Stationary remote sensing satellite sight positioning method and system based on real-time recursion

Abstract

The invention provides a stationary remote sensing satellite sight positioning method and system based on real-time recursion. The method comprises the following steps: establishing a sight positioning deviation model caused by reference deformation of a remote sensing instrument; according to the line-of-sight positioning deviation model, constructing a line-of-sight positioning deviation state equation of the remote sensing instrument; according to the line-of-sight positioning deviation model, constructing a line-of-sight positioning deviation state observation equation of the remote sensing instrument; performing reference deformation real-time recursion based on state estimation by combining the state equation and the state observation equation; and according to the real-time recursion model obtained by the module M4, sight line positioning real-time correction is carried out by using a deviation estimation result. According to the stationary remote sensing satellite sight line positioning method based on real-time recursion, the influence of on-orbit long-period deformation on the optical axis direction of a remote sensing instrument can be effectively solved, and compared with a traditional positioning method, the real-time performance of error correction is high, and the positioning precision is guaranteed.

Description

Technical Field

[0001] The present invention relates to the technical field of satellite overall design and image positioning and registration, and in particular to a method and system for positioning a stationary remote sensing satellite line of sight based on real-time recursion. Background Art

[0002] Line of sight positioning is a key link in the processing and application of geostationary remote sensing satellite observation data, which is used to determine the precise location information of the observed target or image. With the continuous development of satellite remote sensing technology and the deepening of data application, the requirements for core indicators such as geometric positioning of remote sensing satellite data products are becoming increasingly higher. Due to the complex thermal environment of geostationary satellites in orbit, the remote sensing instruments experience a process from direct sunlight to complete backlighting within an orbital cycle. The temperature on the surface of the remote sensing instruments will undergo drastic changes. The harsh space environment will cause dynamic deviations in the pointing direction of the optical axis of the remote sensing instruments, which has an important impact on high-precision line of sight positioning. In order to solve the problem of decreased satellite line of sight positioning accuracy caused by the space thermal environment, it is necessary to carry out research on high-precision line of sight positioning methods.

[0003] After literature research, the paper "Analysis of Thermal Deformation of Geosynchronous Orbit Satellites Using Telemetry Data" (Spacecraft Engineering, Vol. 28, No. 5, 2019) proposed that geosynchronous orbit satellites will be affected by the on-orbit environment and produce thermal deformation, which in turn affects the accuracy of the payload's pointing to the ground. Due to the uncertainty of the space environment and the nonlinearity of thermal deformation, thermal deformation on orbit is difficult to quantify. The article studies the law of using real on-orbit telemetry data to analyze the thermal deformation of satellite bodies, regards thermal deformation as a combination of daily and annual cycle terms, establishes a mathematical model in the form of Fourier series, and proposes an estimation method for the thermal deformation parameters of the satellite body using the least squares method. The article proposes that the fitting method requires big data statistics, and the positioning correction is based on historical data, which is not very timely and difficult to adapt to scenarios where the thermal environment changes drastically. This is significantly different from the real-time recursive method proposed in this patent.

[0004] In the paper "Design and Verification of High-resolution Multi-mode Satellite Image Positioning Accuracy Assurance" (Spacecraft Engineering, Vol. 30, No. 3, 2021), the main influencing factors are comprehensively considered in combination with the current design level, and a ground-ground integrated image positioning accuracy assurance system is established, including orbit determination, attitude measurement, time synchronization, structural stability, stability of camera internal orientation elements, ground calibration and processing, etc. Specific system configuration and software algorithm design schemes are proposed for each item, and simulation analysis, testing and experimental methods are adopted for verification. However, the paper does not involve the relevant content of line of sight positioning deviation correction.

[0005] In the paper "Research on High-precision Earth Positioning Technology of Optical Remote Sensing Satellite Geometric Imaging Model" (Network Information Engineering, 2021), the coordinate systems involved in optical remote sensing satellite imaging and their mutual conversion are introduced from the aspects of scanning coordinate system, instantaneous image coordinate system, and sensor coordinate system; the role of geometric imaging model in high-precision positioning technology is analyzed through rigorous geometric imaging model and general mathematical imaging model; finally, the satellite image stereo positioning technology under the background of ephemeris attitude is studied through multi-image joint stereo positioning. However, the paper does not involve the relevant content of line of sight positioning deviation correction.

[0006] In the paper "Analysis of Planar Positioning Accuracy Error of Optical Remote Sensing Satellites" (Space Return and Remote Sensing, 2021), it is proposed that the geometric positioning of optical remote sensing satellites is divided into physical geometric models and general geometric models. The physical geometric model is based on the collinear equation, and the internal orientation elements of the optical remote sensor and the external orientation elements of the satellite platform attitude and orbit are used to jointly establish the precise geometric positioning model of the remote sensing image. Among them, environmental factors such as optical path difference and atmospheric refraction cannot be ignored, and their offset needs to be eliminated through modeling. However, the paper does not involve the relevant content of the correction of line of sight positioning deviation caused by benchmark deformation.

[0007] In the paper “Research on GEO Satellite Image Positioning and Registration Technology and Simulation Verification” (Spacecraft Engineering, Issue 4, 2015), the basic principles of image positioning and registration were introduced, a mathematical model of compensation was established, and a real-time simulation system was used to replace the payload scanning radiometer, atmospheric vertical sounder, attitude and orbit control and other related subsystems to simulate the satellite’s on-orbit working conditions. The image positioning and registration technology was simulated and verified, but the relevant content of line of sight positioning deviation correction was not involved.

[0008] In summary, the market needs a method and system that can effectively solve the impact of long-period deformation on the optical axis pointing of remote sensing instruments and implement a more accurate real-time recursive stationary remote sensing satellite line-of-sight positioning method and system. Summary of the invention

[0009] In view of the defects in the prior art, the object of the present invention is to provide a method and system for positioning the line of sight of a geostationary remote sensing satellite based on real-time recursion.

[0010] A method for positioning a stationary remote sensing satellite line of sight based on real-time recursion provided by the present invention comprises:

[0011] Step S1: Establishing a line-of-sight positioning deviation model caused by remote sensing instrument benchmark deformation;

[0012] Step S2: constructing a state equation of the remote sensing instrument line of sight positioning deviation according to the line of sight positioning deviation model;

[0013] Step S3: constructing a state observation equation of the remote sensing instrument line of sight positioning deviation according to the line of sight positioning deviation model;

[0014] Step S4: combining the state equation and the state observation equation, and performing real-time recursion of the benchmark deformation based on state estimation;

[0015] Step S5: Based on the real-time recursive model obtained in step S4, the deviation estimation result is used to perform real-time correction of line of sight positioning.

[0016] Preferably, the line-of-sight positioning deviation of the remote sensing instrument in step S1 is related to the pointing angle, wherein the pointing direction of the geostationary orbit remote sensing satellite to the earth includes the east-west dimension and the north-south dimension, and the corresponding line-of-sight positioning deviation includes the east-west dimension positioning deviation and the north-south dimension positioning deviation;

[0017] The relationship between the remote sensing instrument line of sight positioning deviation and the pointing angle, that is, the line of sight positioning deviation model is as follows:

[0018]

[0019] Where Δε represents the east-west line of sight positioning deviation caused by the thermal environment, Δη represents the north-south line of sight positioning deviation caused by the thermal environment, ε represents the direction of the remote sensing instrument in the east-west dimension, η represents the direction of the remote sensing instrument in the north-south dimension, c1, c2, c3 represent the east-west dimension benchmark deformation parameters, d1, d2, d3 represent the north-south dimension benchmark deformation parameters.

[0020] Preferably, the line of sight positioning deviation model is based on the satellite thermal deformation mechanism, and the thermal deformation gradient on the satellite will not change suddenly. Therefore, the line of sight positioning deviation caused by the thermal environment has the characteristic of slow change, satisfying:

[0021]

[0022] In the formula, represents the rate of change of the deformation parameter c1 over time, It represents the rate of change of deformation parameter d1 with time, and k1 and k2 are constants.

[0023] Preferably, the remote sensing instrument line of sight positioning deviation state equation includes constructing a state vector X, and the formula is as follows:

[0024]

[0025] Where X is the state vector, c1, c2, c3 represent the east-west datum deformation parameters, d1, d2, d3 represent the north-south datum deformation parameters, represents the rate of change of the deformation parameter c1 over time, represents the rate of change of the deformation parameter d1 over time;

[0026] Combined with the sight line positioning deviation model constructed in step S1, the state equation can be further obtained as follows:

[0027]

[0028] In the formula, is the differential result of the state vector X, W is the system noise vector, and C is the state transfer matrix.

[0029] Preferably, the remote sensing instrument line of sight positioning deviation state observation equation expression is as follows:

[0030] Z=H·X+V

[0031] In the formula, Z represents the state observation vector, X represents the state vector, H represents the state observation matrix, and V represents the observation white noise vector;

[0032] The state observation matrix H includes two-dimensional pointing angles, which are derived according to the line of sight positioning deviation model of step S1 and are expressed as:

[0033]

[0034] Where, ε represents the pointing angle of the remote sensing instrument in the east-west dimension during geometric calibration, and η represents the pointing angle of the remote sensing instrument in the north-south dimension during geometric calibration;

[0035] The state observation is the result of geometric calibration of the geostationary remote sensing satellite, and the expression of the observation vector Z is:

[0036]

[0037] Where Δε is the east-west line of sight positioning deviation caused by the thermal environment, and Δη is the north-south line of sight positioning deviation caused by the thermal environment;

[0038] Preferably, the observable white noise vector V reflects the error of geometric calibration of the remote sensing instrument. The error of geometric calibration of the geostationary satellite remote sensing instrument includes the satellite attitude measurement error, the remote sensing instrument target extraction error, the remote sensing instrument two-dimensional pointing error and the control point geometric error.

[0039] Preferably, the step S4 includes a deformation parameter prediction step, a mean square error prediction step, a filter gain calculation step, a deformation parameter estimation step, and a mean square error estimation step;

[0040] The deformation parameter prediction step includes using a state equation to derive a state vector at the next moment according to a state vector at the current moment to obtain a state vector prediction result, which is expressed as:

[0041] X i / i-1 =C i / i-1 ·X i-1

[0042] In the formula, X i / i-1represents the state vector prediction result at time i, X i-1 represents the state vector at time i-1, C i / i-1 Represents the state transfer matrix at time i;

[0043] The mean square error prediction step includes calculating the proportion of the state observation results in the state estimation, and the calculation formula is as follows:

[0044] P i / i-1 =C i / i-1 ·P i-1 ·C i / i-1 T

[0045] Where P i / i-1 represents the mean square error matrix prediction result at time i, P i-1 represents the mean square error matrix at time i-1, C i / i-1 Represents the state transfer matrix at time i;

[0046] The filter gain calculation step includes: after completing the mean square error matrix prediction, the filter gain matrix calculation formula is calculated as follows:

[0047]

[0048] In the formula, K i represents the filter gain matrix at time i, P i / i-1 represents the mean square error matrix prediction result at time i, H i represents the state observation matrix at time i, (·) -1 Represents the inverse operation of a matrix;

[0049] The deformation parameter estimation step includes, after completing a geometric calibration, using the geometric calibration data to estimate the deformation parameters and correcting the sight positioning deviation model, the expression is:

[0050] X i =X i / i-1 +K i ·(Z i -H i ·X i / i-1 )

[0051] In the formula, X i represents the state vector at time i, X i / i-1 represents the state vector prediction result at time i, K i represents the filter gain matrix at time i, H i represents the state observation matrix at time i;

[0052] The mean square error estimation includes that after completing the state vector estimation of the reference deformation once, the mean square error matrix needs to be iterated once for recursion at the next moment. The expression is:

[0053] P i =(IK i ·H i )·P i / i-1

[0054] Where P i represents the mean square error matrix estimation result at time i, P i / i-1 represents the mean square error matrix prediction result at time i, K i represents the filter gain matrix at time i, H i Indicates P i-1 represents the state observation matrix at time i, and I represents the identity matrix.

[0055] Preferably, an initial value P0 needs to be determined in the mean square error prediction step, and the initial value P0 is:

[0056]

[0057] Where P0 is the initial value of the mean square error matrix of the line-of-sight positioning bias state equation, and ω is the orbital angular velocity of the satellite.

[0058] Preferably, step S5 includes performing real-time recursion according to the state estimation result, calculating the remote sensing instrument positioning deviation at different times, and obtaining the accurate line of sight positioning result of the remote sensing instrument according to the line of sight positioning correction formula.

[0059] A stationary remote sensing satellite line-of-sight positioning system based on real-time recursion provided by the present invention comprises:

[0060] Module M1: Establishing a model of line-of-sight positioning deviation caused by remote sensing instrument benchmark deformation;

[0061] Module M2: constructing a state equation of the remote sensing instrument line of sight positioning deviation according to the line of sight positioning deviation model;

[0062] Module M3: constructing a state observation equation of the remote sensing instrument line of sight positioning deviation according to the line of sight positioning deviation model;

[0063] Module M4: combining the state equation and the state observation equation, and performing real-time recursion of the benchmark deformation based on state estimation;

[0064] Module M5: Based on the real-time recursive model obtained by module M4, the deviation estimation result is used to perform real-time correction of line of sight positioning.

[0065] Compared with the prior art, the present invention has the following beneficial effects:

[0066] The real-time recursion-based line-of-sight positioning method for a stationary remote sensing satellite proposed in the present invention can effectively solve the influence of long-period deformation on the optical axis pointing of remote sensing instruments. Compared with traditional positioning methods, the real-time performance of error correction is high and the positioning accuracy is guaranteed. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0068] Figure 1 It is a flow chart of a method for positioning a stationary remote sensing satellite line of sight based on real-time recursion;

[0069] Figure 2 This is a schematic diagram of the two-dimensional pointing of a geostationary remote sensing satellite for earth observation;

[0070] Figure 3 Schematic diagram of the process of real-time recursion of benchmark deformation based on state estimation. DETAILED DESCRIPTION

[0071] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0072] The present invention utilizes geometric calibration data to carry out real-time and accurate correction of the satellite line-of-sight positioning model.

[0073] Embodiment 1

[0074] According to a method for positioning a stationary remote sensing satellite based on real-time recursion provided by the present invention, Figure 1 As shown, including:

[0075] Step S1: Establish a line-of-sight positioning deviation model caused by baseline deformation of remote sensing instruments. Establishing a line-of-sight positioning deviation model caused by baseline deformation clarifies that the line-of-sight positioning deviation of remote sensing instruments is related to the pointing angle. When the instrument's optical axis points to different positions on the surface, the corresponding pointing deviation is also inconsistent. Therefore, it is necessary to establish the relationship between the positioning deviation and the pointing angle. Specifically, during the earth observation process of a geostationary remote sensing satellite, the pointing observation of different areas of the earth's surface is achieved by adjusting the two-dimensional pointing angle of the remote sensing instrument's optical axis. For ease of description, the direction of the satellite's two-dimensional observation of the earth can be defined as the east-west dimension and the north-south dimension, such as Figure 2 shown.

[0076] According to the positioning principle of remote sensing instruments, line-of-sight positioning deviation includes east-west positioning deviation and north-south positioning deviation. Under the influence of thermal environment, the line-of-sight positioning deviation of remote sensing instruments is related to the pointing angle. The optical axis of the instrument points to different positions on the surface, and the corresponding pointing deviation is also inconsistent. Therefore, it is necessary to establish the relationship between positioning deviation and pointing angle:

[0077]

[0078] In the formula, Δε represents the east-west line of sight positioning deviation caused by the thermal environment, Δη represents the north-south line of sight positioning deviation caused by the thermal environment, ε represents the direction of the remote sensing instrument in the east-west dimension, η represents the direction of the remote sensing instrument in the north-south dimension, c1, c2, c3 represent the east-west dimension benchmark deformation parameters, d1, d2, d3 represent the north-south dimension benchmark deformation parameters. According to the above expressions, it can be concluded that parameters c2 and d2 reflect the relationship between the line of sight positioning deviation and the east-west dimension pointing angle, parameters c3 and d3 reflect the relationship between the line of sight positioning deviation and the north-south dimension pointing angle, and parameters c1 and d1 reflect the relationship between the line of sight positioning deviation and the benchmark deformation. Since the on-board benchmark deformation has time-varying characteristics, parameters c1 and d1 also have time-varying characteristics.

[0079] The line-of-sight positioning deviation model takes into account the thermal deformation mechanism of the satellite. The thermal deformation gradient on the satellite will not change suddenly. Therefore, the line-of-sight positioning deviation caused by the thermal environment has the characteristic of slow change, satisfying:

[0080]

[0081] In the formula, represents the rate of change of the deformation parameter c1 over time, It represents the rate of change of deformation parameter d1 with time, and k1 and k2 are constants.

[0082] Step S2: Based on the line of sight positioning deviation model, construct the state equation of the remote sensing instrument line of sight positioning deviation. The state quantities in the state equation of the remote sensing instrument line of sight positioning deviation include the change rate of the east-west datum deformation parameter, the north-south datum deformation parameter and the thermal deformation parameter over time. In order to realize the identification of the datum deformation parameter, construct the state vector X, and the expression can be written as:

[0083]

[0084] In the above formula, X is the state vector, c1, c2, c3 represent the east-west datum deformation parameters, d1, d2, d3 represent the north-south datum deformation parameters, represents the rate of change of the deformation parameter c1 over time, Indicates the rate of change of the deformation parameter d1 over time.

[0085] Combined with the sight positioning deviation model constructed in step S1, the state vector X is differentiated. Considering that the result of the first differentiation of parameters c1 and d1 is constant k1 and k2, and the result after two differentiations is 0, the state equation can be further obtained as follows:

[0086]

[0087] In the formula, is the differential result of the state vector X; W is the system noise vector, which indicates the stability of thermal deformation on the satellite; C is the state transfer matrix, which is expressed as:

[0088]

[0089] Step S3: Construct the state observation equation of the line of sight positioning deviation of the remote sensing instrument according to the line of sight positioning deviation model. The state observation matrix in the state observation equation of the line of sight positioning deviation of the remote sensing instrument includes a two-dimensional pointing angle, and the state observation quantity is the result of the geometric calibration of the geostationary remote sensing satellite. The satellite can identify the optical axis pointing deviation of the payload through geometric calibration in orbit. The principle of geometric calibration is to observe the control points with known geometric information, compare the line of sight positioning results of the satellite with the geometric information of the control points, and solve the two-dimensional line of sight positioning deviation of the payload. For geostationary remote sensing satellites, the available geometric control points include landmarks with obvious geometric features or stars in space.

[0090] In order to solve the parameters in the state equation, it is necessary to construct the observation equation, which is expressed as follows:

[0091] Z=H·X+V

[0092] In the above formula, Z represents the state observation vector, X represents the state vector, H represents the state observation matrix, and V represents the observation white noise vector.

[0093] The expression of the observation vector Z can be expanded as:

[0094]

[0095] In the above formula, Δε is the east-west line of sight positioning deviation caused by the thermal environment, and Δη is the north-south line of sight positioning deviation caused by the thermal environment. The observation vector Z can be solved by satellite observation of landmarks or stars.

[0096] The state observation matrix H can be derived according to the line of sight positioning deviation model in step S1, and its expanded expression can be written as:

[0097]

[0098] In the formula, ε represents the pointing angle of the remote sensing instrument in the east-west dimension during geometric calibration, and η represents the pointing angle of the remote sensing instrument in the north-south dimension during geometric calibration. The observed white noise vector V reflects the error of the geometric calibration of the remote sensing instrument. Generally, the error of the geometric calibration of the geostationary satellite remote sensing instrument includes the attitude measurement error of the satellite, the target extraction error of the remote sensing instrument, the two-dimensional pointing error of the remote sensing instrument, and the geometric error of the control point.

[0099] Step S4: Combining the state equation and the state observation equation, and performing real-time recursion of the benchmark deformation based on state estimation. The step S4 includes a deformation parameter prediction step, a mean square error prediction step, a filter gain calculation step, a deformation parameter estimation step, and a mean square error estimation step.

[0100] The deformation parameter prediction step includes using a state equation to derive a state vector at the next moment according to a state vector at the current moment to obtain a state vector prediction result. The specific expression is:

[0101] X i / i-1 =C i / i-1 ·X i-1

[0102] In the above formula, X i / i-1 represents the state vector prediction result at time i, X i-1 represents the state vector at time i-1, C i / i-1 Represents the state transfer matrix at time i.

[0103] The mean square error prediction step includes calculating the proportion of the state observation results in the state estimation, and the calculation formula is as follows:

[0104] P i / i-1 =C i / i-1 ·P i-1 ·C i / i-1 T

[0105] Where P i / i-1 represents the mean square error matrix prediction result at time i, P i-1 represents the mean square error matrix at time i-1, C i / i-1 Represents the state transfer matrix at time i. The core issue of mean square error matrix prediction is the determination of the initial value P0, which needs to be analyzed in combination with the actual physical meaning of the state vector. The state vector established by the present invention mainly includes deformation parameters and the rate of change of deformation parameters. According to the on-orbit experience of geostationary remote sensing satellites, the magnitude of on-orbit deformation parameters is generally close to 0.001 radians, and the initial value of the rate of change of deformation parameters is estimated based on the amount of change of deformation parameters within one orbital cycle. According to the above analysis, the initial value P0 is:

[0106]

[0107] Where P0 is the initial value of the mean square error matrix of the line-of-sight positioning bias state equation, and ω is the orbital angular velocity of the satellite.

[0108] The filter gain calculation step includes: after completing the mean square error matrix prediction, the filter gain matrix calculation formula is calculated as follows:

[0109]

[0110] In the formula, K i represents the filter gain matrix at time i, P i / i-1 represents the mean square error matrix prediction result at time i, H i represents the state observation matrix at time i, (·) -1 Represents the matrix inversion operation.

[0111] The deformation parameter estimation step includes, after completing a geometric calibration, using the geometric calibration data to estimate the deformation parameters and correcting the sight positioning deviation model, the expression is:

[0112] X i =X i / i-1 +K i ·(Z i -H i ·X i / i-1 )

[0113] In the formula, X i represents the state vector at time i, X i / i-1 represents the state vector prediction result at time i, K i represents the filter gain matrix at time i, H i Represents the state observation matrix at time i.

[0114] The state vector X at the i-th moment i The expanded form is as follows:

[0115]

[0116] Where c1(i), c2(i), and c3(i) represent the east-west datum deformation parameters at the i-th moment, d1(i), d2(i), and d3(i) represent the north-south datum deformation parameters at the i-th moment. represents the rate of change of the deformation parameter c1 at the i-th moment, Represents the rate of change of the deformation parameter d1 at the i-th moment.

[0117] The mean square error estimation includes that after completing the state vector estimation of the reference deformation once, the mean square error matrix needs to be iterated once for recursion at the next moment. The expression is:

[0118]

[0119] Where P i represents the mean square error matrix estimation result at time i, P i / i-1 represents the mean square error matrix prediction result at time i, K i represents the filter gain matrix at time i, H i Indicates P i-1 represents the state observation matrix at time i, and I represents the identity matrix.

[0120] Furthermore, if Figure 3 As shown, the real-time delivery process of benchmark deformation based on state estimation in the present invention is specifically described as follows:

[0121] The real-time recursion of the benchmark deformation based on state estimation includes a state vector calculation loop and a gain calculation loop. The state vector calculation loop estimates the state vector according to the state vector prediction result and the observation vector, and uses the state vector estimation result as the state vector of the next cycle for iterative calculation. The gain calculation loop predicts the mean square error matrix, calculates the filter gain, and estimates the mean square error matrix according to the initial mean square error matrix, and circulates in sequence to ensure that a new filter gain can be calculated in each cycle.

[0122] Step S5: Based on the real-time recursive model obtained in step S4, the deviation estimation result is used to perform real-time correction of line of sight positioning. Specifically, firstly, real-time recursion is performed based on the state estimation result to calculate the positioning deviation of the remote sensing instrument at different times, and the accurate line of sight positioning result of the remote sensing instrument is obtained according to the line of sight positioning correction formula. According to the real-time recursive model, the line of sight positioning deviation of the remote sensing instrument at the i-th moment can be calculated, and the expression is:

[0123]

[0124] Where Δε(i) represents the east-west line of sight positioning deviation of the remote sensing instrument at the i-th moment, Δη(i) represents the north-south line of sight positioning deviation of the remote sensing instrument at the i-th moment, ε represents the direction of the remote sensing instrument in the east-west dimension, η represents the direction of the remote sensing instrument in the north-south dimension, c1, c2, c3 represent the east-west dimension benchmark deformation parameters, d1, d2, d3 represent the north-south dimension benchmark deformation parameters.

[0125] The actual pointing angle of the remote sensing instrument after correction is:

[0126]

[0127] Where ε1 and η1 represent the pointing angles of the remote sensing instrument after correction, ε and η represent the pointing angles of the remote sensing instrument before correction, and Δε and Δη represent the line of sight positioning deviations.

[0128] The present invention aims to solve the problem of reduced satellite line-of-sight positioning accuracy caused by the space thermal environment. The present invention is also applicable to the identification and correction of line-of-sight positioning errors of stationary remote sensing satellites, which is of great significance to improving the positioning accuracy of remote sensing instruments.

[0129] Embodiment 2

[0130] The present invention also provides a stationary remote sensing satellite line of sight positioning system based on real-time recursion. The stationary remote sensing satellite line of sight positioning system based on real-time recursion can be realized by executing the process steps of the stationary remote sensing satellite line of sight positioning method based on real-time recursion, that is, those skilled in the art can understand the stationary remote sensing satellite line of sight positioning method based on real-time recursion as a preferred implementation of the stationary remote sensing satellite line of sight positioning system based on real-time recursion.

[0131] A stationary remote sensing satellite line-of-sight positioning system based on real-time recursion provided by the present invention comprises:

[0132] Module M1: Establish a line-of-sight positioning deviation model caused by the benchmark deformation of the remote sensing instrument. In module M1, the line-of-sight positioning deviation of the remote sensing instrument is related to the pointing angle. The pointing direction of the geostationary orbit remote sensing satellite to the earth includes the east-west dimension and the north-south dimension, and the corresponding line-of-sight positioning deviation includes the east-west dimension positioning deviation and the north-south dimension positioning deviation. The relationship between the line-of-sight positioning deviation of the remote sensing instrument and the pointing angle, that is, the line-of-sight positioning deviation model is as follows:

[0133]

[0134] In the formula, Δε represents the east-west line of sight positioning deviation caused by the thermal environment, Δη represents the north-south line of sight positioning deviation caused by the thermal environment, ε represents the direction of the remote sensing instrument in the east-west dimension, η represents the direction of the remote sensing instrument in the north-south dimension, c1, c2, c3 represent the east-west dimension benchmark deformation parameters, d1, d2, d3 represent the north-south dimension benchmark deformation parameters. The line of sight positioning deviation model is based on the satellite thermal deformation mechanism. The thermal deformation gradient on the satellite will not change suddenly. Therefore, the line of sight positioning deviation caused by the thermal environment has the characteristics of slow change and satisfies:

[0135]

[0136] In the formula, represents the rate of change of the deformation parameter c1 over time, It represents the rate of change of deformation parameter d1 with time, and k1 and k2 are constants.

[0137] Module M2: Based on the line of sight positioning deviation model, the state equation of the line of sight positioning deviation of the remote sensing instrument is constructed. The state equation of the line of sight positioning deviation of the remote sensing instrument includes constructing the state vector X, and the formula is as follows:

[0138]

[0139] Where X is the state vector, c1, c2, c3 represent the east-west datum deformation parameters, d1, d2, d3 represent the north-south datum deformation parameters, represents the rate of change of the deformation parameter c1 over time, Indicates the rate of change of the deformation parameter d1 over time.

[0140] Combined with the sight positioning deviation model constructed by module M1, the state equation can be further obtained as follows:

[0141]

[0142] In the formula, is the differential result of the state vector X, W is the system noise vector, and C is the state transfer matrix.

[0143] Module M3: Based on the line of sight positioning deviation model, the state observation equation of the line of sight positioning deviation of the remote sensing instrument is constructed. The expression of the state observation equation of the line of sight positioning deviation of the remote sensing instrument is as follows:

[0144] Z=H·X+V

[0145] In the formula, Z represents the state observation vector, X represents the state vector, H represents the state observation matrix, and V represents the observation white noise vector. The state observation matrix H includes two-dimensional pointing angles, which are derived according to the line of sight positioning deviation model of module M1 and are expressed as follows:

[0146]

[0147] In the formula, ε represents the pointing angle of the remote sensing instrument in the east-west dimension during geometric calibration, and η represents the pointing angle of the remote sensing instrument in the north-south dimension during geometric calibration. The state observation is the result of the geometric calibration of the geostationary remote sensing satellite, and the expression of the observation vector Z is:

[0148]

[0149] Where Δε is the east-west line of sight positioning error caused by the thermal environment, and Δη is the north-south line of sight positioning error caused by the thermal environment. The observable white noise vector V reflects the error of the geometric calibration of the remote sensing instrument. The error of the geometric calibration of the geostationary satellite remote sensing instrument includes the attitude measurement error of the satellite, the target extraction error of the remote sensing instrument, the two-dimensional pointing error of the remote sensing instrument, and the geometric error of the control point.

[0150] Module M4: Combine the state equation and the state observation equation to perform real-time recursion of the benchmark deformation based on state estimation. Module M4 includes deformation parameter prediction step, mean square error prediction step, filter gain calculation step, deformation parameter estimation step, and mean square error estimation step. The deformation parameter prediction step includes using the state equation to derive the state vector at the next moment based on the state vector at the current moment to obtain the state vector prediction result, which is expressed as:

[0151] X i / i-1 =C i / i-1 ·X i-1

[0152] In the formula, X i / i-1 represents the state vector prediction result at time i, X i-1 represents the state vector at time i-1, C i / i-1 Represents the state transfer matrix at time i. The mean square error prediction step includes calculating the proportion of state observation results in state estimation, and the calculation formula is as follows:

[0153] P i / i-1 =C i / i-1 ·P i-1 ·C i / i-1 T

[0154] Where P i / i-1 represents the mean square error matrix prediction result at time i, P i-1 represents the mean square error matrix at time i-1, C i / i-1 Represents the state transfer matrix at time i. The initial value P0 needs to be determined in the mean square error prediction step. The initial value P0 is:

[0155]

[0156] Where P0 is the initial value of the mean square error matrix of the line of sight positioning deviation state equation, and ω is the orbital angular velocity of the satellite. The filter gain calculation steps include: After completing the mean square error matrix prediction, the calculation formula of the filter gain matrix is ​​expanded as follows:

[0157] K i =P i / i-1 ·H i T ·(H i ·P i / i-1 ·H i T ) -1

[0158] In the formula, K i represents the filter gain matrix at time i, P i / i-1 represents the mean square error matrix prediction result at time i, H irepresents the state observation matrix at time i, (·) -1 Represents the inverse operation of the matrix. The deformation parameter estimation step includes using the geometric calibration data to estimate the deformation parameters after completing a geometric calibration, and correcting the line of sight positioning deviation model. The expression is:

[0159] X i =X i / i-1 +K i ·(Z i -H i ·X i / i-1 )

[0160] In the formula, X i represents the state vector at time i, X i / i-1 represents the state vector prediction result at time i, K i represents the filter gain matrix at time i, H i Represents the state observation matrix at time i. The mean square error estimation includes that after completing the state vector estimation of the benchmark deformation, the mean square error matrix needs to be iterated once for the recursion at the next moment. The expression is:

[0161] P i =(IK i ·H i )·P i / i-1

[0162] Where P i represents the mean square error matrix estimation result at time i, P i / i-1 represents the mean square error matrix prediction result at time i, K i represents the filter gain matrix at time i, H i Indicates P i-1 represents the state observation matrix at time i, and I represents the identity matrix.

[0163] Module M5: Based on the real-time recursive model obtained by module M4, the deviation estimation results are used to perform real-time correction of line of sight positioning. Module M5 includes real-time recursion based on the state estimation results, calculating the positioning deviation of the remote sensing instrument at different times, and obtaining the accurate line of sight positioning result of the remote sensing instrument according to the line of sight positioning correction formula.

[0164] Those skilled in the art know that, in addition to realizing the system and its various devices, modules, and units provided by the present invention in a purely computer-readable program code, it is entirely possible to realize the same functions in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered as a hardware component, and the devices, modules, and units included therein for realizing various functions can also be regarded as structures within the hardware component; the devices, modules, and units for realizing various functions can also be regarded as both software modules for realizing the method and structures within the hardware component.

[0165] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A method for positioning a stationary remote sensing satellite based on real-time recursion, characterized in that: include: Step S1: Establishing a line-of-sight positioning deviation model caused by remote sensing instrument benchmark deformation; Step S2: constructing a state equation of the remote sensing instrument line of sight positioning deviation according to the line of sight positioning deviation model; Step S3: constructing a state observation equation of the remote sensing instrument line of sight positioning deviation according to the line of sight positioning deviation model; Step S4: combining the state equation and the state observation equation, and performing real-time recursion of the benchmark deformation based on state estimation; Step S5: Based on the real-time recursive model obtained in step S4, the deviation estimation result is used to perform real-time correction of line of sight positioning.

2. The method for positioning a stationary remote sensing satellite based on real-time recursion according to claim 1, characterized in that: In step S1, the sight line positioning deviation of the remote sensing instrument is related to the pointing angle, wherein the pointing direction of the geostationary orbit remote sensing satellite to the earth includes the east-west dimension and the north-south dimension, and the corresponding sight line positioning deviation includes the east-west dimension positioning deviation and the north-south dimension positioning deviation; The relationship between the remote sensing instrument line of sight positioning deviation and the pointing angle, that is, the line of sight positioning deviation model is as follows: Where Δε represents the east-west line of sight positioning deviation caused by the thermal environment, Δη represents the north-south line of sight positioning deviation caused by the thermal environment, ε represents the direction of the remote sensing instrument in the east-west dimension, η represents the direction of the remote sensing instrument in the north-south dimension, c1, c2, c3 represent the east-west dimension benchmark deformation parameters, d1, d2, d3 represent the north-south dimension benchmark deformation parameters.

3. The method for positioning a stationary remote sensing satellite based on real-time recursion according to claim 2, characterized in that: The line-of-sight positioning deviation model is based on the satellite thermal deformation mechanism. The thermal deformation gradient on the satellite will not change suddenly. Therefore, the line-of-sight positioning deviation caused by the thermal environment has the characteristic of slow change. When the following conditions are met: In the formula, represents the rate of change of the deformation parameter c1 over time, It represents the rate of change of deformation parameter d1 with time, and k1 and k2 are constants.

4. The method for positioning a stationary remote sensing satellite based on real-time recursion according to claim 1, characterized in that: The state equation of the remote sensing instrument line of sight positioning deviation includes constructing a state vector X, and the formula is as follows: Where X is the state vector, c1, c2, c3 represent the east-west datum deformation parameters, d1, d2, d3 represent the north-south datum deformation parameters, represents the rate of change of the deformation parameter c1 over time, represents the rate of change of the deformation parameter d1 over time; Combined with the sight line positioning deviation model constructed in step S1, the state equation can be further obtained as follows: In the formula, is the differential result of the state vector X, W is the system noise vector, and C is the state transfer matrix.

5. The method for positioning a stationary remote sensing satellite based on real-time recursion according to claim 1, characterized in that: The observation equation expression of the remote sensing instrument line of sight positioning deviation state is as follows: Z=H·X+V In the formula, Z represents the state observation vector, X represents the state vector, H represents the state observation matrix, and V represents the observation white noise vector; The state observation matrix H includes two-dimensional pointing angles, which are derived according to the line of sight positioning deviation model of step S1 and are expressed as: Where, ε represents the pointing angle of the remote sensing instrument in the east-west dimension during geometric calibration, and η represents the pointing angle of the remote sensing instrument in the north-south dimension during geometric calibration; The state observation is the result of geometric calibration of the geostationary remote sensing satellite, and the expression of the observation vector Z is: Where Δε is the east-west line of sight positioning deviation caused by the thermal environment, and Δη is the north-south line of sight positioning deviation caused by the thermal environment.

6. The method for positioning a stationary remote sensing satellite based on real-time recursion according to claim 5, characterized in that: The observable white noise vector V reflects the error of the geometric calibration of the remote sensing instrument. The error of the geometric calibration of the geostationary satellite remote sensing instrument includes the satellite attitude measurement error, the remote sensing instrument target extraction error, the remote sensing instrument two-dimensional pointing error and the control point geometric error.

7. The method for positioning a stationary remote sensing satellite based on real-time recursion according to claim 1, characterized in that: The step S4 includes a deformation parameter prediction step, a mean square error prediction step, a filter gain calculation step, a deformation parameter estimation step, and a mean square error estimation step; The deformation parameter prediction step includes using a state equation to derive a state vector at the next moment according to a state vector at the current moment to obtain a state vector prediction result, which is expressed as: X i / i-1 =C i / i-1 ·X i-1 Where, X i / i-1 represents the state vector prediction result at time i, X i-1 represents the state vector at time i-1, C i / i-1 Represents the state transfer matrix at time i; The mean square error prediction step includes calculating the proportion of the state observation results in the state estimation, and the calculation formula is as follows: P i / i-1 =C i / i-1 ·P i-1 ·C i / i-1 T Where P i / i-1 represents the mean square error matrix prediction result at time i, P i-1 represents the mean square error matrix at time i-1, C i / i-1 Represents the state transfer matrix at time i; The filter gain calculation step includes: after completing the mean square error matrix prediction, the filter gain matrix calculation formula is calculated as follows: K i =P i / i-1 ·H i T ·(H i ·P i / i-1 ·H i T ) -1 In the formula, K i represents the filter gain matrix at time i, P i / i-1 represents the mean square error matrix prediction result at time i, H i represents the state observation matrix at time i, (·) -1 Represents the inverse operation of a matrix; The deformation parameter estimation step includes, after completing a geometric calibration, using the geometric calibration data to estimate the deformation parameters and correcting the sight positioning deviation model, the expression is: X i =X i / i-1 +K i ·(Z i -H i ·X i / i-1 ) Where, X i represents the state vector at time i, X i / i-1 represents the state vector prediction result at time i, K i represents the filter gain matrix at time i, H i represents the state observation matrix at time i; The mean square error estimation includes that after completing the state vector estimation of the reference deformation once, the mean square error matrix needs to be iterated once for recursion at the next moment. The expression is: P i =(I-K i ·H i )·P i / i-1 Where P i represents the mean square error matrix estimation result at time i, P i / i-1 represents the mean square error matrix prediction result at time i, K i represents the filter gain matrix at time i, H i Indicates P i-1 represents the state observation matrix at time i, and I represents the identity matrix.

8. The method for positioning a geostationary remote sensing satellite based on real-time recursion according to claim 1, characterized in that: In the mean square error prediction step, an initial value P0 needs to be determined, and the initial value P0 is: Where P0 is the initial value of the mean square error matrix of the line-of-sight positioning bias state equation, and ω is the orbital angular velocity of the satellite.

9. The method for positioning a geostationary remote sensing satellite based on real-time recursion according to claim 1, characterized in that: Step S5 includes performing real-time recursion based on the state estimation result, calculating the remote sensing instrument positioning deviation at different times, and obtaining the accurate line of sight positioning result of the remote sensing instrument according to the line of sight positioning correction formula.

10. A geostationary remote sensing satellite line-of-sight positioning system based on real-time recursion, characterized in that: include: Module M1: Establishing a model of line-of-sight positioning deviation caused by remote sensing instrument benchmark deformation; Module M2: constructing a state equation of the remote sensing instrument line of sight positioning deviation according to the line of sight positioning deviation model; Module M3: constructing a state observation equation of the remote sensing instrument line of sight positioning deviation according to the line of sight positioning deviation model; Module M4: combining the state equation and the state observation equation, and performing real-time recursion of the benchmark deformation based on state estimation; Module M5: Based on the real-time recursive model obtained by module M4, the deviation estimation result is used to perform real-time correction of line of sight positioning.

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