# Moving Target Detection and Parameter Estimation via a Modified Imaging STAP with a Large Baseline in Multistatic GEO SAR

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## Abstract

**:**

## 1. Introduction

## 2. Special Problems of Multistatic GEO SAR MTI

#### 2.1. Geometry of Multistatic GEO SAR

#### 2.2. Ship Oscillatory Motions Effects

#### 2.3. Near-Field Effects

#### 2.4. Errors Induced by Curved Trajectories

## 3. High-Precision Multi-Channel Signal Model in Multistatic GEO SAR

#### 3.1. High-Precision Signal Model of Reference Channel

#### 3.2. Multi-Channel Signal Model with Large Baseline

#### 3.3. Azimuthal Spectrum of Multi-Channel Data Based on High-Order Expansion

## 4. Modified Imaging STAP Method in Near Field

#### 4.1. Clutter Suppression and Beamforming

#### 4.2. Moving Target Imaging

#### 4.3. Parameters Estimation

#### 4.4. Theoretical Analysis of the Proposed Method’s Performance

#### 4.4.1. SCNR Analysis

#### 4.4.2. Computational Complexity Analysis

## 5. Simulation and Discussion

#### 5.1. Error Analysis of Range Model

#### 5.1.1. Error Analysis of Path Difference

^{4}orders of magnitude at the equator.

#### 5.1.2. Error Analysis of Range Model

^{4}orders of magnitude at the equator. The results in Figure 7a,c are similar to the results in Figure 8a,c because the range model’s phase errors were mainly produced by the path difference model’s errors. Thus, only the method based on the fourth-order phase signal is effective for the multistatic GEO SAR system.

#### 5.2. Results of Modified ISTAP Method in Near Field

#### 5.2.1. Clutter Suppression and Motion Parameters Estimation

#### 5.2.2. Performance Analysis of SCNR and Minimum Detectable Velocity

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

## Appendix B

## Appendix C

## Appendix D

^{3}orders of magnitude smaller than the derivative of ${\mathsf{\Theta}}_{c}\left(nT\right)$. Then, it can be obtained that $\frac{\partial {\mathsf{\Theta}}_{m}\left(nT\right)}{\partial \left(nT\right)}\approx 0$. Therefore, when the principle of stationary phase is utilized to solve the expression of signal in the range-Doppler domain, ${\mathsf{\Theta}}_{m}\left(nT\right)$ will not affect the location of the stagnation point. If the stagnation point is ${t}_{k}\left({f}_{a}\right)$, after the Fourier transforms, the signal ${\tilde{S}}_{m}\left(r,nT,{\mathbf{\vartheta}}_{s}\right)$ can be represented as:

## References

- Long, T.; Dong, X.; Hu, C.; Zeng, T. A New Method of Zero-Doppler Centroid Control in GEO SAR. IEEE Geosci. Remote Sens. Lett.
**2010**, 8, 512–516. [Google Scholar] [CrossRef] - Tomiyasu, K. Synthetic aperture radar in geosynchronous orbit. In Proceedings of the Antennas and Propagation Society International Symposium, Washington, DC, USA, 15–19 March 1978; Institute of Electrical and Electronics Engineers (IEEE): Piscataway, NJ, USA, 1978. [Google Scholar]
- Hu, C.; Long, T.; Li, X.; Gao, Y. Geo SAR interferometry: Theory and feasibility study. In Proceedings of the IET International Radar Conference (IET), Xi’an, China, 14–16 April 2013; p. 496. [Google Scholar]
- Li, Y.; Ao, D.; Dumitru, C.O.; Hu, C.; Datcu, M. Super-resolution of geosynchronous synthetic aperture radar images using dialectical GANs. Sci. China Inf. Sci.
**2019**, 62, 209302. [Google Scholar] [CrossRef] [Green Version] - Hu, C.; Zhang, B.; Dong, X.; Li, Y. Geosynchronous SAR Tomography: Theory and First Experimental Verification Using Beidou IGSO Satellite. IEEE Trans. Geosci. Remote Sens.
**2019**, 57, 6591–6607. [Google Scholar] [CrossRef] - Zheng, W.; Hu, J.; Zhang, W.; Yang, C.; Li, Z.; Zhu, J. Potential of geosynchronous SAR interferometric measurements in estimating three-dimensional surface displacements. Sci. China Inf. Sci.
**2017**, 60, 060304. [Google Scholar] [CrossRef] - Dong, X.; Hu, J.; Hu, C.; Long, T.; Li, Y.; Tian, Y. Modeling and Quantitative Analysis of Tropospheric Impact on Inclined Geosynchronous SAR Imaging. Remote Sens.
**2019**, 11, 803. [Google Scholar] [CrossRef] [Green Version] - Hu, C.; Liu, Z.; Long, T. An improved focusing method for geosynchronous SAR. Adv. Space Res.
**2013**, 51, 1773–1783. [Google Scholar] [CrossRef] - Ruiz-Rodon, J.; Broquetas, A.; Makhoul, E.; Guarnieri, A.M.; Rocca, F. Nearly Zero Inclination Geosynchronous SAR Mission Analysis With Long Integration Time for Earth Observation. IEEE Trans. Geosci. Remote Sens.
**2014**, 52, 6379–6391. [Google Scholar] [CrossRef] - Guarnieri, A.M.; Leanza, A.; Recchia, A.; Tebaldini, S.; Venuti, G. Atmospheric Phase Screen in GEO-SAR: Estimation and Compensation. IEEE Trans. Geosci. Remote Sens.
**2018**, 56, 1668–1679. [Google Scholar] [CrossRef] - Guarnieri, A.M.; Broquetas, A.; Recchia, A.; Rocca, F.; Ruiz-Rodon, J. Advanced Radar Geosynchronous Observation System: ARGOS. IEEE Geosci. Remote Sens. Lett.
**2015**, 12, 1406–1410. [Google Scholar] [CrossRef] [Green Version] - Guarnieri, A.M.; Bombaci, O.; Catalano, T.; Germani, C.; Köppel, C.; Rocca, F.; Wadge, G. ARGOS: A fractioned geosynchronous SAR. Acta Astronaut.
**2019**, 164, 444–457. [Google Scholar] [CrossRef] - Guarnieri, A.M.; Broquetas, A.; López-Dekker, F.; Rocca, F. A geostationary MIMO SAR swarm for quasi-continuous observation. In Proceedings of the IEEE International Geoscience and Remote Sensing Symposium, Milan, Italy, 26–31 July 2015. [Google Scholar]
- Guarnieri, A.M.; Rocca, F. Options for continuous radar Earth observations. Sci. China Inf. Sci.
**2017**, 60, 060301. [Google Scholar] [CrossRef] - Hu, C.; Chen, Z.; Dong, X.; Cui, C. Multistatic Geosynchronous SAR Resolution Analysis and Grating Lobe Suppression Based on Array Spatial Ambiguity Function. IEEE Trans. Geosci. Remote Sens.
**2020**, 58, 1–19. [Google Scholar] [CrossRef] - Chen, Z.; Dong, X.; Li, Y.; Hu, C. Formation Design for Single-Pass GEO InSAR Considering Earth Rotation Based on Coordinate Rotational Transformation. Remote Sens.
**2020**, 12, 573. [Google Scholar] [CrossRef] [Green Version] - Wu, J.; Sun, Z.; An, H.; Qu, J.; Yang, J. Azimuth Signal Multichannel Reconstruction and Channel Configuration Design for Geosynchronous Spaceborne–Airborne Bistatic SAR. IEEE Trans. Geosci. Remote Sens.
**2018**, 57, 1861–1872. [Google Scholar] [CrossRef] - An, H.; Wu, J.; Sun, Z.; Yang, J. A Two-Step Nonlinear Chirp Scaling Method for Multichannel GEO Spaceborne–Airborne Bistatic SAR Spectrum Reconstructing and Focusing. IEEE Trans. Geosci. Remote Sens.
**2019**, 57, 3713–3728. [Google Scholar] [CrossRef] - Melzi, M.; Hu, C.; Dong, X.; Li, Y.; Cui, C. Velocity Estimation of Multiple Moving Targets in Single-Channel Geosynchronous SAR. IEEE Trans. Geosci. Remote Sens.
**2020**, 58, 19. [Google Scholar] [CrossRef] - Zhang, Y.; Xiong, W.; Dong, X.; Hu, C.; Sun, Y. GRFT-Based Moving Ship Target Detection and Imaging in Geosynchronous SAR. Remote Sens.
**2018**, 10, 2002. [Google Scholar] [CrossRef] [Green Version] - Tian, H.; Cao, J.; Zhang, S.; Wang, W.-Q.; Ding, H. Moving Target Detection and Imaging for Geosynchronous SAR. In Proceedings of the IGARSS 2018–2018 IEEE International Geoscience and Remote Sensing Symposium, Valencia, Spain, 22–27 July 2018; Institute of Electrical and Electronics Engineers (IEEE): Valencia, Spain; pp. 2833–2836. [Google Scholar]
- Li, Z.; Bao, Z.; Wang, H.; Liao, G. Performance improvement for constellation SAR using signal processing techniques. IEEE Trans. Aerosp. Electron. Syst.
**2006**, 42, 436–452. [Google Scholar] [CrossRef] - Dong, Q.; Xing, M.-D.; Xia, X.-G.; Zhang, S.; Sun, G.-C. Moving Target Refocusing Algorithm in 2-D Wavenumber Domain after BP Integral. IEEE Geosci. Remote Sens. Lett.
**2017**, 15, 127–131. [Google Scholar] [CrossRef] - Tan, W.; Xu, W.; Huang, P.; Huang, Z.; Qi, Y.; Han, K. Investigation of Azimuth Multichannel Reconstruction for Moving Targets in High Resolution Wide Swath SAR. Sensors
**2017**, 17, 1270. [Google Scholar] [CrossRef] [Green Version] - Zheng, H.; Wang, J.; Liu, X. Ground Moving Target Indication for High-Resolution Wide-Swath Synthetic Aperture Radar Systems. IEEE Geosci. Remote Sens. Lett.
**2017**, 14, 749–753. [Google Scholar] [CrossRef] - Brennan, L.E.; Reed, L.S. Theory of Adaptive Radar. IEEE Trans. Aerosp. Electron. Syst.
**2007**, 9, 237–252. [Google Scholar] [CrossRef] - Brennan, L.; Mallett, J.; Reed, I. Adaptive arrays in airborne MTI radar. IRE Trans. Antennas Propag.
**1976**, 24, 607–615. [Google Scholar] [CrossRef] - Klemm, R. Principles of Space-Time Adaptive Processing; Institute of Electical Engineering: London, UK, 2006. [Google Scholar]
- Guerci, J.R. Space-Time Adaptive Processing for Radar; Artech House: New York, NY, USA, 2003. [Google Scholar]
- Peckham, C.D. Reduced-rank STAP performance analysis. IEEE Trans. Aerosp. Electron. Syst.
**2000**, 36, 664–676. [Google Scholar] [CrossRef] - Melvin, W.L. Space-Time Adaptive Radar Performance in Heterogeneous Clutter. IEEE Trans. Aerosp. Electron. Syst.
**2000**, 36, 621–633. [Google Scholar] [CrossRef] - Ender, J.H.G. Space-time processing for multi-channel synthetic aperture radar. Electron. Commun. Eng. J.
**2002**, 11, 29–38. [Google Scholar] [CrossRef] - Cerutti-Maori, D.; Sikaneta, I.; Gierull, C.H. Optimum SAR/GMTI Processing and Its Application to the Radar Satellite RADARSAT-2 for Traffic Monitoring. IEEE Trans. Geosci. Remote Sens.
**2012**, 50, 3868–3881. [Google Scholar] [CrossRef] - Cerutti-Maori, D.; Sikaneta, I. Optimum GMTI Processing for Space-based SAR/GMTI Systems—Simulation Results. In Proceedings of the 8th European Conference on Synthetic Aperture Radar, Aachen, Germany, 8–10 June 2010; VDE: Frankfurt, Germany, 2011. [Google Scholar]
- Cerutti-Maori, D.; Sikaneta, I. Optimum GMTI Processing for Space-based SAR/GMTI Systems—Theoretical Derivation. In Proceedings of the 8th European Conference on Synthetic Aperture Radar, Aachen, Germany, 8–10 June 2010; VDE: Frankfurt, Germany, 2011. [Google Scholar]
- Hu, C.; Long, T.; Liu, Z.; Zeng, T.; Tian, Y. An Improved Frequency Domain Focusing Method in Geosynchronous SAR. IEEE Trans. Geosci. Remote Sens.
**2013**, 52, 5514–5528. [Google Scholar] [CrossRef] - Cui, C.; Liu, X.; Dong, X.; Hu, C.; Li, Y. Moving target modelling and indication in MIMO GEO SAR. J. Eng.
**2019**, 2019, 5529–5533. [Google Scholar] [CrossRef] - Doerry, A.W. Ship Dynamics for Maritime ISAR Imaging; U.S. Department of Energy Office of Scientific and Technical Information: Oak Ridge, TN, USA, 2008.
- Kraus, J.D.; Marhefka, R.J. Antennas for All Applications; McGraw Hill: New York, NY, USA, 2002. [Google Scholar]
- Xiong, W.; Zhang, Y.; Dong, X.; Cui, C.; Liu, Z.; Xiong, M. A Novel Ship Imaging Method with Multiple Sinusoidal Functions to Match Rotation Effects in Geosynchronous SAR. Remote Sens.
**2020**, 12, 2249. [Google Scholar] [CrossRef] - Long, T.; Hu, C.; Ding, Z.; Dong, X.; Tian, W.; Zeng, T. Geosynchronous SAR: System and Signal Processing; Springer: Singapore, 2018. [Google Scholar]
- Fertig, L.B. Analytical expressions for space-time adaptive processing (STAP) performance. IEEE Trans. Aerosp. Electron. Syst.
**2015**, 51, 42–53. [Google Scholar] [CrossRef] - Hu, C.; Tian, Y.; Yang, X.; Zeng, T.; Long, T.; Dong, X. Background Ionosphere Effects on Geosynchronous SAR Focusing: Theoretical Analysis and Verification Based on the BeiDou Navigation Satellite System (BDS). IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens.
**2016**, 9, 1143–1162. [Google Scholar] [CrossRef] - Ward, K.D.; Tough, R.J.A.; Watts, S. Sea clutter: Scattering, the K distribution and radar performance. Waves Random Complex Media
**2007**, 17, 233–234. [Google Scholar] [CrossRef] - Ding, Z.; Zhang, T.; Li, Y.; Li, G.; Dong, X.; Zeng, T.; Ke, M. A Ship ISAR Imaging Algorithm Based on Generalized Radon-Fourier Transform With Low SNR. IEEE Trans. Geosci. Remote Sens.
**2019**, 57, 6385–6396. [Google Scholar] [CrossRef] - Zhang, Y.; Mu, H.; Xiao, T.; Jiang, Y.; Ding, C. SAR imaging of multiple maritime moving targets based on sparsity Bayesian learning. IET Radar Sonar Navig.
**2020**, 14, 1717–1725. [Google Scholar] [CrossRef] - Raney, R.K. Synthetic Aperture Imaging Radar and Moving Targets. IEEE Trans. Aerosp. Electron. Syst.
**1971**, 7, 499–505. [Google Scholar] [CrossRef]

**Figure 1.**Geometry and formation configuration of multistatic geosynchronous synthetic aperture radar (GEO SAR).

**Figure 5.**Slant range errors of the equivalent linear model induced by curved trajectories: (

**a**) range errors in the reference channel; (

**b**) inter-channel path difference errors, with a channel separation of 2 km.

**Figure 7.**The phase error of path difference model in the different orbital position: (

**a**) Far-field assumption model error (Equator); (

**b**) Near-field model error (Equator); (

**c**) Far-field assumption model error (Perigee); (

**d**) Near-field model error (Perigee).

**Figure 8.**The phase error of range model in the different orbital position: (

**a**) Far-field assumption model error (Equator); (

**b**) Near-field model error (Equator); (

**c**) Far-field assumption model error (Perigee); (

**d**) Near-field model error (Perigee).

**Figure 9.**Raw data for the reference channel: (

**a**) Echo received by reference channel; (

**b**) Signal in the range-Doppler domain for the reference channel.

**Figure 10.**Results of the modified ISTAP method in the near field. (

**a**) The result after clutter suppression when the searching parameters (radial velocity is 6 m/s and azimuth velocity is 6 m/s) do not match with the actual motion parameters. (

**b**) The result after imaging with the unmatched parameters. (

**c**) The result after clutter suppression when the searching parameters match with the actual motion parameters. (

**d**) The result after imaging with the matched parameters.

**Figure 11.**The results of velocity searching and imaging: (

**a**) The SNR of output SAR image under different radial velocities; (

**b**) The imaging results of 16 targets where the red cross marks represent the actual position of the targets.

**Figure 12.**Output clutter and noise ratio (SCNR) at the different orbital position with different channel spacing: (

**a**) Equator; (

**b**) Perigee.

Symbol | Explanation | Symbol | Explanation |
---|---|---|---|

$n$ | Slow time | $T$ | Pulse repetition time |

$c$ | Speed of light | ${a}_{a}\left(\xb7\right)$ | The envelope in the azimuth direction |

$\lambda $ | Wavelength | ${a}_{r}\left(\xb7\right)$ | The envelope in range direction |

${\sigma}_{s}^{m}$ | The amplitude of the target received by the mth channel | ${k}_{r}$ | The frequency modulation rate in range direction |

${\phi}_{s}^{m}$ | The phase of the target received by the mth channel | ${\mathbf{\vartheta}}_{s}$ | The set of moving target’s position and its velocity |

${k}_{1}~{k}_{4}$ | Coefficients of each order of the Taylor expansion of the reference channel’s slant range history | ${\mathbf{\vartheta}}_{c}$ | The set of stationary target’s position and its velocity |

${\mathbf{I}}_{M}$ | M-dimensional identity matrix | ${\sigma}_{n}^{2}$ | The variance of thermal noise |

${\phi}_{s}$ | The phase of the target | ${\sigma}_{s}$ | The amplitude of the target |

M | Number of channels | $\Delta {k}_{1}~\Delta {k}_{3}$ | Coefficients of each order of the Taylor expansion of the path difference |

$r$ | The range position in SAR image | $x$ | The azimuth position in SAR image |

**Table 2.**Baseline length and range’s rotation angle limited by the far-field assumption of GEO SAR and a Interferometric Radar Mission (Tandem-L).

Satellite | Slant Range | Wavelength | Baseline Length Limited by the Far-Field Assumption | Range’s Rotation Angle Limited by the Far-Field Assumption |
---|---|---|---|---|

GEO SAR | ~36,000 km | 0.24 m | 1309 m | 0.0016° |

Tandem-L | ~745 km | 0.24 m | 149 m | 0.011° |

Parameters | Values | Parameters | Values |
---|---|---|---|

Semi-major axis | 42,164 km | Sample rate | 20 MHz |

Inclination | 53° | Pulse width | 20 μs |

Eccentricity | 0 | Wavelength | 0.24 m |

Number of channels | 5 | Bandwidth | 18 MHz |

Look angle | 4.65° | Pulse Repetition Frequency | 600 Hz |

Adjacent channel spacings | 5368 m, 2684 m, −2618 m and −5236 m | Observation Time | 60 s |

Target No. | Radial Velocity | Azimuth Velocity | Target No. | Radial Velocity | Azimuth Velocity |
---|---|---|---|---|---|

1 | −1 m/s | −1 m/s | 9 | −3.0147 m/s | −3.0147 m/s |

2 | −5 m/s | −5 m/s | 10 | −6.9825 m/s | −6.9825 m/s |

3 | −15 m/s | −15 m/s | 11 | −11.4486 m/s | −11.4486 m/s |

4 | −30 m/s | −30 m/s | 12 | −24.1429 m/s | −24.1429 m/s |

5 | 1 m/s | 1 m/s | 13 | −29.4437 m/s | −29.4437 m/s |

6 | 5 m/s | 5 m/s | 14 | 3.5543 m/s | 3.5543 m/s |

7 | 15 m/s | 15 m/s | 15 | 19.6818 m/s | 19.6818 m/s |

8 | 30 m/s | 30 m/s | 16 | 20.4853 m/s | 20.4853 m/s |

Target No. | Radial Velocity | Azimuth Velocity | Target No. | Radial Velocity | Azimuth Velocity |
---|---|---|---|---|---|

1 | −1 m/s | −1 m/s | 9 | −3 m/s | −3 m/s |

2 | −5 m/s | −5 m/s | 10 | −7 m/s | −7 m/s |

3 | −15 m/s | −15 m/s | 11 | −11.5 m/s | −11.5 m/s |

4 | −30 m/s | −30 m/s | 12 | −24.1 m/s | −24 m/s |

5 | 1 m/s | 1 m/s | 13 | −29.4 m/s | −29.5 m/s |

6 | 5 m/s | 5 m/s | 14 | 3.5 m/s | 3.5 m/s |

7 | 15 m/s | 15 m/s | 15 | 19.7 m/s | 19.5 m/s |

8 | 30 m/s | 30 m/s | 16 | 20.5 m/s | 20.5 m/s |

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**MDPI and ACS Style**

Dong, X.; Cui, C.; Tian, W.; Li, Y.; Mounir, M.; Hu, C.
Moving Target Detection and Parameter Estimation via a Modified Imaging STAP with a Large Baseline in Multistatic GEO SAR. *Remote Sens.* **2021**, *13*, 346.
https://doi.org/10.3390/rs13030346

**AMA Style**

Dong X, Cui C, Tian W, Li Y, Mounir M, Hu C.
Moving Target Detection and Parameter Estimation via a Modified Imaging STAP with a Large Baseline in Multistatic GEO SAR. *Remote Sensing*. 2021; 13(3):346.
https://doi.org/10.3390/rs13030346

**Chicago/Turabian Style**

Dong, Xichao, Chang Cui, Weiming Tian, Yuanhao Li, Melzi Mounir, and Cheng Hu.
2021. "Moving Target Detection and Parameter Estimation via a Modified Imaging STAP with a Large Baseline in Multistatic GEO SAR" *Remote Sensing* 13, no. 3: 346.
https://doi.org/10.3390/rs13030346