Inter-satellite baseline high-precision measurement and estimation method

Abstract

The application discloses an inter-satellite baseline high-precision measurement and estimation method, and is characterized in that the method comprises the following steps: S1. Estimating and calibrating GNSS measurement information through a star sensor and laser ranging information; S2. Determining a measurement noise variance matrix R, and estimating in combination with satellite motion characteristics and noise characteristics; and S3. Adopting an interactive multiple model unscented Kalman filtering method to perform information processing. In the application, the problems that a measurement scale of an existing method does not meet long-interference baseline measurement requirements, measurement information is single, measurement precision is unknown, and an information processing method is not suitable are overcome, and a method for realizing fusion of GNSS, laser link and star sensor measurement information by using an interactive multiple model unscented Kalman filtering is provided, so that inter-satellite high-precision real-time baseline measurement information is obtained, the demand of future multi-spacecraft formation cooperation for high-precision inter-satellite measurement information is met, and mm-level inter-satellite baseline measurement precision is achieved.

Description

Technical Field

[0001] This invention relates to the field of multi-spacecraft formation collaborative measurement technology, and in particular to a high-precision measurement and estimation method for inter-satellite baselines. Background Technology

[0002] Current spacecraft orbit measurement methods primarily employ ground station Doppler frequency shift orbit determination, GNSS navigation satellite orbit determination, radio signal sources, pulsar navigation, and recursive filtering methods combining ground-sensitive and star-sensitive satellite orbit determination. Ground station orbit determination requires extensive data post-processing before onboard orbit injection, making it a non-real-time orbit determination method used by most spacecraft, as illustrated in patent 20151010107459.6, a method for measuring bistatic differential interferometric baseline coordinates and deformation. GNSS navigation satellite orbit determination accuracy is related to the visibility of the navigation satellite and signal strength, achieving accuracy on the order of 10 cm, as illustrated in patent 201110241765.0, a GPS-based inter-satellite baseline measurement method for formation flying satellites. There are also orbit determination methods based on radio signal sources and pulsar X-ray signals, such as patent 201310263315.0, a non-cooperative radio signal source positioning method based on a high-orbit three-star time difference system, with a positioning accuracy of about 0.5 km; and patent 201210323581.3, a constellation orientation simulation system based on X-ray pulsars, but pulsar navigation applications are currently under research and not yet practical. Satellite orbit estimation methods based on ground-sensitive and star-sensitive direction vectors are suitable for geostationary orbits, with an accuracy on the order of 10 km, such as the 6-month autonomous orbit determination method for the XX-2 / YY-2 satellites.

[0003] Zhang Lei and others from Aerospace Dongfanghong Satellite Co., Ltd. invented a "GPS-based Inter-satellite Baseline Measurement Method for Formation-Orbiting Satellites" (Authorization Announcement No. CN102323597B). This invention utilizes GPS receivers on two satellites to receive navigation satellite signals and calculate their respective positioning information. Then, the information is transmitted via inter-satellite communication between the two satellites to complete the inter-satellite baseline measurement. However, this method only utilizes GPS information and is only suitable for small-scale satellite formation configurations (kilometer-scale), and cannot achieve wide-area long baseline measurements.

[0004] Yang Junwei and others from the 10th Research Institute of China Electronics Technology Group Corporation invented a "High-Precision Relative Positioning Method for Medium- and Long-Baseline GNSS Receivers" (application number CN201510263235.4). This invention utilizes a combination of robust filtering and extended Kalman filtering to achieve medium- and long-baseline relative positioning. However, this invention fails to specify the achievable level of accuracy. Furthermore, the application of extended Kalman filtering to linearize the nonlinear state equation increases computational complexity while sacrificing accuracy, and may even lead to divergence during multi-sensor information fusion.

[0005] Jeffrey H. Hunt invented the "Satellite location determination system" (patent number US67788886B2), which applies femtosecond laser links to the relative positioning of satellites in a constellation, enabling the constellation to maintain a high-precision configuration. However, this method requires that the components of each axis of the baseline in the geocentric inertial coordinate system be known.

[0006] Therefore, this paper proposes a high-precision measurement and estimation method for inter-satellite baselines. Summary of the Invention

[0007] The purpose of this invention is to provide a high-precision measurement and estimation method for inter-satellite baselines in order to solve the above-mentioned problems.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] A method for high-precision measurement and estimation of inter-satellite baselines includes the following steps:

[0010] S1. Estimate and calibrate GNSS measurement information using star sensors and laser ranging information;

[0011] S2. Determine the measurement noise variance matrix R in each model, and estimate it by combining the satellite motion characteristics and noise characteristics;

[0012] S3. An interactive multi-model unscented Kalman filter method is used for information processing;

[0013] The Interactive Multi-Model Unscented Kalman Filter (IMM-UKF) filtering method employs multiple filters in parallel processing, with each filter corresponding to a different state-space model. The model probability is updated based on the model matching likelihood function, and the state estimates corrected by all filters are combined to obtain the state estimate. Compared with unscented Kalman filtering, IMM-UKF has better robustness and can overcome the problem of large errors that may occur in single-model estimation through effective weighted fusion of multiple models.

[0014] S4. Simulation comparison of interferometric baseline measurement methods based on interactive multi-model unscented Kalman filtering method;

[0015] After modeling and simulation analysis of the proposed inter-satellite interferometric baseline measurement and estimation method, considering that the triaxial measurement accuracy of GNSS inter-satellite baseline is better than 30 mm, the laser link distance measurement accuracy is better than 1 μm, and the inter-satellite pointing angle measured by the star sensor as an image sensor is better than 1 arcsecond, after filtering, the overall baseline estimation accuracy can reach within 1 arcsecond.

[0016] Preferably, the method for estimating and calibrating GNSS measurement information using star sensors and laser ranging information in step S1 specifically includes the following steps:

[0017] S11. The Runge-Kutta algorithm is used to discretize the satellite orbit equations to obtain a nonlinear stochastic jump system model and establish the state equations;

[0018] S12. The inter-satellite relative position parameters measured by the star sensor and laser link, as well as the satellite position pseudorange measured by GNSS, are used as a joint measurement vector, including the AB dual-satellite positions measured by GNSS, the AB inter-satellite distance (XYZ) measured by laser, and the satellite relative angles (azimuth and elevation) converted from the inertial attitude measured by the star sensor.

[0019] Preferably, step S3 employs an interactive multi-model unscented Kalman filter method for information processing, specifically including the following steps:

[0020] S31. Input interaction of each model;

[0021] S32. Perform unscented Kalman filtering on each model;

[0022] S33. Update the model probabilities;

[0023] S34. Interaction of outputs from each model.

[0024] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0025] 1. In this application, the inter-satellite interferometric baseline measurement and estimation method is used to add high-precision inter-satellite distance measurement information on the basis of GNSS coarse measurement information, so that the measurement accuracy reaches the millimeter level.

[0026] 2. In this application, laser link pointing and tracking acquisition (TPC) is required during the measurement process, and the data processing after the measurement requires inter-satellite information exchange, which is suitable for multi-satellite formation collaborative missions or satellite constellation collaborative control missions.

[0027] 3. In this application, the measurement cycles of GNSS, star sensors and laser links are different, requiring the design of filter models for asynchronous sampling. GNSS measurement information includes XYZ three-axis position, while the laser link only has one-dimensional measurement information of inter-satellite distance. The measurement equation construction can superimpose different accuracies and different measurement dimensions. Attached Figure Description

[0028] Figure 1 A schematic diagram of a high-precision inter-satellite baseline measurement and estimation method provided according to an embodiment of the present invention is shown.

[0029] Figure 2 This diagram illustrates an inter-satellite interferometric baseline for a high-precision measurement and estimation method for inter-satellite baselines provided by an embodiment of the present invention.

[0030] Figure 3 A diagram illustrating the relationship between satellite attitude measured by a star sensor and inter-satellite baseline direction in a high-precision inter-satellite baseline measurement and estimation method according to an embodiment of the present invention is shown.

[0031] Figure 4 The illustration shows a comparison of baseline measurement errors before filtering and with UKF and IMM-UKF estimation, respectively, for a high-precision inter-satellite baseline measurement and estimation method provided according to an embodiment of the present invention. Detailed Implementation

[0032] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0033] Please see Figure 1-4 The present invention provides a technical solution:

[0034] A method for high-precision measurement and estimation of inter-satellite baselines includes the following steps:

[0035] S1. Estimate and calibrate GNSS measurement information using star sensors and laser ranging information;

[0036] Specifically, the method for estimating and calibrating GNSS measurement information using star sensors and laser ranging information in step S1 includes the following steps:

[0037] S11. The Runge-Kutta algorithm is used to discretize the satellite orbit equations to obtain a nonlinear stochastic jump system model and establish the state equations;

[0038] like Figure 1 As shown, the positions and velocities of satellite A and satellite B in the geocentric inertial coordinate system are respectively... From satellite orbital dynamics, the state equation is obtained (12-dimensional, but only 6-dimensional is shown for satellite A as an example):

[0039]

[0040] Where μ is the Earth's gravitational coefficient, R e The radius of the Earth;

[0041] S12. The inter-satellite relative position parameters measured by the star sensor and the laser link, as well as the satellite position pseudorange measured by GNSS, are used as a joint measurement vector, including the AB dual-satellite positions (XYZ) measured by GNSS, the AB inter-satellite distance measured by laser, and the satellite relative angles (azimuth and elevation angles) converted from the inertial attitude measured by the star sensor.

[0042] GNSS can measure the positions of satellites A and B, a laser link can measure the distance between the two satellites, and a star sensor, acting as an image sensor, can obtain the azimuth of the baseline between the two satellites. By fusing these three types of measurement information, the measurement equation is obtained:

[0043]

[0044] In the measurement equation, the first 6 lines are the positions of satellites A and B obtained by GNSS, the 7th line is the distance between satellites A and B obtained by the laser link, the last two lines are the baseline azimuth obtained by the star sensor, and V is the measurement noise.

[0045] This section further explains how the star sensor obtains the azimuth information about the baseline for the last two lines, such as... Figure 3 As shown, assume that the body coordinate system of satellite A is O. A x A y A z A Satellite B's body coordinate system is O. B x B y B z B Let's assume that satellite A's laser is installed at -x A The laser of satellite B is mounted on the x axis. B The positions of satellites A and B in the geocentric inertial coordinate system are (x, y). A y A , z A ), (x B y B , z B When establishing a laser link, x should be satisfied. A axis, x B The axes are in the same direction and are also in the same direction as the baseline between the two satellites. Assuming that the relative attitude of satellites A and B is measured by the star sensor as an image sensor in Euler angles (pitch angles), Let yaw angle ψ and roll angle γ represent the attitude of the satellite relative to the geocentric inertial frame. Then, the direction cosine matrix between the satellite's attitude and the geocentric inertial frame is:

[0046]

[0047] Among them, B GThe first column represents the unit vector of the satellite's x-axis in the geocentric inertial frame, while the unit vector of the baseline between the two satellites in the geocentric inertial frame is:

[0048]

[0049] By making these two vectors equal, the conversion between satellite attitude and inter-satellite baseline direction can be achieved. It's worth noting that the information output by the star sensor is a quaternion; converting it to Euler angles always yields B. G .

[0050] S2. Determine the measurement noise variance matrix R in each model, and estimate it by combining the satellite motion characteristics and noise characteristics;

[0051] Generally, the measurement noise variance matrix is ​​closely related to the measurement accuracy of the sensor, that is, it is related to the measurement accuracy of GNSS and laser links. The measurement variance requires long-term probability statistics and it is difficult to give an accurate value. Therefore, among multiple models, the first model takes the upper bound of the estimated noise variance, and the second takes the lower bound of the estimated noise variance. You can also add models to cover more possibilities.

[0052] S3. An interactive multi-model unscented Kalman filter method is used for information processing;

[0053] Specifically, step S3 employs an interactive multi-model unscented Kalman filter method for information processing, which includes the following steps:

[0054] S31. Input interaction of each model;

[0055] From state estimation Compared with the model probability μ of each filter in the previous step j (k-1) yields the mixed state estimate Covariance P oj (k-1 / k-1), using the mixed estimate as the initial state of the current loop, the specific parameters are calculated as follows:

[0056] The predicted probability of model j is:

[0057]

[0058] Mixture probability from model i to model j:

[0059]

[0060] The mixed-state estimate of model j is:

[0061]

[0062] Estimation of the mixture covariance of model j:

[0063]

[0064] S32. Perform unscented Kalman filtering on each model;

[0065] a. Using an unscented transformation, obtain 2n+1 Sigma points X. (i) (k / k) and its corresponding weight ω (i) .

[0066]

[0067] b. Calculate the one-step prediction of the Sigma point.

[0068] X (i) (k+1|k)=f[X (i) (k|k)]

[0069] c. Calculate the one-step prediction of the system state variables and the covariance matrix.

[0070]

[0071] d. Substitute the Sigma point set into the observation equation to obtain the predicted observations.

[0072] Z (i) (k+1|k)=h[X (i) (k+1|k)]

[0073] e. Weight the observations of the Sigma point set and sum them to obtain the mean and covariance of the system predictions.

[0074]

[0075] f. Calculate the Kalman gain matrix

[0076]

[0077] g. Computational system's state update matrix and covariance update matrix

[0078]

[0079] S33. Update the model probabilities;

[0080] The likelihood function is used to update the model probability μ. j (k), the likelihood function of model j is:

[0081]

[0082] in,

[0083]

[0084] The probability of model j is:

[0085]

[0086] Note: c is the normalization coefficient;

[0087] S34. Interaction of outputs from each model;

[0088] Based on the model probabilities, the estimation results of each filter are weighted and combined to obtain the overall state estimate:

[0089]

[0090] S4. Simulation comparison of the interferometric baseline measurement method based on the interactive multi-model unscented Kalman filter (IMM-UKF) method;

[0091] By subtracting the position coordinates of satellites A and B, the interferometric baseline can be obtained.

[0092] [x A -x B y A -y B z A -z B ] T ;

[0093] Laser link ranging accuracy is higher than that of GNSS, such as Figure 3 As shown, a simulation comparison is performed between GNSS-only and the IMM-UKF-based interferometric baseline measurement method. The simulation conditions are: baseline length on the order of kilometers, GNSS measurement error (standard deviation) of 0.01m, laser link measurement error of 10⁻⁶m, and star sensor measurement accuracy on the order of arcseconds. Figure 4 It is evident that the interferometric baseline measurement method based on IMM-UKF achieves the fusion of measurement information, which significantly improves measurement accuracy compared to using only GNSS information.

[0094] The table below shows a comparison of simulation results under different simulation conditions. It can be seen that both the UKF (Unscented Kalman Filter) and IMM-UKF (Interactive Multi-Model Unscented Kalman Filter) methods improve measurement accuracy by fusing various measurement information. However, the IMM-UKF method has higher accuracy than the UKF method.

[0095]

[0096] The above description of the embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for high-precision measurement and estimation of inter-satellite baselines, characterized in that, Includes the following steps: S1. Estimate and calibrate GNSS measurement information using star sensors and laser ranging information; S2. Determine the measurement noise variance matrix R, and estimate it by combining the satellite motion characteristics and noise characteristics; S3. An interactive multi-model unscented Kalman filter method is used for information processing; S4. Simulation comparison of interferometric baseline measurement methods based on interactive multi-model unscented Kalman filtering method; The method for estimating and calibrating GNSS measurement information using star sensors and laser ranging information in step S1 specifically includes the following steps: S11. The Runge-Kutta algorithm is used to discretize the satellite orbit equations to obtain a nonlinear stochastic jump system model and establish the state equations; Let the positions and velocities of satellite A and satellite B in the geocentric inertial coordinate system be respectively... From satellite orbital dynamics, the state equation is obtained: Where μ is the Earth's gravitational coefficient, R e The radius of the Earth; S12. The inter-satellite relative position parameters measured by the star sensor and the laser link, as well as the satellite position pseudorange measured by GNSS, are used as a joint measurement vector, including the AB dual-satellite positions measured by GNSS, the AB inter-satellite distance measured by laser, and the satellite relative angle converted from the inertial attitude measured by the star sensor. GNSS measures the positions of satellites A and B, the laser link measures the distance between the two satellites, and the star sensor, acting as an image sensor, obtains the azimuth of the baseline between the two satellites. These three measurements are fused to obtain the measurement equation: In the measurement equation, the first 6 lines are the positions of satellites A and B obtained by GNSS, the 7th line is the distance between satellites A and B obtained by the laser link, the last two lines are the baseline azimuth obtained by the star sensor, and V is the measurement noise. Explain how the azimuth information about the baseline for the last two lines is obtained from the star sensor, assuming that the body coordinate system of satellite A is O. A x A y A z A Satellite B's body coordinate system is O. B x B y B z B Let's assume that the laser of satellite A is installed at -x A The laser of satellite B is mounted on the x axis. B The positions of satellites A and B in the geocentric inertial coordinate system are (x, y). A y A , z A ), (x B y B , z B When establishing a laser link, x should be satisfied. A axis, x B With the axes aligned in the same direction and also aligned with the baseline direction between the two satellites, assuming the relative attitude of satellites A and B, measured by the star sensor as an image sensor, is represented by Euler angles, then the direction cosine matrix between the satellite's relative attitude and the geocentric inertial frame is: Among them, B G The first column represents the unit vector of the satellite's x-axis in the geocentric inertial frame, while the unit vector of the baseline between the two satellites in the geocentric inertial frame is: By making these two vectors equal, the conversion between satellite attitude and inter-satellite baseline direction is achieved. The information output by the star sensor is a quaternion, which is converted into Euler angles to obtain B. G .

2. The method for high-precision measurement and estimation of inter-satellite baselines according to claim 1, characterized in that, Step S3 employs an interactive multi-model unscented Kalman filter method for information processing, specifically including the following steps: S31. Input interaction of each model; S32. Perform unscented Kalman filtering on each model; S33. Update the model probabilities; S34. Interaction of outputs from each model.

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