Comments on ‘Constrained total least‐squares localisation algorithm using time difference of arrival and frequency difference of arrival measurements with sensor location uncertainties’

2014 ◽  
Vol 8 (6) ◽  
pp. 692-693 ◽  
Author(s):  
Fuyong Qu ◽  
Xiangwei Meng
Keyword(s):  
Least Squares ◽  
Total Least Squares ◽  
Time Difference ◽  
Frequency Difference ◽  
Sensor Location ◽  
Time Difference Of Arrival

scholarly journals Constrained total least squares localization using angle of arrival and time difference of arrival measurements in the presence of synchronization clock bias and sensor position errors

2019 ◽  
Vol 15 (7) ◽  
pp. 155014771985859
Author(s):  
Ruirui Liu ◽  
Ding Wang ◽  
Jiexin Yin ◽  
Ying Wu
Keyword(s):  
Lower Bound ◽  
Least Squares ◽  
Total Least Squares ◽  
Time Difference ◽  
Angle Of Arrival ◽  
Order Error ◽  
Time Difference Of Arrival ◽  
Position Errors ◽  
Sensor Position ◽  
Cramer Rao Lower Bound

Based on measurements of angle of arrival and time difference of arrival, a method is proposed to improve the accuracy of localization with imperfect sensors. A derivation of the Cramér–Rao lower bound and the root mean square error is presented aimed at demonstrating the significance of taking synchronization errors into consideration. Subsequently, a set of pseudo-linear equations are constructed, based on which the constrained total least squares optimization model has been formulated for target localization and the Newton iteration is applied to obtain the source position and clock bias simultaneously. The theoretical performance of the constrained total least squares localization algorithm subject to sensor position errors and synchronization clock bias is derived, and a framework for the performance analysis is developed. In addition, the first-order error analysis illustrates that the proposed method can achieve the Cramér–Rao lower bound under moderate Gaussian noises by a mathematic derivation. Finally, simulation results are presented that verify the validity of the theoretical derivation and superiority of the new algorithm.

scholarly journals Time Difference of Arrival (TDoA) Localization Combining Weighted Least Squares and Firefly Algorithm

Sensors ◽  
2019 ◽  
Vol 19 (11) ◽  
pp. 2554 ◽  
Author(s):  
Peng Wu ◽  
Shaojing Su ◽  
Zhen Zuo ◽  
Xiaojun Guo ◽  
Bei Sun ◽  
...  
Keyword(s):  
Least Squares ◽  
Firefly Algorithm ◽  
Weighted Least Squares ◽  
Initial Position ◽  
Time Difference ◽  
Sensor Nodes ◽  
Passive Location ◽  
Search Region ◽  
Time Difference Of Arrival ◽  
Location Methods

Time difference of arrival (TDoA) based on a group of sensor nodes with known locations has been widely used to locate targets. Two-step weighted least squares (TSWLS), constrained weighted least squares (CWLS), and Newton–Raphson (NR) iteration are commonly used passive location methods, among which the initial position is needed and the complexity is high. This paper proposes a hybrid firefly algorithm (hybrid-FA) method, combining the weighted least squares (WLS) algorithm and FA, which can reduce computation as well as achieve high accuracy. The WLS algorithm is performed first, the result of which is used to restrict the search region for the FA method. Simulations showed that the hybrid-FA method required far fewer iterations than the FA method alone to achieve the same accuracy. Additionally, two experiments were conducted to compare the results of hybrid-FA with other methods. The findings indicated that the root-mean-square error (RMSE) and mean distance error of the hybrid-FA method were lower than that of the NR, TSWLS, and genetic algorithm (GA). On the whole, the hybrid-FA outperformed the NR, TSWLS, and GA for TDoA measurement.

scholarly journals A Virtualization Approach to Correct Systematic Errors in Measured TDOA and FDOA for Low Orbit Dual-Satellite Positioning Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Gang Li ◽  
Min Zhou ◽  
Hongwen Tang ◽  
Hongbin Chen
Keyword(s):  
Systematic Errors ◽  
Time Difference ◽  
Frequency Difference ◽  
Reference Station ◽  
Virtual Reference ◽  
Time Difference Of Arrival ◽  
Positioning Accuracy ◽  
Positioning Systems ◽  
Location System ◽  
Measured Time

The low-orbit dual-satellite passive location system provides a cost-efficient and easy implementation platform, by which positions of unknown emitters on the Earth can be determined through measuring both the time and the frequency differences by two low-orbit satellites in space. However, in reality, this dual-satellite location system has low positioning accuracy because of the existence of systematic errors. In this paper, in order to address the problem of low positioning accuracy in low-orbit dual-satellite systems, a virtualization approach, consisting of the establishment of the virtual reference station and virtual frequency conversion, is proposed to correct systematic errors in the system. Specifically, we first analyze the coming source of systematic errors in the dual-satellite location system, and then, a virtual reference station and virtual frequency are constructed to correct errors in the measured time difference of arrival and the frequency difference of arrival, respectively. Simulation results show that systematic errors caused by the measured time difference of arrival can be significantly reduced, and the correction efficiency, defined as a ratio between remaining errors after implementing the proposed method over uncorrected ones, for the measured frequency difference of arrival, largely relies on both the virtual frequency and the transmission frequency of reference stations.

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