A SAR offshore target positioning method and system based on Doppler shift estimation

Abstract

The application provides a SAR offshore target positioning method and system based on Doppler shift estimation, which is used for monitoring and positioning of offshore ship targets and belongs to the technical field of ocean monitoring. The application solves the problem that the existing technology brings great influence on sea area image geometric calibration and high-precision positioning of sea area targets when realizing target positioning by using remote sensing images. The application obtains Doppler shift estimation parameters by using AIS data and SAR data required for positioning, and calculates Doppler shift deviation. After Doppler shift compensation of SAR targets, AIS and SAR targets are associated and matched based on the characteristics of AIS data and SAR data and through an associated matching model, and finally, the same point pairs required for positioning are obtained. A SAR weak intersection area network adjustment model considering Doppler shift error is constructed, and the overall positioning of SAR images is realized based on the same point pairs required for final positioning and the Doppler shift deviation. The application is used for monitoring and positioning of offshore ship targets.

Description

Technical Field

[0001] A SAR maritime target localization method and system based on Doppler displacement estimation is proposed for the monitoring and localization of maritime ship targets, belonging to the field of marine monitoring technology. Technical Background

[0002] With global economic integration and the increasing frequency of human activities at sea, ships, as the main carriers of maritime activities, are of great significance for emergency rescue, disaster prevention and mitigation, shipping control, reconnaissance and surveillance.

[0003] Currently, traditional land-based, airborne, and shipborne radar technologies are insufficient for monitoring wide-area ship targets. However, with the development of satellite technology, which boasts wide detection range, minimal geographical limitations, and high resolution, it has gradually become the primary equipment for maritime surveillance. Synthetic Aperture Radar (SAR), in particular, employs active microwave technology, allowing it to penetrate clouds and fog and operate in all weather conditions, giving it a unique advantage in ship surveillance. Furthermore, Automatic Identification Systems (AIS) also offer the advantage of all-weather operation, using a passive signal reception mode to provide real-time static and dynamic information on ships in the sea area, making it another commonly used device in ship surveillance. Especially with the further development of spaceborne AIS technology, the monitoring range of shore-based AIS has been extensively expanded, achieving global maritime ship monitoring.

[0004] Wide-area maritime target surveillance needs to focus on solving three key issues: maritime target detection, classification and identification, and target positioning. Among these, target positioning plays a prominent role in data application. Although both SAR and AIS systems can perform ship target surveillance and positioning, they exhibit different characteristics and have their own shortcomings: (1) SAR systems, as the main body of target detection, can display target information in objective and vivid images. However, due to the influence of satellite orbit errors, system time delay errors, and Earth curvature, the positioning accuracy of SAR image data is not high. Even with low-orbit satellites, the positioning error in ocean areas without control points is on the order of tens to hundreds of meters. In addition, due to the defects of the imaging system, the Doppler frequency shift of moving ships in SAR images will cause a large positional shift in the images, making it difficult to achieve accurate positioning of ship targets. (2) AIS, as a passive detection system, has high positioning accuracy and identifiable static information. It can effectively improve the target positioning capability in surveillance and is a reliable data source for positioning and a basis for target classification. However, AIS signals are difficult to acquire (primarily because they cannot be used as the primary means of large-scale ship monitoring). For example, many small fishing vessels in the sea are not equipped with AIS, and AIS signals cannot be acquired in a timely manner when they are silent. Furthermore, in certain special operations, information in AIS can be altered to create a deceptive effect, reducing data reliability. Due to these characteristics, AIS can only serve as an auxiliary means of ship monitoring, improving target detection capabilities by leveraging its strengths and mitigating its weaknesses. Therefore, how to fully utilize the respective advantages of SAR and AIS to achieve efficient and accurate ship target surveillance and positioning is a pressing issue in the field of maritime monitoring.

[0005] In summary, the existing technology has the following technical problems:

[0006] When using remote sensing imagery to locate targets, high-precision ground static control points are still often required. However, for vast sea areas, reliable ground static control information is difficult to obtain or impossible to obtain, which has a significant impact on the geometric calibration of sea area images and the high-precision positioning of sea targets. Summary of the Invention

[0007] The purpose of this invention is to provide a SAR maritime target positioning method and system based on Doppler displacement estimation, which solves the problem that when using remote sensing images to achieve target positioning, most existing technologies still require the assistance of high-precision ground static control points. However, for vast sea areas, reliable ground static control information is difficult to obtain or impossible to obtain, which has a significant impact on the geometric calibration of sea area images and the high-precision positioning of sea area targets.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0009] A SAR maritime target localization method based on Doppler displacement estimation includes the following steps:

[0010] S1. Obtain the AIS and SAR data required for positioning;

[0011] S2. Obtain Doppler displacement estimation parameters using AIS and SAR data, and calculate the Doppler displacement deviation. The Doppler displacement estimation parameters include radial velocity, closest slant range, and equivalent radar velocity.

[0012] S3. After compensating for the Doppler displacement of the SAR target, based on the characteristics of AIS data and SAR data, and through the association matching model, the AIS and SAR targets are associated and matched to obtain the corresponding point pairs required for final positioning.

[0013] S4. Construct a SAR weak intersection area network adjustment model that takes into account Doppler displacement error, and realize the overall positioning of SAR images based on the corresponding point pairs and Doppler displacement deviation required for final positioning.

[0014] Furthermore, the specific steps of step S2 are as follows:

[0015] Step S2.1: Obtaining radial velocity and nearest slant distance

[0016] Based on the ground speed and heading from AIS data and the target incident angle from the synthetic aperture radar SAR image, the radial velocity of the moving target is obtained using the velocity projection formula:

[0017]

[0018] Among them, v r1 The radial velocity of the moving target is obtained based on the velocity projection formula. χ is a linear coefficient, which takes a value of 1 when the synthetic aperture radar is in ascending orbit mode and a value of -1 when it is in descending orbit mode. t Indicates the speed over ground. θ represents the angle between the ship's heading relative to the ground and the direction of the image distance, and θ represents the magnitude of the target's incident angle in the SAR image;

[0019] By fitting the AIS trajectory from AIS data and the SAR satellite trajectory from SAR data, a tilt range function that varies between the two over time is constructed. The formula for the radial distance of the moving target, i.e., the tilt range function of the moving target, is as follows:

[0020]

[0021] Among them, R m (t) represents the tilt range of the moving target, (Δx) m (t),Δy m (t),Δzm (t) represents the distance between the moving vessel and the SAR platform in the three-dimensional x, y, and z directions;

[0022] Inclination range R of moving target m (t) Differentiating the derivative yields the radial velocity of the moving target at the imaging moment, which is the radial velocity v of the moving target relative to the SAR platform. rm (t);

[0023] At the same time, take R m The time when (t) reaches its minimum value is taken as the imaging center time of the moving target, denoted as t. c Minimum distance R m (t c This is the nearest slant distance R0 in the Doppler displacement parameters, and t c The ship's position at any given time is determined as the imaging position of a virtual stationary target, and the tilt range R between the virtual stationary target and the SAR platform is established. s (t), the formula for the radial distance of a stationary target is:

[0024]

[0025] Among them, R s (t) represents the tilt range of the virtual stationary target, (Δx) s (t),Δy s (t),Δz s (t) represents the distance between the virtual stationary ship and the SAR platform in the three-dimensional x, y, and z directions;

[0026] The tilt range R of the virtual stationary target s Differentiating (t) yields the radial velocity v of the stationary target relative to the SAR platform. rs (t);

[0027] Based on the obtained imaging center time t of the moving target c Subtracting the two radial velocities at this moment yields the increase in radial velocity v due to the motion of the moving target relative to the stationary target, based on the radial distance formula. r2 The formula is:

[0028] v r2 =v rm (t c )-v rs (t c )

[0029] The radial velocity v of the moving ship target was obtained using the velocity projection formula and the radial distance formula. r1 v r2 With the nearest slope distance R0;

[0030] Step S2.2: Obtaining the equivalent radar velocity

[0031] The center time t of the moving target imaging c The radial velocity v of the virtual stationary target rs (t) Take the derivative and obtain the equivalent radar velocity using the stationary target's acceleration and its frequency modulation at zero Doppler moment; the specific steps are as follows:

[0032] Synthetic Aperture Radar Actual Velocity v s The following relationship exists between the radar and the equivalent radar velocity v:

[0033]

[0034] Among them, v g The speed at which the synthetic aperture radar beam moves across the ground;

[0035] The frequency modulation of a stationary target at the zero Doppler moment is expressed as:

[0036]

[0037] Where v is the equivalent radar velocity, λ is the carrier wavelength of the synthetic aperture radar transmitted pulse, and R0 is the closest slant range;

[0038] According to t c The acceleration A of a stationary target at any given time s (t c ) and its zero Doppler time modulation frequency k a_SAR Correspondence:

[0039]

[0040] Thus, the equivalent radar velocity v can be calculated;

[0041] Step S2.3: Doppler displacement parameter check

[0042] The difference between the radial velocities obtained from the velocity projection formula and the radial distance formula is used as the first check item, and the difference between the ship's bearing velocity obtained from the velocity projection formula and the radial distance formula is used as the second check item.

[0043] For the ship's bearing velocity difference check item, in the velocity projection formula, it is transformed into calculating the ship's bearing velocity, and the formula is as follows:

[0044]

[0045] Among them, v x1 The azimuth velocity of the ship is obtained based on the velocity projection formula, where χ is the linear coefficient and v t Indicates the speed over ground. Indicates the angle between the ship's heading relative to the ground and the direction of the image distance;

[0046] The azimuth velocity of a ship can be calculated using the radial distance formula, i.e., based on the radial velocity v of the moving target. rs The derivative of (t) yields the acceleration A of the moving target. m Formula (t) utilizes the time t at the center of the moving target's imaging. c Corresponding acceleration A m (t c The ship's azimuth velocity is obtained by using its echo Doppler frequency modulation; the specific steps are as follows:

[0047] The Doppler modulation frequency of the moving target echo is expressed as:

[0048]

[0049] Where v is the radar equivalent velocity, v a R0 represents the velocity component along the track direction in the SAR slant range plane, λ is the carrier wavelength of the synthetic aperture radar transmitted pulse, and R0 is the closest slant range.

[0050] Also taking into account the effects of satellite orbit and Earth's rotation, the azimuth velocity v of a ship on the sea surface... x2 v in the slant distance plane a Existence Relationship: This results in the following Doppler frequency modulation transformation of the moving target echo:

[0051]

[0052] According to t c The acceleration A of the moving target at any given time m (t c ) and its echo Doppler modulation frequency k ad Correspondence:

[0053]

[0054] Based on the calculated A m (t c The ship's azimuth velocity v at the sea surface can be calculated by combining R0, the equivalent radar velocity v obtained in the previous step, and the equivalent radar velocity v. x2 This is compared with the ship's azimuth velocity v obtained by velocity projection. x1 By making a mistake, we obtain the second check item;

[0055] Based on multiple first check items and corresponding multiple second check items, AIS data with smaller values ​​for both the first and second check items are selected as the basis for subsequent SAR image geometric positioning. After the check, three Doppler displacement estimation parameters are obtained: radial velocity, nearest slant range, and equivalent radar velocity. The Doppler displacement deviation Δx caused by the target motion is obtained using the displacement formula. AIS data with larger values ​​for the two check items are discarded.

[0056]

[0057] In the formula, v r v corresponding to the first check item after the check r2 .

[0058] Furthermore, the specific steps of step S3 are as follows:

[0059] Step S3.1: Obtain the features of SAR and AIS data: SAR data consists of ship SAR traces. Feature extraction is performed on the detected ship targets. The extracted features include target position information, ship length, ship width, heading, and ship speed estimated based on the ship's wake. AIS data consists of ship AIS traces, including static and dynamic information of the ship target, specifically including position information, ship length, ship width, speed, and heading.

[0060] Step S3.2: Select the same features in AIS data and SAR data, and associate them through the association matching model to obtain the corresponding point pairs required for positioning. Optimize the AIS control points in the corresponding point pairs that meet the check items. That is, use the specific location of the GPS antenna provided by AIS in the ship to transform the ship's GPS antenna position to the center of the ship to obtain the final corresponding point pairs required for positioning. The association matching model is based on the latitude and longitude location information of both AIS data and SAR data as the association attribute features.

[0061] The specific steps for obtaining the required pairs of identically named points for location by using an association matching model are as follows:

[0062] First, perform temporal and spatial calibration on the shared features in the selected AIS and SAR data to obtain the necessary point data for association, specifically:

[0063] Based on the imaging time of the center of a single SAR image, data from AIS data within five minutes before and after this time are acquired. The data is sorted and classified by the ship identification number and timestamp of all ships' AIS data within the range of the acquired single SAR image. That is, AIS data is classified according to ship identification number, and data of each category is sorted and stored according to timestamp.

[0064] Next, using the sorted and classified stored ship AIS data and the Doppler displacement estimation method, the zero Doppler time and corresponding latitude and longitude coordinates of each ship are obtained. Then, inverse Doppler displacement compensation is performed to transform the AIS ship latitude and longitude to the SAR image position to obtain the latitude and longitude after inverse displacement compensation. This is used as the standard point data associated with AIS, that is, the AIS latitude and longitude coordinates are obtained.

[0065] Before association matching, for SAR images, Mercator projection is performed using the provided initial RPC parameters and elevation data provided by ENVI. After target detection, the planar coordinates of SAR ship targets are obtained.

[0066] Convert AIS latitude and longitude coordinates to Mercator projection plane coordinates to achieve temporal and spatial registration of SAR and AIS data;

[0067] Then, based on the time- and space-registered data, the associated matching point data is obtained using an association matching model. The association matching model is a global nearest neighbor association matching model, which is expressed as follows:

[0068]

[0069] Where k represents the total association cost, and the best match is achieved when the total association cost is minimized. ij A binary function that is either 0 or 1. When it is 1, it indicates that the i-th AIS track is associated with the j-th SAR track; when it is 0, it indicates that they are not associated. ij The substitution value is calculated from the Euclidean distance between AIS data and SAR data, where m and n are the maximum values ​​of i and j, respectively.

[0070] The cost matrix is ​​obtained by combining the cost values, and global minimum distance point matching is performed based on the cost matrix. When the distance between the associated points is within the judgment threshold, the point association is successful and the association result is saved. Otherwise, the association fails and the point pair is deleted to obtain the correct AIS and SAR positioning corresponding point pairs, including the latitude and longitude coordinates of the ship center point corresponding to the AIS and the image point coordinates of the ship center in the SAR image. The latitude and longitude coordinates of the ship center point corresponding to the AIS are the object control points of the AIS, and the image point coordinates of the ship center in the SAR image are the image control points of the AIS.

[0071] Furthermore, the specific steps of step S4 are as follows:

[0072] Step S4.1: Construct a SAR weak intersection area network adjustment model that takes into account Doppler displacement error. The SAR weak intersection area network adjustment model is a rational function model with additional parameters. Affine transformation is used as the model for image-side compensation to optimize the rational function model. The parameters to be solved include the affine transformation coefficients in the six affine transformations of the SAR image and the ground three-dimensional coordinates of the connection points.

[0073] The affine transformation model is as follows:

[0074]

[0075] In the formula, (Δc0, Δr0) represents the difference between the measured coordinates of the image point and the coordinates calculated by the rational function model; a0, b0, a1, a2, b1, b2 are affine transformation coefficients; a0, b0 are the image-side coordinate translation parameters in the SAR image; and a1, a2, b1, b2 are the scaling coefficients of the image-side coordinates in the SAR image. Measure the coordinates of image points in SAR images;

[0076] In the affine transformation model, the Doppler displacement bias Δx obtained in step S2 is added to the azimuth direction to compensate for the Doppler displacement error of the SAR moving target. The azimuth displacement of the moving target, i.e., the Doppler displacement bias Δx, is obtained from the Doppler displacement parameters, and is further calculated from the azimuth resolution x of the SAR image. res The azimuth deviation of the moving target in the image direction is obtained as follows: The affine transformation model changes as follows:

[0077]

[0078] Using an affine transformation model that takes into account Doppler displacement error and an RFM model of the image to be adjusted, a regional network adjustment model is established:

[0079]

[0080] Where (c,r) are the coordinates of the image point in the SAR image calculated by the rational function model, and ε L ,ε S Let (Lat, Lon, Hei) be the random error in the SAR image, and (Lat, Lon, Hei) be the three-dimensional spatial coordinates of the ground point, including two types: tie points and control points, which are represented by (Lat1, Lon1, Hei1) and (Lat2, Lon2, Hei2) respectively.

[0081] Substituting the varying affine transformation model (Δc, Δr) into the above regional network adjustment model, the error equation is expanded as follows:

[0082]

[0083] For each SAR tie point and the optimized AIS control point, the corresponding error equation is obtained from the above formula:

[0084]

[0085] Among them, V L V S This represents the column and row residual values ​​of the image point coordinates for SAR tie points and AIS control points. Δa0, Δa1, Δa2, Δb0, Δb1, and Δb2 are the affine transformation coefficient corrections for each SAR image scene, and (ΔLat, ΔLon, ΔHei) are the three-dimensional spatial coordinate corrections for the ground points. It also includes tie points and control points, with each tie point and control point represented by (ΔLat1, ΔLon1, ΔHei1) and (ΔLat2, ΔLon2, ΔHei2), respectively. The partial derivative symbol F represents taking the partial derivative with respect to each parameter. L0 and F S0 When taking an initial value for an unknown, F L and F S The optimized AIS control points include the optimized AIS object control points and the optimized AIS image control points.

[0086] For the connection points, the error equation matrix simplifies to:

[0087] V1=A1x+B1t1-L1,P1

[0088] Where V1 represents the residual vector of the image point of the connection point, x and t1 are the affine transformation coefficient correction matrix and the three-dimensional coordinate correction matrix of the connection point for each SAR image, c1 and B1 are the coefficient matrices of x and t1 respectively, L1 is the constant vector, and P1 is the weight matrix.

[0089] Before adjustment, the initial three-dimensional coordinates of the connection points are obtained as input, and the spatial forward intersection model is used for solution. The spatial forward intersection model is as follows:

[0090]

[0091] For control points, the simplified error equation is expressed as:

[0092] V² = A²x + B²t² - L², P²

[0093] Where V2 represents the control point image point residual vector, t2 represents the control point three-dimensional coordinate correction matrix, A2 and B2 are the coefficient matrices corresponding to x and t2, L2 is the constant vector, and P2 is the weight matrix;

[0094] The SAR weak intersection regional network adjustment model requires changes to the error equations of the aforementioned connection points. The correction of the three-dimensional coordinates (Lat1, Lon1, Hei1) in the regional network adjustment model is changed to a correction of the two-dimensional plane coordinates (Lat1, Lon1). For obtaining the initial values ​​of the three-dimensional coordinates of the connection points, the solution of the three-dimensional coordinates (Lat1, Lon1, Hei1) in the spatial forward intersection model is also changed to a correction of the two-dimensional plane coordinates (Lat1, Lon1). A weak forward intersection model is established, and the elevation is interpolated using SRTM to iteratively solve for the initial values ​​of the three-dimensional coordinates of the connection points.

[0095] For control points in the SAR weak intersection area network adjustment model, they are treated as weighted observations, and the weighted observation error equation for the control points is established:

[0096]

[0097] Among them, V Lat V Lon V Hei This represents the ground coordinate residual value of the control point. This is an approximation of the control point value, which is the same as the control point value, meaning the last term of the error equation is zero.

[0098] The error equation simplifies to:

[0099] V3 = Et2 - L3, P3

[0100] Where E is the corresponding identity matrix, L3 is a constant vector, and P3 is the weight matrix;

[0101] Combining the above error equations for connection points, control points, and weighted observations of control points, the combined error equations are expressed as follows:

[0102] V = Ax + Bt - L, P

[0103]

[0104] Where V represents the residual vector, x and t are the affine transformation coefficients of each SAR image and the corrections of the three-dimensional spatial coordinates of the ground points, including two types: tie points and control points, A and B are the coefficient matrices of x and t, L is the constant vector, and P is the weight matrix.

[0105] Based on the principle of least squares adjustment, the above error equation is normalized, and the normal equation is expressed as follows:

[0106]

[0107] Where T represents the matrix transpose;

[0108] First, eliminate the unknown ground coordinate t, and then solve only for the affine transformation coefficient correction x for each SAR image. The modified normal equation is expressed as follows:

[0109] x = M -1 W

[0110] Where M = A T PA-A T PB(B T PB) -1 B T PA, W = A T PL-A T PB(B T PB) -1 B T PL;

[0111] Step S4.2: Based on the SAR weak intersection area network adjustment model and overall solution steps established in step S4.1, perform the solution; the specific steps are as follows:

[0112] The input data includes the pixel coordinates, ground coordinates, and Doppler displacement pixel deviation of the AIS control points, the pixel coordinates and initial ground coordinates of the SAR image's tie points, the SAR image's RPC parameters, and the SRTM elevation. The pixel coordinates, ground coordinates, and Doppler displacement pixel deviation of the AIS control points can be obtained through correlation matching in step S3. The pixel coordinates of the SAR image's tie points are obtained using an automatic matching algorithm or manually selected. The initial ground coordinates are obtained from the SAR weak intersection area network adjustment model in step S4.1. The SAR image's RPC parameters are obtained from the image's built-in .rpb file, and the SRTM elevation is obtained from an open-source 30m resolution SRTM. Interpolation is then performed to obtain finer grid data.

[0113] The affine transformation parameters are solved again based on the input and the modified normal equations until they stabilize. The solution is then stopped to obtain the affine transformation parameters and the three-dimensional coordinates of the tie points for each SAR image. Otherwise, the affine transformation corrections for each SAR image are obtained by solving the modified normal equations. The affine transformation parameters in the next input are then updated, and the object coordinates of the tie points are obtained based on the established weak forward intersection model and SRTM interpolation. These coordinates are then used as the initial values ​​for the next iteration.

[0114] Finally, based on the acquired affine transformation parameters, SAR images, RPC parameters, and SRTM elevation data, the SAR images are orthorectified to obtain the final overall positioning SAR images.

[0115] A SAR maritime target positioning system based on Doppler displacement estimation includes:

[0116] Acquisition module: Acquires AIS and SAR data required for positioning;

[0117] Doppler displacement deviation calculation module: Uses AIS data and SAR data to obtain Doppler displacement estimation parameters and calculates the Doppler displacement deviation. The Doppler displacement estimation parameters include radial velocity, closest slant range and equivalent radar velocity.

[0118] Same-name point pair matching module: After compensating for the Doppler displacement of the SAR target, the module uses the features of AIS data and SAR data and an association matching model to match the AIS and SAR targets to obtain the same-name point pairs required for final positioning.

[0119] The positioning module constructs a SAR weak intersection area network adjustment model that takes into account Doppler displacement error, and realizes the overall positioning of SAR images based on the corresponding point pairs and Doppler displacement deviation required for final positioning.

[0120] Furthermore, the specific implementation steps of the Doppler displacement deviation calculation module are as follows:

[0121] Step S2.1: Obtaining radial velocity and nearest slant distance

[0122] Based on the ground speed and heading from AIS data and the target incident angle from the synthetic aperture radar SAR image, the radial velocity of the moving target is obtained using the velocity projection formula:

[0123]

[0124] Among them, v r1 The radial velocity of the moving target is obtained based on the velocity projection formula. χ is a linear coefficient, which takes a value of 1 when the synthetic aperture radar is in ascending orbit mode and a value of -1 when it is in descending orbit mode. t Indicates the speed over ground. θ represents the angle between the ship's heading relative to the ground and the direction of distance to the image, and θ represents the magnitude of the target's incident angle in the SAR image;

[0125] By fitting the AIS trajectory from AIS data and the SAR satellite trajectory from SAR data, a tilt range function that varies between the two over time is constructed. The formula for the radial distance of the moving target, i.e., the tilt range function of the moving target, is as follows:

[0126]

[0127] Among them, R m (t) represents the tilt range of the moving target, (Δx) m (t),Δy m (t),Δz m(t) represents the distance between the moving vessel and the SAR platform in the three-dimensional x, y, and z directions;

[0128] Inclination range R of moving target m (t) Differentiating the derivative yields the radial velocity of the moving target at the imaging moment, which is the radial velocity v of the moving target relative to the SAR platform. rm (t);

[0129] At the same time, take R m The time when (t) reaches its minimum value is taken as the imaging center time of the moving target, denoted as t. c Minimum distance R m (t c This is the nearest slant distance R0 in the Doppler displacement parameters, and t c The ship's position at any given time is determined as the imaging position of a virtual stationary target, and the tilt range R between the virtual stationary target and the SAR platform is established. s (t), the formula for the radial distance of a stationary target is:

[0130]

[0131] Among them, R s (t) represents the tilt range of the virtual stationary target, (Δx) s (t),Δy s (t),Δz s (t) represents the distance between the virtual stationary ship and the SAR platform in the three-dimensional x, y, and z directions;

[0132] The tilt range R of the virtual stationary target s Differentiating (t) yields the radial velocity v of the stationary target relative to the SAR platform. rs (t);

[0133] Based on the obtained imaging center time t of the moving target c Subtracting the two radial velocities at this moment yields the increase in radial velocity v due to the motion of the moving target relative to the stationary target, based on the radial distance formula. r2 The formula is:

[0134] v r2 =v rm (t c )-v rs (t c )

[0135] The radial velocity v of the moving ship target was obtained using the velocity projection formula and the radial distance formula. r1 v r2 With the nearest slope distance R0;

[0136] Step S2.2: Obtaining the equivalent radar velocity

[0137] The center time t of the moving target imaging c The radial velocity v of the corresponding virtual stationary target rs (t) Take the derivative and obtain the equivalent radar velocity using the stationary target's acceleration and its frequency modulation at zero Doppler moment; the specific steps are as follows:

[0138] Synthetic Aperture Radar Actual Velocity v s The following relationship exists between the radar and the equivalent radar velocity v:

[0139]

[0140] Among them, v g The speed at which the synthetic aperture radar beam moves across the ground;

[0141] The frequency modulation of a stationary target at the zero Doppler moment is expressed as:

[0142]

[0143] Where v is the equivalent radar velocity, λ is the carrier wavelength of the synthetic aperture radar transmitted pulse, and R0 is the closest slant range;

[0144] According to t c The acceleration A of a stationary target at any given time s (t c ) and its zero Doppler time modulation frequency k a_SAR Correspondence:

[0145]

[0146] Thus, the equivalent radar velocity v can be calculated;

[0147] Step S2.3: Doppler displacement parameter check

[0148] The difference between the radial velocities obtained from the velocity projection formula and the radial distance formula is used as the first check item, and the difference between the ship's bearing velocity obtained from the velocity projection formula and the radial distance formula is used as the second check item.

[0149] For the ship's bearing velocity difference check item, in the velocity projection formula, it is transformed into calculating the ship's bearing velocity, and the formula is as follows:

[0150]

[0151] Among them, v x1 The azimuth velocity of the ship is obtained based on the velocity projection formula, where χ is the linear coefficient and v t Indicates the speed over ground. Indicates the angle between the ship's heading relative to the ground and the direction of the image distance;

[0152] The azimuth velocity of a ship can be calculated using the radial distance formula, i.e., based on the radial velocity v of the moving target. rs The derivative of (t) yields the acceleration A of the moving target. m Formula (t) utilizes the time t at the center of the moving target's imaging. c Corresponding acceleration A m (t c The ship's azimuth velocity is obtained by using its echo Doppler frequency modulation; the specific steps are as follows:

[0153] The Doppler modulation frequency of the moving target echo is expressed as:

[0154]

[0155] Where v is the radar equivalent velocity, v a R0 represents the velocity component along the track direction in the SAR slant range plane, λ is the carrier wavelength of the synthetic aperture radar transmitted pulse, and R0 is the closest slant range.

[0156] Also taking into account the effects of satellite orbit and Earth's rotation, the azimuth velocity v of a ship on the sea surface... x2 v in the slant distance plane a Existence Relationship: This results in the following Doppler frequency modulation transformation of the moving target echo:

[0157]

[0158] According to t c The acceleration A of the moving target at any given time m (t c ) and its echo Doppler modulation frequency k ad Correspondence:

[0159]

[0160] Based on the calculated A m (t c The ship's azimuth velocity v at the sea surface can be calculated by combining R0, the equivalent radar velocity v obtained in the previous step, and the equivalent radar velocity v. x2 This is compared with the ship's azimuth velocity v obtained by velocity projection. x1 By making a mistake, we obtain the second check item;

[0161] Based on multiple first check items and corresponding multiple second check items, AIS data with smaller values ​​for both the first and second check items are selected as the basis for subsequent SAR image geometric positioning. After the check, three Doppler displacement estimation parameters are obtained: radial velocity, nearest slant range, and equivalent radar velocity. The Doppler displacement deviation Δx caused by the target motion is obtained using the displacement formula. AIS data with larger values ​​for the two check items are discarded.

[0162]

[0163] In the formula, v r v corresponding to the first check item after the check r2 .

[0164] Furthermore, the specific implementation steps of the same-name point pair matching module are as follows:

[0165] Step S3.1: Obtain the features of SAR and AIS data: SAR data consists of ship SAR traces. Feature extraction is performed on the detected ship targets. The extracted features include target position information, ship length, ship width, heading, and ship speed estimated based on the ship's wake. AIS data consists of ship AIS traces, including static and dynamic information of the ship target, specifically including position information, ship length, ship width, speed, and heading.

[0166] Step S3.2: Select the same features in AIS data and SAR data, and associate them through the association matching model to obtain the corresponding point pairs required for positioning. Optimize the AIS control points in the corresponding point pairs that meet the check items. That is, use the specific location of the GPS antenna provided by AIS in the ship to transform the ship's GPS antenna position to the center of the ship to obtain the final corresponding point pairs required for positioning. The association matching model is based on the latitude and longitude location information of both AIS data and SAR data as the association attribute features.

[0167] The specific steps for obtaining the required pairs of identically named points for location by using an association matching model are as follows:

[0168] First, perform temporal and spatial calibration on the shared features in the selected AIS and SAR data to obtain the necessary point data for association, specifically:

[0169] Based on the imaging time of the center of a single SAR image, data from AIS data within five minutes before and after this time are acquired. The data is sorted and classified by the ship identification number and timestamp of all ships' AIS data within the range of the acquired single SAR image. That is, AIS data is classified according to ship identification number, and data of each category is sorted and stored according to timestamp.

[0170] Next, using the sorted and classified stored ship AIS data and the Doppler displacement estimation method, the zero Doppler time and corresponding latitude and longitude coordinates of each ship are obtained. Then, inverse Doppler displacement compensation is performed to transform the AIS ship latitude and longitude to the SAR image position to obtain the latitude and longitude after inverse displacement compensation. This is used as the standard point data associated with AIS, that is, the AIS latitude and longitude coordinates are obtained.

[0171] Before association matching, for SAR images, Mercator projection is performed using the provided initial RPC parameters and elevation data provided by ENVI. After target detection, the planar coordinates of SAR ship targets are obtained.

[0172] Convert AIS latitude and longitude coordinates to Mercator projection plane coordinates to achieve temporal and spatial registration of SAR and AIS data;

[0173] Then, based on the time- and space-registered data, the associated matching point data is obtained using an association matching model. The association matching model is a global nearest neighbor association matching model, which is expressed as follows:

[0174]

[0175] Where k represents the total association cost, and the best match is achieved when the total association cost is minimized. ij A binary function that is either 0 or 1. When it is 1, it indicates that the i-th AIS track is associated with the j-th SAR track; when it is 0, it indicates that they are not associated. ij The substitution value is calculated from the Euclidean distance between AIS data and SAR data, where m and n are the maximum values ​​of i and j, respectively.

[0176] The cost matrix is ​​obtained by combining the cost values, and global minimum distance point matching is performed based on the cost matrix. When the distance between the associated points is within the judgment threshold, the point association is successful and the association result is saved. Otherwise, the association fails and the point pair is deleted to obtain the correct AIS and SAR positioning corresponding point pairs, including the latitude and longitude coordinates of the ship center point corresponding to the AIS and the image point coordinates of the ship center in the SAR image. The latitude and longitude coordinates of the ship center point corresponding to the AIS are the object control points of the AIS, and the image point coordinates of the ship center in the SAR image are the image control points of the AIS.

[0177] Furthermore, the specific implementation steps of the positioning module are as follows:

[0178] Step S4.1: Construct a SAR weak intersection area network adjustment model that takes into account Doppler displacement error. The SAR weak intersection area network adjustment model is a rational function model with additional parameters. Affine transformation is used as the model for image-side compensation to optimize the rational function model. The parameters to be solved include the affine transformation coefficients in the six affine transformations of the SAR image and the ground three-dimensional coordinates of the connection points.

[0179] The affine transformation model is as follows:

[0180]

[0181] In the formula, (Δc0, Δr0) represents the difference between the measured coordinates of the image point and the coordinates calculated by the rational function model; a0, b0, a1, a2, b1, b2 are affine transformation coefficients; a0, b0 are the image-side coordinate translation parameters in the SAR image; and a1, a2, b1, b2 are the scaling coefficients of the image-side coordinates in the SAR image. Measure the coordinates of image points in SAR images;

[0182] In the affine transformation model, the Doppler displacement bias Δx obtained in step S2 is added to the azimuth direction to compensate for the Doppler displacement error of the SAR moving target. The azimuth displacement of the moving target, i.e., the Doppler displacement bias Δx, is obtained from the Doppler displacement parameters, and is further calculated from the azimuth resolution x of the SAR image. res The azimuth deviation of the moving target in the image direction is obtained as follows: The affine transformation model changes as follows:

[0183]

[0184] Using an affine transformation model that takes into account Doppler displacement error and an RFM model of the image to be adjusted, a regional network adjustment model is established:

[0185]

[0186] Where (c,r) are the coordinates of the image point in the SAR image calculated by the rational function model, and ε L ,ε S Let (Lat, Lon, Hei) be the random error in the SAR image, and (Lat, Lon, Hei) be the three-dimensional spatial coordinates of the ground point, including two types: tie points and control points, which are represented by (Lat1, Lon1, Hei1) and (Lat2, Lon2, Hei2) respectively.

[0187] Substituting the varying affine transformation model (Δc, Δr) into the above regional network adjustment model, the error equation is expanded as follows:

[0188]

[0189] For each SAR tie point and the optimized AIS control point, the corresponding error equation is obtained from the above formula:

[0190]

[0191] Among them, V L V SThis represents the column and row residual values ​​of the image point coordinates for SAR tie points and AIS control points. Δa0, Δa1, Δa2, Δb0, Δb1, and Δb2 are the affine transformation coefficient corrections for each SAR image scene, and (ΔLat, ΔLon, ΔHei) are the three-dimensional spatial coordinate corrections for the ground points. It also includes tie points and control points, with each tie point and control point represented by (ΔLat1, ΔLon1, ΔHei1) and (ΔLat2, ΔLon2, ΔHei2), respectively. The partial derivative symbol F represents taking the partial derivative with respect to each parameter. L0 and F S0 When taking an initial value for an unknown, F L and F S The optimized AIS control points include the optimized AIS object control points and the optimized AIS image control points.

[0192] For the connection points, the error equation matrix simplifies to:

[0193] V1=A1x+B1t1-L1,P1

[0194] Where V1 represents the residual vector of the image point of the connection point, x and t1 are the correction matrices of the affine transformation coefficients and the three-dimensional coordinate correction matrices of the connection point for each SAR image, A1 and B1 are the coefficient matrices of x and t1 respectively, L1 is the constant vector, and P1 is the weight matrix.

[0195] Before adjustment, the initial three-dimensional coordinates of the connection points are obtained as input, and the spatial forward intersection model is used for solution. The spatial forward intersection model is as follows:

[0196]

[0197] For control points, the simplified error equation is expressed as:

[0198] V² = A²x + B²t² - L², P²

[0199] Where V2 represents the control point image point residual vector, t2 represents the control point three-dimensional coordinate correction matrix, A2 and B2 are the coefficient matrices corresponding to x and t2, L2 is the constant vector, and P2 is the weight matrix;

[0200] The SAR weak intersection regional network adjustment model requires changes to the error equations of the aforementioned connection points. The correction of the three-dimensional coordinates (Lat1, Lon1, Hei1) in the regional network adjustment model is changed to a correction of the two-dimensional plane coordinates (Lat1, Lon1). For obtaining the initial values ​​of the three-dimensional coordinates of the connection points, the solution of the three-dimensional coordinates (Lat1, Lon1, Hei1) in the spatial forward intersection model is also changed to a correction of the two-dimensional plane coordinates (Lat1, Lon1). A weak forward intersection model is established, and the elevation is interpolated using SRTM to iteratively solve for the initial values ​​of the three-dimensional coordinates of the connection points.

[0201] For control points in the SAR weak intersection area network adjustment model, they are treated as weighted observations, and the weighted observation error equation for the control points is established:

[0202]

[0203] Among them, V Lat V Lon V Hei This represents the ground coordinate residual value of the control point. This is an approximation of the control point value, which is the same as the control point value, meaning the last term of the error equation is zero.

[0204] The error equation simplifies to:

[0205] V3 = Et2 - L3, P3

[0206] Where E is the corresponding identity matrix, L3 is a constant vector, and P3 is the weight matrix;

[0207] Combining the above error equations for connection points, control points, and weighted observations of control points, the combined error equations are expressed as follows:

[0208] V = Ax + Bt - L, P

[0209]

[0210] Where V represents the residual vector, x and t are the affine transformation coefficients of each SAR image and the corrections of the three-dimensional spatial coordinates of the ground points, including two types: tie points and control points, A and B are the coefficient matrices of x and t, L is the constant vector, and P is the weight matrix.

[0211] Based on the principle of least squares adjustment, the above error equation is normalized, and the normal equation is expressed as follows:

[0212]

[0213] Where T represents the matrix transpose;

[0214] First, eliminate the unknown ground coordinate t, and then solve only for the affine transformation coefficient correction x for each SAR image. The modified normal equation is expressed as follows:

[0215] x = M -1 W

[0216] Where M = A T PA-A T PB(B T PB) -1 B T PA, W = A T PL-A T PB(B T PB) -1 B T PL;

[0217] Step S4.2: Based on the SAR weak intersection area network adjustment model and overall solution steps established in step S4.1, perform the solution; the specific steps are as follows:

[0218] The input data includes the pixel coordinates, ground coordinates, and Doppler displacement pixel deviation of the AIS control points, the pixel coordinates and initial ground coordinates of the SAR image's tie points, the SAR image's RPC parameters, and the SRTM elevation. The pixel coordinates, ground coordinates, and Doppler displacement pixel deviation of the AIS control points can be obtained through correlation matching in step S3. The pixel coordinates of the SAR image's tie points are obtained using an automatic matching algorithm or manually selected. The initial ground coordinates are obtained from the SAR weak intersection area network adjustment model in step S4.1. The SAR image's RPC parameters are obtained from the image's built-in .rpb file, and the SRTM elevation is obtained from an open-source 30m resolution SRTM. Interpolation is then performed to obtain finer grid data.

[0219] The affine transformation parameters are solved again based on the input and the modified normal equations until they stabilize. The solution is then stopped to obtain the affine transformation parameters and the three-dimensional coordinates of the tie points for each SAR image. Otherwise, the affine transformation corrections for each SAR image are obtained by solving the modified normal equations. The affine transformation parameters in the next input are then updated, and the object coordinates of the tie points are obtained based on the established weak forward intersection model and SRTM interpolation. These coordinates are then used as the initial values ​​for the next iteration.

[0220] Finally, based on the acquired affine transformation parameters, SAR images, RPC parameters, and SRTM elevation data, the SAR images are orthorectified to obtain the final overall positioning SAR images.

[0221] Compared with the prior art, the advantages of the present invention are as follows:

[0222] I. This invention utilizes AIS and SAR data to accurately acquire the Doppler displacement parameters of moving targets: radial velocity, closest slant range, and equivalent radar velocity, thereby restoring the position of moving targets in SAR imagery. Based on Doppler displacement compensation, corresponding AIS and SAR point pairs for positioning are obtained through correlation matching. Finally, a weak intersection area network adjustment model that takes into account Doppler displacement errors is established, and differentially positioned AIS points are used as control information, thereby improving the positioning accuracy of SAR images in the sea area and providing a reference for wide-area ship target surveillance and positioning using SAR imagery.

[0223] II. The present invention provides a method for locating maritime targets using SAR. Existing technologies mainly rely on high-precision control points on land for image correction and positioning, but there are no effective control points in the sea area. Therefore, it is difficult to implement traditional methods for locating ships in the sea area. Attached Figure Description

[0224] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0225] Figure 1 This is a schematic diagram of the process of the present invention;

[0226] Figure 2 This is a schematic diagram of the Doppler displacement deviation estimation results of the present invention;

[0227] Figure 3 The diagram shows the correlation results after Doppler displacement compensation according to the present invention. (a) shows the correlation results before displacement compensation and its partial enlarged view, and (b) shows the correlation results after displacement compensation and its partial enlarged view.

[0228] Figure 4 The diagram shows the adjustment results of the SAR weak intersection area network on the Gaofen-3 SAR image according to the present invention. (a) is the error distribution map of the uncontrolled adjustment, (b) is the error distribution map of the one-point adjustment of the translation model, (c) is the error distribution map of the four-point adjustment of the linear model, and (d) is the error distribution map of the four-point adjustment of the affine transformation model. Detailed Implementation

[0229] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0230] This invention first utilizes joint processing of AIS and SAR data to obtain three Doppler displacement estimation parameters: radial velocity, nearest slant range, and equivalent radar velocity. This addresses the inaccuracy of displacement parameters in traditional Doppler displacement estimation methods. The displacement formula effectively compensates for Doppler displacement deviations in SAR-driven vessels. Simultaneously, based on positional features and a correlation model, AIS and SAR targets are correlated and matched to obtain dynamic corresponding point pairs required for maritime image positioning. Furthermore, traditional regional network adjustment models often use stereo image pairs with large intersection angles. Direct calculation in common processing of adjacent images on the same track or adjacent images on different tracks with the same direction can cause elevation anomalies and model non-convergence. Therefore, this invention, based on dynamic AIS control information and Doppler displacement parameters, constructs a SAR weak intersection regional network adjustment model that considers Doppler displacement errors. SRTM elevation is interpolated as a known value, resolving the aforementioned non-convergence problem. Subsequently, based on AIS data, the overall positioning accuracy of SAR images is improved, providing a reference for maritime target positioning.

[0231] The basic idea of ​​this invention is as follows: First, a method for solving the Doppler displacement estimation parameters of SAR moving targets is constructed to obtain three important parameters: radial velocity, nearest slant range, and equivalent radar velocity, in order to obtain the displacement deviation value. Then, after Doppler displacement compensation of moving targets in SAR images, AIS and SAR targets are matched based on positional features and correlation models to obtain the corresponding point pairs required for image positioning. Finally, a SAR weak intersection area network adjustment model that takes into account Doppler displacement error is constructed, and AIS control points are added to the model as weighted observations to improve the overall positioning accuracy of SAR images based on AIS.

[0232] A SAR maritime target localization method based on Doppler displacement estimation includes the following steps:

[0233] A SAR maritime target localization method based on Doppler displacement estimation, characterized by the following steps:

[0234] S1. Obtain the AIS and SAR data required for positioning;

[0235] S2. Obtain Doppler displacement estimation parameters using AIS and SAR data, and calculate the Doppler displacement deviation. The Doppler displacement estimation parameters include radial velocity, closest slant range, and equivalent radar velocity.

[0236] The specific steps are as follows:

[0237] Step S2.1: Obtaining radial velocity and nearest slant distance

[0238] Automatic Identification System (AIS) can provide dynamic information such as ship track, ground speed, and ground heading, as well as static information such as ship size, type, and identification number. Based on the ground speed and ground heading from AIS data and the target incident angle from the synthetic aperture radar (SAR) image, the radial velocity of the moving target is obtained using a velocity projection formula:

[0239]

[0240] Among them, v r1 The radial velocity of the moving target is obtained based on the velocity projection formula. χ is a linear coefficient, which takes a value of 1 when the synthetic aperture radar is in ascending orbit mode and a value of -1 when it is in descending orbit mode. t Indicates the speed over ground. θ represents the angle between the ship's heading relative to the ground and the direction of the image distance, and θ represents the magnitude of the target's incident angle in the SAR image;

[0241] By fitting data to AIS and SAR satellite trajectories, a tilt range function that varies between the two over time is constructed. The formula for the radial distance of the moving target, i.e., the tilt range function of the moving target, is as follows:

[0242]

[0243] Among them, R m (t) represents the tilt range of the moving target, (Δx) m (t),Δy m (t),Δz m (t) represents the distance between the moving vessel and the SAR platform in the three-dimensional x, y, and z directions;

[0244] Inclination range R of moving target m Differentiating (t) yields the radial velocity v of the moving target relative to the SAR platform. rm (t). Meanwhile, take R. m The time when (t) reaches its minimum value is taken as the imaging center time of the moving target, denoted as t. c Minimum distance R m (t c This is the nearest slant distance R0 in the Doppler displacement parameters. And t... cThe ship's position at any given time is determined as the imaging position of a virtual stationary target. Following the same approach, the tilt range R between the virtual stationary target and the SAR platform is established. s (t). The formula for the radial distance of a stationary target is:

[0245]

[0246] Among them, R s (t) represents the tilt range of the virtual stationary target, (Δx) s (t),Δy s (t),Δz s (t) represents the distance between the virtual stationary ship and the SAR platform in the three-dimensional x, y, and z directions;

[0247] Similarly, the tilt range R of the virtual stationary target s Differentiating (t) yields the radial velocity v of the stationary target relative to the SAR platform. rs (t). Based on the obtained imaging center time t of the moving target. c Subtracting the two radial velocities at this moment yields the increase in radial velocity v due to the target's motion relative to the stationary target. r2 The formula is:

[0248] v r2 =v rm (t c )-v rs (t c )

[0249] The radial velocity v of the moving ship target was obtained using the velocity projection formula and the radial distance formula. r1 v r2 With the nearest slope distance R0;

[0250] Step S2.2: Obtaining the equivalent radar velocity

[0251] For radar velocity in the Doppler displacement parameters, directly using the actual velocity of the radar platform will introduce some error, affecting the accuracy of displacement estimation. The time t of the moving target imaging center... c The radial velocity v of the corresponding virtual stationary target rs (t) Take the derivative and obtain the equivalent radar velocity using the stationary target's acceleration and its frequency modulation at zero Doppler moment; the specific steps are as follows:

[0252] The actual speed of the radar v s The following relationship exists between the radar and the equivalent radar velocity v:

[0253]

[0254] Among them, v gLet v be the speed at which the radar beam moves across the ground. In spaceborne SAR systems, the radar platform speed v is affected by the satellite orbit and the Earth's rotation. s and the speed v of the radar beam on the ground g They are not the same. The radar equivalent velocity v is a virtual equivalent parameter with a magnitude between the two, which can simplify the curved geometric model of the spaceborne SAR system to the straight-line model of the airborne radar, thus simplifying the model.

[0255] The frequency modulation of the stationary target at zero Doppler time can be expressed as:

[0256]

[0257] Where v is the radar equivalent velocity, λ is the carrier wavelength of the radar transmitted pulse, and R0 is the closest slant range.

[0258] According to t c The acceleration A of a stationary target at any given time s (t c ) and its zero Doppler time modulation frequency k a_SAR Correspondence:

[0259]

[0260] Thus, the equivalent radar velocity v can be calculated;

[0261] Step S2.3: Doppler displacement parameter check

[0262] To ensure the accuracy of the obtained Doppler displacement parameters, the difference between the radial velocities obtained from the velocity projection formula and the radial distance formula is used as the first check item, and the difference between the ship's azimuth velocity obtained from the velocity projection formula and the radial distance formula is used as the second check item. The radial velocity difference check item can be calculated directly; the ship's azimuth velocity difference check item is obtained by transforming the velocity projection formula into a calculation of the azimuth velocity.

[0263]

[0264] Among them, v x1 The azimuth velocity of the ship is obtained based on the velocity projection formula, where χ is the linear coefficient and v t Indicates the speed over ground. Indicates the angle between the ship's heading relative to the ground and the direction of the image distance;

[0265] The method for determining a ship's azimuth velocity using radial distance is specifically expressed as follows:

[0266] The azimuth velocity of a ship can be calculated using the radial distance formula, i.e., based on the radial velocity v of the moving target. rs The derivative of (t) yields the acceleration A of the moving target.m Formula (t) utilizes the time t at the center of the moving target's imaging. c Corresponding acceleration A m (t c The ship's azimuth velocity is obtained by using its echo Doppler frequency modulation; the specific steps are as follows:

[0267] The echo Doppler modulation frequency of the moving target is expressed as:

[0268]

[0269] Where v is the radar equivalent velocity, v a Let λ be the velocity component along the track direction in the SAR slant range plane, λ be the carrier wavelength of the radar transmitted pulse, and R0 be the closest slant range. The ship's azimuth velocity v at the sea surface. x2 v in the slant distance plane a Existence Relationship: This results in the following Doppler frequency modulation transformation of the moving target echo:

[0270]

[0271] According to t c The acceleration A of the moving target at any given time m (t c ) and its echo Doppler modulation frequency k ad Correspondence:

[0272]

[0273] Based on the calculated A m (t c The ship's azimuth velocity v at the sea surface can be calculated by combining R0, the equivalent radar velocity v obtained in the previous step, and the equivalent radar velocity v. x2 This is compared with the ship's azimuth velocity v obtained by velocity projection. x1 By making a mistake, we obtain the second check item;

[0274] Based on multiple first check items and corresponding multiple second check items, AIS data with smaller values ​​for both the first and second check items are selected as the basis for subsequent SAR image geometric positioning. After the check, three Doppler displacement estimation parameters are obtained: radial velocity, nearest slant range, and equivalent radar velocity. The Doppler displacement deviation Δx caused by the target motion is obtained using the displacement formula. AIS data with larger values ​​for the two check items are discarded.

[0275]

[0276] In the formula, v r v corresponding to the first check item after the check r2 .

[0277] like Figure 2 As shown, after Doppler displacement correction, the transformed GPS antenna position of the ship can be well aligned with the hull. Meanwhile, in the first three images, the calculated radial velocity difference of the ship is below 0.1 m / s, and the azimuth velocity difference is around 0.1 m / s. These small differences indicate the ship is closer to the hull center, suggesting a relatively stable ship operation and high AIS data quality; therefore, this data is used for subsequent positioning. In the fourth image, the transformed GPS antenna position is at the edge of the hull. Analysis shows a radial velocity difference of 0.402 m / s and an azimuth velocity difference of 1.523 m / s. These errors are significantly larger than in the first three images, indicating lower AIS data quality. Therefore, this type of data is discarded and not used for subsequent positioning.

[0278] S3. After compensating for the Doppler displacement of the SAR target, based on the characteristics of AIS data and SAR data, and through the association matching model, the AIS and SAR targets are associated and matched to obtain the corresponding point pairs required for the final positioning.

[0279] Association matching mainly includes two parts: association feature acquisition and point-track association matching. The association feature acquisition primarily aims to obtain preferred features that facilitate successful matching between AIS and SAR targets. Features include location features, ship length, ship width, speed, and heading. AIS points contain relatively comprehensive static and dynamic target information, all of which are included in the aforementioned features. For SAR imagery, after detecting the ship target, information can be extracted, mainly including target location information, ship length, ship width, heading, and ship speed estimated based on the ship's wake. The same features from AIS and SAR are selected for association; the more association feature attributes obtained, the more accurate the association result. Considering that most commonly used association matching models are based on location features, the latitude and longitude location information of both are used as association attribute features during association. The specific steps are as follows:

[0280] Step S3.1: Obtain the features of SAR and AIS data: SAR data consists of ship SAR traces. Feature extraction is performed on the detected ship targets. The extracted features include target position information, ship length, ship width, heading, and ship speed estimated based on the ship's wake. AIS data consists of ship AIS traces, including static and dynamic information of the ship target, specifically including position information, ship length, ship width, speed, and heading.

[0281] Step S3.2: Select the same features in AIS data and SAR data, and associate them through the association matching model to obtain the corresponding point pairs required for positioning. Optimize the AIS control points in the corresponding point pairs that meet the check items. That is, use the specific location of the GPS antenna provided by AIS in the ship to transform the ship's GPS antenna position to the center of the ship to obtain the final corresponding point pairs required for positioning. The association matching model is based on the latitude and longitude location information of both AIS data and SAR data as the association attribute features.

[0282] The point association matching involves obtaining matching features and then using an association model to find corresponding point pairs between AIS and SAR. The specific processing steps are as follows:

[0283] First, the AIS tracks and SAR data are calibrated temporally and spatially to obtain the necessary point data for correlation. This is based on the SAR imaging center time, specifically:

[0284] Based on the imaging time of the center of a single SAR image, data from AIS within five minutes before and after this time is obtained to reduce the amount of data. The data is then sorted and classified and stored using the ship identification number (MISS) and timestamp.

[0285] Next, using the sorted and classified stored ship AIS data and the Doppler displacement estimation method, the zero Doppler time and corresponding latitude and longitude coordinates of each ship are obtained. Then, inverse Doppler displacement compensation is performed to transform the AIS ship latitude and longitude to the SAR image position to obtain the latitude and longitude after inverse displacement compensation. This is used as the standard point data associated with AIS, that is, the AIS latitude and longitude coordinates are obtained.

[0286] Before association matching, for SAR images, Mercator projection is performed using the provided initial RPC parameters and elevation data provided by ENVI. After target detection, the planar coordinates of SAR ship targets are obtained.

[0287] Convert AIS latitude and longitude coordinates to Mercator projection plane coordinates to achieve temporal and spatial registration of SAR and AIS data;

[0288] Then, based on the time- and space-registered data, the Global Nearest Neighbor (GNN) association model is used to obtain the associated matching point data. The GNN model is represented as follows:

[0289]

[0290] Where k represents the total association cost, and the best match is achieved when the total association cost is minimized. ij A binary function that is either 0 or 1. When it is 1, it indicates that the i-th AIS track is associated with the j-th SAR track; when it is 0, it indicates that they are not associated. ijThe substitution value is calculated from the Euclidean distance between AIS data and SAR data, where m and n are the maximum values ​​of i and j, respectively.

[0291] The cost matrix is ​​constructed by combining cost values, and global minimum distance point matching is performed based on the cost matrix. When the distance between associated points is within a judgment threshold, the point association is successful, and the association result is saved; otherwise, the association fails, and the point pair is deleted. This process yields the correct pair of points with the same name required for AIS and SAR positioning, including the latitude and longitude coordinates of the ship's center point corresponding to the AIS and the image point coordinates of the ship's center in the SAR image. The latitude and longitude coordinates of the ship's center point corresponding to the AIS are the object control points of the AIS, and the image point coordinates of the ship's center in the SAR image are the image control points of the AIS. Figure 3 As shown, the theoretical number of correct matches for the entire map should be 18 pairs. Before Doppler displacement compensation, the number of successful associations for global nearest neighbors was 15 pairs, and after displacement compensation, the number of successful associations increased to 17 pairs. When performing association matching for dense SAR targets based on location features, Doppler displacement compensation can reduce the initial position deviation of moving targets, thereby improving the association success rate and obtaining more correct corresponding point pairs.

[0292] S4. Construct a SAR weak intersection area network adjustment model that takes into account Doppler displacement error, and realize the overall positioning of SAR images based on the corresponding point pairs and Doppler displacement deviation required for final positioning.

[0293] The specific steps are as follows:

[0294] Step S4.1: Construct a SAR weak intersection network adjustment model that takes into account Doppler displacement errors. The SAR weak intersection network adjustment model is a rational function model with additional parameters. Affine transformation is used as the model for image-side compensation to optimize the rational function model. The parameters to be solved include the six affine transformation parameters of the image and the three-dimensional ground coordinates of the tie points.

[0295] The affine transformation model is as follows:

[0296]

[0297] In the formula, (Δc0, Δr0) represents the difference between the measured coordinates of the image point and the coordinates calculated by the rational function model; a0, b0, a1, a2, b1, b2 are affine transformation coefficients; a0, b0 are the image-side coordinate translation parameters in the SAR image; and a1, a2, b1, b2 are the scaling coefficients of the image-side coordinates in the SAR image. Measure the coordinates of image points in SAR images;

[0298] In the affine transformation model, a Doppler displacement bias is added in the azimuth direction to compensate for the Doppler displacement error of the SAR moving target. The azimuth displacement of the moving target, i.e., the Doppler displacement bias Δx, is obtained from the Doppler displacement parameters, and then converted to the azimuth resolution x of the SAR image. res The azimuth deviation of the moving target in the image is obtained as follows: The affine transformation model changes as follows:

[0299]

[0300] Using an affine transformation model that takes into account Doppler displacement error and an RFM model of the image to be adjusted, a regional network adjustment model is established:

[0301]

[0302] Where (c,r) are the coordinates of the image point in the SAR image calculated by the rational function model, and ε L ,ε S Let (Lat, Lon, Hei) be the random error in the SAR image, and (Lat, Lon, Hei) be the three-dimensional spatial coordinates of the ground point, including two types: tie points and control points, which are represented by (Lat1, Lon1, Hei1) and (Lat2, Lon2, Hei2) respectively.

[0303] Substituting the varying affine transformation model (Δc, Δr) into the above regional network adjustment model, the error equation is expanded as follows:

[0304]

[0305] For each SAR tie point and the optimized AIS control point, the corresponding error equation is obtained from the above formula:

[0306]

[0307] Among them, V L V S This represents the column and row residual values ​​of the image point coordinates for SAR tie points and AIS control points. Δa0, Δa1, Δa2, Δb0, Δb1, and Δb2 are the affine transformation coefficient corrections for each SAR image scene, and (ΔLat, ΔLon, ΔHei) are the three-dimensional spatial coordinate corrections for the ground points. It also includes tie points and control points, with each tie point and control point represented by (ΔLat1, ΔLon1, ΔHei1) and (ΔLat2, ΔLon2, ΔHei2), respectively. The partial derivative symbol F represents taking the partial derivative with respect to each parameter. L0 and F S0 When taking an initial value for an unknown, F L and F SThe optimized AIS control points include the optimized AIS object control points and the optimized AIS image control points.

[0308] For the connection points, the error equation matrix simplifies to:

[0309] V1=A1x+B1t1-L1,P1

[0310] Where V1 represents the residual vector of the image point of the connection point, x and t1 are the affine transformation coefficient correction matrix and the three-dimensional coordinate correction matrix of the connection point for each SAR image, c1 and B1 are the coefficient matrices of x and t1 respectively, L1 is the constant vector, and P1 is the weight matrix.

[0311] Before adjustment, the initial three-dimensional coordinates of the connection points are obtained as input, and the spatial forward intersection model is used for solution. The spatial forward intersection model is as follows:

[0312]

[0313] For control points, the simplified error equation is expressed as:

[0314] V² = A²x + B²t² - L², P²

[0315] Where V2 represents the control point image point residual vector, t2 represents the control point three-dimensional coordinate correction matrix, A2 and B2 are the coefficient matrices corresponding to x and t2, L2 is the constant vector, and P2 is the weight matrix;

[0316] For weakly intersected images with an intersection angle of less than 10°, such as adjacent images on the same track and images on adjacent tracks with the same direction, directly using the above-mentioned traditional regional network error equation will result in abnormal solution of the object coordinate elevation values ​​of the connection points and non-convergence of the adjustment results. It is necessary to establish an adjustment model suitable for weakly intersected images.

[0317] The SAR weak intersection regional network adjustment model requires changes to the error equations of the aforementioned connection points. The correction of the three-dimensional coordinates (Lat1, Lon1, Hei1) in the regional network adjustment model is changed to a correction of the two-dimensional plane coordinates (Lat1, Lon1). For obtaining the initial values ​​of the three-dimensional coordinates of the connection points, the solution of the three-dimensional coordinates (Lat1, Lon1, Hei1) in the spatial forward intersection model is also changed to a correction of the two-dimensional plane coordinates (Lat1, Lon1). A weak forward intersection model is established, and the elevation is interpolated using SRTM to iteratively solve for the initial values ​​of the three-dimensional coordinates of the connection points.

[0318] For control points in the SAR weak intersection area network adjustment model, they are treated as weighted observations, and the weighted observation error equation for the control points is established:

[0319]

[0320] Among them, V Lat V Lon V Hei This represents the ground coordinate residual value of the control point. This is an approximation of the control point value, which is the same as the control point value, meaning the last term of the error equation is zero.

[0321] The error equation simplifies to:

[0322] V3 = Et2 - L3, P3

[0323] Where E is the corresponding identity matrix, L3 is a constant vector, and P3 is the weight matrix;

[0324] Combining the above error equations for connection points, control points, and weighted observations of control points, the combined error equations are expressed as follows:

[0325] V = Ax + Bt - L, P

[0326]

[0327] Where V represents the residual vector, x and t are the affine transformation coefficients of each SAR image and the corrections of the three-dimensional spatial coordinates of the ground points, including two types: tie points and control points, A and B are the coefficient matrices of x and t, L is the constant vector, and P is the weight matrix.

[0328] Based on the principle of least squares adjustment, the above error equation is normalized, and the normal equation is expressed as follows:

[0329]

[0330] Where T represents the matrix transpose;

[0331] First, eliminate the unknown ground coordinate t, and then solve only for the affine transformation coefficient correction x for each SAR image. The modified normal equation is expressed as follows:

[0332] x = M -1 W

[0333] Where M = A T PA-A T PB(B T PB) -1 B T PA, W = A T PL-A T PB(B T PB) -1 B T PL;

[0334] Step S4.2: Based on the SAR weak intersection area network adjustment model and overall solution steps established in step S4.1, perform the solution; the specific steps are as follows:

[0335] The input data includes the pixel coordinates, ground coordinates, and Doppler displacement pixel deviation of the AIS control points, the pixel coordinates and initial ground coordinates of the SAR image's tie points, the SAR image's RPC parameters, and the SRTM elevation. The pixel coordinates, ground coordinates, and Doppler displacement pixel deviation of the AIS control points can be obtained through correlation matching in step S3. The pixel coordinates of the SAR image's tie points are obtained using an automatic matching algorithm or manually selected. The initial ground coordinates are obtained from the SAR weak intersection area network adjustment model in step S4.1. The SAR image's RPC parameters are obtained from the image's built-in .rpb file, and the SRTM elevation is obtained from an open-source 30m resolution SRTM. Interpolation is then performed to obtain finer grid data.

[0336] The affine transformation parameters are solved again based on the input and the modified normal equations until they stabilize. The solution is then stopped to obtain the affine transformation parameters and the three-dimensional coordinates of the tie points for each SAR image. Otherwise, the affine transformation corrections for each SAR image are obtained by solving the modified normal equations. The affine transformation parameters in the next input are then updated, and the object coordinates of the tie points are obtained based on the established weak forward intersection model and SRTM interpolation. These coordinates are then used as the initial values ​​for the next iteration.

[0337] Finally, based on the acquired affine transformation parameters, SAR images, RPC parameters, and SRTM elevation data, the SAR images are orthorectified to obtain the final overall positioning SAR images.

[0338] To evaluate the effectiveness of the method of this invention, experiments were conducted on Gaofen-3 QPSI imagery. The imagery consisted of two adjacent images with the same orbital direction and an image intersection angle of 3.3779°. Simultaneously, AIS data corresponding to the images was acquired. During the experiment, DGPS data with high positioning accuracy from the AIS was selected, and Doppler displacement parameters were estimated based on the steps described above. AIS and SAR corresponding point pairs suitable for positioning were also acquired. Finally, based on the established SAR weak intersection area network adjustment model, the affine transformation parameters of the images and the coordinates of the tie points were obtained, and the accuracy was checked based on Google measurement point data.

[0339] The experimental results are shown in Table 1. The table statistically analyzes the connection point errors in uncontrolled adjustment, one-point adjustment using the translation model, four-point adjustment using the linear model, and four-point adjustment using the affine transformation model. It can be seen that in the uncontrolled adjustment, the plane error of the connection points is approximately 33m, and the elevation error is approximately 5m, indicating that directly using image RPC for adjustment has a large error. Using the translation model with one control point for positioning, the plane accuracy is 20.14m, a significant improvement over the initial positioning result, while the elevation accuracy is 3.515m, a smaller improvement. The linear model, using four evenly distributed control points, achieves a plane accuracy of 15.743m, an improvement of about 4m compared to the translation model. The affine transformation model, also using four control points, has better positioning performance because it simultaneously considers the translation, scaling, and rotation errors of the image, achieving a plane accuracy of 15.46m and an elevation accuracy of 3.465m. The above experiments show that the affine transformation model has better performance and higher positioning accuracy than the other two models. It also shows that the AIS position under DGPS positioning has high accuracy. Using it as a control point and using the Doppler displacement compensation weak intersection area network adjustment model for geometric positioning can improve the positioning accuracy of SAR images to a certain extent.

[0340] Table 1 Comparison of AIS control point positioning accuracy in GF-3 imagery.

[0341]

[0342] Figure 4 This is a schematic diagram of the adjustment results of weak intersection network on Gaofen-3 SAR imagery according to the present invention. Figure 4 (a) is a diagram showing the error distribution of uncontrolled adjustment. Figure 4 (b) is a diagram showing the adjustment error distribution at one point of the translation model. Figure 4 (c) is a four-point adjustment error distribution diagram of the linear model. Figure 4 (d) shows the error distribution of the four-point adjustment of the affine transformation model. As can be seen from the figure, under no-control conditions, the plane errors of the connection points uniformly point to the lower left, exhibiting systematic errors. When AIS control points are added, as shown... Figure 4 (d) The systematic error was corrected to a certain extent.

[0343] By orthorectifying the original SAR image based on the acquired affine transformation parameters, SAR image RPC parameters, and SRTM elevation data, the overall positioning accuracy of the image can be improved, thus playing a role in maritime target surveillance and positioning.

Claims

1. A SAR maritime target localization method based on Doppler displacement estimation, characterized in that: Includes the following steps: S1. Obtain the AIS and SAR data required for positioning; S2. Obtain Doppler displacement estimation parameters using AIS and SAR data, and calculate the Doppler displacement deviation. The Doppler displacement estimation parameters include radial velocity, closest slant range, and equivalent radar velocity. S3. After compensating for the Doppler displacement of the SAR target, based on the characteristics of AIS data and SAR data, and through the association matching model, the AIS and SAR targets are associated and matched to obtain the corresponding point pairs required for final positioning. S4. Construct a SAR weak intersection area network adjustment model that takes into account Doppler displacement error, and realize the overall positioning of SAR images based on the corresponding point pairs and Doppler displacement deviation required for final positioning. The specific steps of step S4 are as follows: Step S4.1: Construct a SAR weak intersection area network adjustment model that takes into account Doppler displacement error. The SAR weak intersection area network adjustment model is a rational function model with additional parameters. Affine transformation is used as the model for image-side compensation to optimize the rational function model. The parameters to be solved include the affine transformation coefficients in the six affine transformations of the SAR image and the ground three-dimensional coordinates of the connection points. The affine transformation model is as follows: In the formula, Calculate the difference between the measured coordinates of the image point and the rational function model. For affine transformation coefficients, The image-side coordinate translation parameter in the SAR image. These are the scaling factors for the image-side coordinates in the SAR image, respectively. Measure the coordinates of image points in SAR images; In the affine transformation model, the Doppler displacement obtained in step S2 is added to its orientation direction. To compensate for the Doppler displacement error of SAR moving targets, the azimuth displacement of the moving target, i.e., the Doppler displacement deviation, is obtained from the Doppler displacement parameters. And from the azimuth to resolution of SAR images The azimuth deviation of the moving target in the image direction is obtained as follows: The affine transformation model changes as follows: Using an affine transformation model that takes into account Doppler displacement error and an RFM model of the image to be adjusted, a regional network adjustment model is established: in, The coordinates of image points in the SAR image are calculated using a rational function model. This refers to random errors in SAR images. The three-dimensional coordinates of ground points include two categories: connection points and control points, respectively represented by... and express; The changing affine transformation model Substituting the above regional network adjustment model, the error equation is expanded as follows: For each SAR tie point and the optimized AIS control point, the corresponding error equation is obtained from the above formula: in, , This represents the column and row residual values ​​of the image point coordinates of the SAR tie points and AIS control points. , , , , , The correction number for the affine transformation coefficients of each SAR image. The correction values ​​for the three-dimensional coordinates of ground points also include two categories: tie points and control points. Each tie point and control point is represented by a different value. and express, The partial derivative symbol indicates that the partial derivative is taken with respect to each parameter. and When taking an initial value for an unknown, and The optimized AIS control points include the optimized AIS object control points and the optimized AIS image control points. For the connection points, the error equation matrix simplifies to: in, Represents the residual vector connecting the image points. and For each SAR image scene, there is an affine transformation coefficient correction matrix and a 3D coordinate correction matrix for the tie points. and for and Its corresponding coefficient matrix, A constant vector, The weight matrix; Before adjustment, the initial three-dimensional coordinates of the connection points are obtained as input, and the spatial forward intersection model is used for solution. The spatial forward intersection model is as follows: For control points, the simplified error equation is expressed as: in, Represents the control point image point residual vector. This represents the matrix of corrections for the three-dimensional coordinates of the control points. and for and The corresponding coefficient matrix, A constant vector, The weight matrix; The SAR weak intersection area network adjustment model requires changes to the error equations of the aforementioned connection points, thus transforming the area network adjustment model for three-dimensional coordinates. The correction becomes a correction for two-dimensional plane coordinates. Corrections were made; for obtaining the initial values ​​of the three-dimensional coordinates of the connection points, the spatial forward intersection model was used to align the three-dimensional coordinates. The solution is also transformed into solving for two-dimensional plane coordinates. The correction was made, a weak forward intersection model was established, and the elevation was interpolated using SRTM. The initial values ​​of the three-dimensional coordinates of the connection point were iteratively solved. For control points in the SAR weak intersection area network adjustment model, they are treated as weighted observations, and the weighted observation error equation for the control points is established: in, , , This represents the ground coordinate residual value of the control point. This is an approximation of the control point value, which is the same as the control point value, meaning the last term of the error equation is zero. The error equation simplifies to: in, For the corresponding identity matrix, A constant vector, The weight matrix; Combining the above error equations for connection points, control points, and weighted observations of control points, the combined error equations are expressed as follows: 、 、 、 、 、 in, Represents the residual vector. and For each SAR image, there are affine transformation coefficients and ground point spatial three-dimensional coordinate corrections, including both tie points and control points. and for and Its corresponding coefficient matrix, A constant vector, The weight matrix; Based on the principle of least squares adjustment, the above error equation is normalized, and the normal equation is expressed as follows: in, Indicates matrix transpose; First eliminate the unknowns in the ground coordinates Correction only for the affine transform coefficients of each SAR image. Solving for the equations, the modified normal equations are expressed as follows: in, , ; Step S4.2: Based on the SAR weak intersection area network adjustment model and overall solution steps established in step S4.1, perform the solution; the specific steps are as follows: The input data includes the pixel coordinates, ground coordinates, and Doppler displacement pixel deviation of the AIS control points, the pixel coordinates and initial ground coordinates of the SAR image's tie points, the SAR image's RPC parameters, and the SRTM elevation. The pixel coordinates, ground coordinates, and Doppler displacement pixel deviation of the AIS control points can be obtained through correlation matching in step S3. The pixel coordinates of the SAR image's tie points are obtained using an automatic matching algorithm or manually selected. The initial ground coordinates are obtained from the SAR weak intersection area network adjustment model in step S4.

1. The SAR image's RPC parameters are obtained from the image's built-in .rpb file, and the SRTM elevation is obtained from an open-source 30m resolution SRTM. Interpolation is then performed to obtain finer grid data. The affine transformation parameters are solved again based on the input and the modified normal equations until they stabilize. The solution is then stopped to obtain the affine transformation parameters and the three-dimensional coordinates of the tie points for each SAR image. Otherwise, the affine transformation corrections for each SAR image are obtained by solving the modified normal equations. The affine transformation parameters in the next input are then updated, and the object coordinates of the tie points are obtained based on the established weak forward intersection model and SRTM interpolation. These coordinates are then used as the initial values ​​for the next iteration. Finally, based on the acquired affine transformation parameters, SAR images, RPC parameters, and SRTM elevation data, the SAR images are orthorectified to obtain the final overall positioning SAR images.

2. The SAR maritime target localization method based on Doppler displacement estimation according to claim 1, characterized in that: The specific steps of step S2 are as follows: Step S2.1: Obtaining radial velocity and nearest slant distance Based on the ground speed and heading from AIS data and the target incident angle from the synthetic aperture radar SAR image, the radial velocity of the moving target is obtained using the velocity projection formula: in, The magnitude of the radial velocity of the moving target is obtained based on the velocity projection formula. This is a linearity coefficient, which takes a value of 1 when the synthetic aperture radar is in ascending orbit mode and a value of -1 when it is in descending orbit mode. Indicates the speed over ground. This indicates the angle between the ship's heading relative to the ground and the direction of the image distance. Indicates the magnitude of the target's incident angle in the SAR image; By fitting the AIS trajectory from AIS data and the SAR satellite trajectory from SAR data, a tilt range function that varies between the two over time is constructed. The formula for the radial distance of the moving target, i.e., the tilt range function of the moving target, is as follows: in, Indicates the tilt range of the moving target. For moving ships and SAR platforms in three dimensions , , The magnitude of the distance in the direction; tilt range of moving targets Differentiation yields the radial velocity of the moving target at the imaging moment, which is the radial velocity of the moving target relative to the SAR platform. ; At the same time, take The time when the minimum value is reached is taken as the imaging center time of the moving target, denoted as . minimum distance This is the closest slant distance in the Doppler displacement parameters. and will The ship's position at any given time is determined as the imaging position of a virtual stationary target, and the tilt range between the virtual stationary target and the SAR platform is established. The formula for the radial distance of a stationary target is: in, Indicates the tilt range of a virtual stationary target. For virtual static ships and SAR platforms in three dimensions , , The magnitude of the distance in the direction; tilt range of virtual stationary target Differentiating the values ​​yields the radial velocity of the stationary target relative to the SAR platform. ; Based on the obtained image center time of the moving target Subtracting the two radial velocities at this moment yields the increase in radial velocity due to the motion of the moving target relative to the stationary target, based on the radial distance formula. The formula is: The radial velocity of the moving ship target was obtained using the velocity projection formula and the radial distance formula. , With the nearest slope distance ; Step S2.2: Obtaining the equivalent radar velocity The center time of the moving target imaging Radial velocity corresponding to the virtual stationary target Differentiate and obtain the equivalent radar velocity using the stationary target's acceleration and its frequency modulation at zero Doppler moment; the specific steps are as follows: Synthetic Aperture Radar Actual Velocity With equivalent radar velocity The following relationship exists: in, The speed at which the synthetic aperture radar beam moves across the ground; The frequency modulation of a stationary target at the zero Doppler moment is expressed as: in, For equivalent radar velocity, The carrier wavelength of the transmitted pulse in synthetic aperture radar. The nearest slope distance; according to Acceleration of a stationary target at all times and its zero Doppler time frequency modulation Correspondence: The equivalent radar velocity can then be calculated. ; Step S2.3: Doppler displacement parameter check The difference between the radial velocities obtained from the velocity projection formula and the radial distance formula is used as the first check item, and the difference between the ship's bearing velocity obtained from the velocity projection formula and the radial distance formula is used as the second check item. For the ship's bearing velocity difference check item, in the velocity projection formula, it is transformed into calculating the ship's bearing velocity, and the formula is as follows: in, The azimuth velocity of the ship is obtained based on the velocity projection formula. The coefficients are linear. Indicates the speed over ground. Indicates the angle between the ship's heading relative to the ground and the direction of the image distance; The azimuth velocity of a ship can be calculated using the radial distance formula, i.e., based on the radial velocity of the moving target. Differentiating the derivative yields the acceleration of the moving target. The formula utilizes the time of the center of the moving target's imaging. Corresponding acceleration The ship's azimuth velocity is obtained by using its echo Doppler frequency modulation; the specific steps are as follows: The Doppler modulation frequency of the moving target echo is expressed as: in, For radar equivalent velocity, The velocity components along the track direction in the SAR slant range plane. The carrier wavelength of the transmitted pulse in synthetic aperture radar. The nearest slope distance; Also taking into account the effects of satellite orbits and the Earth's rotation, the azimuth velocity of ships on the sea surface... In the slant distance plane Existence Relationship: This results in the Doppler frequency modulation transformation of the moving target echo being: according to Acceleration of a moving target at all times and its echo Doppler modulation frequency Correspondence: Based on the calculation , and the equivalent radar velocity obtained in the previous step That is, it can calculate the azimuth velocity of ships on the sea surface. The ship's azimuth velocity obtained by projecting it onto the velocity is... By making a mistake, we obtain the second check item; Based on multiple first check items and corresponding second check items, AIS data with simultaneously smaller values ​​for both the first and second check items is selected as the basis for subsequent SAR image geometric positioning. After verification, three Doppler displacement estimation parameters are obtained: radial velocity, nearest slant range, and equivalent radar velocity. The Doppler displacement deviation caused by target motion is then obtained using the displacement formula. AIS data with larger values ​​for the two verification items were removed. ； In the formula, The first check item after the check is checked .

3. The SAR maritime target localization method based on Doppler displacement estimation according to claim 2, characterized in that: The specific steps of step S3 are as follows: Step S3.1: Obtain the features of SAR and AIS data: SAR data consists of ship SAR traces. Feature extraction is performed on the detected ship targets. The extracted features include target position information, ship length, ship width, heading, and ship speed estimated based on the ship's wake. AIS data consists of ship AIS traces, including static and dynamic information of the ship target, specifically including position information, ship length, ship width, speed, and heading. Step S3.2: Select the same features in AIS data and SAR data, and associate them through the association matching model to obtain the corresponding point pairs required for positioning. Optimize the AIS control points in the corresponding point pairs that meet the check items. That is, use the specific location of the GPS antenna provided by AIS in the ship to transform the ship's GPS antenna position to the center of the ship to obtain the final corresponding point pairs required for positioning. The association matching model is based on the latitude and longitude location information of both AIS data and SAR data as the association attribute features. The specific steps for obtaining the required pairs of identically named points through association matching model are as follows: First, perform temporal and spatial calibration on the shared features in the selected AIS and SAR data to obtain the necessary point data for association, specifically: Based on the imaging time of the center of a single SAR image, data from AIS data within five minutes before and after this time are acquired. The data is sorted and classified by the ship identification number and timestamp of all ships' AIS data within the range of the acquired single SAR image. That is, AIS data is classified according to ship identification number, and data of each category is sorted and stored according to timestamp. Next, using the sorted and classified stored ship AIS data and the Doppler displacement estimation method, the zero Doppler time and corresponding latitude and longitude coordinates of each ship are obtained. Then, inverse Doppler displacement compensation is performed to transform the AIS ship latitude and longitude to the SAR image position to obtain the latitude and longitude after inverse displacement compensation. This is used as the standard point data associated with AIS, that is, the AIS latitude and longitude coordinates are obtained. Before association matching, for SAR images, Mercator projection is performed using the provided initial RPC parameters and elevation data provided by ENVI. After target detection, the planar coordinates of SAR ship targets are obtained. Convert AIS latitude and longitude coordinates to Mercator projection plane coordinates to achieve temporal and spatial registration of SAR and AIS data; Then, based on the time- and space-registered data, the associated matching point data is obtained using an association matching model. The association matching model is a global nearest neighbor association matching model, which is expressed as follows: in, This represents the total association cost. The best match is the one where the total association cost is minimized. A binary function that is either 0 or 1; when 1, it represents the first... The AIS point and the first The SAR trace is associated with a certain number of points; a value of 0 indicates no association. The substitution value is calculated from the Euclidean distance between AIS data and SAR data. and They are respectively and The maximum value; The cost matrix is ​​obtained by combining the cost values, and global minimum distance point matching is performed based on the cost matrix. When the distance between the associated points is within the judgment threshold, the point association is successful and the association result is saved. Otherwise, the association fails and the point pair is deleted to obtain the correct AIS and SAR positioning corresponding point pairs, including the latitude and longitude coordinates of the ship center point corresponding to the AIS and the image point coordinates of the ship center in the SAR image. The latitude and longitude coordinates of the ship center point corresponding to the AIS are the object control points of the AIS, and the image point coordinates of the ship center in the SAR image are the image control points of the AIS.

4. A SAR maritime target positioning system based on Doppler displacement estimation, characterized in that: include: Acquisition module: Acquires AIS and SAR data required for positioning; Doppler displacement deviation calculation module: Uses AIS data and SAR data to obtain Doppler displacement estimation parameters and calculates the Doppler displacement deviation. The Doppler displacement estimation parameters include radial velocity, closest slant range and equivalent radar velocity. Same-name point pair matching module: After compensating for the Doppler displacement of the SAR target, the module uses the features of AIS data and SAR data and an association matching model to match the AIS and SAR targets to obtain the same-name point pairs required for final positioning. The positioning module constructs a SAR weak intersection area network adjustment model that takes into account Doppler displacement error, and realizes the overall positioning of SAR images based on the corresponding point pairs and Doppler displacement deviation required for final positioning. The specific implementation steps of the positioning module are as follows: Step S4.1: Construct a SAR weak intersection area network adjustment model that takes into account Doppler displacement error. The SAR weak intersection area network adjustment model is a rational function model with additional parameters. Affine transformation is used as the model for image-side compensation to optimize the rational function model. The parameters to be solved include the affine transformation coefficients in the six affine transformations of the SAR image and the ground three-dimensional coordinates of the connection points. The affine transformation model is as follows: In the formula, Calculate the difference between the measured coordinates of the image point and the rational function model. For affine transformation coefficients, These are the image-side coordinate translation parameters in SAR images. These are the scaling factors for the image-side coordinates in the SAR image, respectively. Measure the coordinates of image points in SAR images; In the affine transformation model, the Doppler displacement obtained in step S2 is added to its orientation direction. To compensate for the Doppler displacement error of SAR moving targets, the azimuth displacement of the moving target, i.e., the Doppler displacement deviation, is obtained from the Doppler displacement parameters. And from the azimuth to resolution of SAR images The azimuth deviation of the moving target in the image is obtained as follows: The affine transformation model changes as follows: Using an affine transformation model that takes into account Doppler displacement error and an RFM model of the image to be adjusted, a regional network adjustment model is established: in, The coordinates of image points in the SAR image are calculated using a rational function model. This refers to random errors in SAR images. The three-dimensional coordinates of ground points include two categories: connection points and control points, respectively represented by... and express; The changing affine transformation model Substituting the above regional network adjustment model, the error equation is expanded as follows: For each SAR tie point and the optimized AIS control point, the corresponding error equation is obtained from the above formula: in, , This represents the column and row residual values ​​of the image point coordinates of the SAR tie points and AIS control points. , , , , , The correction number for the affine transformation coefficients of each SAR image. The correction values ​​for the three-dimensional coordinates of ground points also include two categories: tie points and control points. Each tie point and control point is represented by a different value. and express, The partial derivative symbol indicates that the partial derivative is taken with respect to each parameter. and When taking an initial value for an unknown, and The optimized AIS control points include the optimized AIS object control points and the optimized AIS image control points. For the connection points, the error equation matrix simplifies to: in, Represents the residual vector connecting the image points. and For each SAR image scene, there is an affine transformation coefficient correction matrix and a 3D coordinate correction matrix for the tie points. and for and Its corresponding coefficient matrix, A constant vector, The weight matrix; Before adjustment, the initial three-dimensional coordinates of the connection points are obtained as input, and the spatial forward intersection model is used for solution. The spatial forward intersection model is as follows: For control points, the simplified error equation is expressed as: in, Represents the control point image point residual vector. This represents the matrix of corrections for the three-dimensional coordinates of the control points. and for and The corresponding coefficient matrix, A constant vector, The weight matrix; The SAR weak intersection area network adjustment model requires changes to the error equations of the aforementioned connection points, thus transforming the area network adjustment model for three-dimensional coordinates. The correction becomes a correction for two-dimensional plane coordinates. Corrections were made; for obtaining the initial values ​​of the three-dimensional coordinates of the connection points, the spatial forward intersection model was used to align the three-dimensional coordinates. The solution is also transformed into solving for two-dimensional plane coordinates. The correction was made, a weak forward intersection model was established, and the elevation was interpolated using SRTM. The initial values ​​of the three-dimensional coordinates of the connection point were iteratively solved. For control points in the SAR weak intersection area network adjustment model, they are treated as weighted observations, and the weighted observation error equation for the control points is established: in, , , This represents the ground coordinate residual value of the control point. This is an approximation of the control point value, which is the same as the control point value, meaning the last term of the error equation is zero. The error equation simplifies to: in, For the corresponding identity matrix, A constant vector, The weight matrix; Combining the above error equations for connection points, control points, and weighted observations of control points, the combined error equations are expressed as follows: 、 、 、 、 、 in, Represents the residual vector. and For each SAR image, there are affine transformation coefficients and ground point spatial three-dimensional coordinate corrections, including both tie points and control points. and for and Its corresponding coefficient matrix, A constant vector, The weight matrix; Based on the principle of least squares adjustment, the above error equation is normalized, and the normal equation is expressed as follows: in, Indicates matrix transpose; First eliminate the unknowns in the ground coordinates Correction only for the affine transform coefficients of each SAR image. Solving for the equations, the modified normal equations are expressed as follows: in, , ; Step S4.2: Based on the SAR weak intersection area network adjustment model and overall solution steps established in step S4.1, perform the solution; the specific steps are as follows: The input data includes the pixel coordinates, ground coordinates, and Doppler displacement pixel deviation of the AIS control points, the pixel coordinates and initial ground coordinates of the SAR image's tie points, the SAR image's RPC parameters, and the SRTM elevation. The pixel coordinates, ground coordinates, and Doppler displacement pixel deviation of the AIS control points can be obtained through correlation matching in step S3. The pixel coordinates of the SAR image's tie points are obtained using an automatic matching algorithm or manually selected. The initial ground coordinates are obtained from the SAR weak intersection area network adjustment model in step S4.

1. The SAR image's RPC parameters are obtained from the image's built-in .rpb file, and the SRTM elevation is obtained from an open-source 30m resolution SRTM. Interpolation is then performed to obtain finer grid data. The affine transformation parameters are solved again based on the input and the modified normal equations until they stabilize. The solution is then stopped to obtain the affine transformation parameters and the three-dimensional coordinates of the tie points for each SAR image. Otherwise, the affine transformation corrections for each SAR image are obtained by solving the modified normal equations. The affine transformation parameters in the next input are then updated, and the object coordinates of the tie points are obtained based on the established weak forward intersection model and SRTM interpolation. These coordinates are then used as the initial values ​​for the next iteration. Finally, based on the acquired affine transformation parameters, SAR images, RPC parameters, and SRTM elevation data, the SAR images are orthorectified to obtain the final overall positioning SAR images.

5. A SAR maritime target positioning system based on Doppler displacement estimation according to claim 4, characterized in that: The specific implementation steps of the Doppler displacement deviation calculation module are as follows: Step S2.1: Obtaining radial velocity and nearest slant distance Based on the ground speed and heading from AIS data and the target incident angle from the synthetic aperture radar SAR image, the radial velocity of the moving target is obtained using the velocity projection formula: in, The magnitude of the radial velocity of the moving target is obtained based on the velocity projection formula. This is a linearity coefficient, which takes a value of 1 when the synthetic aperture radar is in ascending orbit mode and a value of -1 when it is in descending orbit mode. Indicates the speed over ground. This indicates the angle between the ship's heading relative to the ground and the direction of the image distance. Indicates the magnitude of the target's incident angle in the SAR image; By fitting the AIS trajectory from AIS data and the SAR satellite trajectory from SAR data, a tilt range function that varies between the two over time is constructed. The formula for the radial distance of the moving target, i.e., the tilt range function of the moving target, is as follows: in, Indicates the tilt range of the moving target. For moving ships and SAR platforms in three dimensions , , The magnitude of the distance in the direction; tilt range of moving targets Differentiation yields the radial velocity of the moving target at the imaging moment, which is the radial velocity of the moving target relative to the SAR platform. ; At the same time, take The time when the minimum value is reached is taken as the imaging center time of the moving target, denoted as . minimum distance This is the closest slant distance in the Doppler displacement parameters. and will The ship's position at any given time is determined as the imaging position of a virtual stationary target, and the tilt range between the virtual stationary target and the SAR platform is established. The formula for the radial distance of a stationary target is: in, Indicates the tilt range of a virtual stationary target. For virtual static ships and SAR platforms in three dimensions , , The magnitude of the distance in the direction; tilt range of virtual stationary target Differentiating the values ​​yields the radial velocity of the stationary target relative to the SAR platform. ; Based on the obtained image center time of the moving target Subtracting the two radial velocities at this moment yields the increase in radial velocity due to the motion of the moving target relative to the stationary target, based on the radial distance formula. The formula is: The radial velocity of the moving ship target was obtained using the velocity projection formula and the radial distance formula. , With the nearest slope distance ; Step S2.2: Obtaining the equivalent radar velocity The center time of the moving target imaging Radial velocity corresponding to the virtual stationary target Differentiate and obtain the equivalent radar velocity using the stationary target's acceleration and its frequency modulation at zero Doppler moment; the specific steps are as follows: Synthetic Aperture Radar Actual Velocity With equivalent radar velocity The following relationship exists: in, The speed at which the synthetic aperture radar beam moves across the ground; The frequency modulation of a stationary target at the zero Doppler moment is expressed as: in, For equivalent radar velocity, The carrier wavelength of the transmitted pulse in synthetic aperture radar. The nearest slope distance; according to Acceleration of a stationary target at all times and its zero Doppler time frequency modulation Correspondence: The equivalent radar velocity can then be calculated. ; Step S2.3: Doppler displacement parameter check The difference between the radial velocities obtained from the velocity projection formula and the radial distance formula is used as the first check item, and the difference between the ship's bearing velocity obtained from the velocity projection formula and the radial distance formula is used as the second check item. For the ship's bearing velocity difference check item, in the velocity projection formula, it is transformed into calculating the ship's bearing velocity, and the formula is as follows: in, The azimuth velocity of the ship is obtained based on the velocity projection formula. The coefficients are linear. Indicates the speed over ground. Indicates the angle between the ship's heading relative to the ground and the direction of the image distance; The azimuth velocity of a ship can be calculated using the radial distance formula, i.e., based on the radial velocity of the moving target. Differentiating the derivative yields the acceleration of the moving target. The formula utilizes the time of the center of the moving target's imaging. Corresponding acceleration The ship's azimuth velocity is obtained by using its echo Doppler frequency modulation; the specific steps are as follows: The Doppler modulation frequency of the moving target echo is expressed as: in, For radar equivalent velocity, The velocity components along the track direction in the SAR slant range plane. The carrier wavelength of the transmitted pulse in synthetic aperture radar. The nearest slope distance; Also taking into account the effects of satellite orbits and the Earth's rotation, the azimuth velocity of ships on the sea surface... In the slant distance plane Existence Relationship: This results in the Doppler frequency modulation transformation of the moving target echo being: according to Acceleration of a moving target at all times and its echo Doppler modulation frequency Correspondence: Based on the calculation , and the equivalent radar velocity obtained in the previous step That is, it can calculate the azimuth velocity of ships on the sea surface. The ship's azimuth velocity obtained by projecting it onto the velocity is... By making a mistake, we obtain the second check item; Based on multiple first check items and corresponding second check items, AIS data with simultaneously smaller values ​​for both the first and second check items is selected as the basis for subsequent SAR image geometric positioning. After verification, three Doppler displacement estimation parameters are obtained: radial velocity, nearest slant range, and equivalent radar velocity. The Doppler displacement deviation caused by target motion is then obtained using the displacement formula. AIS data with larger values ​​for the two verification items were removed. ； In the formula, The first check item after the check is checked .

6. A SAR maritime target positioning system based on Doppler displacement estimation according to claim 5, characterized in that: The specific implementation steps of the same-name point pair matching module are as follows: Step S3.1: Obtain the features of SAR and AIS data: SAR data consists of ship SAR traces. Feature extraction is performed on the detected ship targets. The extracted features include target position information, ship length, ship width, heading, and ship speed estimated based on the ship's wake. AIS data consists of ship AIS traces, including static and dynamic information of the ship target, specifically including position information, ship length, ship width, speed, and heading. Step S3.2: Select the same features in AIS data and SAR data, and associate them through the association matching model to obtain the corresponding point pairs required for positioning. Optimize the AIS control points in the corresponding point pairs that meet the check items. That is, use the specific location of the GPS antenna provided by AIS in the ship to transform the ship's GPS antenna position to the center of the ship to obtain the final corresponding point pairs required for positioning. The association matching model is based on the latitude and longitude location information of both AIS data and SAR data as the association attribute features. The specific steps for obtaining the required pairs of identically named points through association matching model are as follows: First, perform temporal and spatial calibration on the shared features in the selected AIS and SAR data to obtain the necessary point data for association, specifically: Based on the imaging time of the center of a single SAR image, data from AIS data within five minutes before and after this time are acquired. The data is sorted and classified by the ship identification number and timestamp of all ships' AIS data within the range of the acquired single SAR image. That is, AIS data is classified according to ship identification number, and data of each category is sorted and stored according to timestamp. Next, using the sorted and classified stored ship AIS data and the Doppler displacement estimation method, the zero Doppler time and corresponding latitude and longitude coordinates of each ship are obtained. Then, inverse Doppler displacement compensation is performed to transform the AIS ship latitude and longitude to the SAR image position to obtain the latitude and longitude after inverse displacement compensation. This is used as the standard point data associated with AIS, that is, the AIS latitude and longitude coordinates are obtained. Before association matching, for SAR images, Mercator projection is performed using the provided initial RPC parameters and elevation data provided by ENVI. After target detection, the planar coordinates of SAR ship targets are obtained. Convert AIS latitude and longitude coordinates to Mercator projection plane coordinates to achieve temporal and spatial registration of SAR and AIS data; Then, based on the time- and space-registered data, the associated matching point data is obtained using an association matching model. The association matching model is a global nearest neighbor association matching model, which is expressed as follows: in, This represents the total association cost. The best match is the one where the total association cost is minimized. A binary function that is either 0 or 1; when 1, it represents the first... The AIS point and the first The SAR trace is associated with a certain number of points; a value of 0 indicates no association. The substitution value is calculated from the Euclidean distance between AIS data and SAR data. and They are respectively and The maximum value; The cost matrix is ​​obtained by combining the cost values, and global minimum distance point matching is performed based on the cost matrix. When the distance between the associated points is within the judgment threshold, the point association is successful and the association result is saved. Otherwise, the association fails and the point pair is deleted to obtain the correct AIS and SAR positioning corresponding point pairs, including the latitude and longitude coordinates of the ship center point corresponding to the AIS and the image point coordinates of the ship center in the SAR image. The latitude and longitude coordinates of the ship center point corresponding to the AIS are the object control points of the AIS, and the image point coordinates of the ship center in the SAR image are the image control points of the AIS.

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