Geosynchronous Research Articles

CF-LSTM-based post-maneuver position prediction for GEO spacecraft

Prediction of the position of Geosynchronous (GEO) spacecraft after a maneuver is crucial for space domain awareness (SDA), as it can enhance the flexibility of the space surveillance network (SSN). The longitude is a unique parameter that can be freely assigned to GEO spacecraft. In this paper, we propose a prediction model for the longitude of a GEO spacecraft based on Causal Feature Long Short-Term Memory networks (CF-LSTM). Initially, we analyze the historical data of GEO spacecraft in a time-series geographic position and identify the causal parameters of longitude using the Gaussian perturbation equation. Subsequently, we present the CF-LSTM to predict the longitude. Our experimental analysis shows that the proposed method reduces the mean absolute error (MAE) and mean square error (MSE) by 60.92% and 18.75%, respectively, compared to conventional LSTM.

Impact Analysis and Compensation Methods of Frequency Synchronization Errors in Distributed Geosynchronous Synthetic Aperture Radar

Frequency synchronization error, as one of the inevitable technical challenges in distributed synthetic aperture radar (SAR), has different impacts on different SAR systems. Multi-monostatic SAR is a typical distributed configuration where frequency synchronization errors are tiny in distributed airborne and low earth orbit (LEO) SAR systems. However, due to the long time delay and long synthetic aperture time, the imaging performance of a multi-monostatic geosynchronous (GEO) SAR system is affected by frequency oscillator errors. In this paper, to investigate the frequency synchronization problem in this configuration, we firstly model the echo signals with the frequency synchronization errors, which can be divided into fixed frequency errors and random phase noise. Secondly, we talk about the impacts of the two kinds of errors on imaging performance. To solve the problem, we thirdly propose an autofocus back-projection (ABP) algorithm, which adopts the coordinate descent method and iteratively adjusts the phase error estimation until the image reaches its maximum sharpness. Based on the characteristics of the frequency synchronization errors, we further propose the Node ABP (NABP) algorithm, which greatly reduces the amount of storage and computation compared to the ABP algorithm. Finally, simulations are carried out to validate the effectiveness of the ABP and NABP algorithms.

Proposal for a realtime Einstein-synchronization-defined satellite virtual clock

Abstract The realization of high performance satellite onboard clock is vital for various PNT applications. For further improvement of the synchronization-based satellite time and frequency references, this paper proposes a geosynchronous (GEO) satellite virtual clock concept based on ground–satellite synchronization and presents a beacon transponder structure for its implementation (scheduled for launch in 2025), which does not require atomic clocks to be mounted on the satellite. Its high performance relies only on minor modifications to the existing transponder structure of GEO satellites. We carefully modeled the carrier phase link and analyzed the factors causing link asymmetry within the special relativity. Considering that the performance of such synchronization-based satellite clocks is primarily limited by the link’s random phase noise, which cannot be adequately modeled, we designed a closed-loop experiment based on commercial GEO satellites for pre-evaluation. This experiment was aimed at extracting the zero-means random part of the ground-satellite Ku-band carrier phase via a feedback loop. Ultimately, we obtained a 1σ value of 0.633 ps (two-way link), following the Gaussian distribution. From this result, we conclude that the proposed real-time Einstein-synchronization-defined satellite virtual clock can achieve picosecond-level replication of onboard time and frequency.

Contribution of BDS-3 observations to the precise orbit determination of LEO satellites: a case study of TJU-01

The precise orbit determination (POD) of scientific low Earth orbit (LEO) satellites is a prerequisite for the successful implementation of scientific missions. In recent years, global navigation satellite systems have become the main means of determining the orbits of LEO satellites. The global navigation satellite system receiver onboard the Tianjin University No. 1 (TJU-01) satellite receives both GPS and BDS-2/3 signals, with the addition of BDS-2/3 observations playing an important role in improving the POD of LEO satellites. This study comprehensively analyzes the spaceborne GPS/BDS data quality, including BDS-2/3 and GPS code multipath errors. Appreciable code multipath errors are found for the B1I signal of BDS-2 medium Earth orbit (MEO) satellites at elevations higher than 40°, whereas slight near-field relevant multipath errors of both frequencies are found for GPS and BDS-3 MEO satellites. The GPS and BDS-2/3 code multipath errors are estimated through elevation/azimuth-relevant piece-wise modeling and applied in the POD calculations. Several schemes, namely GPS-based, BDS-based, BDS-based without geo-synchronous (GEO) satellites, and GPS/BDS combined schemes, are designed to evaluate the POD performance. Fourteen days of data are calculated and the average three-dimensional (3D) orbital root mean square (RMS) of orbit overlapping differences obtained from GPS-based and BDS-based POD (without GEO satellites) solutions are 37.4 and 27.1 mm, respectively. The BDS-based solutions are obviously better than the GPS-based solutions, mainly owing to better data availability. The GPS/BDS combined solutions have the best accuracy, with a 3D RMS value of 20.6 mm. In addition, when BDS GEO satellites are included, the 3D RMS of the overlapping orbit differences reduces to 32.9 and 27.4 mm for BDS-based and GPS/BDS combined solutions, respectively. Double-difference (DD) and single-difference (SD) integer ambiguity resolution (IAR) are adopted to further improve the POD performance. The fixed orbit of the TJU-01 satellite is solved through DD IAR and SD IAR, and the contribution of the TJU-01 satellite to ambiguity fixing is analyzed. Relative to the float solution, the improvements made using the two ambiguity fixing approaches are equivalent, both being approximately 13%. The importance of this research is not only the precise determination of the orbit of TJU-01 for occultation service but also the demonstration of the contribution of BDS observations to the performance of the POD of LEO satellites.

Electrostatic Potential Shielding in Representative Cislunar Regions

Touchless potential sensing of neighboring spacecraft using photoemissions and secondary electron emissions has been investigated for geosynchronous (GEO) applications. As more missions are being sent to cislunar space, this technology may be extended there as well. However, the complexity of the cislunar environment presents novel challenges for touchless potential sensing technology. A chief issue is shorter Debye lengths than in GEO regions, which can be as low as 10 m in the cislunar regions. Therefore, a model for the electric and potential fields surrounding a charged spacecraft in short Debye regions around the moon is investigated. The vacuum (Laplace) and Debye–Hückel models are presented and effective Debye lengths are used to expand the models and better represent the environment. The effective Debye length has previously been investigated in low Earth orbit (LEO), quiet GEO, and asteroid environments but has not been found in the cislunar plasma environment, and a larger effective Debye length may allow touchless potential sensing using electron emissions to be possible at farther, safer distances than expected. Once the effective Debye lengths and associated models are established, the relationship between effective Debye lengths and touchless potential sensing capabilities is explored through computations in NASCAP-2k, a spacecraft–plasma interaction software. The developed methods are then used to determine whether passive and active touchless potential sensing is feasible in cislunar regions with nonnegligible electrostatic potential shielding.

GEO spacecraft maneuver detection based on causal inference

Geosynchronous (GEO) spacecraft maneuver detection is deemed crucial for space domain awareness (SDA) as it helps to maintain catalogs of high value resident space objects (RSOs). However, several difficulties in resolving maneuver time and requirements for historical data quality still exist for the current research. This paper proposes a method based on causal inference for accurate and timely detection of the maneuver using real-time observational data from optical sensors. Firstly, the residual information of time series observations is obtained through counterfactual reasoning. Secondly, according to the Gaussianity of the optical sensor observation noise, a structural causal equation (SCE) of the residuals of time series observations is derived. Lastly, the maneuver is abstracted as a soft intervention, and the minimum average treatment effect (MATE) is proposed to estimate the effect of the maneuver and used as a feature parameter to identify the GEO spacecraft maneuver. After experimental analysis, the detection rate and detection timeliness of the proposed method reach more than 90%, a significant improvement compared with the conventional χ2, skewness, and kurtosis test methods.

Prediction model of GEO spacecraft position after maneuver based on causal Bayesian network

Predicting the position of Geosynchronous (GEO) spacecraft under maneuver is a crucial work for space domain awareness (SDA) as it can help to improve the flexibility and operational efficiency of space surveillance network (SSN). The longitude is a unique freely assigned parameter for GEO spacecraft, in this paper, a predictive model of GEO spacecraft longitude based on causal Bayesian network is proposed. Firstly, the causal parameters of longitude is found by Gaussian perturbation equation. Secondly, the Markov order of the causal parameters is obtained by transfer entropy. Finally, the linear expressions for Gaussian functions is proved and a causal Bayesian network (CBN) prediction model for longitude is constructed. After experimental analysis, the mean absolute error (MAE) and mean square error (MSE) of the proposed method are decreased by 71.88% and 72.18%, respectively compared with the traditional Long short-term memory (LSTM) method.

Fast Factorized Backprojection Algorithm in Orthogonal Elliptical Coordinate System for Ocean Scenes Imaging Using Geosynchronous Spaceborne–Airborne VHF UWB Bistatic SAR

Geosynchronous (GEO) spaceborne–airborne very high-frequency ultra-wideband bistatic synthetic aperture radar (VHF UWB BiSAR) can conduct high-resolution and wide-swath imaging for ocean scenes. However, GEO spaceborne–airborne VHF UWB BiSAR imaging faces some challenges such as the geometric configuration, huge amount of echo data, serious range–azimuth coupling, large spatial variance, and complex motion error, which increases the difficulty of the high-efficiency and high-precision imaging. In this paper, we present an improved bistatic fast factorization backprojection (FFBP) algorithm for ocean scene imaging using the GEO satellite-unmanned aerial vehicle (GEO-UAV) VHF UWB BiSAR, which can solve the above issues with high efficiency and high precision. This method reconstructs the subimages in the orthogonal elliptical polar (OEP) coordinate system based on the GEO satellite and UAV trajectories as well as the location of the imaged scene, which can further reduce the computational burden. First, the imaging geometry and signal model of the GEO-UAV VHF UWB BiSAR are established, and the construction of the OEP coordinate system and the subaperture imaging method are proposed. Moreover, the Nyquist sampling requirements for the subimages in the OEP coordinate system are derived from the range error perspective, which can offer a near-optimum tradeoff between precision and efficiency. In addition, the superiority of the OEP coordinate system is analyzed, which demonstrates that the angular dimensional sampling rate of the subimages is significantly reduced. Finally, the implementation processes and computational burden of the proposed algorithm are provided, and the speed-up factor of the proposed FFBP algorithm compared with the BP algorithm is derived and discussed. Experimental results of ideal point targets and natural ocean scenes demonstrate the correctness and effectiveness of the proposed algorithm, which can achieve near-optimal imaging performance with a low computational burden.

CubeSat Link Budget: Elements, calculations, and examples

Antenna designs suitable to fly on CubeSats have been of growing interest. The prolific CubeSat antenna literature, however, is contrasted by limited tools for an antenna engineer to develop or understand a CubeSat link budget, which sets the requirements for the spacecraft and ground antenna design. This article presents detailed explanations of the link budget basics, which include not only antenna design terms but also signal processing and system noise parameters. Relations among the data rate, signal-to-noise ratio (SNR), system noise temperature, and antenna gain are reviewed, explained, and applied in three examples of link budgets for CubeSats in low-Earth (LEO), geosynchronous (GEO), and lunar orbits.

Prediction of geosynchronous electron fluxes using an artificial neural network driven by solar wind parameters

There are hundreds of satellites operating at the geosynchronous (GEO) orbit where relativistic electrons can cause severe damage. Thus, predicting relativistic electron fluxes is significant for spacecraft safety. In this study, using GOES satellite data during 2011–2020, we propose two neural network models with two hidden layers to predict geosynchronous relativistic electron fluxes at two energy channels (>0.8 MeV and > 2 MeV). The number of input neurons of the two channels (>0.8 MeV and > 2 MeV) are determined to be 36 and 44, respectively. The > 0.8 MeV model has 22 and 9 neurons in the hidden layers, while the > 2 MeV model has 25 and 15 neurons in the hidden layers. The input parameters include the north–south component of the interplanetary magnetic field, solar wind speed, solar wind dynamic pressure and solar wind proton density. Through the analysis of different time delays, we determine that the optimal time delays of two energy channels (>0.8 MeV and > 2 MeV) are 8 days and 10 days, respectively. The training set and validation set (Jan 2011-Dec 2018) are divided by the 10-fold cross-validation method, and the remaining data (Jan 2019-Feb 2020) is used to analyze the model performance as a test set. The prediction results of both energy channels show good agreement with satellite observations indicated by low RMSE (∼0.3 cm-2sr-1s−1), high PE (∼0.8) and CC (∼0.9). These results suggest that only using solar wind parameters is capable of obtaining reasonable predictions of geosynchronous relativistic electron fluxes.

A Novel Frequency-Domain Focusing Method for Geosynchronous Low-Earth-Orbit Bistatic SAR in Sliding-Spotlight Mode

The low-earth-orbit synthetic aperture radar (SAR) can achieve enhanced remote-sensing capabilities by exploiting the large-scale and long-duration beam coverage of a geosynchronous (GEO) SAR illuminator. Different bistatic imaging modes can be implemented by the steering of an antenna beam onboard the LEO receiver, such as high-resolution sliding-spotlight mode. In this paper, the accurate focusing of GEO-LEO bistatic SAR (GEO-LEO BiSAR) in sliding-spotlight mode is investigated. First, the two major problems of the accurate bistatic range model, i.e., curved trajectory within long integration time and ‘stop-and-go’ assumption error, for sliding-spotlight GEO-LEO BiSAR are analyzed. Then, a novel bistatic range model based on equivalent circular orbit trajectory is proposed to accurately represent the range history of GEO-LEO BiSAR in sliding-spotlight mode. Based on the proposed range model, a frequency-domain imaging method is put forward. First, a modified two-step preprocessing method is implemented to remove the Doppler aliasing caused by azimuth variance of Doppler centroid and beam steering. Then, an azimuth trajectory scaling is formulated to remove the azimuth variance of motion parameters due to curved trajectory. A modified frequency-domain imaging method is derived to eliminate the 2-D spatial variance and achieve accurate focusing of the echo data. Finally, imaging results and analysis on both simulated data and real data from an equivalent BiSAR experiment validate the effectiveness of the proposed method.

Fuzzy-CNN Based Multi-Task Routing for Integrated Satellite-Terrestrial Networks

The integrated satellite-terrestrial network (ISN) is an emerging framework that complements the ground 5G network with global network access. The satellite layer consists of Low Earth Orbit (LEO) and Geosynchronous (GEO) satellites for long-distance and high-throughput data transmission with low latency. However, traditional ground routing strategies are not appropriate in ISN, considering the dynamic motion and different capabilities of satellites. Moreover, multi-type tasks need to be allocated with optimal inter-satellite transmission links (ISL) to ensure both the load balance of ISN and the quality of experience (QoE) of subscribers. In this paper, we combine the Software Defined Networking (SDN), AI technique, and fuzzy logic to optimize multi-task routing in ISN. The GEO satellites and the ground computing center (GCC) are set as the joint control plane. The load information of ISN at different times is collected by GEO controllers and made into a multi-D matrix. The GCC collects the historical traffic data from GEO controllers for convolutional neural network (CNN) model training and updating. The GEO satellites utilize the trained CNN model to make path allocation decisions and issue flow tables to LEO satellites. Further, considering the CNN judgment may contradict the user QoE, we use fuzzy logic to evaluate task requirements to improve the CNN output for optimal ISN path allocation. The simulation results demonstrate that the fuzzy-CNN based multi-task routing (FCMR) method has better traffic control performance and path finding flexibility under different ISN conditions.

Model-Data Co-Driven Integration of Detection and Imaging for Geosynchronous Targets With Wideband Radar

The high orbit height and long coherent processing interval (CPI) of geosynchronous (GEO) targets lead to the problems of ultralow signal-to-noise ratio (ULSNR) and complex signal modulation, posing great challenges to the traditional radar target detection and imaging algorithms. To address the problems, this article proposes a novel model-data codriven integration algorithm of detection and imaging for GEO targets with wideband radar. In this technique, underpinned by the transformation relationships between multiple spatial coordinate systems and the orbit prior information of GEO targets, we deduce the analytical expressions of the effective rotational vector of GEO targets so as to accomplish the model-driven optimal subaperture selection for integration of detection and imaging (OSASIDI). This considerably improves the processing performance and algorithm efficiency compared with traditional data-driven methods at ULSNR. In addition, we derive the radar equation of GEO targets for integration of detection and imaging in detail, which guides OSASIDI by analyzing the impacts of different parameters on detection and imaging performance. Aiming at the complex signal modulation problem caused by ultralong CPI (ULCPI) during the optimal subaperture (OSA) at ULSNR, we innovatively propose a model-data codriven integration of detection and imaging algorithm (MDCDIDI), which can eliminate the complex spatial-time-variant motion errors caused by the dual time-variant characteristic (DTVC) of effective rotational vector, so as to realize the focus-before-detection and obtain the well-focused inverse synthetic aperture radar (ISAR) images. Extensive experimental results from simulated data, which are generated from actual GEO parameters and the computer-aided-design (CAD) model of the Tiangong-I (TG-I) satellite, corroborate the effectiveness of the proposed algorithm.

Coherence-Based Geosynchronous SAR Tomography Employing Formation Flying: System Design and Performance Analysis

Coherence-based synthetic aperture radar (SAR) tomography (TomoSAR) exploits the complex coherences of SAR images to achieve 3-D imaging. Utilizing two-sensor spaceborne SAR formation flying to realize coherence-based TomoSAR has attracted increasing attention because temporal decorrelation-free interferograms can be constructed; therefore, TomoSAR has excellent potential for inverting the vertical structures of natural scenes such as forests and glaciers. However, low earth orbit (LEO) TomoSAR is disadvantaged by limited data and nonuniform sampling in the elevation direction. Geosynchronous (GEO) TomoSAR can overcome these limitations owing to its short revisit time of no more than 24 h. For the first time, this article discusses coherence-based TomoSAR exploiting GEO SAR formation flying. The benefits of GEO-formation coherence-based TomoSAR, including the low cost of slave satellites, rich data sets, and uniform sampling, are noted. The key problems of system design, including the formation design and data acquisition, are discussed. A formation design method based on the minimum along-track baseline is proposed that can realize uniform elevation sampling. The geometric correlation of a general SAR observation geometry is derived; on this basis, an optimal data acquisition method based on the optimal height measurement Cramer-Rao lower bound (CRLB) is proposed. Finally, the performance of GEO-formation coherence-based TomoSAR is analyzed; in particular, the ambiguity height in the altitude direction, the Rayleigh resolution in the altitude direction, and the theoretical optimal geometric correlation are evaluated. Finally, computer simulations validate the proposed formation design method, data acquisition scheme, and performance analysis formula.

Assessment of time spent in the LEO, GEO, and semi-synchronous zones by spacecraft on long-term reentering disposal orbits

The U.S. Government Orbital Debris Mitigation Standard Practices (ODMSP) released in December 2019 include a disposal option to use orbital eccentricity growth for long-term reentry within 200 years. Long-term reentry is beneficial for orbital debris mitigation because it offers a large reduction in long-term collision risk in the regions above low Earth orbit (LEO) compared to use of storage disposal orbits. As a condition for use of this option, the ODMSP specifies a 25-year limit on cumulative time a disposed spacecraft can spend in designated altitude zones that are frequently used by operational spacecraft. An analysis was performed to determine the time spent by disposed spacecraft in the geosynchronous (GEO) zone, the LEO zone, and the semi-synchronous zone for three classes of reentering disposal orbits above LEO: (1) near-circular inclined geosynchronous orbits (IGSOs), (2) eccentric IGSOs (Tundra orbits), and (3) GPS orbits. Long-term disposal orbit propagations over 200-years were performed using the Aerospace high-precision integration code TRACE. Collision probability with operational satellites in the various zones is determined using the Aerospace Debris Environment Projection Tool suite in order to check the trend with time in zone. Results of the study showed that time in zones is less than 25 years when orbital lifetime is less than 200 years, thereby clearing the way for using the new long-term re-entry option relative to this condition. The absolute numerical value of collision probability with operational satellites was found to vary substantially with disposal orbit case and zone. For most cases, results show a clear trend between time in zone and collision probability with some spread. An exception is the GEO zone, for which results show a trend but a wide spread. This may be because most GEO satellites are confined to a ring instead of the shell represented by an altitude zone.

Segmented sliding mode control-based CubeSat rapid attitude manoeuvre in low magnetic environment

The rapid attitude manoeuvre is a control challenge for a CubeSat in low magnetic environments, which include lunar orbits, geosynchronous (GEO) orbits or other higher Earth orbits. Therefore, a rapid attitude manoeuvre control method based on the segmented sliding mode was proposed for CubeSat in a low magnetic environment. The segmented sliding mode control algorithm was applied to the CubeSat attitude manoeuvre control, where the segmented sliding mode surface was designed to guarantee fast convergence to the origin point of the whole attitude manoeuvre process, and the hyperbolic tangent function was used in the reaching law of the controller to alleviate reaction saturation of the wheels. In addition, innovative control strategies were proposed for the hybrid actuators of the reaction wheels and microthrusters, and a guide rail of the microthruster was innovatively designed to move the microthruster to offset the change in moment of inertia caused by propellant consumption. Finally, hardware-in-loop simulation results reveal that our method has a stronger anti-saturation ability and faster manoeuvre speed than the traditional control method, and the operational life cycle of the thrusters can be accordingly increased.

Navigator Notes

Navigator Notes

Study on Optimal Broadcast Ephemeris Parameters for GEO/IGSO Navigation Satellites.

This paper proposes new sets of suitable broadcast ephemeris parameters for geosynchronous (GEO) and inclined geosynchronous (IGSO) navigation satellites (NSs). Despite the increasing number of GEO and IGSO NSs, global positioning system (GPS)-type ephemeris parameters are still widely used for them. In an effort to provide higher fit accuracy, we analyze a variety of broadcast ephemeris parameters for GEO and IGSO satellites along with their orbital characteristics and propose optimal sets of parameters. Nonsingular elements and orbital plane rotation are adopted for alleviating/avoiding the singularity issues of GEO satellites. On the basis of 16 parameters of GPS LNAV, we add one to four parameters out of 28 correction ones to determine optimal sets of ephemeris parameters providing higher accuracy. All possible parameter sets are tested with the least-square curve fit for four BeiDou GEOs and six BeiDou IGSOs. Their fit accuracies are compared to determine the optimal broadcast ephemeris parameters that provide minimum fit errors. The set of optimal ephemeris parameters depends on the type of orbit. User range error (URE) accuracies of the proposed optimal ephemeris parameters ensure results within 2.4 cm for IGSO and 3.8 cm for GEO NSs. Moreover, the experimental results present common parameter sets for both IGSO and GEO for compatibility and uniformity. Compared with four conventional/well-known sets of ephemeris parameters for BeiDou, our proposed parameters can enhance accuracies of up to 34.5% in terms of URE. We also apply the proposed optimal parameter sets to one GEO and three IGSO satellites of QZSS. The effects of fitting intervals, number of parameters, total bits, and orbit types on the fit accuracy are addressed in detail.

Simultaneous Moving and Stationary Target Imaging for Geosynchronous Spaceborne-Airborne Bistatic SAR Based on Sparse Separation

In synthetic aperture radar (SAR) imaging, moving target is generally mixed with stationary targets. Meanwhile, the image of a moving target is distorted and displaced due to the lack of its prior velocity information. Furthermore, imaging of a moving target for geosynchronous (GEO) spaceborne-airborne bistatic SAR (GEO SA-BiSAR) is a more challenging problem because the echo is sub-Nyquist sampled in azimuth. In this article, a simultaneous moving and stationary target imaging method for GEO SA-BiSAR is proposed. First, range models and the corresponding echo models of moving and stationary targets are established. The observation models for both moving and stationary targets with two receiving channels are derived based on the inverse of an efficient imaging algorithm. After that, the imaging problem of moving and stationary targets is modeled as a joint velocity estimation and sparse decomposition problem, which aims at optimizing the entropy of the moving target image and residual error of the formed images at the same time. Finally, a joint optimization method based on the particle swarm optimization (PSO) method and alternating direction method of multipliers (ADMM) is applied to achieve the imaging of moving and stationary targets and estimation of the moving target velocity. With two receiving channels, the accurate separation and focusing of stationary and moving targets as well as the precise estimation of moving target velocity can be achieved with sub-Nyquist sampling echo. Simulation results are presented to validate the effectiveness of the proposed method.

Background Tropospheric Delay in Geosynchronous Synthetic Aperture Radar

Spaceborne synthetic aperture radar (SAR) has been treated as a weather independent system for a long time. However, with the development of advanced SAR configurations, e.g., high resolution, bistatic, geosynchronous (GEO), the influence of tropospheric propagation error, which strongly depends on the weather, has begun to receive attention. In this paper, we focus on the effect of deterministic background tropospheric delay (BTD) during the image formation of GEO SAR. First, the decorrelation problems caused by the spatial variation and BTD are presented. Second, by combining with the SAR imaging geometry, the BTD error is decomposed as constant error, spatially variant error, and time variant error, the influences of which are analyzed under different circumstances. Third, an imaging method starting from the meteorological parameters and the GEO SAR systematic parameters is proposed to deal with the decorrelation problems. Finally, simulations with the dot-matrix targets are performed to validate the imaging method.