High‐precision hyperboloid location method using passive time‐difference‐of‐arrival measurements

Lei, Wenying; Chen, Baixiao

doi:10.1049/iet-rsn.2012.0244

Cited by 8 publications

(5 citation statements)

References 21 publications

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“…where ∆ is the PDE error that corresponds to the effective SNR which is obtained using (33) and that of matrix a is: 14 …”

Section: Appendix A: Derivation Of Relative Grs Geometry and Pd Matrimentioning

confidence: 99%

“…Due to this nonlinearity, several methods are developed to solve these equations [12][13][14][15][16][17][18][19][20][21][22][23][24][25] either in linear/closed-form method or nonlinear/open-form method [1,12]. In the nonlinear method, the first step is to linearize the nonlinear hyperbolic equations using series expansion such as the Taylor series expansion method [13][14][15]. An initial random position of emitter is first inputted and iteratively refined to the final position estimate by minimizing the least square (LS) cost function.…”

mentioning

confidence: 99%

“…This means the accuracy in the PE depends on the GRS configuration. Several studies are carried out on the best GRS configuration for high PE accuracy [14,[30][31][32]. For a few GRSs of 4 or less, simple configurations such as squares and equilateral triangles result in better PE accuracy.…”

mentioning

confidence: 99%

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Position Estimation Error Performance Model for a Minimum Configuration 3-D Multilateration

Yaro¹,

Sha’ameri²,

Kamel³

2018

IJEEI

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A multilateration system estimates the position of emitter using time difference of arrival (TDOA) measurements with a lateration algorithm. It involves solving a set of hyperbolic plane equations to determine the position of the emitter given the TDOA measurements that corresponds to the path difference (PD) measurement in distance. A performance model is developed using the relative maximum error bound (RMEB) which relates the plane equation condition number, the relative ground receiving station (GRS) geometry and the PD measurement error to estimate the position estimation (PE) error. By using air traffic monitoring for civil aviation as an application, Monte Carlo simulation verifies the PE error of the performance model for a square GRS configuration. The coverage assumed a 360 0 bearing, a range of up to 200 km and a maximum altitude of 15 km. Simulation results also show that the performance model estimates the horizontal position error with a maximum absolute error of 0.1 km up to a range of 200 km at an altitude of 15 km and a minimum absolute error of 0.2 km at an altitude of 15 km.

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“…where ∆ is the PDE error that corresponds to the effective SNR which is obtained using (33) and that of matrix a is: 14 …”

Section: Appendix A: Derivation Of Relative Grs Geometry and Pd Matrimentioning

confidence: 99%

mentioning

confidence: 99%

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Position Estimation Error Performance Model for a Minimum Configuration 3-D Multilateration

Yaro¹,

Sha’ameri²,

Kamel³

2018

IJEEI

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“…The current satellite interference source localization methods mainly use the time difference of arrival (TDOA) and the frequency difference of arrival (FDOA) measured by the signals received from the main satellite and the adjacent satellites to determine the location. The localization methods can be classified into analytical methods [ 8 , 9 , 10 , 11 , 12 , 13 , 14 ], optimized solutions [ 15 , 16 , 17 , 18 , 19 , 20 ], and intelligent algorithms [ 21 , 22 , 23 ] in recent years. The analytical methods derive the closed-form solution of the nonlinear localization equation set based on mathematical approximation and the intermediate variable.…”

Section: Introductionmentioning

confidence: 99%

A Tri-Satellite Interference Source Localization Method for Eliminating Mirrored Location

Huo¹,

Bai²,

Jiang³

et al. 2021

Sensors

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With the increase in satellite communication interference, the tri-satellite time difference of arrival (TDOA) localization technique, which is an effective method to determine the location of the interference using sensors or antennas, has been developed rapidly. The location of the interference source is determined through the intersection of the TDOA lines of position (LOP). However, when the two TDOA LOP have two mirrored intersection points, it is theoretically difficult to determine the real location. Aiming at this problem, a method for eliminating mirrored location based on multiple moment TDOA is proposed in this paper. First, the TDOA results are measured at multiple moments using the cross-ambiguity function (CAF), and the localization equation set is established based on the World Geodetic System (WGS)-84 earth ellipsoid model. Then, the initial location result can be obtained by solving the equation set through the Newton iteration method. Finally, the high-precision location result after eliminating the mirrored location is obtained after the single moment localization based on the initial location. Simulation experiments and real measured data processing results verify the effectiveness of the proposed method. It still has good robustness under the condition of large measurement errors and deviations from the prior initial values.

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“…radar, sonar, and wireless networks [1]. A series of works on TDOA localisation algorithms have been published [2][3][4][5]. Generally, the attainable mean-square errors (MSEs) of these algorithms are lower bounded by the Cramer-Rao bound (CRB).…”

Section: Introductionmentioning

confidence: 99%

Optimal and fast sensor geometry design method for TDOA localisation systemswith placement constraints

Zhang

Mao

Zhao

et al. 2019

IET signal process.

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The sensor geometry design problem of time difference of arrival (TDOA) localisation systems based on Cramer-Rao bound is studied. Sensor placement constraints are considered, which means the available placement area is limited. This makes sensor geometry design a sensor selection problem. In two-dimensional (2D) TDOA localisation or 3D TDOA localisation on the earth surface, sensor selection can be implemented through solving a fractional integer programming problem. However, traditional fractional integer programming methods are either suboptimal or too time consuming. For this reason, a new method named path-varying sphere decoding is proposed in two steps. In step one, the programming problem is relaxed into two sphere decoding (SD) subproblems. Solving these subproblems leads to the optimal solution, and the required computational complexity is much less than those of traditional optimal methods. In step two, the structure of the cost function is explored. This makes it possible to calculate the path-varying upper-bound of a quadratic function. Thus the quadratic function constraint used in one SD subproblem becomes tighter and the calculation speed is enhanced. Theory analyses and simulation results show that the proposed method is not only optimal but also much faster than traditional optimal methods when solving large-scale programming problems.

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High‐precision hyperboloid location method using passive time‐difference‐of‐arrival measurements

Cited by 8 publications

References 21 publications

Position Estimation Error Performance Model for a Minimum Configuration 3-D Multilateration

Position Estimation Error Performance Model for a Minimum Configuration 3-D Multilateration

A Tri-Satellite Interference Source Localization Method for Eliminating Mirrored Location

Optimal and fast sensor geometry design method for TDOA localisation systemswith placement constraints

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