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doi: 10.3934/jimo.2021092

## Collaborative mission optimization for ship rapid search by multiple heterogeneous remote sensing satellites

 Beijing Institute of Remote Sensing Information, Beijing 100089, China

* Corresponding author: Bitao Jiang

Received  February 2021 Revised  March 2021 Published  April 2021

Fund Project: This paper is supported by the National Natural Science Foundation of China (Grant Nos: 91638301)

Multiple heterogeneous satellites mission optimization is a typical kind of non-deterministic polynomial-time hard (NP-hard) problem, and some complicated scenarios bring new challenges. A novel method of missing ship rapid search using multiple grouped heterogeneous satellites is introduced in this paper. The focus is on optimization of collaborative mission optimization for various satellites including low-earth orbit (LEO) satellite and geostationary orbit (GEO) satellites. A fast coverage of the wide sea area using imaging satellites with narrow coverage range has become the most important part to tackle this problem. However, due to different imaging mechanisms of heterogeneous satellites and other constraints, it brings a great challenge to construct the optimization model. A constrained optimization problem model considering the cooperation between LEO and GEO satellites is constructed. A solution strategy based on bi-level metaheuristic algorithm is designed. The time optimal solution of the collaborative task planning between LEO and GEO satellites can be obtained based on the optimal attitude maneuver path of GEO satellites. Thus, wide-area search for missing ships can be conducted in an effective way. The effectiveness of the proposed method is verified by an example.

Citation: Qian Zhao, Bitao Jiang, Xiaogang Yu, Yue Zhang. Collaborative mission optimization for ship rapid search by multiple heterogeneous remote sensing satellites. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021092
##### References:

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##### References:
LEO satellite observation
GEO satellite observation
The relationship between ship speed and coverage area
Mesh generation considering ship moving
General structure of solution method
Coverage ratio of task area over 17:29:08
Results of outer layer optimization
LEO Mission Selected
Results of inner layer optimization problems
GEO Satellite Optimal Path
Satellite Orbit Parameters
 $\boldsymbol{a(km)}$ $\boldsymbol{e}$ $\boldsymbol{i(rad)}$ $\boldsymbol{raan(rad)}$ $\boldsymbol{ w(rad)}$ $\boldsymbol{GEO}$ 42166.3 0 0 2.6180 0 $\boldsymbol{LEO-1 }$ 6978 0 0.6981 0.7854 2.0944 $\boldsymbol{LEO-2 }$ 6978 0 0.6981 0.7854 4.1888 $\boldsymbol{LEO-3 }$ 6978 0 0.6981 0.7854 6.2832 $\boldsymbol{LEO-4 }$ 6978 0 0.6981 1.5708 2.0944 $\boldsymbol{LEO-5 }$ 6978 0 0.6981 1.5708 4.1888 $\boldsymbol{LEO-6 }$ 6978 0 0.6981 1.5708 6.2832 $\boldsymbol{LEO-7 }$ 6978 0 0.6981 2.3562 2.0944 $\boldsymbol{LEO-8 }$ 6978 0 0.6981 2.3562 4.1888 $\boldsymbol{LEO-9 }$ 6978 0 0.6981 2.3562 6.2832 $\boldsymbol{LEO-10 }$ 6978 0 0.6981 3.1416 2.0944 $\boldsymbol{LEO-11 }$ 6978 0 0.6981 3.1416 4.1888 $\boldsymbol{LEO-12 }$ 6978 0 0.6981 3.1416 6.2832 $\boldsymbol{LEO-13 }$ 6978 0 0.6981 3.9270 2.0944 $\boldsymbol{LEO-14 }$ 6978 0 0.6981 3.9270 4.1888 $\boldsymbol{LEO-15 }$ 6978 0 0.6981 3.9270 6.2832 $\boldsymbol{LEO-16 }$ 6978 0 0.6981 4.7124 2.0944 $\boldsymbol{LEO-17 }$ 6978 0 0.6981 4.7124 4.1888 $\boldsymbol{LEO-18 }$ 6978 0 0.6981 4.7124 6.2832 $\boldsymbol{LEO-19 }$ 6978 0 0.6981 5.4978 2.0944 $\boldsymbol{LEO-20 }$ 6978 0 0.6981 5.4978 4.1888 $\boldsymbol{LEO-21 }$ 6978 0 0.6981 5.4978 6.2832 $\boldsymbol{LEO-22 }$ 6978 0 0.6981 6.2832 2.0944 $\boldsymbol{LEO-23 }$ 6978 0 0.6981 6.2832 4.1888 $\boldsymbol{LEO-24 }$ 6978 0 0.6981 6.2832 6.2832
 $\boldsymbol{a(km)}$ $\boldsymbol{e}$ $\boldsymbol{i(rad)}$ $\boldsymbol{raan(rad)}$ $\boldsymbol{ w(rad)}$ $\boldsymbol{GEO}$ 42166.3 0 0 2.6180 0 $\boldsymbol{LEO-1 }$ 6978 0 0.6981 0.7854 2.0944 $\boldsymbol{LEO-2 }$ 6978 0 0.6981 0.7854 4.1888 $\boldsymbol{LEO-3 }$ 6978 0 0.6981 0.7854 6.2832 $\boldsymbol{LEO-4 }$ 6978 0 0.6981 1.5708 2.0944 $\boldsymbol{LEO-5 }$ 6978 0 0.6981 1.5708 4.1888 $\boldsymbol{LEO-6 }$ 6978 0 0.6981 1.5708 6.2832 $\boldsymbol{LEO-7 }$ 6978 0 0.6981 2.3562 2.0944 $\boldsymbol{LEO-8 }$ 6978 0 0.6981 2.3562 4.1888 $\boldsymbol{LEO-9 }$ 6978 0 0.6981 2.3562 6.2832 $\boldsymbol{LEO-10 }$ 6978 0 0.6981 3.1416 2.0944 $\boldsymbol{LEO-11 }$ 6978 0 0.6981 3.1416 4.1888 $\boldsymbol{LEO-12 }$ 6978 0 0.6981 3.1416 6.2832 $\boldsymbol{LEO-13 }$ 6978 0 0.6981 3.9270 2.0944 $\boldsymbol{LEO-14 }$ 6978 0 0.6981 3.9270 4.1888 $\boldsymbol{LEO-15 }$ 6978 0 0.6981 3.9270 6.2832 $\boldsymbol{LEO-16 }$ 6978 0 0.6981 4.7124 2.0944 $\boldsymbol{LEO-17 }$ 6978 0 0.6981 4.7124 4.1888 $\boldsymbol{LEO-18 }$ 6978 0 0.6981 4.7124 6.2832 $\boldsymbol{LEO-19 }$ 6978 0 0.6981 5.4978 2.0944 $\boldsymbol{LEO-20 }$ 6978 0 0.6981 5.4978 4.1888 $\boldsymbol{LEO-21 }$ 6978 0 0.6981 5.4978 6.2832 $\boldsymbol{LEO-22 }$ 6978 0 0.6981 6.2832 2.0944 $\boldsymbol{LEO-23 }$ 6978 0 0.6981 6.2832 4.1888 $\boldsymbol{LEO-24 }$ 6978 0 0.6981 6.2832 6.2832
Constant Parameters
 $\textbf{Parameters}$ $\boldsymbol{Value}$ $\boldsymbol{Unit}$ Orbit perturbation constant J2 0.001082629989052 — Gravity acceleration of earth's sea level ge 0.00980665 km/s$^2$ Gravitational constant $\mu$ 398600.4418 km$^2$/s$^2$ Radius of the earth Re 6.378137e3 km Ship maximum speed $v_{max}$ 20 km/hour Imaging width of LEO satellite $D_{LEO}$ 250km km Imaging width of GEO satellite $D_{GEO}$ 250km km Maximum angular velocity of GEO satellite $w_{max}$ 1e-4 deg/hour Single imaging time of GEO satellite $t_{single}$ 20 s
 $\textbf{Parameters}$ $\boldsymbol{Value}$ $\boldsymbol{Unit}$ Orbit perturbation constant J2 0.001082629989052 — Gravity acceleration of earth's sea level ge 0.00980665 km/s$^2$ Gravitational constant $\mu$ 398600.4418 km$^2$/s$^2$ Radius of the earth Re 6.378137e3 km Ship maximum speed $v_{max}$ 20 km/hour Imaging width of LEO satellite $D_{LEO}$ 250km km Imaging width of GEO satellite $D_{GEO}$ 250km km Maximum angular velocity of GEO satellite $w_{max}$ 1e-4 deg/hour Single imaging time of GEO satellite $t_{single}$ 20 s
Access calculation results
 $\textbf{Meta Mission No.}$ $\textbf{Satellite No.}$ $\textbf{Grid No.}$ ${\textbf{Observation Time (hour)}}$ $\boldsymbol{1}$ 4 1 0.119444 $\boldsymbol{2}$ 4 2 0.113889 $\boldsymbol{3}$ 4 3 0.108333 $\boldsymbol{4}$ 4 11 0.125 $\boldsymbol{5}$ 4 12 0.122222 $\boldsymbol{6}$ 4 21 0.133333 $\boldsymbol{7}$ 7 7 1.625 $\boldsymbol{8}$ 7 8 1.619444 $\boldsymbol{9}$ 7 16 1.636111 $\boldsymbol{10}$ 7 17 1.633333 $\boldsymbol{11}$ 7 18 1.627778 $\boldsymbol{12}$ 7 26 1.641667 $\boldsymbol{13}$ 7 27 1.641667 $\boldsymbol{14}$ 7 35 1.655556 $\boldsymbol{15}$ 7 36 1.652778 $\boldsymbol{16}$ 7 37 1.644444 $\boldsymbol{17}$ 7 45 1.663889 $\boldsymbol{18}$ 7 46 1.658333 $\boldsymbol{19}$ 7 54 1.675 $\boldsymbol{20}$ 7 55 1.669444
 $\textbf{Meta Mission No.}$ $\textbf{Satellite No.}$ $\textbf{Grid No.}$ ${\textbf{Observation Time (hour)}}$ $\boldsymbol{1}$ 4 1 0.119444 $\boldsymbol{2}$ 4 2 0.113889 $\boldsymbol{3}$ 4 3 0.108333 $\boldsymbol{4}$ 4 11 0.125 $\boldsymbol{5}$ 4 12 0.122222 $\boldsymbol{6}$ 4 21 0.133333 $\boldsymbol{7}$ 7 7 1.625 $\boldsymbol{8}$ 7 8 1.619444 $\boldsymbol{9}$ 7 16 1.636111 $\boldsymbol{10}$ 7 17 1.633333 $\boldsymbol{11}$ 7 18 1.627778 $\boldsymbol{12}$ 7 26 1.641667 $\boldsymbol{13}$ 7 27 1.641667 $\boldsymbol{14}$ 7 35 1.655556 $\boldsymbol{15}$ 7 36 1.652778 $\boldsymbol{16}$ 7 37 1.644444 $\boldsymbol{17}$ 7 45 1.663889 $\boldsymbol{18}$ 7 46 1.658333 $\boldsymbol{19}$ 7 54 1.675 $\boldsymbol{20}$ 7 55 1.669444
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