Velocity Estimation for Space Infrared Dim Targets Based on Multi-Satellite Observation and Robust Locally Weighted Regression
"> Figure 1
<p>Schematic of the target position vector transformation process. (The red font is the position vector in the corresponding coordinate frame, and the blue font is the transition matrix.)</p> "> Figure 2
<p>Imaging of an ideal target (<b>a</b>) and a space moving target (<b>b</b>).</p> "> Figure 3
<p>Schematic of multi-satellite cross-positioning.</p> "> Figure 4
<p>Flowchart of the proposed space IR targets velocity estimation method.</p> "> Figure 5
<p>Schematic of the orbits of the three observation satellites.</p> "> Figure 6
<p>MAE of velocity estimation under different scenarios: (<b>a</b>) <span class="html-italic">X</span>-axis; (<b>b</b>) <span class="html-italic">Y</span>-axis; (<b>c</b>) <span class="html-italic">Z</span>-axis; (<b>d</b>) Overall velocity.</p> "> Figure 7
<p>Display of instantaneous velocity estimation within 40–60 s: (<b>a</b>) <span class="html-italic">X</span>-axis; (<b>b</b>) <span class="html-italic">Y</span>-axis; (<b>c</b>) <span class="html-italic">Z</span>-axis; (<b>d</b>) Overall velocity.</p> "> Figure 8
<p>MAE of overall velocity estimation under different parameters: (<b>a</b>) Iteration; (<b>b</b>) Polynomial degree; (<b>c</b>) Window size.</p> "> Figure 9
<p>The impact of different measurement error factors on velocity estimation accuracy: (<b>a</b>) MAE; (<b>b</b>) RMSE.</p> "> Figure 10
<p>The impact of different numbers of satellites on velocity estimation accuracy: (<b>a</b>) MAE; (<b>b</b>) RMSE.</p> ">
Abstract
:1. Introduction
2. Space-Based IR Multi-Satellite Observation Model
2.1. Space Target Observation Model
2.2. Target IR Image Plane Extraction
2.3. Multi-Satellite Cross-Positioning
3. Velocity Estimation Based on Robust Locally Weighted Regression
3.1. Locally Weighted Regression
3.2. Robust Locally Weighted Regression
3.3. Velocity Estimation and Accuracy Analysis
4. Experiment and Analysis
4.1. Simulation Parameter Settings
4.2. Comparative Experiment
4.3. Analysis of Impact Factors
4.3.1. Parameter Analysis for Proposed Method
4.3.2. Measurement Error Analysis
4.3.3. Satellite Number Analysis
5. Discussion
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
- Fontana, S.; Di Lauro, F. An Overview of Sensors for Long Range Missile Defense. Sensors 2022, 22, 9871. [Google Scholar] [CrossRef]
- Zhou, X.; Ni, X.; Zhang, J.; Weng, D.; Hu, Z.; Chen, F. A novel detection performance modular evaluation metric of space-based infrared system. Opt. Quantum Electron. 2022, 54, 274. [Google Scholar] [CrossRef]
- He, B.; Li, H.; Li, G.; Pei, Z.; Jiang, T. Simulation modeling and detection performance analysis of space-based infrared early warning system. In Proceedings of the 2022 IEEE 5th International Conference on Information Systems and Computer Aided Education (ICISCAE), Dalian, China, 23–25 September 2022; pp. 969–977. [Google Scholar]
- Yılmaz, Ö.; Aouf, N.; Checa, E.; Majewski, L.; Sanchez-Gestido, M. Thermal analysis of space debris for infrared-based active debris removal. Proc. Inst. Mech. Eng. Part G J. Aerosp. Eng. 2019, 233, 811–822. [Google Scholar] [CrossRef]
- Erlandson, R.E.; Taylor, J.C.; Michaelis, C.H.; Edwards, J.L.; Brown, R.C.; Swaminathan, P.K.; Kumar, C.K.; Hargis, C.B.; Goldberg, A.C.; Klatt, E.M.; et al. Development of Kill Assessment Technology for Space-Based Applications. Johns Hopkins APL Tech. Dig. 2010, 29, 289. [Google Scholar]
- Wang, Y.; Chen, X.; Gong, C.; Rao, P. Non-Ellipsoidal Infrared Group/Extended Target Tracking Based on Poisson Multi-Bernoulli Mixture Filter and B-Spline. Remote Sens. 2023, 15, 606. [Google Scholar] [CrossRef]
- Hu, Y.; Ma, Y.; Pan, Z.; Liu, Y. Infrared Dim and Small Target Detection from Complex Scenes via Multi-Frame Spatial–Temporal Patch-Tensor Model. Remote Sens. 2022, 14, 2234. [Google Scholar] [CrossRef]
- Zhang, Y.; Leng, K.; Park, K.S. Infrared detection of small moving target using spatial–temporal local vector difference measure. IEEE Geosci. Remote Sens. Lett. 2022, 19, 1–5. [Google Scholar] [CrossRef]
- Zhang, S.; Rao, P.; Zhang, H.; Chen, X.; Hu, T. Spatial Infrared Objects Discrimination based on Multi-Channel CNN with Attention Mechanism. Infrared Phys. Technol. 2023, 104670. [Google Scholar] [CrossRef]
- Chen, L.; Rao, P.; Chen, X.; Huang, M. Local Spatial–Temporal Matching Method for Space-Based Infrared Aerial Target Detection. Sensors 2022, 22, 1707. [Google Scholar] [CrossRef]
- Du, J.; Lu, H.; Zhang, L.; Hu, M.; Deng, Y.; Shen, X.; Li, D.; Zhang, Y. DP–MHT–TBD: A Dynamic Programming and Multiple Hypothesis Testing-Based Infrared Dim Point Target Detection Algorithm. Remote Sens. 2022, 14, 5072. [Google Scholar] [CrossRef]
- Sheng, W. Research on Target Tracking Technologies for Space-Based Optical Surveillance System; National University of Defense Technology: Changsha, China, 2011. [Google Scholar]
- Lih, Y.; Kirubarajan, T.; Bar-Shalom, Y.; Yeddanapudi, M. Trajectory and launch point estimation for ballistic missiles from boost phase LOS measurements. In Proceedings of the 1999 IEEE Aerospace Conference, Proceedings (Cat. No. 99TH8403), Snowmass, CO, USA, 7 March 1999; Volume 4, pp. 425–442. [Google Scholar]
- Aghav, S.T.; Gangal, S.A. Simplified orbit determination algorithm for low earth orbit satellites using spaceborne gps navigation sensor. Artif. Satell. 2014, 49, 81–99. [Google Scholar] [CrossRef]
- Julier, S.J.; Uhlmann, J.K. Unscented filtering and nonlinear estimation. Proc. IEEE 2004, 92, 401–422. [Google Scholar] [CrossRef]
- Liu, J.; Luo, Q.; Lou, J.; Li, Y. Space infrared tracking of a hypersonic cruise vehicle using an adaptive scaling UKF. Aerospace Syst. 2020, 3, 287–296. [Google Scholar] [CrossRef]
- Arasaratnam, I.; Haykin, S. Cubature kalman filters. IEEE Trans. Autom. Control. 2009, 54, 1254–1269. [Google Scholar] [CrossRef]
- Zou, T.; Situ, W.; Yang, W.; Zeng, W.; Wang, Y. A Method for Long-Term Target Anti-Interference Tracking Combining Deep Learning and CKF for LARS Tracking and Capturing. Remote Sens. 2023, 15, 748. [Google Scholar] [CrossRef]
- Huang, P.; Li, H.; Wen, G.; Wang, Z. Application of Adaptive Weighted Strong Tracking Unscented Kalman Filter in Non-Cooperative Maneuvering Target Tracking. Aerospace 2022, 9, 468. [Google Scholar] [CrossRef]
- Cui, N.G.; Zhang, L.; Wang, X.G.; Yang, F.; Lu, B. Application of adaptive high-degree cubature Kalman filter in target tracking. Acta Aeronaut. Astronaut. Sin. 2015, 36, 3885–3895. [Google Scholar]
- Ding, W.Z.; Zhang, Z.Y.; Yang, H. Analysis of target positioning accuracy based on method of double satellite optical tracking. Acta Astron. Sin. 2017, 58, 40. [Google Scholar]
- Zhao, J.B.; Xu, T.T.; Yang, X.B.; Yong, Q. Stereo celestial positioning of space-based double satellites to space target. Opt. Precis. Eng. 2021, 12, 2902–2914. [Google Scholar] [CrossRef]
- Duan, C.; Feng, B.; Zhang, K.; Xue, J.; Zhang, Q. A Novel Constellation Selection Strategy of Multi-Satellite Joint Positioning. In Proceedings of the 2021 13th International Conference on Wireless Communications and Signal Processing (WCSP), Changsha, China, 20–22 October 2021; pp. 1–5. [Google Scholar]
- Zhao, H.; Yan, Y.; Shi, X. A dynamic localization network for regional navigation under global navigation satellite system denial environments. Int. J. Distrib. Sens. Netw. 2019, 15, 1550147719834427. [Google Scholar] [CrossRef]
- Holt, C.C. Forecasting seasonals and trends by exponentially weighted moving averages. Int. J. Forecast. 2004, 20, 5–10. [Google Scholar] [CrossRef]
- Widrow, B. The LMS algorithm. In Cybernetics 2.0: A General Theory of Adaptivity and Homeostasis in the Brain and in the Body; Springer International Publishing: Cham, Switzerland, 2022; pp. 23–31. [Google Scholar]
- Schafer, R.W. What is a Savitzky-Golay filter? [lecture notes]. IEEE Signal Process. Mag. 2011, 28, 111–117. [Google Scholar] [CrossRef]
- Cleveland, W.S.; Devlin, S.J. Locally weighted regression: An approach to regression analysis by local fitting. J. Am. Stat. Assoc. 1988, 83, 596–610. [Google Scholar] [CrossRef]
- Chen, J.-H.; Lu, S.-L. A New Sum of Squares Exponentially Weighted Moving Average Control Chart Using Auxiliary Information. Symmetry 2020, 12, 1888. [Google Scholar] [CrossRef]
- Mabude, K.; Malela-Majika, J.C.; Castagliola, P.; Shongwe, S.C. Generally weighted moving average monitoring schemes: Overview and perspectives. Qual. Reliab. Eng. Int. 2021, 37, 409–432. [Google Scholar] [CrossRef]
- Ochieng, P.J.; Maróti, Z.; Dombi, J.; Krész, M.; Békési, J.; Kalmár, T. Adaptive Savitzky–Golay Filters for Analysis of Copy Number Variation Peaks from Whole-Exome Sequencing Data. Information 2023, 14, 128. [Google Scholar] [CrossRef]
- Guo, D.; Yang, G.; Qi, B.; Wang, C. A Fast Ground Segmentation Method of LiDAR Point Cloud From Coarse-to-Fine. IEEE Sens. J. 2022, 23, 1357–1367. [Google Scholar] [CrossRef]
- Alqasrawi, Y.; Azzeh, M.; Elsheikh, Y. Locally weighted regression with different kernel smoothers for software effort estimation. Sci. Comput. Program. 2022, 214, 102744. [Google Scholar] [CrossRef]
- Zhang, W.; Zhao, S.; Pan, H.; Zhao, X. A locally weighted linear regression look-up table-based iterative reconstruction method for dual spectral CT. IEEE Trans. Biomed. Eng. 2023. [Google Scholar] [CrossRef]
- Hu, Y.; Zhang, X.; Chen, L. Strategy design and sensor scheduling for optical navigation of low earth orbit satellites. IEEE Sens. J. 2018, 18, 9802–9811. [Google Scholar] [CrossRef]
- Hu, Y.; Li, K.; Liang, Y.; Chen, L. Review on strategies of space-based optical space situational awareness. J. Syst. Eng. Electron. 2021, 32, 1152–1166. [Google Scholar]
- Wang, X. Study of 3D Computer Vision for Photoelectric Theodolite Tracking Aircraft; The Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences: Changchun, China, 2010. [Google Scholar]
- Li, M.; Yan, C.; Hu, C.; Liu, C.; Xu, L. Space target detection in complicated situations for wide-field surveillance. IEEE Access 2019, 7, 123658–123670. [Google Scholar] [CrossRef]
- Chen, Z.; Hu, Z.; Su, X.; Hu, T.; Chen, F. A Large-Aperture Remote Sensing Camera Calibration Method Based on Stellar and Inner Blackbody. IEEE Trans. Geosci. Remote Sens. 2022, 60, 1–9. [Google Scholar] [CrossRef]
- Li, Z.; Zhao, Q.; Gong, W. Distorted point spread function and image reconstruction for ghost imaging. Opt. Laser Eng. 2021, 139, 106486. [Google Scholar] [CrossRef]
- Xie, K.; Han, Y.; Xue, M. Analysis of passive location accuracy in LEO infrared early warning constellation. Signal Process. 2008, 3, 343–348. [Google Scholar]
Satellite 1 | Satellite 2 | Satellite 3 | |
---|---|---|---|
Latitude angle | |||
Orbit inclination angle | |||
RAAN | |||
Focal plane size | 512 × 512 | ||
Pixel size | |||
Aperture | |||
Focal | |||
Frame frequency | 10 Hz | ||
Observation time | 100 s |
Scenario | ||||
---|---|---|---|---|
0 | 0 | 0 | 0 | 0 |
1 | 10 | 10 | 10 | 0.1 |
2 | 20 | 20 | 20 | 0.2 |
3 | 30 | 30 | 30 | 0.3 |
4 | 40 | 40 | 40 | 0.4 |
5 | 50 | 50 | 50 | 0.5 |
Scenario | MSP | MSP-LMS | MSP-LWR | MSP-ASG | Proposed Method | |||||
---|---|---|---|---|---|---|---|---|---|---|
MAE | RMSE | MAE | RMSE | MAE | RMSE | MAE | RMSE | MAE | RMSE | |
0 | 0.0331 | 0.4223 | 1.4303 | 2.9179 | 0.0663 | 1.4507 | 0.0354 | 0.4280 | 0.0733 | 1.6640 |
1 | 1939.4755 | 3811.0791 | 17.7091 | 59.4185 | 20.3960 | 43.1666 | 21.5942 | 47.8943 | 15.1737 | 35.4483 |
2 | 5242.1767 | 8056.9157 | 41.0581 | 102.0510 | 33.9207 | 74.9259 | 44.6317 | 91.6023 | 29.8266 | 63.2735 |
3 | 8582.6232 | 11,823.3344 | 63.7244 | 145.7770 | 50.8750 | 119.5350 | 58.8795 | 132.0521 | 45.6544 | 101.3857 |
4 | 11,795.9802 | 15,510.8994 | 87.3195 | 192.7804 | 68.7979 | 144.9957 | 80.4788 | 189.4000 | 59.9750 | 116.5446 |
5 | 15,424.1788 | 19,591.5688 | 108.3511 | 239.5455 | 95.8185 | 194.1914 | 104.6386 | 232.1873 | 81.9898 | 161.8585 |
MSP | MSP-LMS | MSP-LWR | MSP-ASG | Proposed Method | |
---|---|---|---|---|---|
Time (s) | 0.0115 | 0.2925 | 0.0381 | 0.1782 | 0.1517 |
Scenario | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
E1 | E2 | E3 | E4 | Overall | E1 | E2 | E3 | E4 | Overall | |
1 | 0.75 | 5.31 | 4.25 | 14.01 | 15.17 | 2.18 | 9.26 | 7.04 | 28.22 | 35.44 |
2 | 1.21 | 9.04 | 9.96 | 24.10 | 29.82 | 3.32 | 17.63 | 15.14 | 52.17 | 63.27 |
3 | 1.88 | 15.04 | 13.42 | 41.26 | 45.65 | 4.34 | 26.40 | 20.81 | 82.91 | 101.38 |
4 | 2.98 | 16.83 | 19.07 | 56.64 | 59.97 | 6.10 | 31.77 | 28.66 | 111.92 | 116.54 |
5 | 4.24 | 21.79 | 21.30 | 60.22 | 81.98 | 7.95 | 42.84 | 34.13 | 124.51 | 161.85 |
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Zhang, S.; Rao, P.; Zhang, H.; Chen, X. Velocity Estimation for Space Infrared Dim Targets Based on Multi-Satellite Observation and Robust Locally Weighted Regression. Remote Sens. 2023, 15, 2767. https://doi.org/10.3390/rs15112767
Zhang S, Rao P, Zhang H, Chen X. Velocity Estimation for Space Infrared Dim Targets Based on Multi-Satellite Observation and Robust Locally Weighted Regression. Remote Sensing. 2023; 15(11):2767. https://doi.org/10.3390/rs15112767
Chicago/Turabian StyleZhang, Shenghao, Peng Rao, Hao Zhang, and Xin Chen. 2023. "Velocity Estimation for Space Infrared Dim Targets Based on Multi-Satellite Observation and Robust Locally Weighted Regression" Remote Sensing 15, no. 11: 2767. https://doi.org/10.3390/rs15112767