Unmanned Airborne Bistatic Interferometric Synthetic Aperture Radar Data Processing Method Using Bi-Directional Synchronization Chain Signals

: The bistatic Interferometric Synthetic Aperture Radar (InSAR) system can overcome the physical limitations imposed by the baseline of monostatic dual-antenna InSAR. It provides greater ﬂ exibility and can enhance elevation measurement accuracy through a well-designed baseline con ﬁ guration. Unmanned aerial vehicles (UAVs) equipped with bistatic InSAR, having relatively low cost and high ﬂ exibility, are useful for mapping and land resource exploration. However, due to challenges including spatiotemporal synchronization and motion errors, there are limited reports on UAV-borne bistatic InSAR. This paper proposes a comprehensive method for processing data from small UAV-borne bistatic InSAR by integrating two-way synchronization chain signals. The proposed method includes compensation for time and phase synchronization errors, trajectory re ﬁ nement with synchronized chain and Position and Orientation System (POS) data, high-precision bistatic InSAR imaging, and interferometric processing. Height inversion results based on the proposed method are also provided, which demonstrate the e ﬀ ectiveness of the proposed method in improving the accuracy of interferometric measurement at calibration points from 0.66 m to 0.42 m.


Introduction
Interferometric Synthetic Aperture Radar (InSAR) [1] technology generally refers to cross-track SAR interferometry, which is a remote sensing method that obtains the elevation of a target using interferometric processing.Applications of InSAR include terrain mapping, surface deformation monitoring, and urban planning.Interferometric SAR can be formed using various methods, including monostatic re-tracking or repeated flight interferometry, monostatic dual-antenna interferometry, and bistatic interferometry.Among them, the baseline length of the bistatic interferometric SAR [2] system can break through the physical limitations imposed on the baseline length of the monostatic dual-antenna and has a greater degree of freedom, which is important for measuring elevation accurately, and has a great application prospect.
However, the clocks of the bistatic SAR transceiver system use different frequency sources, resulting in an inevitable synchronization error between the first and the second.These errors in time and phase will degrade the SAR imaging quality and phase accuracy.In addition, there is no physical connection between the first and second antennas of bistatic interferometric SAR, which is a purely flexible baseline.The maintenance of baseline configuration and high-accuracy measurement are also challenges for bistatic interferometric SAR.
Bistatic interferometric SAR can be categorized explicitly into airborne, spaceborne, and other types based on the carrying platforms.Specifically, space-borne SARs are unaffected by air currents, making it easier for space-borne SARs to form a relatively stable baseline configuration and maintain the synchronization chain.TerraSAR-X/TanDEM-X is the first international spaceborne bistatic interferometric SAR system, which has acquired a large amount of data and completed the production of global highprecision DEM data products, thus expanding the scientific and commercial applications of spaceborne bistatic interferometric SAR [3,4].The Lutan-1 (LT-1) mission is China's first civilian spaceborne bistatic synthetic aperture radar mission, consisting of two fully polarimetric L-band SAR satellites successfully launched on 26 January and 28 February 2022, respectively.LT-1 continuously provides high-quality observation data and interferometric data products for land monitoring and other purposes [5,6].
The success of the above bistatic interferometric SAR constellation shows that the current problems of time and phase synchronization, as well as baseline measurement of spaceborne InSAR, have been well resolved.The technical approaches mainly include using ultra-high stability optical clocks, setting ground calibration points, GNSS clockbased synchronization, continuous wave signal pair transmission, pulse signal pair transmission, etc.The TanDEM-X SAR system solves the phase synchronization problem by adopting the synchronization scheme of two-way transmission of alternating pulses, which ensures that the time synchronization error is less than 5 µs within 600 s [7].LT-1 constellation adopts an advanced uninterrupted phase synchronization scheme.The synchronization pulses are exchanged immediately after the end time of the radar echo reception window and before the start time of the next pulse repetition interval without interrupting the normal operation of the SAR.The uninterrupted synchronization scheme has a high synchronization accuracy with a residual phase standard deviation (STD) lower than 0.3° [8].
However, on the one hand, the stability of the crystal oscillator used in airborne SAR is not as high as that of spaceborne SAR due to cost considerations.This leads to more prominent time and phase synchronization problems in airborne bistatic interferometric SAR.On the other hand, the baseline configuration of airborne bistatic InSAR is not easy to maintain, and the accuracy of the baseline measurements is also often limited due to the influence of the airflow.Therefore, the implementation of airborne bistatic interferometric SAR is challenging, and few related results have been reported.To the best of the authors' knowledge, only ESA has carried out the BelSAR bistatic interferometric experiment [9].The BelSAR radar sensors were mounted on two Cessna 208 aircraft and synchronized by means of a technique based on a dedicated high-precision GPSDO system with a 10 MHz reference clock and a pulse-per-second output to synchronize the receivers with the transmitters [10].However, no interferometric results or accuracy verification obtained from this experiment have been seen, indicating that this technique is far from reliable.Although there are few reports on airborne bistatic InSAR data processing methods, relevant research exists in bistatic SAR imaging, airborne SAR motion compensation, and interferometric processing.
As for the bistatic SAR imaging algorithm, in order to solve the frequency domain form in bistatic SAR imaging, Loffeld, Ding et al. converted bistatic SAR echo data into monostatic SAR data.This method is clear and simple, but the accuracy of the approximation is relatively low in the case of a larger scene [11].Loffeld et al. directly introduced the approximation into the frequency domain to obtain an approximate analytical expression of the 2D spectrum and then derived the bistatic SAR imaging algorithm on this basis.This method results in a relatively high accuracy but is very complicated [12].Ender and Giroux et al. obtained an exact implicit expression for the 2D spectrum based on numerical calculations and a wave number domain algorithm by phase decomposition [13,14].Qiu et al. proposed a bistatic SAR imaging algorithm based on a modified hyperbolic equivalent model [15] that can be used in the case of short bistatic baselines and a nonlinear CS algorithm [16] that can be used in the case of long baselines.
In terms of motion compensation, the separation of the transmitter and the receiver further complicates the motion error.On the one hand, step-by-step compensation is needed because of the two-dimensional space-variant motion error.Generally, motion errors are divided into the following categories and are compensated for separately: space-invariant motion error, range-variant motion error, and azimuth-variant motion error.In particular, the step-by-step compensation of range-invariant and range-variant errors is usually called a two-step motion compensation algorithm [17].The one-step motion compensation algorithm is an improved version of the two-step motion compensation algorithm, which can compensate for the space-invariant motion error and the range-variant motion error before the imaging process and effectively reduce the residual error before imaging [18,19].The azimuth-variant motion error is generally compensated on coarsely focused SAR images, and the precise terrain and aperturedependent motion compensation (PTA) algorithm can effectively compensate for the residual azimuth-variant motion error in SAR images, but the envelope of a SAR image is required to be completely corrected in this method.In airborne SAR imaging processing, the Range Migration Algorithm (RMA) or Omega-K algorithm is a commonly used imaging algorithm in engineering, but the residual error will be coupled with the RMA algorithm, thus causing a large envelope error, which will seriously reduce the compensation effect of PTA [20,21].Therefore, when higher accuracy is required, the BP algorithm is often used, sacrificing efficiency for processing accuracy [22].
In terms of airborne interferometric processing, the majority of research has been conducted on airborne monostatic dual-antenna InSAR.For example, Fangfang Li et al. experimented with airborne dual-antenna InSAR data and proposed a motion compensation method based on height iteration [23].Mao et al. addressed multipath effects in airborne dual-antenna InSAR systems by proposing a theoretical model for calculating multipath errors [24].Erxue Chen et al. used airborne X-band dual-antenna single-polarization InSAR data to estimate forest tree height [25].However, the method for processing airborne bistatic InSAR has been rarely reported.
In recent years, the rapid development of SAR miniaturization technology and UAV technology has brought more possibilities to realize bistatic interferometry using a small UAV platform.Small UAV-based bistatic InSAR is one of the directions for the development of low-cost and efficient airborne interferometric SAR technology.However, small UAV-borne SAR often requires higher cost control and is more susceptible to airflow, further increasing the difficulty of bistatic InSAR processing.To the best of the authors' knowledge, there has been no systematic research on small UAV-borne bistatic InSAR imaging and interferometric processing methods in the world.
The Aerospace Information Research Institute, Chinese Academy of Sciences, led the design and development of the first international unmanned airborne bistatic interferometric SAR system [26], and flight experiments were carried out at the Bailing Airport in Inner Mongolia.In [26], the authors describe the program design, basic composition, and main performance of the system, as well as the program and implementation of the first flight experiment.
This paper focuses on the small UAV-borne bistatic InSAR system and establishes a comprehensive method for high-precision synchronization error compensation, imaging processing, and interferometric processing.Firstly, a phase and time error compensation method based on the bistatic synchronization chain is derived, and the synchronization chain is used to compensate for the time and phase errors of the second station.Then, combining the synchronization chain information and POS data, an optimization method is used to refine the second station trajectory and improve the trajectory accuracy of the second station POS.In terms of imaging, high-precision motion compensation using Doppler bandwidth segmentation and sub-aperture image synthesis combined with the RMA algorithm is used for motion compensation and the imaging of echo data.On this basis, interferometric error calibration and interferometric processing are carried out, and high-precision elevation measurement results are obtained.
The sections of this paper are organized as follows.Section 2 introduces the key synchronization chain scheme of the small UAV-borne bistatic InSAR system.Section 3 provides an overview of the data processing method for bistatic InSAR, including the synchronization error compensation method, the POS trajectory refinement method, the high-precision bistatic InSAR imaging processing method, and the interferometric processing method.Section 4 presents the experimental results, validating the effectiveness of the proposed methods.Section 5 concludes this paper.

Bidirectional Synchronization Chain Scheme
To ensure coherence during flight between the first and second station images of the small UAV-borne bistatic InSAR system, strict requirements are placed on time synchronization and phase (frequency) synchronization.Time synchronization refers to the clock alignment between two independent SAR channels or clock error measurement and compensation.The bistatic interferometric SAR system adopts a one-transmitter-tworeceiver operating mode, and the transmitter-receiver timing between the two channels is required to be accurate to the microsecond or even the nanosecond level.Establishing the correlation between complex image pairs becomes impossible when the system timing is disrupted.As a result, the clock alignment of the two channels or the measurement and the compensation of the error is one of the synchronization problems that need to be solved.The existing time synchronization methods for bistatic SAR include the carrying clock method, the one-way timing method, and the two-way clock comparison method [27].The time synchronization scheme of this system uses the direct one-way timing method.The timing reference module of the synchronized clock reference signal provides a time synchronization reference for each radar extension.The system uses the respective crystal oscillator in the triggering of the echo recording window, which is triggered according to a fixed pulse repetition frequency, and presets a periodic compensation mechanism to ensure the validity of the echo recording.The compensation mechanism is counteracted by appropriate post-processing methods to bring the echo data back to their normal state.
Phase synchronization is the core problem and technical difficulty of the UAV bistatic InSAR system.This challenge arises due to the independent frequency sources used for receiving echo signals in InSAR systems, directly impacting the coherence of complex image pairs and the interferometric phase accuracy [28].Generally, the phase synchronization method of frequency sources can be divided into four types: the independent frequency source synchronization method, the data-based synchronization method, the direct synchronization method, and the indirect synchronization method.Based on the form of the transmitted synchronization signal and the use of the synchronization signal, the direct synchronization method can be further divided into the synchronization chain method and the reference signal transmission chain method.This system uses a two-way synchronization chain to realize phase synchronization.In a twoway synchronization chain, the transmitted synchronization signals contain synchronization error information between frequency sources.Each station records this information and uses it for synchronization error compensation during imaging processing, ultimately realizing phase synchronization between stations.The synchronization chain in this system uses a scheme of signal pair transmission between bistatic stations, i.e., after the first station sends the synchronization signal to the second station, the second station sends the synchronization signal from the second station to the first station after a certain delay, so as to realize the transmission of two-way synchronization signals.The first and second stations each record the synchronization signal for subsequent imaging processing.Figure 1 shows a schematic diagram of the twoway synchronization chain of the bistatic InSAR system.0 ( ) cos( 2( )) The timing of the synchronization chain is designed to first handshake through 100 pulses and then perform the normal operating timing.In each pulse repetition time (PRT), synchronization pulses are first transmitted and received, followed by radar pulse transmission and echo reception.Once the first and second establish connection and synchronization, the first station controls the PRT according to the first's crystal oscillator and the second station controls the PRT using its own crystal oscillator frequency source.Each station opens the echo acceptance window and starts the working time sequence according to a certain time delay.
Because the time synchronization error in the bistatic InSAR system is coupled into the phase synchronization, the phase synchronization technique is combined with the time synchronization scheme to establish a direct wave communication link between the bistatic InSAR system.The synchronization signals received by the first and second stations through two-way synchronization are compensated for the periodic position jumps caused by time synchronization.After that, the phase synchronization information of the echo is obtained by extracting the peak phase of the synchronized signal after pulse compression.Based on this phase synchronization information, the length of the timevarying baseline can be calculated and used to refine the POS data of the second station.

Overall Processing Flow for Small UAV Bistatic InSAR
The overall processing flow and methodology of bistatic InSAR is as follows.Firstly, the synchronization data obtained from the two-way synchronization chain is used to compensate for the time and phase errors of the second echoes, followed by first-second radar data imaging.The data processing of bistatic SAR is carried out using the equivalent processing method of converting bistatic SAR data to monostatic SAR data, combining the bistatic synchronization chain and POS data to improve the track accuracy of the second POS.Then, an imaging method based on Doppler bandwidth segmentation and sub-aperture image synthesis with high-precision motion compensation combined with the RMA algorithm is used for motion compensation and imaging the echo data.Finally, the interferometric processing and elevation inversion of bistatic SAR are realized through the steps of complex image registration, calibration of interferometric system parameters such as baseline, interferometric phase filtering and unwrapping, and height inversion.In this section, each part of the processing method will be introduced.

Time and Phase Synchronization Error Compensation Methods
Firstly, based on the assumption that the fast and slow times are not coupled, let the slow time be  and the fast time be  .Located at the  th timing, the emitted synchronization signal is as follows: where T is the pulse width of the transmitted signal (0.5 µs in this system), fT0 is the central frequency of the first station, and φT(•) is the time-varying phase of the first station.
Let the distance between the transmitter and receiver platforms at this point be where   ,   ,   and   ,   ,   are the positions of the transmitter and receiver at time  .
The demodulated signal received by the receiver is then where fR0 is the central frequency of the second station and φR(•) is the time-varying phase of the second station.Taking the peak phase after compression of the direct wave pulse is equivalent to taking the phase at t = 0, with After receiving the direct wave signal, the receiver will transmit the direct wave signal at a small interval, and the start delay of the current sequence is Δt0 = 2 us.In other words, the direct wave signal is produced by the receiver itself.The signal is as follows The transmitter receives and demodulates this signal and obtains Pulse compression of this direct wave signal to take the peak phase is equivalent to taking the phase of the t = 0 moment By comparing   , 0 and   , 0 and averaging both phases, we have For the first term ①, because Δt0 = 2 µs, a crystal oscillator frequency error of 100 MHz can reach 10 −8 .Because the system operates at a central frequency of 1.5 GHz, this term is 0.0054 degrees and can be neglected.The second term ② represents the phase introduced by the baseline, and the baseline can be calculated based on this term.The third term ③ is the synchronous phase error term, which can be neglected as long as the phase remains stable at the microsecond level.Based on previous test data, this error term is less than 0.1 degrees.Through theoretical and experimental data analysis, both terms ① and ③ in the above equation can be ignored.Consequently, based on the second term, the calibration method for the baseline is given by The subtraction of   , 0 and   , 0 yields the result in the following equation where the first term ① is the phase error caused by the inconsistency in frequency sources, which changes linearly with azimuth time  .The second term ② is approximately zero and can be ignored due to      .And the third term ③ is the synchronous phase error excluding the linear phase.Further neglecting the variation in the above phase with fast time, we have: Assuming the SAR signal transmitted by the first station is where Δt1 is the time difference between the transmission of the SAR signal and the synchronization signal,  is the linear frequency modulation rate, and  is the pulse width of the SAR signal.After reflection from the ground target, the signal received by the second station is given by and the synchronous phase error is given by Neglecting the variation in the phase error with fast time, we have As a result, the term   , 0   , 0 /2 in Equation ( 11) represents the synchronous phase error that needs to be compensated in the second station SAR echo.
During the above analysis on phase synchronization, it is assumed that the reference time  at the beginning of each PRT is the same, and both first and second stations are based on the same  .However, due to the existence of time synchronization errors, this assumption does not hold, and the effect of time synchronization needs to be further considered.In this paper, the UAV bistatic SAR system adopts relatively low crystal oscillator stabilization of 10 −7 orders of magnitude for the first and second stations for cost consideration.In order to avoid the impact of the time drift of the second station relative to the first station on the integrity of the echo acquisition, an echo recording window compensation mechanism with a period of 6.3 s and an offset of 1 us is pre-set in the actual system, which makes the echo data appear jagged.By analyzing the phase composition of the echo signal from the second station, it can be observed that the samples in the range direction are not aligned, and there is a term related to the azimuthal moment j,  , which is exactly the time offset that needs to be compensated by means of envelope alignment.This is compensated by performing an FFT along the distance direction, multiplying the distance direction frequency domain by exp 2  , and then changing back to the time domain.
From the above analysis, the overall processing steps are as follows: 1. Perform pulse compression and peak phase extraction on the direct wave signal received by the receiver at each  moment to obtain   ,  ; 2. Perform pulse compression and peak phase extraction on the direct wave signal received at the transmitter at each  moment to obtain  ,  ;

Trajectory Refinement Method Combining Synchronization Chain and POS Data
Due to the limitation of the carrying capacity of the UAV platform, it is difficult to use traditional inertial measurement devices with large size, heavy weight, high power consumption, and high accuracy, and the carrier POS accuracy is limited to a certain extent.Because the time-varying baseline can be extracted from the synchronous signal chain, the second station's trajectory can be optimized using this baseline, thus contributing to trajectory refinement and improving the accuracy of interferometric measurement.We propose the following optimization method for refining the trajectory at each azimuth moment of the second station: where RB is the baseline length according to the two-way synchronization chain (Equation ( 9)), and (X1,Y1,Z1) and (X2,Y2,Z2) are the positions of the first and second station according to the POS data, respectively. ⃗   ,   ,   is the baseline vector from the POS data,  ⃗   Δ,   Δ,   Δ is the optimized baseline vector, and (Δx, Δy, Δz) is the amount to be optimized.In the above equation, the first term is the baseline length constraint term, aiming to make the optimized trajectory's baseline length as close as possible to the baseline length obtained from the two-way synchronous chain.The second term is the baseline direction constraint term, aligning the optimized baseline with the original baseline direction, where p is the weight (chosen as 0.2 in this study).Using these constraints, the trajectory of the second station is optimized and solved for each azimuth moment.The second station trajectory is refined by smoothing and filtering the offset and removing outliers.

High-Precision Bistatic InSAR Imaging Processing Methods
Because the UAV platform is relatively light and small, the motion state of the carrier is disturbed by the airflow, leading to large position and attitude errors.Trajectory measurement error will lead to baseline error.At the same time, the deviation of the trajectory after airflow and the trajectory measurement error together lead to residual error after motion compensation, which cannot be canceled out in the case of the firstsecond station carrier flying independently.This error makes the SAR image geometrically distorted and increases the difficulty of registration.The error also results in phase fluctuation, which affects the accuracy of the unmanned aircraft-carried bistatic SAR inversion DEM.Effectively compensating the motion error with range and azimuth variability using high-precision imaging algorithms is an important task in imaging processing.
Figure 2 shows the UAV bistatic SAR imaging processing flow.For the second station, when the baseline is short, the center of the first station and second station positions can be used as the equivalent center position of the bistatic SAR.The hyperbolic equivalent approximation model of the bistatic SAR is used for the derivation of the ω-k algorithm, and the motion compensation and imaging methods consistent with the monostatic SAR are used for processing.The raw SAR echoes are first range-compressed, and a one-step motion compensation is performed using the filtered and refined trajectory to remove the spacevariance in the motion error along with range direction.After that, resampling in azimuth is performed to homogenize the pulse sending and receiving intervals.Then, azimuthal FFT is performed to divide the sub-aperture in the azimuthal frequency domain, each subaperture datum is imaged separately using the ω-k algorithm, and the PTA method is used to compensate for the motion error within the aperture.Finally, all the sub-aperture images are coherently synthesized to obtain high-precision imaging processing results.
This imaging processing flow is similar for both the first and second stations, but there are two differences.First, the reference trajectories for the first station and the second station are different.For the first station, the reference track is a straight line fitted by the first station trajectory; for the second station, the motion compensation is based on the transmitting and receiving reference tracks.Secondly, the azimuth resampling method is different.For the first station, the azimuth resampling is directly based on the first inertial navigation data and the first echo pulse timestamps.While for the second station, the azimuth resampling method of bistatic SAR is used to obtain accurate azimuth resampling results.The method is described in more detail in Section 3.3.2.

One-Step Motion Compensation Algorithm Based on High-Precision Inertial Navigation
By recording the precise position of the first station at each sampling moment through high-precision inertial navigation, the motion error can be calculated using airborne geometry.The one-step motion compensation algorithm processes the timedomain echo signal after range compression before imaging, corrects the envelope error along the range direction by interpolation, and compensates for the phase error.The onestep motion compensation algorithm has higher accuracy when compared with the classical two-step motion compensation algorithm.It can compensate for more motion errors before imaging and can compensate for the envelope error of range varying with a higher accuracy.
Figure 3shows the flight geometry of the aircraft considering the trajectory offset, where  is the actual position of the target at a certain orientation moment, and  and  are the slant range from the target to the actual position of the aircraft and the slant range from the target to the ideal position of the aircraft, respectively.While applying the one-step motion compensation algorithm, based on the approximation of the center of the beam, it is assumed that the target is located at the center of the beam, i.e.,  , and the slant ranges from that point to the ideal position and the actual position of the aircraft,  and  , are used to calculate the motion error, so the compensated error is The residual error is In general, the residual error  is much smaller than one distance unit.

Bistatic SAR Echo Azimuth Resampling
As the aircraft cannot maintain an ideal uniform linear motion during flight, and there is acceleration along the flight direction, i.e., there is a change in velocity, which in turn causes the spatial spacing between pulses to be non-uniform.For monostatic SAR systems, azimuth resampling is often used to compensate for non-uniform spatial intervals between pulses, but in bistatic SAR, the spatial intervals between transmit and receive are non-uniform, and resampling becomes difficult due to the two platforms.
We propose to compensate for motion errors along the flight direction by using a bistatic SAR echo azimuth resampling method with an equivalent average sampling moment, which is as follows.
When the receiving/transmitting antenna is moving at a uniform linear speed, let the range history of the nth pulse transmitting/receiving moment be where Δη = 1/PRF.Similarly, with motion error along the flight direction, the range history at the nth pulse transmit/receive moment is Therefore, the transmitting antenna and receiving antenna can be regarded as moving at a uniform speed at  and  , respectively.The nth pulse is transmitted and received at Δ Δ Δ / and Δ Δ Δ / , respectively.Since transmitting and receiving should be regarded as simultaneous under the stop-go assumption, it is assumed that the n pulse under the motion error along flight direction is transmitted and received, respectively, at this moment.

𝜂 𝑛Δ𝜂 (21)
Based on the above equivalent moments, azimuth resampling (e.g., using Lagrange interpolation) can be performed on the bistatic SAR echoes to obtain the echo signal under uniform motion.

Highly Accurate Motion Compensation Method Based on Doppler Bandwidth Segmentation and Sub-Aperture Image Superposition
From the above discussion, it can be seen that there is still residual error in the signal processed by one-step motion compensation, although the residual error is generally much smaller than one range unit.But after the processing of frequency domain algorithms such as the range migration algorithm, the residual error will be amplified and cause serious envelope disorder, which can easily exceed one range unit.In this case, onestep motion compensation is not enough to obtain a well-focused image.
In order to deal with the problem of envelope disorder caused by residual motion error after the range migration algorithm, we propose a high-precision motion compensation method based on Doppler bandwidth segmentation and sub-aperture image superpostion.The echo data after one-step motion compensation are divided into multiple sub-apertures along the Doppler bandwidth in the 2D frequency domain, and each sub-aperture is zeroed to the original length and transformed to the 2D time domain.According to the time-frequency relationship, the corresponding squint angle of view of each sub-aperture is computed, and the residual error caused by the one-step mapping algorithm using the center-beam approximation is compensated.The sub-images are obtained by using a range migration algorithm for imaging each sub-aperture echo.For each sub-image, the residual error is further reduced, which is not enough to cause envelope disorder for more than one range unit, and then, the PTA algorithm is used to compensate for all the intra-aperture motion errors for each sub-image.Finally, the errorfree image is coherently summed to obtain the high-resolution big picture.

Interferometric Calibration
Interferometric calibration mainly contains slant range calibration, baseline length calibration, baseline angle calibration, and interference phase calibration.

Slant range calibration
Here, only the slant range error ΔR of the first station image needs to be calibrated, and the slant range error calibration is obtained by optimizing the following objective function: where  and  _ are the slant range of the first station image and the measured slant range from the position of the first station antenna phase center to the target point, respectively.

Baseline length and baseline angle calibration
The first station data are selected as the reference image for the calibration of baseline length and baseline angle.In order to avoid the influence of the phase error between channels, the measured position of the calibrator is used as the true value, and its distance to the reference straight-line trajectory of each channel is calculated so as to carry out the calibration of the baseline and baseline angle.The calibration formula is as follows: where the baseline length B and the baseline angle α are the quantities to be calibrated, and θ is the look angle of the first image. and  are the slant ranges of the ith calibrator in the first and second images, respectively.

Interferometric Processing
Interferometric processing mainly includes first-second complex image registration, flat-earth phase removal, phase filtering, phase unwrapping, elevation inversion, and accuracy analysis.

Complex image registration and generation of the interference phase
By using the coordinate relationship of homonymous points in the two complex images, the second complex image is resampled so that it corresponds to the first image pixels.Generally, coherence is used as a quality evaluation metric for complex image registration.The interferometric phase image is obtained by multiplying the conjugate of the aligned complex images and calculating the phase.

Flat-earth phase removal
Since the phase history grows with increasing transmit time, interference fringes are also present on flat terrain and vary linearly with the slant range, which is called the flatearth phase.Due to the long baseline of the bistatic station, the fringes are very dense, and the terrain undulations cause large phase variations; removing the flat-earth phase is an important step in order to facilitate the subsequent phase unwrapping.Using the calibrated baseline length, baseline angle, and interferometric phase error, the flat-earth phase can be removed using the following expression:

Phase filtering
There is still a large number of noisy phases in the phase map after flat phase removal, which come from thermal noise decoherence, baseline decoherence, alignment error decoherence, and other factors.In order to obtain high-quality interferometric phase maps and reduce the influence of phase noise, it is necessary to choose a better filtering method as well as a suitable filtering window.In this paper, the classical Goldstein phase filtering method is used [29].In view of the fact that some regions are relatively noisy, which affects the overall phase unwrapping, the low-coherent regions are first screened, and their neighboring phases are used for fitting and interpolation to obtain the estimated phases of the low-coherent regions.

Phase unwrapping
Because of undulating terrain, the interferometric phase variation beyond 2 π will be entangled in (−π, π], which is not the complete interferometric phase corresponding to the elevation, so phase unwrapping is required.We use the classical minimum cost flow method for phase unwrapping [30].The phase after unwrapping is still relative and differs from the absolute phase value by a constant, which can be calculated from any ground control point.

Elevation inversion
The following height inversion formula was used to perform the elevation inversion using the unwrapped phase: where  is the height of the phase center of the first antenna, and  and  are the constant values of the unwrapping phase and its difference from the absolute phase, respectively.

Experiment
In order to verify the effectiveness of the established unmanned airborne bistatic InSAR synchronization compensation as well as the high-precision imaging processing flow and the elevation inversion capability of the system, we carried out the bistatic SAR ground test and the first integrated calibration flight experiment.

Bistatic SAR Ground Test
The UAV bistatic interferometric SAR processing technology proposed in this paper mainly includes two parts: one is the phase synchronization technology based on the bidirectional synchronous chain, and the other is the high-precision bistatic InSAR imaging processing method based on the synchronous chain and high-precision POS data.Among them, the metric requirements of the design of the system synchronization error are less than 5 degrees after compensation, and the time synchronization error is 1 ns.In order to verify the effectiveness of the error compensation algorithm, we designed a ground test experiment for the synchronous system and completed the test in the laboratory in July 2022.
The phase synchronization test scheme divides the signal of the first station into two channels after passing through the optical delay line: one into the receiving channel of the second station and the other into the receiving channel of the first station.The transmit signal of the synchronization chain enters the receiving channel of the second station and is fed back to the synchronization chain of the first station through the power amplifier.The phase error of the second station is corrected by the synchronization signal of the first station.The phase consistency of the echo signal of the second is then compared.
Figure 4 shows the ground static measurement results of the bidirectional synchronization chain technology of the bistatic interferometric SAR system, and the results of the synchronization signal pulse compression of the second radar after pulse compression, range sampling, envelope shift, and phase synchronization error compensation.Figure 4a shows the position of the peak point of the pulse compression after the synchronization error of the target echo signal of the second radar is compensated.It can be seen that the envelope error of the residual time synchronization is less than 0.1 sampling points (sampling rate of 1.25 GHz), that is, 0.08 ns. Figure 4b shows the phase of the peak point position of the pulse compression after the synchronization error of the target echo signal of the second radar is compensated.It can be seen that the residual random phase error after phase synchronization compensation is less than ±0.6 degrees, and it can be concluded that the synchronization error of the system is 1.2°, which meets the metric requirement of better than 5°.For wire-feed laboratory tests, the following conclusions can be drawn: The peak point position of the synchronization signal is consistent after calibration, and the residual envelope error of time synchronization is less than 1 ns.After phase calibration of the peak point of the synchronization signal, it is consistent after the system clock is thermally stabilized.The stabilization time needs to be turned on for more than 40 min, and the stable synchronization phase accuracy is 1.2°.
The compensation data obtained by the synchronous signal can be used to compensate for the envelope and phase of the radar signal data.The ideal point target result can be obtained through two-dimensional compression after the radar signal compensation, and the sidelobe situation is ideal.Using bistatic synchronization and radar signal compensation technology, it can provide a highly stable synchronous phase, which can meet the requirements of the UAV bistatic L-band interferometric SAR system.

Bistatic SAR Flight Experiment
The first integrated calibration flight experiment was conducted on 17-29 August 2022, at Bailing Airport, Darhan Muminggan United Banner, Inner Mongolia.Figure 5 shows the optical image of the experiment site and the deployment of the calibrator.Table 1 lists the basic parameters of the bistatic flight experiment as well as the SAR payload parameters.The payloads for the first and second stations were the same.Figure 6 shows the image after range compression before and after echo envelope alignment of the second station, which indicates that the time synchronization error is well compensated.The compensation term is shown in Figure 7.    Figure 10 shows both baselines as extracted from the synchronization signal and as calculated using GPS.The differences can be observed in the bottom figure in Figure 10.

Results of the Second Station Trajectory Refinement
The POS data of the second station is refined using the baseline constraint based on the synchronization signal, as described in Section 3.2.Figure 11 shows the correction values for the second station's trajectory in the x-, y-, and z-directions for each sampling point.From Figure 12, it can be observed that with the corrected the second station trajectory, the calculated baseline length (in green) closely matches the baseline extracted from the synchronization signal (in red).Figure 13 illustrates that the difference between these two baseline lengths is mainly within 1 mm, which will be advantageous for interferometric inversion.

Bistatic InSAR Imaging Results
Now we apply the synchronization phase compensation shown in Figures 7 and 8 to the imaging processing flow as described in Section 3.3.Figure 14 presents images of the second station without synchronous phase compensation and with synchronous phase compensation.It can be observed that uncompensated phase errors lead to the defocusing of the targets, as shown in the green boxes in the top image in Figure 14.The targets are focused after synchronous phase compensation, as shown in the yellow boxes in the bottom image in Figure 14.This clearly demonstrates the necessity and effectiveness of compensating for phase synchronization errors.Figure 15 shows the imaging results of the second station before and after trajectory refinement, indicating that the images are well focused, and the difference between the two amplitude images is barely noticeable because of the small trajectory refinement.The phase image will be influenced in later interferometric processing.The imaging quality tests on calibration points are shown in Figure 16, demonstrating that both the first and second stations are well focused.The resolutions measured by the corner reflectors are listed in Table 2.  Interferometric processing and elevation inversion are carried out according to the results of interferometric calibration.Firstly, the airport area in the first image and second image (as in Figure 17) is selected for interferometric co-registration.The interferometric phase image (Figure 18) and inversion height (Figure 19) are calculated using a 5 × 5 window after co-registration.The elevation and elevation error statistics of the 14 calibration points are shown in Table 3 and Figure 20.It can be seen that the elevation error RMS of all 14 calibration points improved greatly from 0.66 m to 0.42 m after trajectory refinement.We also measured the Copernicus DEM error and found that the RMS of all calibration points is 0.87 m, considering land surface elevation varies over several years.

Discussion
The bistatic Interferometric Synthetic Aperture Radar (InSAR) system has many advantages, but it faces serious problems such as spatiotemporal, phase synchronization, and motion error, which poses a huge challenge to the processing of SAR data under complex flight conditions of UAVs.In addition, there are few reports of relevant research on UAV bistatic InSAR.Therefore, we proposed several methods to comprehensively process bistatic InSAR data of small UAVs with bidirectional synchronous chain signals, including synchronous processing system based on a bidirectional synchronous chain, a trajectory refinement method using synchronous chain and positioning system (POS) data, high-precision bistatic InSAR imaging processing, and interference processing algorithms.
The synchronous processing system plays a crucial role in the high-coherence imaging results of the bistatic InSAR.The methods in this paper have several advantages, such as (1) High accuracy of the synchronous processing.(2) The method deals with both phase synchronization error and residual time synchronization error.(3) The synchronization signal can additionally provide the ability for baseline calibration and track refinement.However, there is some room for improvement in this synchronization processing method: (1) The synchronization method relies on the hardware support of a complex synchronization system, which requires complex ground testing and work timing requirements.Therefore, it has the potential for modularization, miniaturization, and universalization to reduce the resource occupation of the entire interferometric system.(2) The robustness and reliability of the synchronous processing algorithm under harsh conditions need to be verified in the future, which requires more experimental application in advance.(3) There is room for algorithm development and upgrading in terms of multi-station synchronization.
One of the key processes in this paper is the bistatic high-precision imaging algorithm.As detailed in this paper, the bistatic imaging algorithm based on the orbit refinement processing of bistatic synchronization and the motion compensation processing for the bistatic flight system is novel.The proposed motion compensation method is suitable for situations with large motion errors or high radar resolution requirements.
Another key process is the bistatic interferometric processing and flight experimental data processing.We calibrated interferometric error based on several calibrators and obtained reliable elevation of calibrators.As can be seen in Figure 18, the coherent phase shows the contrast before and after phase compensation, which demonstrates the effectiveness of our method.The elevation and elevation error of the 14 calibrators indicates the improvement in the refinement of trajectory in Table 3 and Figure 20, and it shows better accuracy than Copernicus DEM.
There are some artifact signals in the interferometric phase image in Figure 18, and they are interference fringes in the strong scattering sidelobe area.The white areas of the amplitude image include calibrators, airport ground facilities, wire fence, etc.The sidelobes at the same distance to the radar have the same phase, so the interference phase in the area covered by the sidelobes is still fringed after flat-earth phase removal.We can also see abnormal elevation in same areas in Figure 19.Since we calculate the height of calibrators via extracting the scattering center phase of the calibrators, the results remain accurate.
Due to the constraints of the field conditions, the types of ground objects in this experimental scene are too scarce, and there are strong scattering interferences such as wire fences and steel frames, which lead to some interference in the images.The range of the calibrators is not large enough, which is not conducive to studying the relationship between the time-varying baseline and the phase of the azimuth.It is better to study the influence of azimuth time-varying baselines on the accuracy of interferometric SAR and optimization methods.

Conclusions
This paper presents the overall processing workflow and methods for UAV-borne bistatic InSAR using the two-way synchronization chain and POS data.The methods include error compensation for time and phase synchronization, trajectory refinement combining the synchronization chain and POS data, high-precision bistatic InSAR imaging processing, and interferometric processing.The results indicate that the proposed processing methods effectively process data from UAV-borne bistatic InSAR and improve interferometric elevation accuracy through trajectory refinement.The research demonstrates the potential of UAV-borne dual/distributed InSAR applied in complex terrain areas.

Figure 1 .
Figure 1.Schematic of the two-way synchronization chain for a bistatic InSAR system.

3 .
Calculate the baseline length inversion result   ,    ,  /2 for subsequent interferometric processing; 4. Calculate the synchronization phase compensation term   ,    ,  /2 and compensate for the received echo signals at each  moment; 5. Perform envelope alignment, in which the echo is transformed by FFT along the range direction, multiplied by exp 2  in the range direction in the frequency domain, and then transformed back to the time domain to obtain the envelope aligned second echo for subsequent imaging.

Figure 3 .
Figure 3. Schematic diagram of the geometric relationship of bistatic SAR.

Figure 4 .
Figure 4. Measurement results of second radar after time and phase synchronization.(a)envelope of the synchronization signal after pulse compression; (b) the phase of the peak of the synchronization pulse after compression

Figure 5 .
Figure 5. Optical image and corner reflector distribution.

Figures 8
Figures8 and 9show the second phase synchronization compensation phases calculated according to the procedure in Section 3.1 and the error after removing the linear term.

Figure 10 .
Figure 10.(Top) Baseline as extracted from the synchronization signal and as calculated using GPS.(Bottom) Difference between the two baselines.

Figure 11 .
Figure 11.The correction values for the second station's trajectory.

Figure 12 .
Figure 12.Baseline as extracted from the synchronization signal and as calculated using GPS.

Figure 13 .
Figure 13.The difference between the refined baseline and the baseline extracted from the synchronization signal.

Figure 14 .
Figure 14.Imaging results (top) before and (bottom) after synchronization phase compensation.

Figure 17 .
Figure 17.SAR images of an area of the airport.

Figure 20 .
Figure 20.Inversion height error before and after refinement.

Table 3 .
Table of height errors before and after trajectory refinement.