Demonstration of Simultaneous Localization and Imaging With Multirotor-Borne MiniSAR

This article extends the segmental aperture imaging (SAI) algorithm, which tackles the challenges of synthetic aperture radar (SAR) imaging of miniaturized synthetic aperture radar (MiniSAR) onboard multirotor unmanned aerial vehicle (UAV). The SAI algorithm is developed based on an accurate phase error model of both translational and rotational motion of UAV. It does require auxiliary positioning data such as global positioning system/inertial navigation system. We further extend it to simultaneously estimate and reconstruct the three-dimensional (3-D) trajectory of UAV from parameters derived from SAI motion compensation. Thus, it in fact accomplishes the simultaneously location and imaging (SLAI) using UAV-borne radar. It is first validated and evaluated via raw signal simulation using realistic trajectory data. For experiment purpose, a multirotor-borne MiniSAR system FUSAR-Ku is developed. Experimental results show that the proposed algorithm can achieve decimeter-resolution imaging performance as measured by various metrics, while simultaneously accomplishing centimeter-to-decimeter 3-D self-positioning capability. It is a first demonstration of SLAI mode with a multirotor-borne MiniSAR.

the characteristics of small size, light weight, and low power consumption (SWaP), and is generally equipped on small mobile platform, such as unmanned aerial vehicles (UAVs) [1]- [8]. The portable system setup and easy experimental preparation make it possible to acquire SAR images with multiple incident angles and multiple orbits more flexibly [9]. It is convenient for various applications such as local terrain mapping or target scattering measurement [10]. MiniSAR can also perform data fusion with spaceborne SAR and manned airborne SAR to form a multiheight, multidimensional, and multilevel remote sensing system. Various remote sensing systems have Manuscript  reference clocks, so data fusion at the signal level is complex. The usual practice is to fuse the data at the pixel level. That is, after each sensor is imaged, the two-dimensional (2-D) imaging results are fused. We generally use the spatial correlation of the target to perform geometric registration, geocoding, and other operations on the image, and then perform stitching and fusion [11]. For small maneuvering platforms, not only high-resolution and high-precision imaging algorithms are required, but also high-sampling rate positioning information to better restore the motion features of the platform [12]. Due to the SWaP of the multirotor UAVs (multirotors) platform, and the rapid development of high-speed digital processing technology, MiniSAR systems mostly use FMCW technology to reduce the system ADC sampling rate and the cost of analog circuits [3], [4]. In 2004, Brigham-Young University Microwave Earth Remote Sensing developed a low-cost mi-croASAR system with a center frequency of 5.56 GHz (C-band) and a bandwidth of 80 MHz [13]. The power is 16 W, and the weight of the main components of the whole system is about 2 kg. In order to pursue portability, the noise suppression ratio and channel isolation of the system are low, resulting in a low signal-to-noise ratio and strong speckle noise in the image. Its imaging algorithm adopts classic back projection algorithm, and uses high-precision (accuracy about one-tenth of a wavelength) global positioning system (GPS) data for motion compensation [14]. In the case of continuous waves, it does not consider the intrapulse modulation caused by platform movement, which causes the signal model violating the "stop-and-go" model assumption. In 2005, Delft University of Technology developed an X-band SAR system, named TuDelft, mounted on a fixed-wing UAV [15], which solved the problems of continuous intrapulse motion and frequency nonlinearity. Sandia Laboratory of the United States and the German European Aeronautic Defence and Space Company (EADS) have successively developed the Ka-band Mini-SAR and MiSAR [16], [17]. The quality of the system imaging results completely depends on the accuracy of the GNSS system [17]. Later, Germany's MIRANDA35 system [17] and SUMATRA system [18], China's NUAA-MiniSAR [9], IECAS-SAR [8] are the first to use auto-focusing algorithm, such as map-drift [19], phase gradient auto-focus [20], [21], and minimum entropy auto-focus [22], which does not rely on inertial navigation system (INS) for high-resolution imaging. These autofocusing algorithms have the disadvantages of only estimating the second-order error, requiring isolated feature points, and high computational complexity [23]- [25]. This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ However, most MiniSAR systems and algorithms are developed to work onboard stationary platforms such as fixed-wing UAVs, and often mounted with stabilizing technologies such as antenna servo systems. The challenges of multirotor-borne MiniSAR imaging can be summarized as unstable trajectories, unique maneuvering errors, inaccurate positioning, and orientation information, which are described in detail in [26]. To address these challenges, the segmental aperture imaging (SAI) algorithm is proposed [26]. The basic idea is to perform imaging segment by segment independently along the trajectory. For each stable segment, its accurate trajectory is estimated by fitting a polynomial phase history function. Segmental motion compensation is then performed to obtain focused segmental subimages which are then further stitched together to form the complete SAR image.
UAV MiniSAR has the characteristics of miniaturization, low test cost, and high freedom of laboratory parameters such as orbit and incidence angle. In order to give full play to its advantages, we need to obtain the position information of the platform at the same time in the imaging. If the MiniSAR finds a target of interest during the mission, it can interact with the UAV navigation system to adjust the flight trajectory in time for multiangle and multiorbit illumination. It provides a basis for the follow-up UAV intelligence and cluster work. Ultimately, we achieve two goals: 1) We use SLAI to provide alternative positioning approach in GPS-denied situation, to accomplish imaging without auxiliary positioning; and 2) the relative positioning of the SLAI with respect to the observed scene. Provide a technical approach for autonomous navigation and exploration for UAV.
Scholars from Delft University, The Netherlands, believe that the platform trajectory shows the periodic swing in coherent integration time [27], [28]. They use multibeams to illuminate the reference target on both sides of the trajectory. And then, they estimated the motion parameters of the platform after imaging, achieving an accuracy close to the resolution. Referring to this idea, under the condition of the motion trajectory closing to a straight line or a curve with a slight curvature, when imaging with single-channel data, the incident angle difference between segments is used to estimate the motion trajectory of the platform, making it possible to positioning and imaging simultaneously; moreover, after calculating the precise trajectory of each channel, we can correct the relative phase difference to achieve the effect of phase preservation.
In this article, the SAI algorithm is further extended for simultaneously location and imaging (SLAI), where it estimates and reconstructs the 3-D trajectory of the platform based on parameters derived from the motion compensation of SAI. An image correction scheme is also proposed, which is crucial for real data processing. A newly built FUSAR-Ku system onboard a multirotor platform is presented. The algorithm is applied to the system and demonstrates superior focusing and positioning performance to conventional methods. It demonstrated, for the first time, SLAI with a multirotor-borne radar.
The reminder of the article is organized as follows. Section II introduces the design and development of FUSAR-Ku system. Section III presents the algorithm extensions on SLAI, and image correction. In Section IV, a simulation using real radar Fig. 1. Block diagram of FUSAR-Ku MiniSAR system, including control unit, transmitter and receiver unit, digital signal source unit, signal acquisition and processing unit, navigation and control unit, and power supply unit. system parameters and motion trajectories are carried out to demonstrate the extended algorithm. Experimental results are shown in Section V. Section VI concludes the article.

II. FUSAR-KU SYSTEM
A multirotor-borne MiniSAR system named FUSAR-Ku is developed for experiment purpose. A block diagram of our system is shown in Fig. 1. The system consisting of control unit, transmitter and receiver unit, signal acquisition and processing unit, navigation and control unit, and power supply unit is mounted onboard a UAV platform equipped with a navigation device.
The control unit controls the overall timing of the system and synchronizes the time of each sensor in the system. The transmitter and receiver unit include transmitter and receiver channels, as shown in Fig. 1. The transmit channel contains a waveform generator, which generates a sawtooth wave signal with a bandwidth of 300 MHz. It is then multiplied and mixed with a 13 GHz local oscillator to obtain an FMCW with a center frequency of 15.2 GHz (Ku-band) and a max bandwidth of 1.2 GHz. Finally, it is radiated to the imaging area via the transmitting antennas (Tx antennas), followed by a power amplifier. System specifications are the transmitter power of 5 W, the antenna gain of 23 dB, and the system noise figure of 4 dB, while sweep time can be adjusted between 500 and 2000 μs.
After the receiving antennas (Rx antennas) receive the echo signal, it is amplified by a low-noise amplifier and mixed with the reference signal by dechirp operation to obtain the beat signal. The ADC samples the beat signal and stores it in the solid-state disk (SSD). Simultaneously, the dechirp operation has reduced the sampling rate to 25 MHz. The ground workstation reads the raw data stored in the SSD through the USB3.0 interface and uses the SAI algorithm to perform high-resolution imaging on the ground [26].
The system includes two Tx antennas and two Rx antennas, which are H and V polarization modes, respectively. Four channels of fully polarized (HH, HV, VH, VV) raw data can be obtained in one flight. The radar system itself and it being mounted on a multirotor are pictured in Fig. 2. The antenna is installed perpendicular to the right side of its nose, and the antenna points to the right. The incident angle is 65°. The distance between the two antennas is 50 cm.
We have installed GPS, INS, and real-time kinematic (RTK) antennas on the multirotor for the navigation and control unit to fly according to the planned trajectory. The weight is 1.1 kg, and the positioning accuracy is 1.5-3 m. The digital signal processing (DSP) connects UAV navigation system with MiniSAR. The DSP reads the latitude, longitude, and altitude coordinates of the current platform, and controls MiniSAR to turn ON/OFF the transmitter and receiver at the desired position. Note that the GPS/INS measurements are later used for validation purpose only, but not used for imaging. It means that the radar system itself does not rely on the GPS/INS. Instead, the radar could be used simultaneously as a positioning system to replace GPS/INS if real-time imaging is implemented in future.
The control unit, transmitter and receiver unit, digital signal source unit, signal acquisition and processing unit, and navigation and control unit are all integrated into one box as shown in Fig. 2. And the power supply unit ensures the continuous operation of the system, which is provided by a 10 000 mA lithium battery. The system weighs about 6 kg.

A. Phase Estimation
A comprehensive signal model tailored for MiniSAR onboard multirotor platform is derived in [26], which described the relationship between the errors of the platform motion speed, attitude angle, and vibration frequency and the phase error of the target echo. The instantaneous phase is derived as follows: where η means the azimuth sampling time and φ o (η) represents the ideal phase without errors. It is approximated as a secondorder polynomial of η, the first-order coefficient is related to the Doppler center, and the second-order coefficient is related to the Doppler frequency modulation slope.
φ e (η) describes the phase error due to platform position and attitude errors where λ is the wavelength of the transmitted signal, θ in is the incident angle of the system, and θ e is the angle between the error vector and the line of sight (LoS). The error vector is the position error (Δx, Δy, Δz) after the rotation of the attitude angle (roll angle, yaw angle, and pitch angle). Δx, Δy, and Δz represent the error projections in the X, Y, and Z directions, respectively, which are obtained from the system original position error and attitude angle error through rotation and translation transformation, and they have different values at each Doppler frequency sampling point. φ s (η) represents the phase error caused by high-frequency vibration where w r is the frequency of high-frequency vibration and ξ indicates the projection of the vibration magnitude A r in the LoS where θ s e , θ y e , and θ r e are obtained by projecting the position and attitude coupling errors on the XOY plane, the YOZ plane, and the XOZ plane, respectively.
The SAI algorithm [26] can be used to estimate the position and attitude of platform simultaneously while performing autofocusing for imaging. Considering the instability of the motion of platform, we divide the echo signal into M segments along the azimuth dimension, and perform polynomial fitting on the phase segment by segment. Equations (1)-(4) establishes the relationship between the motion parameters and the instantaneous phase.
In segment q, q = 1 . . . M, we extract the phase φ q (η q ) from the raw data, and the fitted instantaneous phaseφ q (η q ) can be expressed as follows: where η q means the azimuth time of segment q, β q and α q are the coefficients of the second-order and first-order terms of the fitted phase, respectively, and ϕ 0,q is a constant term caused by high-frequency vibration. The estimated value of ξ for the qth segment is as follows: where c is the speed of light, K r means the frequency slope of transmitted signal, and R s,q is the reference range of segment q, calculated from the shortest slant range and the squint angle. By analyzing the high-frequency components of φ q (η q ), we can estimate the phase error caused by high-frequency vibration φ s,q (η q ).
According to (1), we can estimate the phase errors φ e,q (η q ) of segment q After obtaining the phase errors of each orderφ e,q (η q ), φ s (η q ), phase compensation is performed on the raw data after range compression, and finally the focused SAR image can be obtained by multiplying the matched filter.

B. Platform Positioning, Trajectory Reconstruction, and SLAI
We write the phase φ(η) in (5) as a Taylor expansion, and we obtain the relationship between the Doppler frequency slope K a,q and the Doppler center f dc,q in the qth segment and the coefficients of the first-order and second-order terms The estimated value of β q and α q are in [26,Eqs. (17), (18)]. Substitute the estimated values of β q and α q into (7) and (8), and then add the second and first derivatives of the higher order phaseφ s,q (η q ) to obtain the estimated values of the K a,q and the Doppler center f dc,q where d(·) dη q denotes the derivative with respect to η q . The instantaneous velocityv q and squint angle θ s,q are calculated from the relationship between the estimated phase historyφ q (η q ) and the Doppler parameters K a,q and f dc,q , and details are in (22) in [26]. λ is the wavelength.
Assuming in segment q, we consider the trajectory of the multirotor to be linear, as shown in Fig. 3, the blue line. In the XYZ coordinate system of segment q, the linear trajectory coordinates are as follows: ∫v q sin θ s,q dη q ∫v q sin (θ in + θ e ) dη q + ∫v q cos θ s,q dη q R s,q cos θ s,q cos θ in + θ e + ∫v q cos (θ in + θ e ) dη q ⎤ ⎦ .
The track coordinates of the adjacent segment q + 1 can also be written in the form of (12) in the q + 1 coordinate system [X q+1 in q+1 , Y q+1 in q+1 , Z q+1 in q+1 ] T . As shown in Fig. 4, there is a rotation angle (θ x,q+1 , θ y,q+1 , θ z,q+1 ) in the coordinate system between two adjacent segments. Let us use the coordinate system of segment q as the reference coordinate system. Choose at least three points in the area where the two apertures intersect. The coordinates are [Q 1,q , Q 2,q , Q 3,q ] 3×3 in Fig. 3. Schematic diagram of trajectory estimation. The blue one is the segment q coordinate system, and the green one is the segment q + 1 coordinate system. There is a rotation angle between the two coordinate systems. The blue point is the point of the complete aperture in the segment q. The point of the full aperture among the green points segment q + 1. The red point is the point where the two apertures intersect, and it is the point of incomplete aperture in both segments. segment q, and the coordinates are [Q 1,q+1 , Q 2,q+1 , Q 3,q+1 ] 3×3 in segment q + 1.
According to the rotation matrix, the relationship between the two coordinates is as follows: cos θ y,q+1 0 − sin θ y,q+1 Solving the rotation angle directly will increase the difficulty of the solution, so we choose three points to solve the rotation matrix Υ Calculate the coordinates of the platform trajectory of segment q + 1 in the q coordinate system ⎡ The above operation is conducted section by section to unify all segment trajectory in the reference segment coordinate system.
Note that, in this part, the Y-axis in the coordinate system here represents the slant range, as shown in Fig. 3. It is the azimuth-slant range-altitude coordinate system. After that, we project the slant range to the ground range according to the imaging geometry, where the error caused by the roll angle will be introduced. If an absolute position of a group of Q points in the image can be obtained (such as the coordinate of the WGS-84 coordinate system), the absolute position of the estimated trajectory can then be estimated accordingly.
The proposed method has, in fact, established an SLAI algorithm for multirotor-borne radar for the first time. Based on this, more interesting topics could be studied in the future.

C. Image Correction
UAV has relatively poor wind resistance. Large fluctuations may appear in one section of the image, while other sections are very stable. At this time, it is not only the phase of the echo signal that is affected, but its amplitude may also be affected. According to the radar equation, if the system remains unchanged, and the RCS of target area observed by the radar system does not change significantly, the echo power is inversely proportional to the fourth power of the range. The image will be distorted by this received power relationship. Moreover, when stitching segments, there may be differences in amplitude for different segments. Thus, each segment image is corrected by multiplying a scale factor which is estimated by matching the brightness histograms of different segment images.
When a multirotor flies in a certain direction, its pitch angle will affect the beam center direction. Therefore, MiniSAR will change from side view to slightly squint view. As shown in Fig. 4, ABCD and A'B'C'D' are two identical rectangles with edges l 1 and l 2 , which are located on the XOY plane with distance y 0 to the X-axis, and the perpendicular slant range of the flight track is R 0 . For the squint view case, the rectangular target will become a parallelogram. The following processing steps will correct such distortion effect.
First, from the geometric relationships, the angle of deformation can be obtained in where θ d is the squint angle. As shown in Fig. 5, in Step 1, the original SAR image is first transformed from azimuth time domain η to the azimuth frequency domain f d , i.e., S r (t, η) → S r (t, f d ).
In Step 2, we transform parallelogram to rectangle by multiplying a phase factor as where f d indicates the Doppler center and v is the speed of the platform. Subsequently, it is transformed back to the azimuth time domain S GC r (t, η), and a scaling factor of t is applied, i.e.
Now we have corrected the parallelogram A'B'C'D' to the rectangle with the same size of ABCD. Next, we need to compensate the shift in range dimension. First, transform S GC r (t , η) to the range frequency domain S GC r (t , η) and then multiply a phase factor as follows: Finally, transform S GC r (f , η) back to the range time domain and it will restore the undistorted image.
If one wants to further perform geocoding, at least three reference corner reflectors or a landmark building with known  SIMULATION   Fig. 6. Imaging geometry of the simulation case where a 7 × 7 point target grid is in the scene center. Simulation parameters are listed in Table I. latitude and longitude coordinates should be included in the image. Additionally, these reference coordinates can be used to estimate the latitude and longitude coordinates of the platform trajectory.

IV. SIMULATION ANALYSES
In this section, raw signals are simulated using the parameters shown in Table I to validate the SLAI algorithm. It employs the FMCW mode and observes a 7×7 grid point targets with a horizontal and vertical spacing of 25 m. The simulated scene is shown in Fig. 6. The platform flies from −200 m to +200 m along the X-axis. The simulation uses the actual platform trajectory measured by GPS/INS in an experiment of the FUSAR-Ku, so the trajectory contains realistic position error and attitude error, but the vibration error cannot be completely restored due to the low sampling rate of GPS/INS. The data of platform position and attitude are shown in Fig. 7(a) and (b), respectively. The pitch angle and roll angle of the multirotor will change in stages due to its maneuvering features and the SWaP of platform. The accumulation angular variation range is greater than 6°, where the center direction of the beam is rotated, resulting in a coupling phase that cannot be ignored.
The SAI algorithm is used to focus the simulated echo data. First, the entire original data is divided into six overlapping segments along the azimuth direction. The total length of the azimuth dimension of the simulated data is 398.894 m, and the lattice target covers the range of −80-80 m in the azimuth direction, of which segments 3, 4, and 5 contain the complete target area. The lengths of each section are 160.51, 123.89, and 267.67 m, respectively. The squint angles were 8.4°, −2.1°, and 3.2°, respectively. One of the imaging results of a segment is shown in Fig. 7(c). Then, motion compensation and imaging are performed on each segment separately. Finally, the final imaging results of each segment are stitched to obtain the entire image, as shown in Fig. 7(d).
The segment imaging results have incomplete apertures on both sides, so the focusing results of the point target will have azimuthal broadening. The mainlobe 3 dB width of azimuth point spread function (PSF) is 14.11 cm. The peak side lobe ration (PSLR) is about 10.28 dB. The resolution is the same everywhere in the final imaging range. The 3 dB mainlobe width of azimuth PSF is 9.46 cm, which is close to the theoretical value of 9.42 cm. Slight degradation might be caused by segment stitching, and the resolution loss is less than λ/4. It will not affect the coherent processing of SAR images. The PSLR is about 13.25 dB, close to the theoretical value.
In the simulation, we take GPS/INS as the true value of the platform motion trajectory. According to simulated data, we can calculate the phase variation range during the entire flight process. After removing the constant phase of the reference slant range, the reference phase curve is shown by the blue line in Fig. 7(e). The reference phase variation range is from −40 to 80 rad. Although the overall shape is approximately a second-order curve, the high-order phase term is obviously superimposed, and the curve is asymmetrical, which means the azimuth Doppler center is not zero.
The final phase history estimated by the SAI algorithm is shown as the red line in Fig. 7(e). The SAI algorithm adopts a local linear substitution method, such as the enlarged part in the green box. The estimation accuracy of the complete phase history estimated and the reference phase history is less than 2 rad.
According to the estimated parameters of each segment, the trajectory of each segment is calculated according to (12). The trajectory coordinates are in the XYZ coordinate system, where the X-axis represents the azimuth dimension, the Y-axis represents the ground range dimension, which is the projected component of the slant range on the ground, and the Z-axis represents the altitude dimension.
We further stitch the estimated trajectories of each segment. During the imaging process of the SAI algorithm, multiple subimages like Fig. 7(c) will be generated. First, 3-4 strong points are extracted in the intersection area of segments, such as the point in red box in Fig. 7(c). Using the subaperture spectrum and the correlation of the phase-Doppler curve, the transformation matrix is calculated. Finally, the segment q + 1 of trajectories are transformed to segment q + 1, and stitching in turn to obtain the final complete trajectory, as shown in Fig. 7(a).
The trajectory estimation error is shown in Fig. 7(f), which shows that we can achieve centimeter-level accuracy in azimuth dimension (X-axis) and ground range dimension (Y-axis), and decimeter-level accuracy in height dimension (Z-axis). Because the SAR image is a 2-D image, and there is overlapping in the measurement process, the estimation error of the altitude dimension exceeds that of other dimensions. The estimation accuracy of the azimuth dimension (X-axis) and ground range dimension (Y-axis) is positively related to the PRF and bandwidth. When the azimuth interval is less than λ/4, its estimation accuracy can reach λ/10. Since multiple pulses, which contain the reference strong scatterers, are highly correlated after compensating for the Doppler shift, the azimuth estimation has high accuracy. On the slant range dimension, we can only rely on the signal chirp. Therefore, the estimation accuracy of the ground range dimension is basically in the same order as the range resolution.

V. EXPERIMENTAL RESULTS
From 2020 to 2021, we have conducted a number of flight experiments with the FUSAR-Ku system to verify the SLAI algorithm. The experiments were carried out on the Handan and Jiangwan campuses of Fudan University. We designed multiple parallel trajectories across the campus. During the flight, we encountered sunny and moderate rain. Ground winds are between level 3 to 6. The algorithm works robustly in these environments. The altitude of platform is about 450 m, and the swath is about 1400 m. Reference slant range is 912 m. The platform speed is 10-15 m/s. The system setup was shown in Fig. 2. Other parameters are shown in Table I. In the experimental preparation stage, four corner reflectors were placed on the ground. We plan to use it as a calibrator for the geometric correction as described in Section III-C, and also use it for radiometric and polarimetric calibration. The ground station uses RTK antenna to communicate with the UAV, and displays the flight status of the multirotor in real time.
The results of imaging and trajectory estimation using the SLAI algorithm are shown in Fig. 8. It shows estimated trajectories and imaging results in azimuth dimensions from −200 to 200 m. From the results of trajectory estimation, it can be seen that the platform is intermittently affected by wind, which leads to large fluctuations along the trajectory (> 10λ). In Fig. 8(a), the reconstructed trajectories are compared in three dimensions relative to the GPS/INS measurements. The estimation errors are shown and evaluated in Fig. 8(b). The experimental trajectory estimation results are basically consistent with the simulation results. The errors of the azimuth dimension (X-axis), ground range dimension (Y-axis), and altitude dimension (Z-axis) are centimeter-level, centimeter-level, and decimeter-level, respectively. Note that the actual positioning error should be better as this is the sum of both the GPS/INS measurement error and the SLAI error.
By accurately reconstructing the trajectory of platform, we can also use the relative position between the platform and reference targets in the illuminated scene to geometrically correct the image. Take the imaging result of Guanghua Tower as an example, as shown in Fig. 8(c), the edge of the building is annotated by a red box, and it can be seen that the red box is a parallelogram, which should appear as a rectangle. For geometric correction, four corner reflectors were used as reference targets. During the experimental preparation stage, their latitude and longitude were recorded and the estimated trajectories can be converted into the WGS84 geographic coordinate system. After correction by the method in Section III-C, the results shown in Fig. 8(d) are obtained. Apparently, the shape of the building after correction denoted by yellow box appears to be correct. The optical photo of Guanghua Tower is shown in Fig. 8(e) as a reference. The imaging effect of the point target is illustrated by the focusing effect of four corner reflectors. Their 3 dB mainlobe width is about 9.53-9.98 cm, PSLR is between 13.01 and 13.27 dB, and entropy is between 0.31 and 0.67.
According to the ratio of the peak value of the reference target to the theoretical value in the image, the image is radiometrically corrected to calibrate the dynamic range of the image. Then, according to the theoretical corner reflector scattering matrix, the Quegan algorithm is used to perform polarization calibration on the image. The imaging results of the quadpolarization channels (HH/HV/VH/VV) are decomposed, and the difference channel, the cross channel, and the sum channel are used to form an RGB pseudocolor image. As shown in Fig. 9, the color distributions of the pseudocolor images of the Gymnasium and Science Building are consistent with the scattering properties of the target. Buildings parallel to the flight trajectory are equivalent to the dihedral angle of the vertical incidence of electromagnetic waves, and the co-polarization channels are stronger, which is red in the pseudocolor image. Plants such as sycamore trees are mainly multipe scattering components, and thus the cross-polarization channels are strong, which is green in the pseudocolor image.
Finally, the slant range-azimuth image can be projected to the ground range-azimuth image, and the affine matrix of the SAR image can be calculated according to the geographic coordinates of the estimated trajectory, and the image can be geocoded. As shown in Fig. 9, it is the complete SAR image of the Handan campus, and the upper right corner is the campus image captured by camera on a drone. The comparison of optical images and SAR images of typical buildings is shown in Fig. 9.

VI. CONCLUSION
This study proposes the novel SLAI algorithm specifically for MiniSAR onboard small platforms such as multirotors. It achieves SAR imaging without auxiliary positioning such as GNSS/INS. In addition, it can simultaneously estimate accurate position of the platform while performing SAR imaging. Thus, it realizes SLAI on multirotor with radar sensor only. Experimental results with the FUSAR-Ku system demonstrate superior performance of the SLAI algorithm, i.e., 0.1 m-resolution imaging is achieved with the Ku-band radar with simultaneously centimeter-to-decimeter level of positioning accuracy. The resolution and accuracy of the final image are demonstrated, and the phase estimation error is less than 2 rad.
The current implementation of SLAI takes advantage of parallel processing. It has the possibility of being improved into real-time processing. For example, the sequential processing step of segment stitching can be further parallelized in a recursive fashion. There are additional works for full processing of the FUSAR-Ku system. For example, this system is designed as a polarimetric SAR interferometry (PolInSAR) system with two dual-pol antennas. It is also necessary to continue to study the coherent processing between range/azimuth multichannels. The multirotor-borne MiniSAR will open a wide range of applications in surveying, monitoring, disaster relief, and defense areas.