Augmented Lagrange geolocation algorithm using TDOA measurements and calibration sources in the presence of satellite position errors

Chen, Xin; Wang, Ding; Yin, Jianxin; Jia, Changgui

doi:10.1016/j.aeue.2019.152900

Cited by 6 publications

(7 citation statements)

References 35 publications

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“…with T ¼ diagf1; 1; 1=ð1 − e 2 Þg, which can be deduced from Equation (4). Considering the above quadratic ellipsoidal Earth constraint, the CRB of z under this constraint can be expressed as [2] CRB…”

Section: Crbs For Position Estimation Of Transmitter On Earthmentioning

confidence: 99%

“…Following the similar derivation in [2] and substituting Equation (69) into Equation (72), CRB ðIÞ NC ðzÞ is equivalent to…”

Section: Crbs For Position Estimation Of Transmitter On Earthmentioning

confidence: 99%

“…We now introduce the ellipsoidal Earth constraint:

{boldz}^{normalT} T z - r_{e}^{2} = 0,

with

T = diag {1, 1, 1 / (1 - e^{2})}

, which can be deduced from Equation (). Considering the above quadratic ellipsoidal Earth constraint, the CRB of

z

under this constraint can be expressed as [2]

CR {boldB}_{NC}^{(I)} (boldz) = CR {boldB}^{'}_{NC} (boldz) - CR {boldB}^{'}_{NC} (boldz) \cdot T z {(z^{T} boldT \cdot boldCR {B^{'}}_{NC} (z) \cdot boldT boldz)}^{- 1} {boldz}^{normalT} T \cdot CR {boldB}^{'}_{NC} (boldz) .

…”

Section: Crbs For Position Estimation Of Transmitter On Earthmentioning

confidence: 99%

“…Especially, passive geolocation of a transmitter on Earth has many applications, such as interference localisation and space electronic reconnaissance [1]. To localise an object on Earth, geolocation systems based on the satellite platform have been used widely in recent years due to their advantages of large coverage and high location accuracy [2].…”

Section: Introductionmentioning

confidence: 99%

“…To deal with this problem, a constrained total least squares (CTLS) algorithm based on TDOA measurements and calibration sources was investigated in Ref. [2]. In the second category, the statistical property of satellite position errors is assumed to facilitate robust localisation.…”

Section: Introductionmentioning

confidence: 99%

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Single‐step geolocation for a non‐circular source in the presence of satellite orbit perturbations

Yin

Wang

Nie³

et al. 2021

IET Signal Processing

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This study addresses the problem of geolocating a strictly non-circular source on the surface of Earth by a cluster of passive satellites. The known satellite positions and velocities are subject to random errors. The authors propose a single-step satellite geolocation algorithm that directly localises the transmitter from sensor outputs using the information of time delays and Doppler shifts but without explicitly estimating them. It exploits the non-circular property of signals and a priori information of satellite orbit error distribution to jointly calibrate orbit errors and determine the longitude and latitude of the transmitter based on the ellipsoidal Earth model, which integrates an alternating iteration scheme for the estimation of various unknowns instead of the exhaustive grid search. Additionally, a detailed Cramér-Rao bound (CRB) derivation is presented for the single-step satellite geolocation of a non-circular source on Earth with and without satellite orbit perturbations, and it is proved that these CRBs are lower than the associated CRBs for a circular source. The simulation results illustrate that the proposed method asymptotically attains the associated CRB, and shows greater performance robustness to signal-to-noise ratio (SNR) and satellite orbit errors compared with conventional twostep satellite geolocation approaches.

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Section: Crbs For Position Estimation Of Transmitter On Earthmentioning

confidence: 99%

“…Following the similar derivation in [2] and substituting Equation (69) into Equation (72), CRB ðIÞ NC ðzÞ is equivalent to…”

Section: Crbs For Position Estimation Of Transmitter On Earthmentioning

confidence: 99%

“…We now introduce the ellipsoidal Earth constraint: