Single-target orbit determination method, device, medium and product based on multi-satellite observation

Abstract

A single-target orbit determination method, device, medium and product based on multi-satellite observation belong to the technical field of space target tracking orbit, and solve the problem of low tracking accuracy for orbit flying targets. The method comprises the following steps: creating a line-of-sight unit vector from an observation node to a target node in a satellite body coordinate system; converting the line-of-sight unit vector into an inertial coordinate system; obtaining observation values of each observation satellite; obtaining an observation model of multi-observation satellites observing a single target; obtaining a state model of the multi-observation satellites observing the single target; performing linearization and discretization processing on the observation model and the state model; performing extended Kalman filtering iterative calculation and completing target observation orbit determination. The application is suitable for the field of space target detection technology and space-based optical observation.

Description

Technical Field

[0001] This application relates to the field of space target tracking orbit technology, and in particular to the tracking of orbital flying targets. Background Technology

[0002] Space target tracking utilizes the dynamic models of the target and satellite, along with prior information about the target, to adjust the sensor's pointing direction in real time. Combined with real-time tracking algorithms, the target's initial ephemeris can be updated to enhance tracking. To determine whether a space object is trackable, the angular velocity threshold for sensor pointing needs to be increased to ensure the sensor can catch up with the target.

[0003] To obtain high-quality tracking data, most space target tracking missions are performed by observation satellites equipped with Space Visible Light Cameras (SSOs). For example, ideally, in December, a Dawn-Dusk Sun-synchronous satellite at an altitude of 800 km can track a geostationary object continuously for more than 3 hours per day. Similar to general surveillance, tracking low Earth orbit (LEO) targets is the most challenging due to their high relative speeds.

[0004] Early target tracking by spaceborne optical cameras was accomplished by a single satellite. Related work primarily focused on developing real-time tracking algorithms to support tracking tasks. These included numerous linear and nonlinear algorithms, such as KF, EKF, and UKF, for space target tracking. More recently, some researchers have dedicated themselves to developing a more robust filter to handle measurement glitches and sparse measurement problems frequently encountered in practical applications, as well as for tracking maneuverable targets.

[0005] However, SBO observations have inherent limitations, namely that SBO sensors can only obtain directional information of the observed space object. Therefore, the target's orientation in the observation frame always has the greatest estimation uncertainty. Furthermore, due to the limitations of SBO observations, tracking continuity is usually not ideal, especially for tracking LEO targets.

[0006] Therefore, to improve tracking performance, multiple satellites are needed to perform the task. This necessitates finding new technologies to support single-target tracking with multiple observation satellites. Summary of the Invention

[0007] The purpose of this invention is to solve the problem of low tracking accuracy for orbital targets in existing systems, and to provide a method, device, medium and product for determining the orbit of a single target based on multi-satellite observation.

[0008] This invention is achieved through the following technical solution: In one aspect, this invention provides a method for determining the orbit of a single target based on multi-satellite observations, the method comprising:

[0009] Step 1: Establish a multi-star observation angle measurement model, which specifically includes:

[0010] Step 1.1: By measuring the azimuth and elevation angles of the target satellite in the observation satellite's body coordinate system, create a line-of-sight unit vector from the observation node to the target node in the observation satellite's body coordinate system;

[0011] Step 1.2 Convert the line-of-sight unit vector from the observation node to the target node in the observation satellite body coordinate system into a line-of-sight unit vector in the inertial coordinate system;

[0012] Step 1.3: Obtain the observation values ​​for each observation satellite;

[0013] Step 1.4: Process the observations from each satellite to obtain the observation model for a single target observed by multiple satellites:

[0014]

[0015] in, , This represents the observed value when the Kth observation satellite observes the target. , , Let K be the position component of the Kth observation satellite in the inertial frame.

[0016] The target's state vector represents the target's position and velocity.

[0017] Step 2: Obtain the state model for single-target observation by multiple observation satellites;

[0018] Step 3: Linearize and discretize the observation model and the state model;

[0019] Step 4: Perform extended Kalman filter iterative calculations and complete target observation and orbit determination.

[0020] Further, in step 1.1, the line-of-sight unit vector from the observation node to the target node in the satellite body coordinate system is:

[0021]

[0022] Where Az is the azimuth angle of the target satellite in the observation satellite's own system, and El is the elevation angle of the target satellite in the observation satellite's own system.

[0023] Further, step 1.2 specifically includes:

[0024] Step 1.2.1, The line-of-sight unit vector, transformed from the satellite's intrinsic coordinate system to the LVLH relative motion coordinate system of the observed star, is as follows:

[0025]

[0026] in, , and These are the three Euler angles: roll, pitch, and yaw.

[0027] Step 1.2.2, will The line-of-sight unit vector is transformed from the LVLH relative motion coordinate system of the observed star to the inertial coordinate system, specifically as follows:

[0028]

[0029] Where i is the orbital inclination of the observed star. It is the right ascension of the ascending node. It is the sum of the angular distance from the pericenter and the true pericenter angle.

[0030] Further, step 1.3 specifically includes:

[0031] Define two planes, each containing the target and the corresponding observed satellite node, and each plane is described by a point and the plane's normal vector;

[0032] The points on the first plane are the observation satellite nodes, and the normal vector of the first plane is defined as:

[0033]

[0034] in, The unit vector representing the observed satellite position is given by the observed satellite position. Since it is a known quantity, the vector is known. Let be the normal vector of the first plane. The unit vector of the line of sight of the observation satellite in the inertial coordinate system;

[0035]

[0036] The expression for the first plane is:

[0037]

[0038] Where x, y, and z are the position components of the observed target in the inertial frame; , , To observe the position components of the satellite in an inertial frame;

[0039] The points in the second plane are still the observed satellite nodes, and the normal vector of the second plane is defined as:

[0040]

[0041] in, For the second plane normal vector, To observe the unit vector of the satellite's line of sight in the inertial coordinate system;

[0042] The expression for the second plane is:

[0043]

[0044] By combining the two planar expressions, we can obtain the equation for the measurement values ​​from the observed satellite to the target:

[0045] ;

[0046] The observed values ​​(x, y, z) can be obtained by solving the equation for the measured values.

[0047] Furthermore, in step 2, the state model for single-target observation by multiple observation satellites includes the state vector of the target and the state vector of the Kth observation satellite:

[0048] The target's state vector consists of the target's position and velocity.

[0049]

[0050] in, The location of the target. The speed of the target;

[0051] The state vector of the Kth observation satellite is the satellite's own position and velocity:

[0052]

[0053] in, In order to observe the satellite's own position, To observe the satellite's own speed.

[0054] Furthermore, the linearization and discretization processing of the state model specifically includes:

[0055] The state differential equation of the target is:

[0056]

[0057] , The target's position and velocity vectors;

[0058] Discretize it, and we have the target state discretization equation:

[0059]

[0060] for The status of the target at any given moment.

[0061] Furthermore, the observation model's discretization process specifically includes:

[0062] The discretized model and matrix of the measurement equation are as follows:

[0063]

[0064]

[0065] In the formula, The measurement equation is after discretization. for The position of the target satellite's inertial frame as observed by the satellite at any given time. for The position of the satellite's inertial frame is constantly monitored.

[0066] Secondly, the present invention provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, it executes the steps of a single-target orbit determination method based on multi-star observation as described above.

[0067] Thirdly, the present invention provides a computer-readable storage medium storing a plurality of computer instructions, the plurality of computer instructions being used to cause a computer to execute a single-target orbit determination method based on multi-satellite observation as described above.

[0068] Fourthly, the present invention provides a computer program product, which, when executed by a processor, implements the single-target orbit determination method based on multi-satellite observation as described above.

[0069] The beneficial effects of this invention are:

[0070] Compared with traditional single-satellite observation for target orbit determination, the dual-satellite observation in this invention can achieve observation convergence faster under the same observation conditions, and the observation and orbit determination accuracy is higher.

[0071] Furthermore, although the EKF single-star observation orbit determination can eventually achieve stable positioning and convergence under suitable initial state errors, the convergence time and the estimation error of final positioning and velocity will also increase as the initial state error increases. In contrast, the dual-star observation orbit determination in this invention is less affected by measurement errors and initial state errors, making it more suitable for high-precision orbit determination.

[0072] This invention summarizes the traditional single-satellite angle-only observation model and proposes a line-of-sight-based multi-satellite orbit determination observation model. It presents an EKF filtering model and the application of the new observation model to EKF. Simulations of single-satellite and multi-satellite orbit determination under a two-body model are performed to analyze the impact of parameters such as initial state error and observation angle noise on filtered orbit determination. Furthermore, simulations of the target observable window are conducted based on a space-based optical camera observation constraint model. Based on the simulation results, it is evident that under favorable observation conditions, two-satellite orbit determination achieves higher accuracy and faster convergence, while being less affected by measurement errors and initial state errors, making it more suitable for high-precision orbit determination and a priority consideration in task allocation.

[0073] This invention is applicable to the field of space-based optical observation in space target detection technology. Attached Figure Description

[0074] To more clearly illustrate the technical solution of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0075] Figure 1 This is the extended Kalman filtering process of the present invention;

[0076] Figure 2-3 This is experimental data from multi-satellite observations;

[0077] Figure 4-5 This is experimental data from single-star observations. Detailed Implementation

[0078] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0079] Specific Implementation Method 1: A method for determining the orbit of a single target based on multi-satellite observations, the method comprising:

[0080] Step 1: Establish a multi-star observation angle measurement model, which specifically includes:

[0081] Step 1.1: By measuring the azimuth and elevation angles of the target satellite in the observation satellite's body coordinate system, create a line-of-sight unit vector from the observation node to the target node in the observation satellite's body coordinate system;

[0082] Step 1.2 Convert the line-of-sight unit vector from the observation node to the target node in the observation satellite body coordinate system into a line-of-sight unit vector in the inertial coordinate system;

[0083] Step 1.3: Obtain the observation values ​​for each observation satellite;

[0084] Step 1.4: Process the observations from each satellite to obtain the observation model for a single target observed by multiple satellites:

[0085]

[0086] in, , This represents the observed value when the Kth observation satellite observes the target. , , Let K be the position component of the Kth observation satellite in the inertial frame.

[0087] The target's state vector represents the target's position and velocity.

[0088] Step 2: Obtain the state model for single-target observation by multiple observation satellites;

[0089] Step 3: Linearize and discretize the observation model and the state model;

[0090] Step 4: Perform extended Kalman filter iterative calculations and complete target observation and orbit determination.

[0091] This implementation provides the following technology:

[0092] 1. Establish a multi-star observation model based solely on angle measurement.

[0093] Observation model:

[0094] The angle measurement of a space-based optical camera can be summarized into two angle measurements: the azimuth (Az) and elevation (El) of the target satellite in the observation satellite's body coordinate system. Through angle measurement, a line-of-sight unit vector from the observation node to the target node can be created in the observation satellite's body coordinate system.

[0095] When multiple observation satellites observe a single target, the multiple observation satellites create multiple line-of-sight unit vectors.

[0096] When using line-of-sight (LOS) angle measurements to observe targets and estimate orbits in an inertial frame, two orthogonal planes are created for each observation satellite, intersecting the observation node and the target. Two planes are defined, each containing the target and the corresponding observation satellite node, requiring a point on the plane and the plane's normal vector. The point on each plane represents the position of the observation node. The normal vector of the first plane is defined as the cross product of the satellite's LOS unit vector and its position unit vector. The normal vector of the second plane is calculated by cross-product of the normal vector of the first plane and the observation satellite's LOS unit vector.

[0097] Using the equations for each plane as the measurement model, the terms containing the measured values ​​(elevation (E1) and azimuth (A2)) are isolated on one side of the equation. The terms containing the measured values ​​are the components of the normal vector of each plane. This yields a measurement model for multi-star observations using only angle measurements.

[0098] State model:

[0099] The target's state vector represents its position and velocity, while the observation satellite's state vector represents its position and velocity.

[0100] 2. Multi-satellite observation EKF filtering orbit determination

[0101] Linearization and discretization: The state equations of multi-satellite measurements are nonlinear and continuous, requiring linear discretization; the measurement equations are nonlinear and discrete, requiring linearization.

[0102] After performing the linear discretization process, it can be done according to... Figure 1 The process involves extended Kalman filtering iterative calculations to complete the target observation and orbit determination. Here, P, R, and Q represent the covariances of state, measurement, and process noise, respectively.

[0103] This implementation presents a high-precision orbit determination technical solution, creating an observation model for observing a single target by an observation satellite. This model enables faster convergence of observations under the same observation conditions and achieves higher orbit determination accuracy.

[0104] Specific implementation method two is a further limitation on the single-target orbit determination method based on multi-satellite observation described in implementation method one. In this implementation method, step 1.1 is further limited, specifically including:

[0105] In step 1.1, the line-of-sight unit vector from the observation node to the target node in the satellite body coordinate system is:

[0106]

[0107] Where Az is the azimuth angle of the target satellite in the observation satellite's own system, and El is the elevation angle of the target satellite in the observation satellite's own system.

[0108] This implementation creates a line-of-sight unit vector from the observation node to the target node in the observation satellite body coordinate system, which is used to establish a multi-satellite observation angle measurement model.

[0109] Specific implementation method three is a further limitation on the single-target orbit determination method based on multi-satellite observation described in implementation method two. In this implementation method, step 1.2 is further limited, specifically including:

[0110] Step 1.2 specifically includes:

[0111] Step 1.2.1, The line-of-sight unit vector, transformed from the satellite's intrinsic coordinate system to the LVLH relative motion coordinate system of the observed star, is as follows:

[0112]

[0113] in, , and These are the three Euler angles: roll, pitch, and yaw.

[0114] Step 1.2.2, will The line-of-sight unit vector is transformed from the LVLH relative motion coordinate system of the observed star to the inertial coordinate system, specifically as follows:

[0115]

[0116] Where i is the orbital inclination of the observed star. It is the right ascension of the ascending node. It is the sum of the angular distance from the pericenter and the true pericenter angle.

[0117] In this embodiment, the multi-star angle measurement model is established in an inertial coordinate system, so it is necessary to convert the line-of-sight unit vector in this system.

[0118] Specific implementation method four is a further limitation on the single-target orbit determination method based on multi-satellite observation described in implementation method three. In this implementation method, step 1.3 is further limited:

[0119] Step 1.3 specifically includes:

[0120] Define two planes, each containing the target and the corresponding observed satellite node, and each plane is described by a point and the plane's normal vector;

[0121] The points on the first plane are the observation satellite nodes, and the normal vector of the first plane is defined as:

[0122]

[0123] in, The unit vector representing the observed satellite position is given by the observed satellite position. Since it is a known quantity, the vector is known. Let be the normal vector of the first plane. The unit vector of the line of sight of the observation satellite in the inertial coordinate system;

[0124]

[0125] The expression for the first plane is:

[0126]

[0127] Where x, y, and z are the position components of the observed target in the inertial frame; , , To observe the position components of the satellite in an inertial frame;

[0128] The points in the second plane are still the observed satellite nodes, and the normal vector of the second plane is defined as:

[0129]

[0130] in, For the second plane normal vector, To observe the unit vector of the satellite's line of sight in the inertial coordinate system;

[0131] The expression for the second plane is:

[0132]

[0133] By combining the two planar expressions, we can obtain the equation for the measurement values ​​from the observed satellite to the target:

[0134] .

[0135] In this embodiment, when multiple satellites use line-of-sight angle measurements to observe the target and estimate its orbit in an inertial frame, two orthogonal planes will be created for each observation satellite, which intersect with the observation node and the target.

[0136] Specific implementation method five is a further limitation on the single-target orbit determination method based on multi-satellite observation described in implementation method one. In this implementation method, the state model for single-target observation by multiple observation satellites in step 2 is further defined, specifically including:

[0137] In step 2, the state model for single-target observation by multiple observation satellites includes the target's state vector and the state vector of the Kth observation satellite:

[0138] The target's state vector consists of the target's position and velocity.

[0139]

[0140] in, The location of the target. The speed of the target;

[0141] The state vector of the Kth observation satellite is the satellite's own position and velocity:

[0142]

[0143] in, In order to observe the satellite's own position, To observe the satellite's own speed.

[0144] This implementation method yields a state model for single-target observation using multiple observation satellites.

[0145] Specific implementation method six is ​​a further limitation on the single-target orbit determination method based on multi-satellite observations described in implementation method one. In this implementation method, the linearization and discretization processing of the state model is further limited, specifically including:

[0146] The linearization and discretization of the state model specifically includes:

[0147] The state differential equation of the target is:

[0148]

[0149] , The target's position and velocity vectors;

[0150] Discretize it, and we have the target state discretization equation:

[0151]

[0152] for The status of the target at any given moment.

[0153] The linearized and discretized equations in this embodiment are used for subsequent EKF filtering iterative calculations.

[0154] Specific implementation method seven is a further limitation on the single-target orbit determination method based on multi-satellite observations described in implementation method one. In this implementation method, the personalized discretization processing of the observation model is further limited, specifically including:

[0155] The observation model's discretization process specifically includes:

[0156] The discretized model and matrix of the measurement equation are as follows:

[0157]

[0158]

[0159] In the formula, The measurement equation is after discretization. for The position of the target satellite's inertial frame as observed by the satellite at any given time. for The position of the satellite's inertial frame is constantly monitored.

[0160] Specific implementation method eight, this implementation method is an embodiment of the single-target orbit determination method based on multi-satellite observation as described above, specifically including:

[0161] 1. Establish a multi-star observation model based solely on angle measurement.

[0162] Step 1: By measuring the azimuth (Az) and elevation (El) angles of the target satellite in the observation satellite's body coordinate system, create a line-of-sight unit vector from the observation node to the target node in the observation satellite's body coordinate system. .

[0163]

[0164] Step Two: The multi-star angle measurement model is established in an inertial coordinate system, therefore, it is necessary to transform the line-of-sight unit vector in this system. The process is as follows:

[0165] First of all Transformation from the satellite's intrinsic coordinate system to the LVLH relative motion coordinate system of the observed star , and These are the three Euler angles: roll, pitch, and yaw.

[0166]

[0167] Next, LOS is transferred from the LVLH relative motion coordinate system of the observed star to the inertial coordinate system. i It is the orbital inclination of the observed star. It is the right ascension of the ascending node. It is the sum of the angular distance from the pericenter and the true anterior angle:

[0168]

[0169] Step 3: When multiple observation satellites are observing a single target, each satellite can establish a Line of Sight (LOS). Following the method above, N observation satellites establish N unit line-of-sight vectors in inertial frames (simplified as...). ):

[0170]

[0171] Step 4: Obtain the observation values ​​for each observation satellite.

[0172] When multiple satellites use line-of-sight angle measurements to observe targets and estimate orbits in an inertial frame, two orthogonal planes will be created for each observation satellite, intersecting with the observation node and the target.

[0173] Define two planes, each containing the target and the corresponding observed satellite node, and each plane is described by a point and the plane's normal vector.

[0174] The point on the first plane is the observation satellite node, and its normal vector is defined as the unit vector of the line of sight in the inertial frame of the observation satellite. The cross product with the unit vector R.

[0175]

[0176] in, The unit vector representing the observed satellite position is given by the observed satellite position. Since it is a known quantity, the vector is known. Let be the normal vector of the first plane. This is the unit vector of the line of sight of the observation satellite in the inertial coordinate system.

[0177]

[0178] Therefore, the expression for the first plane is:

[0179]

[0180] in, x, y, z To observe the position components of the target in the inertial frame; , , To observe the position component of the satellite in the inertial frame.

[0181] The points on the second plane are still observation satellite nodes, and the normal vector is calculated by cross product of the normal vector of the first plane and the line-of-sight unit vector of the observation satellite.

[0182]

[0183] in, Let this be the normal vector of the second plane. This is the unit line-of-sight vector of the observation satellite in the ECI frame.

[0184] The expression for the second plane is:

[0185]

[0186] Therefore, by combining the two planar expressions, we can obtain the equation for the measurement value from the observed satellite to the target:

[0187]

[0188] The observed values ​​(x, y, z) can be obtained by solving the equation for the measured values.

[0189] Step 5: Process the observations from each satellite to obtain an observation model for a single target observed by multiple satellites.

[0190] By processing the measurements from the observed satellites, we can obtain:

[0191]

[0192] Clearly, for each observation satellite, two measurements will be provided; that is, for the Kth observation satellite, we have:

[0193]

[0194] In the formula, , This represents the observed value when the Kth observation satellite observes the target.

[0195] For multiple observation satellites, the measurements from each satellite are combined, and the target position is represented by... The alternative representation yields the observation model for a single target observed by multiple observation satellites (this model is the measurement equation without discretization):

[0196]

[0197] Step Six: Obtain the state model for single-target observation by multiple observation satellites. The state model includes the target's state vector and the state vector of the Kth observation satellite:

[0198] The target's state vector consists of its position and velocity.

[0199]

[0200] in, The location of the target. The speed of the target.

[0201] The state vector of the observation satellite (Kth satellite) is the position and velocity of the observation satellite itself, and this state vector is a known quantity.

[0202]

[0203] in, In order to observe the satellite's own position, To observe the satellite's own speed.

[0204] Step 7: Linearization and discretization of the observation model and state model.

[0205] The state equations for multi-satellite measurements are nonlinear and continuous, requiring linearization and discretization.

[0206] The measurement equation is nonlinear and discrete, and needs to be linearized.

[0207] The state differential equation of the target is:

[0208]

[0209] , Let be the target's position and velocity vectors. Discretizing them, we have:

[0210]

[0211] for The state of the target at any given time. k represents... Various data are processed at all times, with the subscript k.

[0212] when Enough hours Available Expanding to a Taylor series:

[0213]

[0214]

[0215] Substituting into the discretization equation of the target state, we have:

[0216]

[0217] This represents the error vector during linearization. This represents the state noise covariance matrix, and this represents the solution of the covariance.

[0218] Jacobian matrix at the state estimate for:

[0219]

[0220]

[0221] In the formula, The Earth's gravitational constant has a value of [value missing]. km 3 / s 2 , This is the state estimate at time t. This is the estimated position of the target at that moment. This corresponds to the time.

[0222] The discretized model and matrix of the measurement equation are as follows:

[0223]

[0224]

[0225] In the formula, The measurement equation is after discretization. for The position of the target satellite's inertial frame as observed by the satellite at any given time. for Observe the position of the satellite's inertial frame at all times.

[0226] Step 8: Perform extended Kalman filter iterative calculations and complete target observation and orbit determination.

[0227] After completing the linear discretization process of the observation model and the state model, according to Figure 1 The process involves extended Kalman filtering iterative calculations and target observation and orbit determination.

[0228] Where P, R, and Q represent the covariances of state, measurement, and process noise, respectively. The specific process is as follows:

[0229] 1) Obtain the initial state estimate of a single target measured by multiple satellites.

[0230] In order to obtain an initial state estimate, in addition to providing an initial error, some literature uses the Herrick Gibbs method.

[0231]

[0232] Represents the i-th measurement value, where:

[0233]

[0234]

[0235] Once the three locations are determined, the velocity at the second time point is determined as follows:

[0236]

[0237] and:

[0238] In the formula, , , For the time corresponding to the i-th measurement value, the target x-coordinate and the three coordinate components of the first plane normal vector.

[0239] Therefore, the initial state estimate for multi-star measurements is:

[0240]

[0241] 2) Calculate the Kalman gain and update the measurement.

[0242] Based on the initial state estimation and initial error covariance estimation Calculate the Kalman gain K k .

[0243]

[0244] In the formula, the subscript k represents State and error at time

[0245] Based on the calculated Kalman gain, update the initial state estimate from the first iteration or the predicted state estimate from subsequent iterations. And update the error coequation .

[0246]

[0247] In the formula, I is the identity matrix.

[0248] 3) Calculate the target state vector forward, and calculate the target state vector and error covariance at the next moment.

[0249] Based on the updated state and error from the measurement, update and predict the state and error for the next time step.

[0250] The differential equation is:

[0251]

[0252]

[0253] In the formula,

[0254]

[0255] For target state estimation, Let Q represent the direction cosine matrix of the coordinate transformation, and let Q be the covariance matrix of the process noise.

[0256] Integrating the two differential equations above yields the predicted state value for the next time step. and error prediction value .

[0257] 2) and 3) Through continuous iteration, the observations of multiple observation satellites on a single target will converge to the true value, thereby obtaining the target's state vector (position and velocity) information.

[0258] By following the steps described above, the observation and orbit determination process of a single target satellite by multiple observation satellites can be achieved.

[0259] The specific technical effects of this invention include:

[0260] The standard deviation of the azimuth and elevation angle measurements for both single-star and multi-star observations (two-star observations were used in the experiment) was 1. The filtering period T is 2s, there is no process noise, and the initial state estimation error is [5,5,5,0.005,0.005,0.005]T (case1), [10,10,10,0.01,0.01,0.01]T (case2) and [20,20,20,0.02,0.02,0.02]T (case3).

[0261] Experimental data such as Figure 2-5 As shown, under the same observation conditions, multi-satellite observations have higher accuracy, faster convergence, and are less affected by measurement errors and initial state errors, making them more suitable for high-precision orbit determination and should be given priority in mission allocation.

[0262] Under single-satellite observation conditions, the final RMS position estimation errors for cases 1, 2, and 3 are 1.23 km, 1.51 km, and 1.9 km, respectively, and the final RMS velocity estimation errors are 0.001 km / s, 0.0013 km / s, and 0.0016 km / s, respectively. It can be seen that EKF single-satellite orbit determination can achieve stable positioning and convergence under suitable initial state errors. However, as the initial state error increases, the convergence time and the estimation errors for final positioning and velocity also increase.

[0263] In multi-satellite observations, the final RMS position estimation errors for cases 1a, 2a, and 3a were 0.61 km, 0.63 km, and 0.65 km, respectively, while the final RMS velocity estimation errors were 0.0009 km / s, 0.0011 km / s, and 0.0012 km / s, respectively. This shows that the initial state estimation has a relatively small impact on the accuracy of multi-satellite orbit determination. Compared to single-satellite observations, the final position and velocity errors from multi-satellite observations are smaller, and the convergence speed is significantly improved (converging in approximately 200 s).

[0264] This application first summarizes the constraint model of space-based optical camera observation based on the basic theory of space-based satellite target observation; then it establishes measurement models for single-satellite observation and multi-satellite observation, as well as an EKF filtering model; finally, it conducts simulation of filtering and positioning of satellite targets and analyzes the influencing factors of orbit determination.

Claims

1. A single-target orbit determination method based on multi-satellite observation, characterized in that, The method comprises: Step 1, establishing a multi-satellite observation only angle measurement model, specifically comprising: Step 1.1, creating a line-of-sight unit vector from the observation node to the target node in the observation satellite body coordinate system through the measurement of the azimuth and elevation angles of the target satellite in the observation satellite body coordinate system; Step 1.2, converting the line-of-sight unit vector from the observation node to the target node in the observation satellite body coordinate system into a line-of-sight unit vector in the inertial coordinate system; Step 1.3, obtaining the observation value of each observation satellite, comprising: For each observation satellite, create two orthogonal planes intersecting the observation node and the target, define two planes, wherein each plane contains the target and the corresponding observation satellite node, and each plane is described by a point and the normal vector of the plane; The point of the first plane is the observation satellite node, and the first plane normal vector is defined as: ， wherein, is the position unit vector of the observation satellite, since the position of the observation satellite is a known quantity, thus the vector is known, is the normal vector of the first plane, is the line-of-sight unit vector of the observation satellite in the inertial coordinate system; ， Wherein, the expression of the first plane is: ， The point of the second plane is still the observation satellite node, and the second plane normal vector is defined as: ， wherein, is the second plane normal vector, is the line-of-sight unit vector of the observation satellite in the inertial coordinate system; The expression of the second plane is: ， The measurement value equation of the observation satellite to the target can be obtained by combining the expressions of the two planes: ， The observation value can be obtained by solving the measurement value equation as (x, y, z); Use the equation of each plane as a measurement model, isolate the terms containing the measurement value and the azimuth angle to one side of the equation, and obtain the measurement model of the multi-satellite observation only angle measurement, wherein the terms containing the measurement value are the components of the normal vector of each plane; Step 1.4, processing the observation value of each satellite to obtain the observation model of multiple observation satellites observing a single target: For observation satellite measurement value processing, the following can be obtained: , For each observation satellite, two measurement values will be provided, that is, for the Kth observation satellite, there are: , For multiple observation satellites, the measurements of each satellite are solved simultaneously, and the target position is represented by instead of the observation model when a single target is observed by multiple observation satellites: ， wherein, , represents the observation value of the Kth observation satellite when observing the target, , , is the position component of the Kth observation satellite in the inertial system ; Step 2, obtaining the state model when multiple observation satellites observe a single target; Step 3, linearizing and discretizing the observation model and the state model; Step 4, Extended Kalman filter iteration is calculated and the target observation orbit is completed.

2. The single-target orbit determination method based on multi-satellite observations according to claim 1, characterized in that, In step 1.1, the line-of-sight unit vector from the observation node to the target node in the observation satellite body coordinate system is: ， Wherein, Az is the azimuth angle of the target satellite in the observation satellite body coordinate system, and El is the elevation angle of the target satellite in the observation satellite body coordinate system.

3. The method for determining the orbit of a single target based on multi-satellite observation according to claim 2, characterized in that, Step 1.2, specifically comprising: Step 1.2.1, from the satellite body frame to the LVLH relative motion frame of the observed satellite, is given by: The line-of-sight unit vector in the LVLH relative motion frame of the observed satellite is given by: ， wherein , and are three Euler angles of roll, pitch and yaw angles; Step 1.2.2, the The line-of-sight unit vector in the inertial coordinate system is transformed from the LVLH relative motion coordinate system of the observed star, specifically: ， where i is the orbital inclination of the observed star, is the right ascension of the ascending node, is the sum of the argument of perigee and the true anomaly.

4. The single-target orbit determination method based on multi-satellite observations according to claim 1, wherein, In step 2, the state model when multiple observation satellites observe a single target comprises a target state vector and a Kth observation satellite state vector: The target state vector is the position and velocity of the target: ， wherein, a position targeted, a speed targeted; The state vector of the Kth observation satellite is the position and velocity of the observation satellite itself: ， wherein, is the position of the observation satellite itself, is the velocity of the observation satellite itself.

5. The method according to claim 1, wherein, The state model linearization and discretization process specifically comprises: The target state differential equation is: ， , Position and velocity vector of the target Discretization of the target state differential equation has the target state discretization equation: ， To the status of the momentary target.

6. The method according to claim 1, wherein, The observation model linearization and discretization process specifically comprises: The measurement equation discretization model and matrix are: ， ， wherein is the discretized measurement equation, is is the inertial system position of the target satellite observed by the satellite at time is is the inertial system position of the observing satellite at time 7.A computer device, comprising a memory and a processor, wherein the memory stores a computer program, and the computer device is configured to perform the method according to any one of claims 1-6. The processor executes the steps of the method of any one of claims 1 to 6 when running the computer program stored in the memory.

8. A computer-readable storage medium, characterized in that, The computer readable storage medium stores a plurality of computer instructions for causing a computer to execute the method of any one of claims 1 to 6.

9. A computer program product, characterised in that, The computer program, which is executed by a processor, implements the method of any one of claims 1 to 6.

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