A steady-state gain correction GNSS autonomous navigation system based on normalized orbital parameters

Abstract

The application relates to a steady-state gain correction GNSS autonomous navigation system based on normalized orbit parameters, which comprises a GNSS information conversion module, an orbit extrapolation updating module, a steady-state gain Kalman filter correction module and a steady-state gain offline calculation module. The application adopts a normalized orbit semi-major axis, an orbit inclination, an ascending node right ascension, an eccentricity vector and a flat latitude amplitude angle as state variables of navigation filter estimation, adopts a Cowell method to perform one-step prediction of the above-mentioned orbit element information, converts position in a WGS84 system output by a GNSS receiver into orbit element information in combination with one-step predicted speed information, and adopts a steady-state gain Kalman filter algorithm to complete filter correction of the above-mentioned orbit element information.

Description

TECHNICAL FIELD

[0001] The application relates to a steady-state gain correction GNSS autonomous navigation system and method based on normalized orbit parameters and belongs to the technical field of autonomous navigation. BACKGROUND

[0002] In order to realize autonomous operation in orbit, an inertial position and speed information of a spacecraft needs to be determined in real time, and autonomous navigation is realized. The autonomous navigation method using GNSS navigation information is the most commonly used method for near-earth orbit spacecrafts. In the design of an on-board control system, if a filter estimation algorithm with constant gain is used, the system has certain advantages, mainly represented as reducing the symbolic calculation amount of the control system, shortening the program running time in the control period, and avoiding the error covariance matrix in the filter program from losing the matrix positive definiteness due to calculation error accumulation. Related designs have been widely used in the star-sensitive / tao-sensitive / gyro combined attitude determination (Satellite Attitude Dynamics and Control, 2001), star-sensitive / gyro combined attitude determination (Star Sensor Measurement Model and Its Application in Satellite Attitude Determination System, 2003; Constant-gain information filter for attitude determinantion of precision pointing spacecraft, 1996).

[0003] Generally, the autonomous navigation algorithm based on GNSS measurement information has the characteristics of time-varying nonlinearity in the system equation, and needs to use the EKF algorithm for filter estimation. The elements of the filter gain matrix have the characteristics of time-varying nonlinearity. SUMMARY

[0004] The technical problem of the application is to overcome the shortcomings of the prior art and provide a steady-state gain correction GNSS autonomous navigation system based on normalized orbit parameters, which is used to solve the problem of autonomous navigation using constant gain correction GNSS output information.

[0005] The technical solution of the application is:

[0006] A steady-state gain correction GNSS autonomous navigation system based on normalized orbit parameters comprises a GNSS information conversion module, an orbit extrapolation update module, a steady-state gain Kalman filter correction module and a steady-state gain offline calculation module.

[0007] The GNSS information conversion module converts GNSS navigation receiver output information according to the position of a satellite in the WGS84 coordinate system at the time ​​​Calculate the satellite's position in the ECI coordinate system Combined with the orbit extrapolation update module outputting the satellite's velocity in the ECI coordinate system after one-step extrapolation, Calculate the normalized orbital feature information at that moment. ;

[0008] The orbit extrapolation update module, based on the output of the Kalman filter correction module for steady-state gain, The satellite's position in the ECI coordinate system after time filtering correction and speed Extrapolation calculation of satellites in Time-normalized orbital element information ;

[0009] The steady-state gain offline calculation module uses a discrete calculation method to calculate the output gain filtering matrix. ;

[0010] The steady-state gain Kalman filter correction module, based on the output of the GNSS information conversion module... Time-normalized orbital element information The extrapolation calculation output by the orbit extrapolation update module Time-normalized orbital element information The gain filtering matrix output by the steady-state gain offline calculation module ,calculate The position of the satellite in the ECI coordinate system estimated by time filtering and speed .

[0011] Furthermore, the GNSS information conversion module calculates normalized orbital element information. Specifically:

[0012] (1) Calculation Navigation information of satellites in the ECI coordinate system The specific calculation formula is as follows:

[0013]

[0014] (2) Calculation Time track semi-major axis The specific calculation formula is as follows:

[0015]

[0016] in, μ It is the gravitational constant;

[0017] (3) Calculation Time eccentricity The specific calculation formula is as follows:

[0018] ;

[0019] (4) Calculation orbital inclination at any moment The specific calculation formula is as follows:

[0020]

[0021]

[0022] in, , , They are respectively Components along the X, Y, and Z axes in the ECI coordinate system;

[0023] (5) Calculation Right ascension of ascending node at moment and latitude angle The specific calculation process is as follows:

[0024] if <1×10 -7 , =0, =arctan2( , );

[0025] if ≥1×10 -7 ,when When ≥0,

[0026] = ,

[0027] when When <0, = ,

[0028] = ;

[0029] in, , , for The components of the satellite's position along the X, Y, and Z axes in the ECI coordinate system at any given time;

[0030] (6) Calculation Argument of perigee at time Peaceful perigee angle The specific calculation process is as follows:

[0031] First, calculate the near-point angle. The calculation formula is:

[0032]

[0033] Second, calculate the true anterior angle. The calculation formula is:

[0034]

[0035] Then, calculate the argument of perigee. ,

[0036]

[0037] Finally, calculate the angle of near-geometry. ,

[0038]

[0039] (7) Calculate Time-normalized orbital element information The specific calculation formula is as follows:

[0040]

[0041] in, The normalized distance unit is bound to the semi-major axis of the satellite's nominal orbit.

[0042] Furthermore, the orbit extrapolation update module, based on the output of the Kalman filter correction module for steady-state gain... The satellite's position in the ECI coordinate system after time filtering correction and speed Extrapolation calculation of satellites in Time-normalized orbital element information The details are as follows:

[0043] (1) Calculate the position, velocity, and acceleration of the first extrapolation.

[0044]

[0045] in, , , The results were obtained by first-order extrapolation. The position, velocity, and acceleration of the satellite in the ECI coordinate system at any given time;

[0046] (2) Calculate the position, velocity, and acceleration of the second extrapolation.

[0047]

[0048] in, , , The results were obtained from second-order extrapolation. The position, velocity, and acceleration of the satellite in the ECI coordinate system at any given time. This is the step size for extrapolation integration;

[0049] (3) Calculate the position, velocity, and acceleration of the third extrapolation.

[0050]

[0051] in, , , The results were obtained from third-order extrapolation. The position, velocity, and acceleration of the satellite in the ECI coordinate system at any given time;

[0052] (4) Calculate the position, velocity, and acceleration of the fourth-order extrapolation.

[0053]

[0054] in, , , The results were obtained from fourth-order extrapolation. The position, velocity, and acceleration of the satellite in the ECI coordinate system at any given time;

[0055] (5) Calculate the position, velocity, and acceleration of the extrapolation step.

[0056]

[0057] in, , The results were obtained by one-step extrapolation of the orbit. The position and velocity of the satellite in the ECI coordinate system at any given time;

[0058] (6) Calculate the orbital elements for one-step extrapolation. .

[0059] Furthermore, step (6) calculates the orbital elements extrapolated in one step. Specifically:

[0060] First, calculate the result obtained by one-step extrapolation. Time track semi-major axis The specific calculation formula is as follows:

[0061]

[0062] Secondly, calculate the result obtained by one-step extrapolation. Time eccentricity The specific calculation formula is as follows:

[0063]

[0064] Third, calculate the result obtained by one-step extrapolation. orbital inclination at any moment The specific calculation formula is as follows:

[0065]

[0066]

[0067] in, , , They are respectively Components along the X, Y, and Z axes in the ECI coordinate system;

[0068] Fourth, calculate the result obtained by one-step extrapolation. Right ascension of ascending node at moment and latitude angle The specific calculation process is as follows:

[0069] if Less than 1×10 -7 , Equal to 0, equals arctan2( , );

[0070] if Greater than or equal to 1×10 -7 ,when When greater than or equal to 0,

[0071] equal

[0072] ,

[0073] when When less than 0, equal

[0074] ,

[0075] equal

[0076] ;

[0077] in, , , for The components of the satellite's position along the X, Y, and Z axes in the ECI coordinate system at any given time;

[0078] Fifth, calculate the result obtained by one-step extrapolation. Argument of perigee at time Peaceful perigee angle The specific calculation process is as follows: first, calculate the near-point angle. The calculation formula is:

[0079]

[0080] Calculate the true anterior angle obtained by one-step extrapolation. The calculation formula is:

[0081]

[0082] Calculate the perigee argument obtained by one-step extrapolation

[0083]

[0084] Calculate the angle of perigee obtained by one-step extrapolation.

[0085]

[0086] Finally, calculate the result obtained by one extrapolation step. Time-normalized orbital element information The specific calculation formula is as follows:

[0087]

[0088] in, It is a normalized distance unit.

[0089] Furthermore, the specific calculation relationship of the Kalman filter correction module for steady-state gain is as follows:

[0090] (1) Calculate the orbital element information of the filtered estimation

[0091]

[0092] in, For filtering estimation Time-normalized orbital element information; , , , , , for The semi-major axis, inclination, right ascension of the ascending node, eccentricity, argument of perigee, and mean perigee angle are estimated by time-lapse filtering.

[0093] (2) Calculate the position and velocity estimated by filtering.

[0094] First, iterative calculation Latitude argument estimated by time-time filtering Initial value for iterative calculation for The iterative formula is

[0095]

[0096] The termination condition for iterative calculation is Or the number of iterations exceeds 10;

[0097] Secondly, calculation True latitude argument estimated by time-lapse filtering The specific calculation formula is as follows:

[0098]

[0099] Third, calculation Time-filtered estimation of orbital semi-path Earth's center distance radial velocity and tangential velocity The specific calculation formula is as follows:

[0100]

[0101]

[0102]

[0103]

[0104] Fourth, calculation The position of the satellite in the ECI coordinate system estimated by time filtering The specific calculation formula is as follows:

[0105]

[0106] Fifth, calculation The satellite velocity in the ECI coordinate system estimated by time filtering The specific calculation formula is as follows:

[0107] .

[0108] Furthermore, the steady-state gain offline calculation module uses a discrete calculation method to calculate the output gain filtering matrix. The specific calculation process is as follows:

[0109] (1) Calculate the system state error transition matrix

[0110] The formula for calculating the system state error transition matrix is ​​as follows:

[0111]

[0112] in, The value is taken as the semi-major axis of the satellite orbit;

[0113] (2) Calculate the system state transition matrix

[0114] The formula for calculating the system state transition matrix is ​​as follows:

[0115]

[0116] in, It is the identity matrix;

[0117] (3) Calculate the discretized system state error matrix

[0118] The formula for calculating the discretized system state error matrix is ​​as follows:

[0119]

[0120] in, The system state error matrix is ​​3×3;

[0121] (4) Calculate the measurement state transition matrix

[0122] The formula for calculating the measurement state transition matrix is ​​as follows:

[0123]

[0124] (5) Calculate the gain filtering matrix

[0125] The error covariance matrix is ​​calculated iteratively, with the initial value of the error covariance matrix being... ;

[0126] The formula for iterative calculation is:

[0127]

[0128] The termination condition for iterative calculation is or the number of iterations exceeds 10 4 Second-rate;

[0129] in, For the firstk The error covariance matrix obtained in the next iteration The i line, number j Column elements, 0 < i , j ≤ 6. Gain Filtering Matrix The value is the gain matrix at the end of the iteration. .

[0130] Furthermore, this invention proposes an autonomous navigation method for a GNSS autonomous navigation system based on steady-state gain correction using normalized orbit parameters, comprising:

[0131] According to the output of the GNSS navigation receiver Position of the time satellite in the WGS84 coordinate system Sidereal hour angle and the precession matrix Calculate the satellite's position in the ECI coordinate system ;

[0132] Combined with the satellite's velocity in the ECI coordinate system after one extrapolation Calculate the normalized orbital feature information at that moment. ;

[0133] Based on the output The satellite's position in the ECI coordinate system after time filtering correction and speed Extrapolation calculation of satellites in Time-normalized orbital element information ;

[0134] The output gain filter matrix is ​​calculated using a discrete calculation method. ;

[0135] according to Time-normalized orbital element information Extrapolation calculation Time-normalized orbital element information Gain filter matrix calculate The position of the satellite in the ECI coordinate system estimated by time filtering and speed .

[0136] The advantages of this invention compared to the prior art are:

[0137] (1) The system and method described in this invention are improved on the basis of the original autonomous navigation algorithm based on GNSS measurement information using EKF, forming an autonomous navigation algorithm with constant gain correction, which effectively reduces the amount of on-board computation and has no special computation operation, making it easy to implement on-board.

[0138] (2) In the design of the on-board control system, the present invention adopts a constant gain filtering estimation algorithm, which has certain advantages for system implementation. The main advantages are that it reduces the symbol calculation of the control system, shortens the program running time in the control cycle, and avoids the error covariance matrix in the filtering program from losing its positive definiteness due to the accumulation of calculation errors. Attached Figure Description

[0139] Figure 1 This is a schematic diagram of the steady-state gain correction GNSS autonomous navigation method based on normalized orbit parameters according to the present invention;

[0140] Figure 2 Position error ( Figure 2 a) Speed ​​error ( Figure 2 b) Schematic diagram of simulation results (GNSS output);

[0141] Figure 3 The position error of the EKF-based GNSS autonomous navigation algorithm ( Figure 3 a) Speed ​​error ( Figure 3 b) Schematic diagram of simulation results;

[0142] Figure 4 To correct the position error of the GNSS autonomous navigation method based on the steady-state gain of normalized orbit parameters ( Figure 4 a) Speed ​​error ( Figure 4 b) is a schematic diagram of the simulation results. Detailed Implementation

[0143] The specific embodiments of the present invention will now be described in further detail with reference to the accompanying drawings.

[0144] This invention proposes using normalized orbital semi-major axis, orbital inclination, right ascension of the ascending node, eccentricity vector, and mean latitude argument as state variables for navigation filtering estimation. The Cowell method is used to perform one-step prediction of the above orbital element information. The position in WGS84 system output by the GNSS receiver is combined with the one-step predicted velocity information to convert it into orbital element information. The steady-state gain Kalman filtering algorithm is used to complete the filtering correction of the above orbital element information.

[0145] The system corresponding to the method of this invention can be approximated as a completely controllable and completely observable steady-state linear system. The gain matrix can converge to the steady-state matrix. Therefore, the steady-state gain matrix can be solved offline on the ground using iterative methods or the Riccati difference equation, and then stored in the onboard computer after being uploaded to the ground. In addition, normalizing the orbital elements can effectively reduce the differences in numerical magnitude between the semi-major axis, eccentricity, and other angular elements, and helps to reduce the accumulation of calculation errors.

[0146] The system of this invention mainly consists of four modules: a GNSS information conversion module 101, an orbit extrapolation update module 102, a Kalman filter correction module for steady-state gain 103, and a steady-state gain offline calculation module 201. A schematic diagram of the specific method is shown below. Figure 1 As shown.

[0147] GNSS information conversion module 101, based on the output of the GNSS navigation receiver... The position of the time satellite in the WGS84 coordinate system (unit: km) and sidereal time angle ( (unit: rad) precession nutation matrix ( ), calculate the satellite's position in the ECI coordinate system ( (unit: km), combined with the orbit extrapolation update module 102 outputting the satellite's velocity in the ECI coordinate system after one-step extrapolation ( (unit: km / s), calculate the normalized orbital element information at that moment. The specific calculation process is as follows:

[0148] (1) Calculation Navigation information of satellites in the ECI coordinate system The specific calculation formula is as follows:

[0149]

[0150] (2) Calculation Time track semi-major axis ( (unit: km), the specific calculation formula is as follows:

[0151]

[0152] in, μ The gravitational constant is 3.986005 × 10⁻⁶. 5 Unit: km 3 / s 2 .

[0153] (3) Calculation Time eccentricity The specific calculation formula is as follows:

[0154]

[0155] (4) Calculation orbital inclination at any moment ( (unit: rad), the specific calculation formula is as follows:

[0156]

[0157]

[0158] in, , , They are respectively The components along the X, Y, and Z axes in the ECI coordinate system, in km.

[0159] (5) Calculation Right ascension of ascending node at time ( (unit: rad) and latitudinal argument ( (unit: rad), the specific calculation process is as follows:

[0160] if Less than 1×10 -7 , Equal to 0, equals arctan2( , );

[0161] if Greater than or equal to 1×10 -7 ,when When greater than or equal to 0,

[0162] equal ;

[0163] when When less than 0,

[0164] equal , equal

[0165] ;

[0166] in, , , for The components of the satellite's position along the X, Y, and Z axes in the ECI coordinate system at any given time;

[0167] (6) Calculation Argument of perigee at time ( (unit: rad) and angle of perigee ( (unit: rad), the specific calculation process is as follows: first calculate the near-point angle ( (unit: rad), the calculation formula is:

[0168]

[0169] Secondly, calculate the true anterior angle ( (unit: rad), the calculation formula is:

[0170]

[0171] Then, calculate the argument of perigee ( (unit: rad)

[0172]

[0173] Finally, calculate the angle of near-geometry ( (unit: rad)

[0174]

[0175] (7) Calculation Time-normalized orbital element information The specific calculation formula is as follows:

[0176]

[0177] in, The normalized distance unit is 42164, expressed in km.

[0178] The orbit extrapolation update module 102, based on the output of the Kalman filter correction module 103 of the steady-state gain, The position of the satellite in the ECI coordinate system after filtering correction (time) (unit: km) and speed ( (unit: km / s), extrapolation calculation of satellite speed at... Time-normalized orbital element information The specific calculation relationships are as follows:

[0179] (1) Calculate the position, velocity, and acceleration of the first extrapolation.

[0180]

[0181] in, , , The results were obtained by first-order extrapolation. The position, velocity, and acceleration of the satellite in the ECI coordinate system at any given time, in km, km / s, and km / s respectively. 2 ;

[0182] (2) Calculate the position, velocity, and acceleration of the second extrapolation.

[0183]

[0184] in, , , The results were obtained from second-order extrapolation. The position, velocity, and acceleration of the satellite in the ECI coordinate system at any given time, in km, km / s, and km / s respectively. 2 , The extrapolation integration step size, in seconds;

[0185] (3) Calculate the position, velocity, and acceleration of the third extrapolation.

[0186]

[0187] in, , , The results were obtained from third-order extrapolation. The position, velocity, and acceleration of the satellite in the ECI coordinate system at any given time, in km, km / s, and km / s respectively. 2 ;

[0188] (4) Calculate the position, velocity, and acceleration of the fourth extrapolation.

[0189]

[0190] in, , , The results were obtained from fourth-order extrapolation. The position, velocity, and acceleration of the satellite in the ECI coordinate system at any given time, in km, km / s, and km / s respectively. 2 ;

[0191] (5) Calculate the position, velocity, and acceleration of the one-step extrapolation.

[0192]

[0193] in, , The results were obtained by one-step extrapolation of the orbit. The satellite's position and velocity in the ECI coordinate system at any given time, in km, km / s, and km / s respectively. 2 ;

[0194] (6) Calculate the orbital elements for one-step extrapolation.

[0195] First, calculate the result obtained by one-step extrapolation. Time track semi-major axis The unit is km, and the specific calculation formula is as follows:

[0196]

[0197] Secondly, calculate the result obtained by one-step extrapolation. Time eccentricity The specific calculation formula is as follows:

[0198]

[0199] Third, calculate the result obtained by one-step extrapolation. orbital inclination at any moment ( (unit: rad), the specific calculation formula is as follows:

[0200]

[0201]

[0202] in, , , They are respectively The components along the X, Y, and Z axes in the ECI coordinate system, in km.

[0203] Fourth, calculate the result obtained by one-step extrapolation. Right ascension of ascending node at time ( (unit: rad) and latitudinal argument ( (unit: rad), the specific calculation process is as follows:

[0204] if Less than 1×10 -7 , Equal to 0,

[0205] equals arctan2( , );

[0206] if Greater than or equal to 1×10 -7 ,when When greater than or equal to 0,

[0207] = ,

[0208] when When less than 0,

[0209] = ,

[0210] equal

[0211] ;in, , , for The components of the satellite's position along the X, Y, and Z axes in the ECI coordinate system at any given time;

[0212] Fifth, calculate the result obtained by one-step extrapolation. Argument of perigee at time ( (unit: rad) and angle of perigee ( (unit: rad), the specific calculation process is as follows: first calculate the near-point angle ( (unit: rad), the calculation formula is:

[0213]

[0214] Calculate the true anterior angle obtained by one-step extrapolation ( (unit: rad), the calculation formula is:

[0215]

[0216] Calculate the perigee argument obtained by one-step extrapolation ( (unit: rad)

[0217]

[0218] Calculate the angle of near perigee obtained by one-step extrapolation ( (unit: rad)

[0219]

[0220] Finally, calculate the result obtained by one extrapolation step. Time-normalized orbital element information The specific calculation formula is as follows:

[0221]

[0222] in, The normalized distance unit is 42164, expressed in km.

[0223] The steady-state gain Kalman filter correction module 103, based on the output of the GNSS information conversion module 101... Time-normalized orbital element information The extrapolation calculation output by the orbit extrapolation update module 102 Time-normalized orbital element information The gain filtering matrix output by the steady-state gain offline calculation module 201 ,calculate The position of the satellite in the ECI coordinate system estimated by time filtering. (unit: km) and speed ( (unit: km / s)

[0224] The specific calculation relationship of the Kalman filter correction module for steady-state gain is as follows:

[0225] (1) Calculate the track element information of the filtered estimate

[0226]

[0227] in, For filtering estimation Time-normalized orbital element information; , , , , , for The time-filtered estimates of the orbit's semi-major axis, orbital inclination (in rad), right ascension of the ascending node (in rad), orbital eccentricity (in rad), argument of perigee (in rad), and mean perigee (in rad);

[0228] (2) Calculate the position and velocity estimated by filtering.

[0229] First, iterative calculation Latitude argument estimated by time-time filtering (Unit: rad, domain: [0, 2π)), initial value for iterative calculation (unit: rad) The iterative formula is

[0230]

[0231] The termination condition for iterative calculation is Or the number of iterations exceeds 10.

[0232] Secondly, calculation True latitude argument estimated by time-lapse filtering (Unit: rad, domain: [0, 2π)), the specific calculation formula is as follows:

[0233]

[0234] Third, calculation Time-filtered estimation of orbital semi-path (unit: km), geocentric distance (unit: km), radial velocity (unit: km / s) and tangential velocity (Unit: km / s), the specific calculation formula is as follows:

[0235]

[0236]

[0237]

[0238]

[0239] Fourth, calculation The position of the satellite in the ECI coordinate system estimated by time filtering. (unit: km), the specific calculation formula is as follows:

[0240]

[0241] Fifth, calculation The satellite's velocity in the ECI coordinate system is estimated by time filtering. (unit: km), the specific calculation formula is as follows:

[0242]

[0243] The steady-state gain offline calculation module 201 calculates the output gain filtering matrix using a discrete calculation method. The specific calculation process is as follows:

[0244] (1) Calculate the system state error transfer matrix

[0245] The formula for calculating the system state error transition matrix is ​​as follows:

[0246]

[0247] in, The value is taken as the semi-major axis of the satellite orbit, in km;

[0248] (2) Calculate the system state transition matrix

[0249] The formula for calculating the system state transition matrix is ​​as follows:

[0250]

[0251] in, It is the identity matrix;

[0252] (3) Calculate the discretized system state error matrix

[0253] The formula for calculating the discretized system state error matrix is ​​as follows:

[0254]

[0255] in, It is a 3×3 system state error matrix.

[0256] (4) Calculate the measurement state transition matrix

[0257] The formula for calculating the measurement state transition matrix is ​​as follows:

[0258]

[0259] (5) Calculate the gain filtering matrix

[0260] The error covariance matrix is ​​calculated iteratively, with the initial value of the error covariance matrix being... The formula for iterative calculation is:

[0261]

[0262] The termination condition for iterative calculation is or the number of iterations exceeds 10 4 Next. Among them, For the first k The error covariance matrix obtained in the next iteration The i line, number j Column elements (0< i , j≤ 6) Gain Filtering Matrix The value is the gain matrix at the end of the iteration. .

[0263] To verify the effectiveness of the present invention, mathematical simulation was used to verify the method described in the present invention. Figure 2 The changes in satellite position and velocity errors obtained by solving the GNSS output measurements are presented. Figure 3 The changes in satellite position and velocity errors estimated by the EKF-based GNSS autonomous navigation algorithm are presented. Figure 4 The variations in satellite position and velocity errors obtained by filtering estimation using the steady-state gain correction GNSS autonomous navigation method based on normalized orbit parameters described in this invention are presented. Simulation results show that the filtering estimation results of the steady-state gain correction GNSS autonomous navigation method based on normalized orbit parameters described in this invention are basically equivalent to the navigation accuracy of the GNSS autonomous navigation algorithm based on EKF.

[0264] The parts of this invention not described in detail are common knowledge to those skilled in the art.

Claims

1. A steady-state gain correction GNSS autonomous navigation system based on normalized orbit parameters, characterized in that... include: GNSS information conversion module, orbit extrapolation update module, steady-state gain Kalman filter correction module, and steady-state gain offline calculation module; The GNSS information conversion module converts data based on the output of the GNSS navigation receiver. Position of the time satellite in the WGS84 coordinate system Sidereal hour angle and the precession matrix Calculate the satellite's position in the ECI coordinate system Combined with the orbit extrapolation update module outputting the satellite's velocity in the ECI coordinate system after one-step extrapolation, Calculate the normalized orbital feature information at that moment. ; The orbit extrapolation update module, based on the output of the Kalman filter correction module for steady-state gain, The satellite's position in the ECI coordinate system after time filtering correction and speed Extrapolation calculation of satellites in Time-normalized orbital element information ; The steady-state gain offline calculation module uses a discrete calculation method to calculate the output gain filtering matrix. ; The steady-state gain Kalman filter correction module, based on the output of the GNSS information conversion module... Time-normalized orbital element information The extrapolation calculation output by the orbit extrapolation update module Time-normalized orbital element information The gain filtering matrix output by the steady-state gain offline calculation module ,calculate The position of the satellite in the ECI coordinate system estimated by time filtering and speed .

2. The GNSS autonomous navigation system based on normalized orbital parameters with steady-state gain correction according to claim 1, characterized in that: The GNSS information conversion module calculates normalized orbital element information. Specifically: (1) Calculation Navigation information of satellites in the ECI coordinate system The specific calculation formula is as follows: (2) Calculation Time track semi-major axis The specific calculation formula is as follows: in, μ It is the gravitational constant; (3) Calculation Time eccentricity The specific calculation formula is as follows: ； (4) Calculation orbital inclination at any moment The specific calculation formula is as follows: in, , , They are respectively Components along the X, Y, and Z axes in the ECI coordinate system; (5) Calculation Right ascension of ascending node at moment and latitude angle The specific calculation process is as follows: if <1×10 -7 , =0, =arctan2( , ); if ≥1×10 -7 ,when When ≥0, = ， when When <0, = , = ； in, , , for The components of the satellite's position along the X, Y, and Z axes in the ECI coordinate system at any given time; (6) Calculation Argument of perigee at time Peaceful perigee angle The specific calculation process is as follows: First, calculate the near-point angle. The calculation formula is: Second, calculate the true anterior angle. The calculation formula is: Then, calculate the argument of perigee. , Finally, calculate the angle of near-geometry. , ； (7) Calculate Time-normalized orbital element information The specific calculation formula is as follows: in, The normalized distance unit is bound to the semi-major axis of the satellite's nominal orbit.

3. The GNSS autonomous navigation system based on normalized orbital parameters with steady-state gain correction according to claim 2, characterized in that: The orbit extrapolation update module updates the orbit based on the output of the Kalman filter correction module for steady-state gain. The satellite's position in the ECI coordinate system after time filtering correction and speed Extrapolation calculation of satellites in Time-normalized orbital element information The details are as follows: (1) Calculate the position, velocity, and acceleration of the first extrapolation. in, , , The results were obtained by first-order extrapolation. The position, velocity, and acceleration of the satellite in the ECI coordinate system at any given time; (2) Calculate the position, velocity, and acceleration of the second extrapolation. in, , , The results were obtained from second-order extrapolation. The position, velocity, and acceleration of the satellite in the ECI coordinate system at any given time. This is the step size for extrapolation integration; (3) Calculate the position, velocity, and acceleration of the third extrapolation. in, , , The results were obtained from third-order extrapolation. The position, velocity, and acceleration of the satellite in the ECI coordinate system at any given time; (4) Calculate the position, velocity, and acceleration of the fourth-order extrapolation. in, , , The results were obtained from fourth-order extrapolation. The position, velocity, and acceleration of the satellite in the ECI coordinate system at any given time; (5) Calculate the position, velocity, and acceleration of the extrapolation step. in, , The results were obtained by one-step extrapolation of the orbit. The position and velocity of the satellite in the ECI coordinate system at any given time; (6) Calculate the orbital elements for one-step extrapolation. .

4. A GNSS autonomous navigation system based on normalized orbital parameters with steady-state gain correction according to claim 3, characterized in that: Step (6) calculates the orbital elements for one-step extrapolation. Specifically: First, calculate the result obtained by one-step extrapolation. Time track semi-major axis The specific calculation formula is as follows: Secondly, calculate the result obtained by one-step extrapolation. Time eccentricity The specific calculation formula is as follows: Third, calculate the result obtained by one-step extrapolation. orbital inclination at any moment The specific calculation formula is as follows: in, , , They are respectively Components along the X, Y, and Z axes in the ECI coordinate system; Fourth, calculate the result obtained by one-step extrapolation. Right ascension of ascending node at moment and latitude angle The specific calculation process is as follows: if Less than 1×10 -7 , Equal to 0, equals arctan2( , ); if Greater than or equal to 1×10 -7 ,when When greater than or equal to 0, equal ,when When less than 0, equal , equal ； in, , , for The components of the satellite's position along the X, Y, and Z axes in the ECI coordinate system at any given time; Fifth, calculate the result obtained by one-step extrapolation. Argument of perigee at time Peaceful perigee angle The specific calculation process is as follows: first, calculate the near-point angle. The calculation formula is: Calculate the true anterior angle obtained by one-step extrapolation. The calculation formula is: Calculate the perigee argument obtained by one-step extrapolation Calculate the angle of perigee obtained by one-step extrapolation. Finally, calculate the result obtained by one extrapolation step. Time-normalized orbital element information The specific calculation formula is as follows: in, It is a normalized distance unit.

5. A GNSS autonomous navigation system based on normalized orbital parameters with steady-state gain correction according to claim 4, characterized in that: The specific calculation relationship of the Kalman filter correction module for steady-state gain is as follows: (1) Calculate the orbital element information of the filtered estimation in, For filtering estimation Time-normalized orbital element information; , , , , , for The semi-major axis, inclination, right ascension of the ascending node, eccentricity, argument of perigee, and mean perigee angle are estimated by time-lapse filtering. (2) Calculate the position and velocity estimated by filtering. First, iterative calculation Latitude argument estimated by time-time filtering Initial value for iterative calculation for The iterative formula is The termination condition for iterative calculation is Or the number of iterations exceeds 10; Secondly, calculation True latitude argument estimated by time-lapse filtering The specific calculation formula is as follows: Third, calculation Time-filtered estimation of orbital semi-path Earth's center distance radial velocity and tangential velocity The specific calculation formula is as follows: Fourth, calculation The position of the satellite in the ECI coordinate system estimated by time filtering The specific calculation formula is as follows: Fifth, calculation The satellite velocity in the ECI coordinate system estimated by time filtering The specific calculation formula is as follows: 。 6. A GNSS autonomous navigation system based on normalized orbital parameters with steady-state gain correction according to claim 5, characterized in that: The steady-state gain offline calculation module uses discrete calculation to calculate the output gain filtering matrix. The specific calculation process is as follows: (1) Calculate the system state error transition matrix The formula for calculating the system state error transition matrix is ​​as follows: in, The value is taken as the semi-major axis of the satellite orbit; (2) Calculate the system state transition matrix The formula for calculating the system state transition matrix is ​​as follows: in, It is the identity matrix; (3) Calculate the discretized system state error matrix The formula for calculating the discretized system state error matrix is ​​as follows: in, The system state error matrix is ​​3×3; (4) Calculate the measurement state transition matrix The formula for calculating the measurement state transition matrix is ​​as follows: (5) Calculate the gain filtering matrix The error covariance matrix is ​​calculated iteratively, with the initial value of the error covariance matrix being... ; The formula for iterative calculation is: The termination condition for iterative calculation is or the number of iterations exceeds 10 4 Second-rate; in, For the first k The error covariance matrix obtained in the next iteration The i line, number j Column elements, 0 < i , j≤ 6. Gain Filtering Matrix The value is the gain matrix at the end of the iteration. .

7. An autonomous navigation method implemented by a GNSS autonomous navigation system based on steady-state gain correction of normalized orbit parameters according to claim 1, characterized in that... include: According to the output of the GNSS navigation receiver Position of the time satellite in the WGS84 coordinate system Sidereal hour angle and the precession matrix Calculate the satellite's position in the ECI coordinate system ; Combined with the satellite's velocity in the ECI coordinate system after one extrapolation Calculate the normalized orbital feature information at that moment. ; Based on the output The satellite's position in the ECI coordinate system after time filtering correction and speed Extrapolation calculation of satellites in Time-normalized orbital element information ; The output gain filter matrix is ​​calculated using a discrete calculation method. ; according to Time-normalized orbital element information Extrapolation calculation Time-normalized orbital element information Gain filter matrix calculate The position of the satellite in the ECI coordinate system estimated by time filtering and speed .

8. A GNSS autonomous navigation system based on normalized orbital parameters with steady-state gain correction according to claim 7, characterized in that: The GNSS information conversion module calculates normalized orbital element information. Specifically: (1) Calculation Navigation information of satellites in the ECI coordinate system The specific calculation formula is as follows: (2) Calculation Time track semi-major axis The specific calculation formula is as follows: in, μ It is the gravitational constant; (3) Calculation Time eccentricity The specific calculation formula is as follows: ； (4) Calculation orbital inclination at any moment The specific calculation formula is as follows: in, , , They are respectively Components along the X, Y, and Z axes in the ECI coordinate system; (5) Calculation Right ascension of ascending node at moment and latitude angle The specific calculation process is as follows: if <1×10 -7 , =0, =arctan2( , ); if ≥1×10 -7 ,when When ≥0, = ， when When <0, = , = ； in, , , for The components of the satellite's position along the X, Y, and Z axes in the ECI coordinate system at any given time; (6) Calculation Argument of perigee at time Peaceful perigee angle The specific calculation process is as follows: First, calculate the near-point angle. The calculation formula is: Second, calculate the true anterior angle. The calculation formula is: Then, calculate the argument of perigee. , Finally, calculate the angle of near-geometry. , (7) Calculate Time-normalized orbital element information The specific calculation formula is as follows: in, The normalized distance unit is bound to the semi-major axis of the satellite's nominal orbit.

9. A GNSS autonomous navigation system based on normalized orbital parameters with steady-state gain correction according to claim 8, characterized in that: The orbit extrapolation update module updates the orbit based on the output of the Kalman filter correction module for steady-state gain. The satellite's position in the ECI coordinate system after time filtering correction and speed Extrapolation calculation of satellites in Time-normalized orbital element information The details are as follows: (1) Calculate the position, velocity, and acceleration of the first extrapolation. in, , , The results were obtained by first-order extrapolation. The position, velocity, and acceleration of the satellite in the ECI coordinate system at any given time; (2) Calculate the position, velocity, and acceleration of the second extrapolation. in, , , The results were obtained from second-order extrapolation. The position, velocity, and acceleration of the satellite in the ECI coordinate system at any given time. This is the step size for extrapolation integration; (3) Calculate the position, velocity, and acceleration of the third extrapolation. in, , , The results were obtained from third-order extrapolation. The position, velocity, and acceleration of the satellite in the ECI coordinate system at any given time; (4) Calculate the position, velocity, and acceleration of the fourth-order extrapolation. in, , , The results were obtained from fourth-order extrapolation. The position, velocity, and acceleration of the satellite in the ECI coordinate system at any given time; (5) Calculate the position, velocity, and acceleration of the extrapolation step. in, , The results were obtained by one-step extrapolation of the orbit. The position and velocity of the satellite in the ECI coordinate system at any given time; (6) Calculate the orbital elements for one-step extrapolation. .

10. A GNSS autonomous navigation system based on normalized orbital parameters with steady-state gain correction according to claim 9, characterized in that: Step (6) calculates the orbital elements for one-step extrapolation. Specifically: First, calculate the result obtained by one-step extrapolation. Time track semi-major axis The specific calculation formula is as follows: Secondly, calculate the result obtained by one-step extrapolation. Time eccentricity The specific calculation formula is as follows: Third, calculate the result obtained by one-step extrapolation. orbital inclination at any moment The specific calculation formula is as follows: in, , , They are respectively Components along the X, Y, and Z axes in the ECI coordinate system; Fourth, calculate the result obtained by one-step extrapolation. Right ascension of ascending node at moment and latitude angle The specific calculation process is as follows: if Less than 1×10 -7 , Equal to 0, equals arctan2( , ); if Greater than or equal to 1×10 -7 ,when When greater than or equal to 0, equal ,when When less than 0, equal , equal ； in, , , for The components of the satellite's position along the X, Y, and Z axes in the ECI coordinate system at any given time; Fifth, calculate the result obtained by one-step extrapolation. Argument of perigee at time Peaceful perigee angle The specific calculation process is as follows: first, calculate the near-point angle. The calculation formula is: Calculate the true anterior angle obtained by one-step extrapolation. The calculation formula is: Calculate the perigee argument obtained by one-step extrapolation Calculate the angle of perigee obtained by one-step extrapolation. Finally, calculate the result obtained by one extrapolation step. Time-normalized orbital element information The specific calculation formula is as follows: in, Normalized distance unit; The specific calculation relationship of the Kalman filter correction module for steady-state gain is as follows: (1) Calculate the orbital element information of the filtered estimation in, For filtering estimation Time-normalized orbital element information; , , , , , for The semi-major axis, inclination, right ascension of the ascending node, eccentricity, argument of perigee, and mean perigee angle are estimated by time-lapse filtering. (2) Calculate the position and velocity estimated by filtering. First, iterative calculation Latitude argument estimated by time-time filtering Initial value for iterative calculation for The iterative formula is The termination condition for iterative calculation is Or the number of iterations exceeds 10; Secondly, calculation True latitude argument estimated by time-lapse filtering The specific calculation formula is as follows: Third, calculation Time-filtered estimation of orbital semi-path Earth's center distance radial velocity and tangential velocity The specific calculation formula is as follows: Fourth, calculation The position of the satellite in the ECI coordinate system estimated by time filtering The specific calculation formula is as follows: Fifth, calculation The satellite velocity in the ECI coordinate system estimated by time filtering The specific calculation formula is as follows: ； The steady-state gain offline calculation module uses discrete calculation to calculate the output gain filtering matrix. The specific calculation process is as follows: (1) Calculate the system state error transition matrix The formula for calculating the system state error transition matrix is ​​as follows: in, The value is taken as the semi-major axis of the satellite orbit; (2) Calculate the system state transition matrix The formula for calculating the system state transition matrix is ​​as follows: in, It is the identity matrix; (3) Calculate the discretized system state error matrix The formula for calculating the discretized system state error matrix is ​​as follows: in, The system state error matrix is ​​3×3; (4) Calculate the measurement state transition matrix The formula for calculating the measurement state transition matrix is ​​as follows: (5) Calculate the gain filtering matrix The error covariance matrix is ​​calculated iteratively, with the initial value of the error covariance matrix being... ; The formula for iterative calculation is: The termination condition for iterative calculation is or the number of iterations exceeds 10 4 Second-rate; in, For the first k The error covariance matrix obtained in the next iteration The i line, number j Column elements, 0 < i , j≤ 6. Gain Filtering Matrix The value is the gain matrix at the end of the iteration. .

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