A precise motion compensation method for SAR imaging using attitude and velocity information

Abstract

The application discloses a kind of accurate motion compensation methods for SAR imaging using attitude and velocity information, belong to radar imaging technical field.The application is modeled to the motion state of aircraft, obtains the position information of more accurate aircraft actual track, obtains more accurate compensation phase by calculating the error of radar actual track and ideal track in radar line-of-sight direction, then carries out motion compensation, can well solve the influence brought by the low sampling rate of GPS to the inaccuracy of positioning actual position, improves imaging quality.In the application, phase compensation only involves the related calculation of inertial navigation system INS data, so as to more accurately estimate line-of-sight error, and therefore the implementation is very simple.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar imaging, and in particular relates to a precise motion compensation method for SAR imaging using attitude and velocity information. Background Art

[0002] Synthetic Aperture Radar (SAR) uses the motion of an aircraft or satellite to form a synthetic aperture, enabling high-resolution ground imaging. By measuring the target's reflected signal, the SAR system synthesizes a long virtual aperture, improving imaging resolution. It is suitable for geological exploration, topographic mapping, environmental monitoring, and military reconnaissance, and is unaffected by weather and lighting conditions, making it widely applicable. However, during aircraft motion, the aircraft is subject to various influences, such as airflow and the aircraft's own instability. Changes in flight speed and direction can cause the aircraft's actual trajectory to deviate from the ideal trajectory. The additional phase caused by trajectory deviation leads to blurring and distortion in the image, necessitating motion compensation to improve image quality.

[0003] In practical applications, the accuracy of motion compensation directly impacts the quality of SAR images. Inaccurate compensation can result in image distortion, blurring, or artifacts. Therefore, motion compensation based on GPS and inertial navigation systems has become a crucial component of SAR imaging systems, ensuring the reliability and accuracy of imaging results.

[0004] The prior art "Using Inertial Navigation and GPS Data for Motion Compensation of Radar Imaging" discloses a motion compensation method based on the aircraft's latitude, longitude, and elevation information recorded by GPS and the attitude data provided by the inertial navigation system. The method calculates the skew moment difference between the aircraft's actual trajectory and the ideal trajectory in the direction of the radar beam, i.e., the line-of-sight error, and then performs motion compensation. However, GPS data may be affected by signal interference, delays, or multipath effects, resulting in low positioning accuracy. Specifically, the GPS sampling rate is much lower than the radar's pulse repetition frequency. Accurate motion compensation requires knowing the aircraft's actual position at each azimuth moment. The aircraft's actual position information provided by GPS cannot meet the requirements for accurate motion compensation. Directly using the position information recorded by GPS and the attitude data provided by the inertial navigation system for motion compensation has limited effect on improving SAR imaging quality. In severe cases, it may even cause the imaging effect to become more blurred or even impossible to image. Summary of the Invention

[0005] The present invention aims to overcome the shortcomings of the prior art by providing a precise motion compensation method for SAR imaging using attitude and velocity information. During synthetic aperture radar imaging, the aircraft's velocity and acceleration information are fully considered. Due to the short timeframe at each azimuth moment, the aircraft's motion state can be modeled as uniformly accelerated linear motion, allowing for a precise estimation of the aircraft's trajectory. This improves the imaging error caused by inaccurate GPS recording of the aircraft's real-time position. By using Taylor expansion to estimate line-of-sight error at each azimuth moment and accumulating line-of-sight errors at each azimuth moment, the method can accurately estimate line-of-sight error at each azimuth moment, thereby performing precise motion compensation. This method provides a precise motion compensation method.

[0006] The technical problem proposed by the present invention is solved as follows:

[0007] A method for accurate motion compensation of SAR imaging using attitude and velocity information comprises the following steps:

[0008] Step 1: Generate a rotation matrix using the roll angle, pitch angle, and yaw angle to convert the velocity in the north-east coordinate system to the imaging coordinate system;

[0009] Step 2: Model the aircraft's motion trajectory in each azimuth time as a uniformly accelerated linear motion model;

[0010] Step 3: Calculate the radar line of sight error generated in each azimuth time, and accumulate the radar line of sight error to obtain the radar line of sight error at any azimuth moment;

[0011] Defining ΔD los (i) is the radar line of sight error generated during the i-th azimuth time, expressed as:

[0012]

[0013] in, Indicates t i Moment D los (PRT) function value, t i Indicates the end time of the i-th azimuth time, t i =i*PRT, where i is a positive integer;

[0014] Expressed as:

[0015]

[0016] in, and They represent the speed of the aircraft along the y-axis in the imaging coordinate system at the start and end times within the i-th azimuth time, and They represent the speed of the aircraft along the z-axis in the imaging coordinate system at the start and end times of the i-th azimuth time respectively;

[0017] Then the radar line of sight error D at the kth azimuth moment is los (k) is expressed as:

[0018]

[0019] Wherein, k is a positive integer;

[0020] Step 4: Calculate the compensation phase at any azimuth moment from the radar line of sight error at that azimuth moment, and use the compensation phase to perform phase compensation on the target echo signal at that azimuth moment;

[0021] Step 5: Using a polar coordinate format algorithm to perform synthetic aperture radar imaging on the target echo signal after phase compensation;

[0022] Step 6: Use the phase gradient autofocusing method to perform precise phase compensation on the image domain data after imaging.

[0023] Furthermore, the specific process of step 1 is:

[0024] The rotation matrices corresponding to the roll angle, pitch angle, and yaw angle are:

[0025]

[0026] Among them, T x is the roll angle θ x The corresponding rotation matrix, T y is the pitch angle θ y The corresponding rotation matrix, T z is the yaw angle θ z The corresponding rotation matrix;

[0027] The velocity conversion relationship in the north-east coordinate system is as follows:

[0028]

[0029] Among them, V n is the north velocity, V e is the eastward velocity, V d is the ground velocity, V x is the velocity of the aircraft along the x-axis in the imaging coordinate system, V y is the speed of the aircraft along the y-axis in the imaging coordinate system, V z is the velocity of the aircraft along the z-axis in the imaging coordinate system.

[0030] Furthermore, in step 2, for any time t within the i-th azimuth time, the distance vector traveled by the aircraft is Expressed as:

[0031]

[0032] in, is the aircraft velocity vector at the starting moment within the i-th azimuth time in the imaging coordinate system, is the aircraft motion acceleration vector in the i-th azimuth time in the imaging coordinate system, and PRT is the radar pulse repetition period.

[0033] Furthermore, the specific process of step 3 is:

[0034] The phase center of the aircraft antenna in the ideal track is taken as the coordinate origin, h is the target height, θ is the irradiation angle of the aircraft radar to the target in the ideal track, and the ideal track of the aircraft moves uniformly along the x-axis of the imaging coordinate system at a speed of v0; the ideal coordinate of the aircraft, that is, the coordinate origin, is (v0t, 0, 0), and the actual coordinate of the aircraft is The coordinates of the imaging target are (0, y0, h), where A y and A z are the accelerations of the aircraft along the y-axis and z-axis in the imaging coordinate system, respectively; y0 is the position of the target along the y-axis in the imaging coordinate system;

[0035] The ideal slant distance is the distance R between the ideal coordinate and the target ref , expressed as:

[0036]

[0037] Among them, r represents the distance between the target and the ideal coordinate, r 2 =y0 2 +h 2 ;

[0038] Taylor expansion of the above equation at t = 0 is retained to the quadratic term, expressed as:

[0039]

[0040] Define the sight coordinate system, with the origin as the ideal coordinate, D los The axis is the radar line of sight, D x Axis is the ideal track direction, D τ The axis is perpendicular to the line of sight and the ideal track direction; in the line of sight coordinate system, the coordinates of the target are (r, 0, 0), and the coordinates of the actual coordinates are (D x (t), D los (t), D τ (t)), expressed as:

[0041]

[0042] In the line of sight coordinate system, the distance R between the actual coordinate and the target real for:

[0043]

[0044] Taylor expansion is performed on the above equation at t = 0, and the quadratic term is retained, which is expressed as:

[0045]

[0046] Among them, D los ′(0) and D los ″(0) represents D los (i) The first and second derivatives at t = 0, D x ′(0) and D τ ′(0) represents D x (t) and D τ (t) first derivative at t = 0;

[0047] Ignoring the last term of Taylor expansion, the above formula can be rewritten as:

[0048]

[0049] The slope range error ΔR is expressed as:

[0050] ΔR=R real -R ref =-D los (t)

[0051] Defining ΔD los (i) is the radar line of sight error generated during the i-th azimuth time, expressed as:

[0052]

[0053] in, Indicates t i Moment D los (PRT) function value, t i Indicates the end time of the i-th azimuth time, t i =i*PRT, where i is a positive integer;

[0054] according to Expressed as:

[0055]

[0056] in, and They represent the speed of the aircraft along the y-axis in the imaging coordinate system at the start and end times within the i-th azimuth time, and They represent the speed of the aircraft along the z-axis in the imaging coordinate system at the start and end times of the i-th azimuth time respectively;

[0057] Then the radar line of sight error D at the kth azimuth time los (k) is expressed as:

[0058]

[0059] Wherein, k is a positive integer.

[0060] Furthermore, in step 4, the compensation phase at the k-th azimuth moment is:

[0061]

[0062] Here, λ represents the wavelength.

[0063] The beneficial effects of the present invention are:

[0064] The method of the present invention models the motion state of an aircraft as uniformly accelerated linear motion in each azimuth time, accurately estimates the motion trajectory of the aircraft, and improves the imaging error caused by the inaccurate recording of the real-time position of the aircraft by the GPS in the prior art; the method of the present invention uses Taylor expansion to estimate the line of sight error at each azimuth time, accumulates the line of sight errors at each azimuth time, and can accurately estimate the line of sight error at each azimuth time, thereby performing accurate motion compensation, and is an accurate motion compensation method; in the method of the present invention, phase compensation only involves relevant calculations of inertial navigation system INS data, thereby more accurately estimating the line of sight error, and is therefore simple to implement.

[0065] In summary, the method of the present invention solves the problem of inaccurate positioning caused by low GPS sampling rate in the prior art; improves the focusing effect of imaging and enhances the quality of the image; and the implementation process does not involve complex calculation processes. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 Schematic diagram of the process of the present invention;

[0067] Figure 2 This is the geometric relationship diagram of airborne SAR imaging;

[0068] Figure 3 This is the PFA imaging effect diagram for the original target echo signal;

[0069] Figure 4 This is the PFA imaging effect diagram after phase compensation using GPS positioning data in the existing technology;

[0070] Figure 5This is a diagram of the PFA imaging effect after phase compensation using the method described in this embodiment;

[0071] Figure 6 For Figure 3 The image is imaged after PGA;

[0072] Figure 7 For Figure 4 The image is imaged after PGA;

[0073] Figure 8 This is an imaging effect diagram of the method of the present invention. DETAILED DESCRIPTION

[0074] The present invention will be further described below with reference to the accompanying drawings and examples.

[0075] This embodiment provides a method for accurate motion compensation of SAR imaging using attitude and velocity information provided by INS. Figure 1 As shown, the following steps are included:

[0076] Step 1: First, coordinate conversion is performed. The roll angle, pitch angle, and yaw angle recorded by the inertial measurement unit (IMU) are used to generate a rotation matrix, and the velocity information (east velocity, north velocity, and ground velocity) in the north-east coordinate system is converted to the imaging coordinate system.

[0077] The specific process of step 1 is:

[0078] The rotation matrices corresponding to the roll angle, pitch angle, and yaw angle are:

[0079]

[0080] Among them, T x is the roll angle θ x The corresponding rotation matrix, T y is the pitch angle θ y The corresponding rotation matrix, T z is the yaw angle θ z The corresponding rotation matrix;

[0081] The velocity conversion relationship in the north-east coordinate system is as follows:

[0082]

[0083] Among them, V n is the north velocity, V e is the eastward velocity, V d is the ground velocity, V x is the velocity of the aircraft along the x-axis in the imaging coordinate system, V y is the speed of the aircraft along the y-axis in the imaging coordinate system, Vz is the velocity of the aircraft along the z-axis in the imaging coordinate system.

[0084] Step 2: Model the trajectory of the aircraft within each azimuth time. Since each azimuth time is extremely short, it can be considered that the aircraft is performing uniformly accelerated linear motion within each azimuth time, that is, within the radar pulse repetition period.

[0085] Assume that the actual trajectory of the radar is different from the ideal trajectory and a phase error is generated in the radar line of sight. The phase error is expressed as follows:

[0086] Δψ ε =a0+a1t+a2t 2 +……

[0087] Among them, a0, a1 and a2 are the coefficients of the 0th power term, 1st power term and 2nd power term of time t respectively;

[0088] Ignore the influence of higher-order phase errors and only perform motion compensation on the primary and secondary phase errors. The primary phase error will cause the image center of mass to change, and the secondary phase difference caused by acceleration will cause the image to defocus. Model the aircraft's motion trajectory within each azimuth time. Since each azimuth time is extremely short, it can be considered that the aircraft is moving in a uniformly accelerated straight line within each azimuth time, that is, within the radar pulse repetition period. For any time t within the i-th azimuth time, the distance vector traveled by the aircraft is for:

[0089]

[0090] in, is the aircraft speed at the start of the i-th azimuth time in the imaging coordinate system, is the aircraft motion acceleration in the i-th azimuth time in the imaging coordinate system, is a constant vector, and PRT is the radar pulse repetition period.

[0091] Step 3: Calculate the line of sight error ΔD at each azimuth moment los (i) and accumulate the radar line of sight error to obtain the radar line of sight error D at the kth azimuth moment. los (k);

[0092] Figure 2 The geometric relationship diagram of airborne SAR imaging is given, and the aircraft motion trajectory is modeled based on the SAR imaging geometric relationship diagram; the phase center of the aircraft antenna in the ideal track is the coordinate origin A, h is the target height, θ is the irradiation angle of the aircraft radar to the target in the ideal track, and the ideal track of the aircraft moves at a constant speed v0 along the x-axis of the imaging coordinate system. The ideal coordinate of the aircraft, that is, the coordinate origin A, is (v0t, 0, 0), and the actual coordinate of the aircraft B is The coordinates of the imaging target Target are (0, y0, h), where A y and A z are the accelerations of the aircraft along the y-axis and z-axis in the imaging coordinate system, and y0 is the position of the target along the y-axis in the imaging coordinate system.

[0093] The ideal slope distance is the distance R between the ideal coordinate A and the target ref :

[0094]

[0095] Among them, r represents the distance between the target and the ideal coordinate A, r 2 =y0 2 +h 2 ;

[0096] Taylor expansion of the above equation at t = 0 is retained to the quadratic term, expressed as:

[0097]

[0098] The distance R between the actual coordinate B and the target real for:

[0099]

[0100] In order to simplify the analysis, another coordinate system is defined: the line of sight coordinate system AD x D los D τ , where D los The axis is the radar line of sight, D x The axis is still in the ideal track direction, D τ The axis is perpendicular to the line of sight and the ideal track direction. The relationship between the line of sight coordinate system and the imaging coordinate system is:

[0101]

[0102] Then in the sight coordinate system, the coordinate of the actual coordinate B is (D x (t), D los (t), D τ (t)), the coordinates of the target are (r, 0, 0), and the distance R between the actual coordinate B and the target real for:

[0103]

[0104] Taylor expansion is performed on the above equation at t = 0, and the quadratic term is retained, which is expressed as:

[0105]

[0106] Among them, D los ′(0) and D los ″(0) represents D los (t) The first and second derivatives at t = 0, D x ′(0) and D τ ′(0) represents D x (t) and D τ (t) The first derivative at t = 0.

[0107] Since r≥D τ ′(0), the last term of Taylor expansion can be ignored. Then the above formula can be rewritten as:

[0108]

[0109] The slope range error is expressed as:

[0110] ΔR=R real -R ref =-D los (t)

[0111] Defining ΔD los (i) is the radar line of sight error at the i-th azimuth moment, expressed as:

[0112]

[0113] in, Indicates t i Moment D los (PRT) function value, t i Indicates the maximum time value within the i-th azimuth time, t i =i*PRT;

[0114] according to It can be expressed as follows:

[0115]

[0116] in, and They represent the speed of the aircraft along the y-axis in the imaging coordinate system at the starting and ending moments within the i-th azimuth time, and they represent the speed of the aircraft along the z-axis in the imaging coordinate system at the starting and ending moments within the i-th azimuth time, respectively.

[0117] Then the radar line of sight error D at the kth azimuth moment is los (k) can be expressed as:

[0118]

[0119] Step 4: The radar sight error D at the k-th azimuth moment is los (k), the compensation phase at that moment can be obtained Then, the phase compensation is performed on the target echo signal at the kth azimuth moment;

[0120] The compensation phase at the kth azimuth moment is:

[0121]

[0122] Here, λ represents the wavelength.

[0123] Step 5: Using the PFA algorithm to perform synthetic aperture radar imaging on the target echo signal after phase compensation;

[0124] Step 6: Use the phase gradient autofocus algorithm (PGA) to perform precise phase compensation on the image domain data after PFA imaging.

[0125] This embodiment provides the following simulation example, and the specific settings of the simulation parameters are as follows: the circular PFA imaging mode is adopted, the distance between the radar and the center of the scene is 3700 meters, and the center carrier frequency of the transmitted signal is 220 GHz;

[0126] Figure 3 The PFA imaging effect diagram is directly performed on the original target echo signal. Due to the difference between the actual trajectory and the ideal trajectory, there is a deviation in the line of sight. The strong scattering points in the imaging scene show that the focusing effect in the range and azimuth directions is not good.

[0127] Figure 4 This is the PFA imaging effect diagram after phase compensation using GPS positioning data in the existing technology. It can be seen that due to the low sampling rate of GPS, the positioning data is inaccurate, and thus phase compensation cannot be performed accurately. Figure 3 Compared with the distance compression effect, the improvement is not significant.

[0128] Figure 5 The PFA imaging effect diagram after phase compensation using the method described in this embodiment shows that after compensating the radar line of sight error in each azimuth, Figure 3 and Figure 4 In comparison, the distance direction can be effectively compressed, and the effect is obvious.

[0129] Figure 6 For Figure 3 The image is imaged after PGA. Since the line of sight error in the range direction is not compensated, the image quality is still not effectively improved.

[0130] Figure 7 For Figure 4The image is imaged after PGA. It can be seen that due to the low sampling rate of GPS, the positioning data is inaccurate, and phase compensation cannot be performed accurately. The edges of the image are blurred, and the points in the distance direction cannot be effectively compressed. Figure 6 Compared with the image quality, the improvement is not significant;

[0131] Figure 8 For Figure 5 The imaging effect diagram after PGA, that is, the imaging effect diagram using the method described in this embodiment, can be seen that both the range and azimuth directions are effectively compressed, which is consistent with the imaging effect diagram of the present embodiment. Figure 6 and Figure 7 In comparison, the imaging quality is greatly improved, which fully demonstrates that the method of the present invention is an accurate motion compensation method.

[0132] In summary, judging from the processing results, the method provided by the present invention has practical value.

Claims

1. A method for accurate motion compensation of SAR imaging using attitude and velocity information, characterized in that: The following steps are involved: Step 1: Generate a rotation matrix using the roll angle, pitch angle, and yaw angle to convert the velocity in the north-east coordinate system to the imaging coordinate system; Step 2: Model the aircraft's motion trajectory in each azimuth time as a uniformly accelerated linear motion model; Step 3: Calculate the radar line of sight error generated in each azimuth time, and accumulate the radar line of sight error to obtain the radar line of sight error at any azimuth moment; Defining ΔD los (i) is the radar line of sight error generated during the i-th azimuth time, expressed as: in, Indicates t i Moment D los (PRT) function value, t i Indicates the end time of the i-th azimuth time, t i =i*PRT, where i is a positive integer; Expressed as: in, and They represent the speed of the aircraft along the y-axis in the imaging coordinate system at the start and end times within the i-th azimuth time, and represents the speed of the aircraft along the z-axis in the imaging coordinate system at the start and end times of the i-th azimuth time; PRT is the radar pulse repetition period, and θ is the irradiation angle of the aircraft radar to the target in the ideal track; Then the radar line of sight error D at the kth azimuth moment is los (k) is expressed as: Wherein, k is a positive integer; Step 4: Calculate the compensation phase at any azimuth moment from the radar line of sight error at that azimuth moment, and use the compensation phase to perform phase compensation on the target echo signal at that azimuth moment; Step 5: Using a polar coordinate format algorithm to perform synthetic aperture radar imaging on the target echo signal after phase compensation; Step 6: Use the phase gradient autofocusing method to perform precise phase compensation on the image domain data after imaging.

2. The method for accurate motion compensation of SAR imaging using attitude and velocity information according to claim 1, characterized in that: The specific process of step 1 is: The rotation matrices corresponding to the roll angle, pitch angle, and yaw angle are: Among them, T x is the roll angle θ x The corresponding rotation matrix, T y is the pitch angle θ y The corresponding rotation matrix, T z is the yaw angle θ z The corresponding rotation matrix; The velocity conversion relationship in the north-east coordinate system is as follows: Among them, V n is the north velocity, V e is the eastward velocity, V d is the ground velocity, V x is the velocity of the aircraft along the x-axis in the imaging coordinate system, V y is the speed of the aircraft along the y-axis in the imaging coordinate system, V z is the velocity of the aircraft along the z-axis in the imaging coordinate system.

3. The method for accurate motion compensation of SAR imaging using attitude and velocity information according to claim 1, characterized in that: In step 2, for any time t within the i-th azimuth time, the distance vector traveled by the aircraft is Expressed as: in, is the aircraft velocity vector at the starting moment within the i-th azimuth time in the imaging coordinate system, is the aircraft motion acceleration vector in the i-th azimuth time in the imaging coordinate system, and PRT is the radar pulse repetition period.

4. The method for accurate motion compensation of SAR imaging using attitude and velocity information according to claim 3, characterized in that: The specific process of step 3 is: The phase center of the aircraft antenna in the ideal track is taken as the coordinate origin, h is the target height, θ is the irradiation angle of the aircraft radar to the target in the ideal track, and the ideal track of the aircraft moves uniformly along the x-axis of the imaging coordinate system at a speed of v0; the ideal coordinate of the aircraft, that is, the coordinate origin, is (v0t,0,0), and the actual coordinate of the aircraft is The coordinates of the imaging target are (0, y0, h), where V y and V z are the speeds of the aircraft along the y-axis and z-axis in the imaging coordinate system, A y and A z are the accelerations of the aircraft along the y-axis and z-axis in the imaging coordinate system, respectively; y0 is the position of the target along the y-axis in the imaging coordinate system; The ideal slant distance is the distance R between the ideal coordinate and the target ref , expressed as: Among them, r represents the distance between the target and the ideal coordinate, r 2 =y0 2 +h 2 ; Taylor expansion of the above equation at t = 0 is retained to the quadratic term, expressed as: Define the sight coordinate system, with the origin as the ideal coordinate, D los The axis is the radar line of sight, D x Axis is the ideal track direction, D τ The axis is perpendicular to the line of sight and the ideal track direction; in the line of sight coordinate system, the coordinates of the target are (r, 0, 0), and the coordinates of the actual coordinates are (D x (t),D los (t),D τ (t)), expressed as: In the line of sight coordinate system, the distance R between the actual coordinate and the target real for: Taylor expansion is performed on the above equation at t = 0, and the quadratic term is retained, which is expressed as: Among them, D los '(0) and D los ”(0) represents D los (t) The first and second derivatives at t = 0, D x '(0) and D τ '(0) represents D x (t) and D τ (t) first derivative at t = 0; Ignoring the last term of Taylor expansion, the above formula can be rewritten as: The slope range error ΔR is expressed as: ΔR=R real -R ref =-D los (t) Defining ΔD los (i) is the radar line of sight error generated during the i-th azimuth time, expressed as: in, Indicates t i Moment D los (PRT) function value, t i Indicates the end time of the i-th azimuth time, t i =i*PRT, where i is a positive integer; according to Expressed as: in, and They represent the speed of the aircraft along the y-axis in the imaging coordinate system at the start and end times within the i-th azimuth time, and They represent the speed of the aircraft along the z-axis in the imaging coordinate system at the start and end times of the i-th azimuth time respectively; Then the radar line of sight error D at the kth azimuth time is los (k) is expressed as: Wherein, k is a positive integer.

5. The method for accurate motion compensation of SAR imaging using attitude and velocity information according to claim 1, characterized in that In step 4, the compensation phase at the kth azimuth moment is: Here, λ represents the wavelength.

Images