Novel cooperative localization method of over-the-horizon shortwave emitters based on direction-of-arrival and time-difference-of-arrival measurements

Wang, Ding; Yin, Jianxin; Zhu, Zhen

doi:10.1360/ssi-2021-0331

Cited by 3 publications

(1 citation statement)

References 42 publications

(4 reference statements)

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“…Based on Equation (3), the CCRLB of

{\mathbf{u}}^{o}

can be obtained by [25–27]:

\mathbf{C}\mathbf{C}\mathbf{R}\mathbf{L}\mathbf{B}=\mathbf{C}\mathbf{R}\mathbf{L}\mathbf{B}-{\mathbf{C}\mathbf{R}\mathbf{L}\mathbf{B}\widetilde{\boldsymbol{\Lambda }}\left({\widetilde{\boldsymbol{\Lambda }}}^{\mathrm{T}}\mathbf{C}\mathbf{R}\mathbf{L}\mathbf{B}\widetilde{\boldsymbol{\Lambda }}\right)}^{-1}{\widetilde{\boldsymbol{\Lambda }}}^{\mathrm{T}}\mathbf{C}\mathbf{R}\mathbf{L}\mathbf{B}={\boldsymbol{\Sigma }}_{1}{{\left({\boldsymbol{\Sigma }}_{1}^{T}{(\text{CRLB})}^{-1}{\boldsymbol{\Sigma }}_{1}\right)}^{-1}\boldsymbol{\Sigma }}_{1}^{\mathrm{T}}

where

\widetilde{\boldsymbol{\Lambda }}={\left[{\boldsymbol{\Lambda }}_{1}{\mathbf{u}}^{o}\right]}^{\mathrm{T}}

and

${\boldsymbol{\Sigma }}_{1}=\left[\begin{array}{@{}c@{}}{\mathbf{I}}_{2}\\ \begin{array}{cc}-\left(1-{e}^{2}\right){\mathbf{u}}_{x}^{o}/{\mathbf{u}}_{z}^{o}& -\left(1-{e}^{2}\right){\mathbf{...

…”

Section: Ccrlbmentioning

confidence: 99%

A two‐stage iterative method for short‐wave source localisation

Jiang,

Tang,

et al. 2023

IET Radar Sonar & Navi

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Short‐wave source localisation has an important role in many fields. A two‐stage iterative algorithm is proposed based on the ionospheric virtual height (IVH) model using the direction of arrival (DOA) and time difference of arrival (TDOA) measurements, which is divided into DOA stage and TDOA stage. The optimisation problem of the TDOA stage can be obtained by using the result of DOA stage and TDOA measurements. During the solution process, the non‐convex quadratic equation constraints are converted to linear constraints, which can lead to the algorithm converges to the global optimal solution and the optimal solution can be analytically solved. The theoretical analysis demonstrates that the localisation accuracy of both stages can reach the corresponding constrained Cramér‐Rao lower bound (CCRLB). And the accuracy of TDOA stage achieves the CCRLB of hybrid localisation. Finally, the performance of the proposed method is demonstrated by simulations.

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“…Based on Equation (3), the CCRLB of

{\mathbf{u}}^{o}

can be obtained by [25–27]:

\mathbf{C}\mathbf{C}\mathbf{R}\mathbf{L}\mathbf{B}=\mathbf{C}\mathbf{R}\mathbf{L}\mathbf{B}-{\mathbf{C}\mathbf{R}\mathbf{L}\mathbf{B}\widetilde{\boldsymbol{\Lambda }}\left({\widetilde{\boldsymbol{\Lambda }}}^{\mathrm{T}}\mathbf{C}\mathbf{R}\mathbf{L}\mathbf{B}\widetilde{\boldsymbol{\Lambda }}\right)}^{-1}{\widetilde{\boldsymbol{\Lambda }}}^{\mathrm{T}}\mathbf{C}\mathbf{R}\mathbf{L}\mathbf{B}={\boldsymbol{\Sigma }}_{1}{{\left({\boldsymbol{\Sigma }}_{1}^{T}{(\text{CRLB})}^{-1}{\boldsymbol{\Sigma }}_{1}\right)}^{-1}\boldsymbol{\Sigma }}_{1}^{\mathrm{T}}

where

\widetilde{\boldsymbol{\Lambda }}={\left[{\boldsymbol{\Lambda }}_{1}{\mathbf{u}}^{o}\right]}^{\mathrm{T}}

and

${\boldsymbol{\Sigma }}_{1}=\left[\begin{array}{@{}c@{}}{\mathbf{I}}_{2}\\ \begin{array}{cc}-\left(1-{e}^{2}\right){\mathbf{u}}_{x}^{o}/{\mathbf{u}}_{z}^{o}& -\left(1-{e}^{2}\right){\mathbf{...

…”

Section: Ccrlbmentioning

confidence: 99%

A two‐stage iterative method for short‐wave source localisation

Jiang,

Tang,

et al. 2023

IET Radar Sonar & Navi

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A Two-Stage Method for Short-Wave Target Localization Using DOA and TDOA Measurements

Jiang

Tang

et al. 2023

IEEE Access

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Fusion of Land-Based and Satellite-Based Localization Using Constrained Weighted Least Squares

Zhao,

Jiang,

Tang

et al. 2024

Sensors

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Combining multiple devices for localization has important applications in the military field. This paper exploits the land-based short-wave platforms and satellites for fusion localization. The ionospheric reflection height error and satellite position errors have a great impact on the short-wave localization and satellite localization accuracy, respectively. In this paper, an iterative constrained weighted least squares (ICWLS) algorithm is proposed for these two kinds of errors. The algorithm converts the nonconvex equation constraints to linear constraints using the results of the previous iteration, thus ensuring convergence to the globally optimal solution. Simulation results show that the localization accuracy of the algorithm can reach the corresponding Constrained Cramér–Rao Lower Bound (CCRLB). Finally, the localization results of the two methods are fused using Kalman filtering. Simulations show that the fused localization accuracy is improved compared to the single-means localization.

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Novel cooperative localization method of over-the-horizon shortwave emitters based on direction-of-arrival and time-difference-of-arrival measurements

Cited by 3 publications

References 42 publications

A two‐stage iterative method for short‐wave source localisation

A two‐stage iterative method for short‐wave source localisation

A Two-Stage Method for Short-Wave Target Localization Using DOA and TDOA Measurements

Fusion of Land-Based and Satellite-Based Localization Using Constrained Weighted Least Squares

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