate the model and performance of instantaneous velocity determination and positioning with LEO satellites. Given a LEO constellation with 288 satellites, we simulate Doppler shift observations at nine multi-GNSS experiment stations. Owing to the lower orbit, the performance of LEO velocity determination is much more sensitive to the initial receiver position error than that of GNSS. Statistical results show that with the initial receiver position error increased from 0.1 to 10 m, the Root Mean Square Errors (RMSEs) increase from 0.73 to 2.65 cm/s, 0.68 to 2.96 cm/s, and 1.67 to 4.15 cm/s in the east, north, and up directions, respectively. The performances with GPS are compared with GPS + LEO, and it is found that LEO Doppler shift observations contribute to GPS velocity determination. As for LEO Doppler positioning, even if more than 30 visible LEO satellites are available, the position dilution of precision values can reach several hundreds. Assuming that the error of LEO Doppler measurements is 0.01 m/s, the instantaneous Doppler positioning accuracy can achieve about a few meters, which is comparable to that of GNSS pseudorange positioning. A constant velocity model is adopted for state transition. Static LEO Doppler positioning results show that an accuracy at centimeter to decimeter level can be achieved after solution convergence. For a static simulated kinematic positioning test, the RMSEs range from a few decimeters to several meters in different regions by giving different constraints. For a dynamic positioning test, the RMSEs are about 2–3 m in high latitude region.

Majorization-Minimization Method for Elliptic Localization in the Absence of Transmitter Position

This paper investigates the problem of elliptic localization in the absence of transmitter position. An efficient iterative method is developed to jointly evaluate the target and transmitter positions. Using the measurement information from the indirect paths reflected from the target and the direct paths between the transmitter and receivers, a non-convex maximum likelihood estimation (MLE) problem is formulated. Owing to the non-convex nature of the issue, we apply the majorization-minimization (MM) principle to address the MLE problem, which iteratively minimizes a convex surrogate function instead of the original objective function. Moreover, the proposed MM method is further extended to tackle a general scenario where both multiple unknown transmitters and receiver position errors are considered. Finally, numerical simulations demonstrate that the proposed MM method outperforms the state-of-the-art methods.

3D TDOA/AOA Localization in MIMO Passive Radar with Transmitter and Receiver Position Errors

This paper deals with the problem of determining the position of a single target from time difference of arrival (TDOA) and angle of arrival (AOA) measurements using multitransmitter multireceiver passive radar system with widely separated antennas. A practically motivating scenario where the transmitter and receiver positions are contaminated by errors is addressed. First, the reduction in localization accuracy due to the presence of transmitter and receiver position errors is derived through the Cramér-Rao lower bound (CRLB) analysis. Then, a novel algebraic localization algorithm based on weighted least squares minimization is proposed that takes the transmitter and receiver position errors into consideration to reduce the estimation error. The proposed solution is shown theoretically to reach the CRLB even when the transmitter and receiver positions have errors. Simulation results also verify the theoretical developments and the performance improvement of the proposed solution over existing algorithms.

PERFORMANCE EVALUATION OF PARABOLIC TROUGH COLLECTOR WITH RECEIVER POSITION ERROR

In the present study, the effect of receiver position error on the optical and thermal performance of a parabolic trough collector (PTC) has been studied. Optical analysis of the PTC has been carried out by using Monte Carlo ray tracing (MCRT) method. The solar heat flux profile obtained from the optical analysis is coupled with the finite volume method (FVM) to study the thermal performance of the PTC. Simulations have been done for experimental SEGS LS2 solar collector used in Sandia National Laboratories. Syltherm 800 has been considered as heat transfer fluid (HTF). Receiver position errors in two directions i.e. along optical axis and lateral direction, have been taken. Results show that the receiver position error substantially influences the solar heat flux distribution and hence the temperature distribution on the absorber tube. The maximum circumferential temperature difference over the absorber tube increases up to by 199.7 K with receiver dislocation along the optical axis. The effects of the receiver position error on the optical efficiency and collector efficiency have also been studied. A maximum drop of 32% in the optical efficiency is observed when the receiver is displaced from the focus by 1.63% of focal length of the collector in both directions. The collector efficiency decreases by up to 14% when the receiver is offset by 1.63% of focal length of the collector along optical axis (away from the trough).

Implementation of new navigation algorithm based on cross-correntropy for precise positioning in low latitude regions of South India

The objective of this article is to develop a new positioning algorithm to estimate the position accurately in low latitude region and assess the algorithm’s performance in terms of accuracy and precision. The Kalman Filter (KF) has been widely recognized as one of the most powerful state estimation techniques in estimating system state variables and suppressing measurement noise. The Kalman Filter is desirable because the uncertainty in the Minimum Mean Square Error (MMSE) estimation can be minimized. In this article, we implemented a new algorithm called as Cross-Correntropy Kalman Filter (CCKF) to enhance the position accuracy and performance of the GPS receiver. Primarily the improvement depends on the Cross-Correntropy criterion which is a measure of local similarity, and a novel Fixed-Point algorithm for updating subsequent estimates. In this work, we present a thorough derivation of the method suggested, how to accurately measure the estimate of the GPS receiver position. Furthermore, in tabular forms, we provide a comparison of receiver position error (X, Y, Z coordinates) and performance metrics (2-D & 3-D) together with graphical representations for both algorithms (KF & CCKF).

Passive radar sparse imaging with transmitter and receiver position errors

Passive radar sparse imaging requires accurate known system observation matrix, but in practical applications there usually exists transmitter and receiver position errors, which would make radar observation matrix partially unknown, resulting in mismatch between echo measurements and observation matrix, thus seriously degrade the performances of traditional sparse imaging algorithms. Here, the passive radar imaging model under position errors of transceivers is established first. Then, an adaptive phase error correction imaging method based on Bayesian compressed sensing is presented, which can deal with transceivers position errors while reconstructing target image simultaneously. Simulation results verify the effectiveness of authors’ method.

Refining Inaccurate Transmitter and Receiver Positions Using Calibration Targets for Target Localization in Multi-Static Passive Radar.

Transmitter and receiver position errors have been known to significantly deteriorate target localization accuracy in a multi-static passive radar (MPR) system. This paper explores the use of calibration targets, whose positions are known to the MPR system, to counter the loss in target localization accuracy arising from transmitter/receiver position errors. This paper firstly evaluates the Cramér–Rao lower bound (CRLB) for bistatic range (BR)-based target localization with calibration targets, which analytically indicates the potential of calibration targets in enhancing localization accuracy. After that, this paper proposes a novel closed-form solution, which includes two steps: calibration step and localization step. Firstly, the calibration step is devoted to refine the inaccurate transmitter and receiver locations using the BR measurements from the calibration targets, and then in the calibration step, the target localization can be accurately achieved by using the refined transmitter/receiver positions and the BR measurements from the unknown target. Theoretical analysis and simulation results indicate that the proposed method can attain the CRLB at moderate measurement noise level, and exhibits the superiority of localization accuracy over existing algorithms.

Bias reduction for TDOA localization in the presence of receiver position errors and synchronization clock bias

Time difference of arrival (TDOA) localization does not require time stamping of the source signal and is playing an increasingly important role in passive location. In addition to measurement noise, receiver position errors and synchronization clock bias are two important factors affecting the performance of TDOA positioning. This paper proposes a bias-reduced solution for passive source localization using TDOA measurements in the presence of receiver position errors and synchronization clock bias. Like the original two-step weighted least-squares solution, the new technique has two stages. In the first stage, the proposed method expands the parameter space in the weighted least-squares (WLS) formulation and imposes a quadratic constraint to suppress the bias. In the second stage, an effective WLS estimator is given to reduce the bias generated by nonlinear operations. With the aid of second-order error analysis, theoretical biases for the original solution and proposed bias-reduced solution are derived, and it is proved that the proposed bias-reduced method can achieve the Cramér–Rao lower bound performance under moderate Gaussian noise, while having smaller bias than the original algorithm. Simulation results exhibit smaller estimation bias and better robustness for all estimates, including those of the source position, refined receiver positions, and clock bias vector, when the measurement noise or receiver position error increases.

Geometric, optical and thermal analysis for solar parabolic trough concentrator efficiency improvement using the Photogrammetry technique under semi-arid climate

The investment of renewable energy, especially the solar energy, seems to be the real alternative and the potential solutions for the classical fuel energy due to its pollutant and limited source. Therefore, the cost and performance are the main criteria to assess a solar power plant. The purpose of this work is to evaluate the optical and thermal efficiencies of a solar Parabolic Trough Concentrated (PTC) installed in the Green Energy Park (GEP) research platform in Benguerir, Morocco. In order to improve the optical efficiency of the system, an optical qualification is necessary because of the difficulties of handling the glasses and the deformations from the ideal design. In this sense, an experimental study was carried out using the robust Photogrammetry measurement technique to perform the geometrical and optical errors of the solar concentrating system. Slope error, misalignment error, and receiver position error has been identified and analyzed. Moreover, the intercept factor and the optical efficiency of the PTC system according to the experimental measurements given by the Photogrammetry technique were determined. Finally, the thermal efficiency of the PTC according to results obtained and the weather conditions climate of Benguerir city extracted by an accurate meteorological station have been performed and analyzed. The results obtained show the relevant impact of the optical efficiency on the thermal energy and the plant performance.

Performance analysis and improvement of direct position determination based on Doppler frequency shifts in presence of model errors: case of known waveforms

The direct position determination (DPD) method based on Doppler frequency shifts for signals with known waveforms is first proposed by Amar and Weiss. Although this method exhibits excellent asymptotic performance, but does not account for the effects of uncertainties in the receiver positions and velocities. These uncertainties may result in a considerable reduction of localization accuracy. In this paper, the statistical performance of the DPD estimator is investigated under receiver position and velocity errors (also called model errors). We derive an analytical expression for the mean square error in the estimated source location in the case where the estimator assumes that the receiver positions and velocities are accurate, but they in fact contain errors. The main difficulty in the mathematical analysis is that the DPD cost function is not explicit with respect to the emitter position. Consequently, some algebraic manipulation is required to derive closed-form expressions for the first- and second-order partial derivatives of the cost function. The Cramer–Rao bounds (CRBs) for the target position estimation are also deduced in the presence and absence of model errors. These CRBs provide insights into the effects of model errors on the localization accuracy. Two improved DPD methods are developed based on our analysis results. The first has lower complexity than the common grid search, and the second exhibits increased robustness to model errors. Simulation results support and corroborate the theoretical developments in this paper.

Performance Analysis and Dimension-Reduction Taylor Series Algorithms for Locating Multiple Disjoint Sources Based on TDOA Under Synchronization Clock Bias

Time difference of arrival (TDOA) localization technology, which does not require the time stamp of the source signals, is playing an increasingly important role in passive localization. Besides TDOA measurement noise and receiver position errors, another factor affecting TDOA positioning accuracy is the synchronization clock bias between different receivers. In this paper, the problem of TDOA source localization is considered under the condition that the TDOA measurements from multiple disjoint sources are subject to the same receiver position displacements and synchronization clock bias. First, based on the orthogonal projection matrix, the Cramer–Rao lower bounds of unknown parameters are derived in the presence of synchronization clock bias. Subsequently, according to the maximum likelihood (ML) criterion and Taylor series (TS) positioning method, the estimates obtained by ignoring the clock bias are shown to be biased, and the mean square error is found to increase quadratically with the 2-norm of the clock bias vector. To suppress the effect of synchronization clock bias, two dimension-reduction TS algorithms are proposed, and their asymptotically optimal performance is demonstrated under first-order error analysis. In addition, an ML-based closed-form solution for the clock bias vector is provided. Finally, simulation results verify the validity of the theoretical derivation and show the superiority of the proposed algorithms compared to the existing closed-form method.

Solar Field Optical Characterization at Stillwater Geothermal/Solar Hybrid Plant

Concentrating solar power (CSP) can provide additional thermal energy to boost geothermal plant power generation. For a newly constructed solar field at a geothermal power plant site, it is critical to properly characterize its performance so that the prediction of thermal power generation can be derived to develop an optimum operating strategy for a hybrid system. In the past, laboratory characterization of a solar collector has often extended into the solar field performance model and has been used to predict the actual solar field performance, disregarding realistic impacting factors. In this work, an extensive measurement on mirror slope error and receiver position error has been performed in the field by using the optical characterization tool called distant observer (DO). Combining a solar reflectance sampling procedure, a newly developed solar characterization program called firstoptic and public software for annual performance modeling called system advisor model (SAM), a comprehensive solar field optical characterization has been conducted, thus allowing for an informed prediction of solar field annual performance. The paper illustrates this detailed solar field optical characterization procedure and demonstrates how the results help to quantify an appropriate tracking-correction strategy to improve solar field performance. In particular, it is found that an appropriate tracking-offset algorithm can improve the solar field performance by about 15%. The work here provides a valuable reference for the growing CSP industry.

Development of an analytical optical method for linear Fresnel collectors

An analytical optical approach—First-principle OPTical Intercept Calculation (FirstOPTIC)—is developed for the optical performance evaluation of linear Fresnel collectors. Instead of treating all optical error sources as probability distributions and convolving them with the sun shape into an overall beam spread function, FirstOPTIC treats mirror slope error, receiver position error, and collector tracking error as geometric modifications to the collector, as interpreted in laboratory measurements. Calculation of intercept factors is analytically derived through a rigorous mathematical model. It is shown through test cases that FirstOPTIC can provide accurate and fast calculation of collector intercept factors as a function of incidence angle. Finally, FirstOPTIC is used to conduct analysis on the incidence angle modifier (IAM) and indicates that the factorized IAM representation with respect to independent transversal and longitudinal components can be a good approximation but in general underestimates the optical performance of a linear Fresnel collector.

Study of the Optical Impact of Receiver Position Error on Parabolic Trough Collectors

A newly developed analytical optical approach—first-principle OPTical intercept calculation (FirstOPTIC)—is employed to study the optical impact of receiver position error on parabolic trough collectors. The FirstOPTIC method treats optical error sources the way they are typically characterized in laboratory measurements using a geometrical or optical interpretation. By analyzing a large number of cases with varying system parameters, such as overall system optical error and the collector's geometrical parameters, a practical correlation between actual measurement data and its corresponding error-convolution approximation for receiver position error is established from parametric study; the correlation enables a direct comparison of receiver position error to the sun shape and other optical error sources (such as mirror specularity and slope error) with respect to the collector optical performance. The effective coefficients that define the correlation of actual measurement data and its error-convolution approximation for receiver position error are also summarized for several existing trough collectors; these make it convenient to characterize the relative impact of receiver position error compared with other optical error sources, which was not straightforward in the past. It is shown that FirstOPTIC is a suitable tool for in-depth optical analysis and fast collector design optimization, which otherwise require computationally intensive ray-tracing simulations.

Static and dynamic performance evaluation of a commercially-available ultra wideband tracking system

Locating and tracking resources (e.g., people, equipment, and materials) is critical in many industrial applications for monitoring productivity and safety. In construction, various technologies (e.g., global positioning systems (GPS), radio frequency identification (RFID) and radio frequency (RF) localization) have been proposed. However, the performance of these types of technologies is not well understood for this particular application. This paper presents a study for evaluating the static and dynamic performance of a commercially-available ultra wideband (UWB) tracking system in free space and under realistic construction environments. In addition, a static performance model for estimating position error as a function of receiver position and initial calibration error was also developed. Results and experiences are in particular useful for researchers or practitioners in need for adapting UWB technology for their application.

Assessment of the Higher Order Ionosphere Error on Position Solutions

This paper presents an assessment of the impact of the higher order ionosphere error on GPS position solutions. Prior studies of higher order ionosphere error are based on simplified ionosphere models, and there is a lack of understanding of their temporal and spatial structures. In this paper, we apply the Appleton-Hartree formula in the computation of the higher order errors by combining vertical electron density profiles obtained from the Arecibo incoherent scatter radar, the International Reference Ionosphere model, total electron content maps derived from the International GNSS Service database, and the International Geomagnetic Reference Field model. The 24-slot GPS baseline constellation is used to compute a receiver position error based on higher order range error. The position error at the Arecibo radar site on a quiet day is used as an example to demonstrate the magnitude, sign, and daily variation patterns of higher order ionosphere induced position error.

Experimental validation of regularized array element localization

This paper examines and validates regularized inversion for array element localization (AEL) by quantitative comparison of inversion results to direct measurements of receiver positions for a full-scale AEL survey. Regularized AEL treats both receiver and source positions as unknown parameters in a ray-based inversion; prior information on source/receiver positions, inter-receiver spacing in depth, and/or a smooth array shape can be included, subject to statistically fitting the acoustic data. Uncertainties in the recovered receiver positions are estimated via Monte Carlo appraisal. To study this approach, a specially stabilized, two-dimensional receiver array and a series of impulsive sources (imploding glass light bulbs) were deployed from shore-fast (motionless) Arctic sea ice. Sources and recordings were not synchronized in time, so AEL inversions are based on relative arrival times. Receiver positions were measured to an uncertainty of ∼5 cm in each dimension [9 cm in three dimensions (3D)] using nonacoustic (optical) methods. Average AEL errors (difference between measured receiver positions and inversion results) of 13 cm in depth, 27 cm in the horizontal, and 30 cm in 3D, as well as good agreement between the measured errors and estimated AEL uncertainties validate the regularized approach and provide benchmarks for acoustic AEL. Receiver-position errors are quantitatively investigated as a function of the number of sources, source-position errors, and different regularizations.

Multistatic localization error due to receiver positioning errors

This paper is a summary of a study of the effect of receiver position errors on the target localization accuracy of a multistatic sonar. The multistatic active system under examination consists of one or more transmitters and receivers, and the target is localized in the horizontal plane by means of echoes from the transmissions. Two-dimensional propagation of sound, with a constant sound speed, is assumed throughout. A simple analytic approach, implemented and illustrated numerically, is derived for calculating the sensitivity to receiver position error over a specified area. For many of the examples considered, there are considerable regions where target localization errors can be unacceptably large even for highly accurate receiver positions.

Travel time tomography simulations for the test ocean constructed for the 124th Meeting of the Acoustical Society of America

Geometric rays were traced for a variety of source–receiver configurations in the test ocean sound-speed field constructed for the 124th Meeting of the Acoustical Society of America. A stochastic inverse incorporating the statistical information distributed with the test ocean was performed using only one-way travel times as data. Realistic errors in travel times and source–receiver positions were allowed for. The travel times were assumed to be contaminated with internal-wave-induced travel time fluctuations. The fluctuation variance increased linearly with range, with a magnitude of 10 ms rms at 1000 km. This internal wave noise can be reduced by a factor of N−1/2 by assuming that the mesoscale sound-speed structure remains static over N internal-wave-induced decorrelation times. Decorrelation times shorter than 10 min have been observed in the North Pacific at 1000-km range, so a daily average can yield a net contamination below 1 ms, neglecting the effects of longer period fluctuations like internal tides. The simulation results are sensitive to the size of the assumed error, and using values below 1 ms can lead to unrealistically good performance. The size of the source–receiver position errors can vary dramatically depending on the navigational techniques used and can have significant effects on the array design problem. These sensitivities will be explored in the process of choosing a source–receiver array adequate to resolve 96% of the sound-speed variance at 700-m depth in the test ocean.