Sensor Control in Anti-Submarine Warfare—A Digital Twin and Random Finite Sets Based Approach
Abstract
:1. Introduction
- Digital twin breaks the barriers between the real ASW and the simulated ASW, and enables real-time communication in both directions.
- Digital twin can make full use of the prediction, evaluation, and analysis ability of simulation system to evaluate available courses of actions for sensor control.
- Digital twin paves a way for the cyber-physical integration of ASW, which is an important bottleneck to enable intelligent and adaptive decision making.
- Digital twin can enable the integrated application of new-generation information technologies, such as internet of things (IoT), 5G, AI, cloud, edge computing, and so on.
- Digital twin can take full advantage of POMDP and the simulation-based approach to support more complex application scenarios.
2. Digital Twin and RFS-Based Framework of Online Sensor Control
3. RFS-Based Modeling of the Simulated ASW
3.1. RFS-Based Data Model
- It is based on the assumption that the studied system is a single dynamic system that is permanently active. It cannot be used for the dynamic system that switches on and off randomly. Switching is quite common for submarine activity, for example, a submarine may enter and leave a battle area at random instance.
- It is based on the assumption that the detection is perfect with no false detections and no missed detections, and it also needs the number and ordering of measurements to be previously designated. Furthermore, it cannot jointly estimate the number of submarines and the states of each submarine.
3.2. RFS-Based Measurement Model
3.3. RFS-Based Simulation Model
4. RFS-Based Data-Assimilation Algorithm
4.1. Data Assimilation with RFS-Based Models
- the posterior submarine’s existence probability ;
- the posterior spatial PDF of denoted by .
4.2. SMC-Based Calculation
5. Computation of Reward Function
5.1. Derivation of Reward Function
5.2. Data-Assimilation-Based Computation
6. Simulation Experiments
6.1. Data-Assimilation Experiment
6.1.1. Experimental Setup
6.1.2. Experimental Results
6.1.3. Sensitivity Analysis
6.2. Online Sensor Control Experiment with Single Submarine
6.2.1. Experimental Setup
6.2.2. Experimental Results
6.2.3. Sensitivity Analysis
6.3. Online Sensor Control Experiment with Multiple Submarines
6.3.1. Experimental Setup
6.3.2. Experimental Results
6.3.3. Sensitivity Analysis
7. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
ASW | Anti-submarine Warfare |
FISST | Finite Set Statistics |
Probability Density Function | |
PF | Particle Filter |
POMDP | Partially Observed Markov Decision Process |
RFS | Random Finite Set |
RMS | Root Mean Square |
SMC | Sequential Monte Carlo |
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Name | Parameter | True Value | Biased Value |
---|---|---|---|
Enemy submarine | Initial speed | 5 knot | 3 knot |
Process noise intensity | 0.0 | 0.2 | |
Initial position | (10,000, 1000) m | (9500, 1000) m | |
Initial heading | −135 deg | −90 deg | |
Survival Probability | 0.99 | - | |
Anti-submarine ship | Initial speed | 4 knot | - |
Initial heading | −50 deg | - | |
Initial position | (0, 0) m | - | |
Detection probability | - | ||
Max detection probability | 0.98 | - | |
Measurement standard deviation | 1 deg | - |
1 | 5 | 10 | 20 | 50 | 80 | 100 | 200 | 500 | 800 | 900 | 1000 | 1500 | 2000 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
25 | 11 | 11 | 3 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
45 | 23 | 37 | 28 | 22 | 15 | 17 | 11 | 9 | 5 | 7 | 6 | 8 | 2 | |
45 | 42 | 27 | 25 | 32 | 30 | 32 | 33 | 30 | 29 | 30 | 30 | 31 | 32 | |
22 | 30 | 29 | 22 | 20 | 16 | 20 | 19 | 19 | 26 | 18 | 15 | 20 | 17 | |
19 | 17 | 14 | 15 | 8 | 12 | 10 | 7 | 12 | 12 | 12 | 10 | 8 | 12 | |
2 | 7 | 10 | 7 | 7 | 8 | 6 | 8 | 6 | 4 | 5 | 8 | 6 | 5 | |
7 | 9 | 5 | 9 | 6 | 6 | 6 | 8 | 6 | 6 | 5 | 4 | 5 | 4 | |
4 | 3 | 6 | 4 | 3 | 5 | 3 | 2 | 3 | 6 | 1 | 7 | 4 | 7 | |
9 | 12 | 9 | 9 | 9 | 8 | 6 | 4 | 5 | 4 | 4 | 3 | 6 | 5 | |
18 | 10 | 12 | 19 | 14 | 13 | 13 | 9 | 11 | 9 | 16 | 13 | 12 | 11 | |
26 | 30 | 28 | 24 | 39 | 32 | 32 | 35 | 30 | 34 | 39 | 28 | 26 | 22 | |
65 | 90 | 82 | 96 | 108 | 120 | 110 | 108 | 104 | 102 | 92 | 106 | 94 | 91 | |
111 | 125 | 142 | 162 | 175 | 192 | 207 | 225 | 242 | 256 | 263 | 266 | 276 | 290 | |
64 | 77 | 81 | 76 | 56 | 43 | 38 | 31 | 23 | 7 | 8 | 4 | 4 | 2 | |
22 | 13 | 7 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
5 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
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Wang, P.; Yang, M.; Peng, Y.; Zhu, J.; Ju, R.; Yin, Q. Sensor Control in Anti-Submarine Warfare—A Digital Twin and Random Finite Sets Based Approach. Entropy 2019, 21, 767. https://doi.org/10.3390/e21080767
Wang P, Yang M, Peng Y, Zhu J, Ju R, Yin Q. Sensor Control in Anti-Submarine Warfare—A Digital Twin and Random Finite Sets Based Approach. Entropy. 2019; 21(8):767. https://doi.org/10.3390/e21080767
Chicago/Turabian StyleWang, Peng, Mei Yang, Yong Peng, Jiancheng Zhu, Rusheng Ju, and Quanjun Yin. 2019. "Sensor Control in Anti-Submarine Warfare—A Digital Twin and Random Finite Sets Based Approach" Entropy 21, no. 8: 767. https://doi.org/10.3390/e21080767