Performance modeling and simulation of space based tracking layer constellation

Yonghong Xue; Shiwei Fan; Kai Qiao; Lei Zhang

doi:10.3788/IRLA20210067

Journals >Infrared and Laser Engineering >Volume 50 >Issue 11 >Page 20210067 > Article

Infrared and Laser Engineering
Vol. 50, Issue 11, 20210067 (2021)

Performance modeling and simulation of space based tracking layer constellation

Yonghong Xue, Shiwei Fan, Kai Qiao, and Lei Zhang

Author Affiliations

Beijing Institute of Tracking and Telecommunication Technology, Beijing 100094, China

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DOI: 10.3788/IRLA20210067 Cite this Article

Yonghong Xue, Shiwei Fan, Kai Qiao, Lei Zhang. Performance modeling and simulation of space based tracking layer constellation[J]. Infrared and Laser Engineering, 2021, 50(11): 20210067 Copy Citation Text

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Abstract

With the rapid development of technology and practical deployment of hypersonic weapon, the United States has carried out a new plan of building Tracking Layer of National Defense Space Architecture (NDSA). Firstly, the main design parameters of tracking layer were introduced; Secondly, the analysis model of tracking layer constellation coverage performance, detection capability and tracking performance were established; Finally, the performance of tracking layer was analyzed through simulation and calculation, and the core capabilities such as the minimum satellites number of the whole constellation, detection sensitivity and optimal global target tracking accuracy were deduced. The analysis results have important reference value for the research of data processing algorithm and the design of similar payload and constellation.

Keywords

coverage performance detection performance hypersonic weapon National Defense Space Architecture (NDSA)tracking layer tracking performance

$ {N_{S}=}\left\{ {

\begin{array}{l} \frac{4 π R^{2}}{{(α H)}^{2}} I n s t a n t a n e o u s f i e l d o f v i e w (I F O V) \\ \frac{4 π R^{2}}{π {(β H / 2)}^{2}} T o t a l f i e l d o f v i e w (T F O V) \end{array}

} \right. $

(1)

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$ \left\{

\begin{array}{l} Q_{f o c}^{(B)} = E_{f o c}^{(B)} \cdot t_{d} \cdot d_{f o c}^{2} \\ Q_{f o c}^{(T)} = E_{f o c}^{(T)} \cdot t_{d} \cdot \int_{y_{c} - \frac{d_{f o c}}{2}}^{y_{c} + \frac{d_{f o c}}{2}} \int_{x_{c} - \frac{- d_{f o c}}{2}}^{x_{c} + \frac{d_{f o c}}{2}} p_{(x_{0}, y_{0})} (x, y) d x d y \end{array}

\right. $

(2)

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$ \left\{

\begin{array}{l} E_{f o c}^{(B)} = \int L_{λ} d λ \cdot \frac{f_{I F O V}^{2} \cdot τ_{0} \cdot π \cdot D^{2} \cdot \cos (θ_{0})}{4 d_{f o c}^{2}} \\ E_{f o c}^{(T)} = \frac{\int τ_{a}^{λ} \cdot I_{λ} d λ}{l^{2}} \cdot \frac{τ_{0} \cdot π \cdot D^{2} \cdot \cos (θ_{1})}{4 d_{f o c}^{2}} \end{array}

\right. $

(3)

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$ CR = \frac{{Q_{\rm foc}^{\left( {\rm T} \right)}}}{{Q_{{\rm{foc}}}^{\left( {\rm{B}} \right)}}} = \frac{{\rho \cdot \displaystyle\int {\tau _a^\lambda \cdot {I_\lambda }{\rm d}\lambda } }}{{{l^2} \cdot f_{{\rm{IFOV}}}^2 \cdot \displaystyle\int {{L_\lambda }} {\rm d}\lambda }} $

(4)

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$ {{\boldsymbol{v}}_T} = \frac{{{\boldsymbol{r}} - {{\boldsymbol{r}}_S}}}{{\left\| {{\boldsymbol{r}} - {{\boldsymbol{r}}_S}} \right\|}} $

(5)

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$ {\rm d}{{\boldsymbol{v}}_T} = {\boldsymbol{H}}\left( {{\rm d}{\boldsymbol{r}} - {\rm d}{{\boldsymbol{r}}_S}} \right) $

(6)

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$ {\boldsymbol{H}}{\rm d}{\boldsymbol{r}} = {\rm d}{{\boldsymbol{v}}_T} + {\boldsymbol{H}}{\rm d}{{\boldsymbol{r}}_S} $

(7)

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\begin{aligned} \boldsymbol H = \\ \frac{(\begin{array}{c} {(y - y_{S})}^{2} + {(z - z_{S})}^{2} & - (x - x_{S}) (y - y_{S}) & - (x - x_{S}) (z - z_{S}) \\ - (x - x_{S}) (y - y_{S}) & {(x - x_{S})}^{2} + {(z - z_{S})}^{2} & - (y - y_{S}) (z - z_{S}) \\ - (x - x_{S}) (z - z_{S}) & - (y - y_{S}) (z - z_{S}) & {(x - x_{S})}^{2} + {(y - y_{S})}^{2} \end{array})}{{‖ \boldsymbol r - {\boldsymbol r}_{S} ‖}^{3}} \end{aligned}

(8)

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$ \left( {

\begin{matrix} {\boldsymbol H}_{1} \\ ⋮ \\ {\boldsymbol H}_{N_{S}} \end{matrix}

} \right){\rm d}{\boldsymbol{r}} = \left( {

\begin{matrix} d {\boldsymbol v}_{T, 1} \\ ⋮ \\ d {\boldsymbol v}_{T, N_{S}} \end{matrix}

} \right) + {{{\rm{\varLambda}} }}\left( {

\begin{matrix} d {\boldsymbol r}_{S, 1} \\ ⋮ \\ d {\boldsymbol r}_{S, N_{S}} \end{matrix}

} \right) $

(9)

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$ {\rm d}{\boldsymbol{r}} = {\left( {{{\boldsymbol{\Sigma }}_H}} \right)^{ - 1}}{{\boldsymbol{C}}_H}\left( {

\begin{matrix} d {\boldsymbol v}_{T, 1} \\ ⋮ \\ d {\boldsymbol v}_{T, N_{S}} \end{matrix}

} \right) + {\left( {{{\boldsymbol{\Sigma }}_H}} \right)^{ - 1}}{{\boldsymbol{B}}_H}\left( {

\begin{matrix} d {\boldsymbol r}_{S, 1} \\ ⋮ \\ d {\boldsymbol r}_{S, N_{S}} \end{matrix}

} \right) $

(10)

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\begin{array}{l} {\boldsymbol Σ}_{H} = \sum_{i = 1}^{N_{S}} {\boldsymbol H}_{i}^{T} {\boldsymbol H}_{i} \\ {\boldsymbol C}_{H} = ({\boldsymbol H}_{1}^{T}, \dots, {\boldsymbol H}_{N_{S}}^{T}) \\ {\boldsymbol B}_{H} = ({\boldsymbol H}_{1}^{T} {\boldsymbol H}_{1}, \dots, {\boldsymbol H}_{N_{S}}^{T} {\boldsymbol H}_{N_{S}}) \end{array}

(11)

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Yonghong Xue, Shiwei Fan, Kai Qiao, Lei Zhang. Performance modeling and simulation of space based tracking layer constellation[J]. Infrared and Laser Engineering, 2021, 50(11): 20210067

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