Ephemeris broadcast and time synchronization method for Beidou pseudolite deformation monitoring

Abstract

The invention relates to an ephemeris broadcast and time synchronization method for Beidou pseudolite deformation monitoring, and belongs to the technical field of satellite positioning. The method comprises the following steps: constructing a linearization error equation based on a pseudo-range observation value, and solving a clock error correction amount in combination with a robust iterative algorithm to improve the time synchronization precision; analyzing ephemeris parameters of the Beidou GEO satellite, calculating earth-fixed coordinates of the Beidou GEO satellite, and rotating and adapting the earth-fixed coordinates; establishing an affine transformation relationship between the pseudo-satellite coordinates and GEO ephemeris, and generating optimized pseudo-satellite ephemeris data; and a time synchronization protocol is designed, and clock skew is compensated through bidirectional timestamp interaction of the main base station and the pseudo satellite. According to the method, nanosecond synchronization of the pseudo-satellite and the real satellite is realized, the ephemeris parameter redundancy problem of the static pseudo-satellite is optimized, multi-system cooperative work is supported, and the deformation monitoring reliability and precision under the complex terrain are remarkably improved.

Description

Technical Field

[0001] The invention belongs to the technical field of satellite positioning, and in particular relates to an ephemeris broadcasting and time synchronization method for Beidou pseudo-satellite deformation monitoring. Background Art

[0002] Beidou pseudo-satellites are fixed signal transmitters deployed on the ground. They simulate Beidou satellite signals (including ephemeris parameters and carrier frequency) to achieve regional enhanced positioning. Their key advantages include: their fixed deployment is unaffected by orbital dynamics, ensuring controllable signal coverage; they can compensate for the lack of visible satellites in mountainous and canyon areas due to terrain obstruction; and they receive Beidou timing signals through the main base station and synchronize the pseudo-satellite clocks, achieving alignment with the Beidou system's time base.

[0003] Due to the steep terrain in mountainous canyon areas, satellite signals are blocked or reflected multiple times, resulting in phase delay and a decrease in signal-to-noise ratio. In addition, the sky view windows on both sides of the canyon are in opposite directions, which significantly reduces the number of shared satellites during synchronous observation, making it difficult to meet the needs of traditional PVT solutions. Heavy rain, vegetation changes, etc. will aggravate signal attenuation and affect the reliability of traditional contact sensors (such as strain gauges and optical fibers).

[0004] Current deformation monitoring technology can only obtain local data and relies on manual collection, making it impossible to achieve real-time monitoring of the entire area. Electrical sensors are susceptible to lightning and corrosion, and data noise is significant under complex geological conditions. Conventional GNSS technology requires at least four visible satellites, which is difficult to meet in high mountain canyons, resulting in positioning failure or a sharp drop in accuracy.

[0005] Pseudo-satellites must achieve nanosecond-level synchronization accuracy with real satellites. However, existing two-way pseudo-range synchronization technology is affected by atmospheric delay and device latency, and error accumulation is particularly problematic in complex terrain. The main base station's oven-controlled crystal oscillator has limited long-term stability, requiring periodic calibration with Beidou timing signals. If the signal is interrupted, synchronization errors can increase significantly. Universal satellite ephemeris is designed based on Kepler orbital parameters and is suitable for dynamic satellites. However, as pseudo-satellites are static nodes, their direct application results in redundant coordinate descriptions and reduced accuracy.

[0006] Although pseudo-satellite coordinate mapping can be established through GEO satellite ephemeris, the problems of rotation matrix modeling error and matrix stability under multipath interference must be solved; the high-power signal of pseudo-satellite may suppress the real satellite signal in the distance. Although pulse modulation technology can alleviate this problem, the multipath delay distribution is exacerbated in the canyon reflection environment; pseudo-satellite needs to work in coordination with real satellites and ground sensors, but the unification of time base and data fusion algorithm have not yet been standardized, which affects the overall reliability of the monitoring system. Summary of the Invention

[0007] In order to solve the above problems existing in the prior art, the present invention provides a method for ephemeris broadcasting and time synchronization for Beidou pseudolite deformation monitoring;

[0008] The purpose of the present invention can be achieved through the following technical solutions:

[0009] S1: Obtain the ground receiver coordinates and pseudo-satellite coordinates, simplify the positioning equation through the pseudo-range observation values ​​of the real satellite, and send ranging signals to the satellite in both directions through the pseudo-satellite;

[0010] S2: Performing Taylor expansion on the geometric distance of the positioning equation to establish a linearized positioning equation, solving the clock error correction in the positioning equation through robust iteration; iteratively updating the weights using the pseudorange measurement noise variance, and outputting the optimal clock error estimate;

[0011] S3: Analyze the ephemeris parameters of the BeiDou GEO satellite, calculate the position of the satellite in the orbital plane, and adapt the coordinates to the Earth-centered Earth-fixed coordinate system through coordinate rotation. Establish an affine transformation relationship between the actual coordinates of the pseudolite and the GEO satellite coordinates, solve the rotation scaling matrix and translation vector in the affine transformation relationship, fit the pseudolite virtual orbit parameters based on the mapping relationship, and generate ephemeris data that conforms to the BeiDou message format;

[0012] S4: The master base station calibrates the local clock using BeiDou timing signals and periodically synchronizes time with pseudolites to compensate for clock deviations.

[0013] Specifically, the simplified positioning equation is:

[0014]

[0015] Among them, ρ i is the pseudorange, (X i ,Y i ,Z i ) is the satellite coordinate or pseudo-satellite coordinate, (X r ,Y r ,Z r ) is the receiver coordinate, c is the speed of light, δt r represents the clock error, is the parameter to be estimated, ε i is the observation noise and other error terms.

[0016] Specifically, the linearized positioning equation is constructed by using the coordinates and pseudo-range observations of the satellite and pseudo-satellite. The geometric distance of the simplified positioning equation is Taylor expanded, and high-order terms are ignored to obtain a linearized error equation. The calculation formula is:

[0017]

[0018] Among them, Δx, Δy, Δz are the receiver position corrections, Δ(δt r ) is the clock error correction, e i is the linearized residual, is the direction cosine matrix element, and the specific calculation is:

[0019] Specifically, the robust iterative method is:

[0020] The observation equation is combined into a matrix form: y = Hx + e, where y is the pseudorange residual vector, H is the design matrix, including direction cosine and clock error coefficients, and x = [Δx, Δy, Δz, Δ(δt r )] T , is the parameter vector to be estimated, e is the noise vector;

[0021] By using the least squares criterion, the goal is to minimize the weighted residual sum of squares:

[0022]

[0023] Where W is the weight matrix, and the initial state is set as a diagonal matrix based on the satellite's altitude angle;

[0024] Decompose the design matrix H into an orthogonal matrix Q and an upper triangular matrix R, H = QR;

[0025] According to the above calculation process, the matrix form of the observation equation is converted into:

[0026] Q T y=Rx+Q T e,

[0027] And solve the parameter vector to be estimated by back substitution method, x=R -1 Q T y; the clock error correction is the last element of the parameter vector to be estimated;

[0028] The weight matrix is ​​updated iteratively, and an optimal clock error estimate is output after convergence.

[0029] Specifically, the objective constraint for solving the affine transformation relationship is to minimize the residual sum of squares, and the calculation formula is:

[0030]

[0031] Solve the rotation and scaling matrix and translation vector using the least squares method, and the solution is:

[0032]

[0033] in, is the center of mass coordinate, Q iis the actual coordinate of the pseudo-satellite, P i are the GEO satellite ECEF coordinates.

[0034] Specifically, the accuracy verification index of the rotation scaling matrix and the translation vector in the affine transformation relationship is the root mean square error. If the root mean square error is greater than the preset accuracy verification threshold, resampling is performed until convergence. The calculation formula is:

[0035]

[0036] Among them, RMSE is the root mean square error, Q i is the actual coordinate of the pseudo-satellite, R is the rotation and scaling matrix, P i is the ECEF coordinate of the GEO satellite, and t is the translation vector.

[0037] Specifically, the virtual orbit parameter fitting adopts an 18-parameter model and is smoothed by cubic spline interpolation.

[0038] Specifically, the time synchronization protocol includes the generation and transmission of timestamps, the estimation and compensation of clock deviations, and the monitoring and feedback of synchronization status.

[0039] Specifically, the main base station calibrates its local clock through the Beidou timing signal and periodically sends time synchronization instructions to the pseudo-satellite. After receiving the instructions, the pseudo-satellite records the local clock reading at the time of reception and immediately replies with a confirmation message, attaching the local clock reading at the time of reply.

[0040] Specifically, the master base station estimates the clock deviation of the pseudo-satellite based on the timestamp of the round-trip message, and compensates for it through the clock deviation correction in the pseudo-range observation value; the status monitoring of the time synchronization includes triggering an alarm mechanism when multiple synchronization failures occur continuously or the deviation exceeds a threshold, and recording an abnormal log.

[0041] The beneficial effects of the present invention are:

[0042] Through the method provided by the present invention, the Beidou pseudo-satellite deformation monitoring system can achieve high-precision time synchronization and ephemeris broadcasting, effectively solving the problem of reduced positioning accuracy caused by satellite signal obstruction in complex terrain. On the one hand, through two-way pseudo-range observation and anti-error iterative algorithm, the present invention improves the accuracy of clock error correction and reduces the impact of atmospheric delay and equipment delay on synchronization accuracy; on the other hand, the use of affine transformation relationship to fit the pseudo-satellite virtual orbit parameters not only reduces the redundancy of coordinate description, but also improves the accuracy and applicability of ephemeris data. In addition, the time synchronization protocol of the present invention ensures the unification of the time reference between the pseudo-satellite and the main base station, improving the overall reliability of the monitoring system. Therefore, the present invention has broad application prospects in the field of deformation monitoring, especially in complex terrain areas such as high mountains and canyons, and can provide strong support for achieving real-time monitoring of the entire area. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] To facilitate understanding by those skilled in the art, the present invention is further described below with reference to the accompanying drawings.

[0044] Figure 1 The present invention is a flowchart of a method for ephemeris broadcasting and time synchronization for Beidou pseudolite deformation monitoring. DETAILED DESCRIPTION

[0045] In order to further illustrate the technical means and effects adopted by the present invention to achieve the predetermined purpose of the invention, the specific implementation methods, structures, features and effects of the present invention are described in detail below in conjunction with the accompanying drawings and preferred embodiments.

[0046] See also Figure 1 A method for broadcasting ephemeris and synchronizing time for deformation monitoring of Beidou pseudo-satellite, comprising:

[0047] Obtain the ground receiver coordinates and pseudo-satellite coordinates, simplify the positioning equation through the pseudo-range observation value of the real satellite, and send ranging signals bidirectionally between the pseudo-satellite and the satellite. The pseudo-range observation equation is:

[0048]

[0049] Among them, ρ i is the pseudorange, (X i ,Y i ,Z i ) is the satellite coordinate or pseudo-satellite coordinate, (X r ,Y r ,Z r ) is the receiver coordinate, c is the speed of light, δt r represents the clock error, is the parameter to be estimated, ε i is the observation noise and other error terms;

[0050] The linearized error equation is constructed using the coordinates and pseudo-range observations of the satellite and pseudo-satellite. The geometric distance of the positioning equation is Taylor expanded, and the high-order terms are ignored to obtain the linearized error equation. The calculation formula is:

[0051]

[0052] Among them, Δx, Δy, Δz are the receiver position corrections, Δ(δt r ) is the clock error correction, e i is the linearized residual, is the direction cosine matrix element, and the specific calculation is:

[0053] Combining the observation equations into matrix form: y=Hx+e, where y is the pseudo-range residual vector, H is the design matrix containing direction cosines and clock bias coefficients, x=[Δx, Δy, Δz, Δ(δt r ) T , is the estimated parameter vector, and e is the noise vector;

[0054] By the least squares criterion, the objective is set to minimize the weighted residual sum of squares:

[0055]

[0056] where W is the weight matrix, and the initial state is set to a diagonal matrix based on the elevation angle of the satellite;

[0057] The design matrix H is decomposed into an orthogonal matrix Q and an upper triangular matrix R, H=QR, which is achieved by Gram-Schmidt orthogonalization or Householder transformation;

[0058] According to the above calculation process, the matrix form of the observation equation is converted to:

[0059] Q T y=R T x+Q

[0060] e,

[0061] The estimated parameter vector x is solved by back substitution method, x=R -1 Q T y; the clock correction amount Δ(δt r ) is the last element of the estimated parameter vector;

[0062] S201: initialize the weight matrix, the initialized matrix element where σ i is the observation noise variance;

[0063] S202: solve the estimated parameter vector by

[0064] S203: calculate the residual and update the weight matrix; the residual e i is the difference between the observed value and the calculated value, and the weight is updated by the robust function; the update calculation formula of the matrix element of the weight matrix is:

[0065]

[0066] where k is the iteration count, k0 and k1 are threshold adjustment factors, and the specific values are k0=1.5σ and k1=3σ;

[0067] S204: repeat S202-S203 until convergence;

[0068] wherein the convergence determination condition comprises: parameter variation ||x (k) -x (k-1) ||<∈1, residual variation ||e (k) -e (k-1) ||<∈2, and maximum iteration number k max is 15;

[0069] After convergence, the final clock error estimate is:

[0070]

[0071] wherein, is the initial clock error value, Δ(δt r ) (k) is the accumulated correction in the iteration process;

[0072] Obtain the ephemeris parameters of the Beidou GEO satellite, the ephemeris parameters comprising Keplerian elements (semi-major axis a, inclination i, eccentricity e, argument of perigee w, mean anomaly M, right ascension of the ascending node Ω), ephemeris reference time, harmonic coefficients of orbit perturbation, and perturbation quantity;

[0073] Calculate the true anomaly according to the mean anomaly in the ephemeris parameters, and determine the position of the satellite in the orbital plane in combination with the semi-major axis and the eccentricity;

[0074] The GEO satellite needs to be rotated by 5° in the coordinate system to adapt to the geocentric and geodetic coordinate system. The rotation formula is:

[0075]

[0076] wherein, R x , R z is the rotation matrix around the X and Z axes, and r is the distance from the satellite to the center of the earth;

[0077] In this embodiment, the enu2ecef function of MATLAB or the Perl script geo::ecef is called to input the longitude, latitude and height parameters, and the ECEF coordinates are calculated in combination with the WGS84 ellipsoid parameters;

[0078] According to the ECEF coordinates of the GEO satellite and the actual coordinates of the pseudo-satellite, a mapping relationship matrix is constructed, and the calculation formula is:

[0079]

[0080] wherein, the ECEF coordinates of the GEO satellite are P i =[X i , Y i, Z i ] T , the pseudo-satellite actual coordinates are Q i = [x i , y i , z i ] T , R is a rotation scaling matrix, and t is a translation vector;

[0081] The affine transformation parameters are solved by minimizing the residual sum of squares; the target constraint is:

[0082]

[0083] The rotation scaling matrix and the translation vector are solved by the least square method, and the solution is:

[0084] R = (P T P) -1 P T Q,

[0085]

[0086] wherein, is the centroid coordinate;

[0087] The root mean square error is taken as the accuracy verification index, if the root mean square error is greater than a preset accuracy verification threshold, resampling is performed until convergence, and the calculation formula is:

[0088]

[0089] According to the inverse matrix of the solved affine transformation parameters, the fixed coordinates of the pseudo-satellite are inversely affine transformed and mapped back to the ephemeris parameter space of the GEO satellite, the 18-parameter model is used to fit the "virtual orbit" parameters of the pseudo-satellite, the parameter legality is checked, and the pseudo-satellite ephemeris data conforming to the Beidou message format is generated.

[0090] In this embodiment, a polynomial fitting algorithm is used to smooth the "virtual orbit" parameters of pseudolites, reducing fluctuations caused by data noise and improving the stability and reliability of ephemeris data. Specifically, cubic spline interpolation or Chebyshev polynomials are used for fitting to ensure minimal error within the fitting interval. A time synchronization protocol is designed to align the time bases of pseudolites with the master base station and real satellites. This protocol includes timestamp generation and transmission, clock bias estimation and compensation, and synchronization status monitoring and feedback. The master base station calibrates its local clock using Beidou timing signals and periodically sends time synchronization commands to the pseudolites. Upon receiving the commands, the pseudolites record the local clock reading at the time of receipt and immediately send an acknowledgment message with the local clock reading at the time of the reply. The master base station estimates the pseudolites' clock bias based on the timestamps of the round-trip messages and compensates for it using the clock correction value in the pseudorange observations. Furthermore, the synchronization status is monitored. If synchronization fails repeatedly or the bias exceeds a threshold, an alarm is triggered and an exception log is recorded.

[0091] The computer storage medium of the embodiment of the present invention may adopt any combination of one or more computer-readable media. The computer-readable medium may be a computer-readable signal medium or a computer-readable storage medium. The computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or component, or any combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof. In this document, a computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in combination with an instruction execution system, device or device.

[0092] A computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, which carries computer-readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A computer-readable signal medium may also be any computer-readable medium other than a computer-readable storage medium that can transmit, propagate, or transport a program for use by or in conjunction with an instruction execution system, apparatus, or device.

[0093] The program code included in the computer-readable medium can be transmitted with any appropriate medium, including but not limited to wireless, electric wire, optical cable, RF or the like, or any suitable combination thereof. The computer program code for performing the operation of the present invention can be written in one or more programming languages ​​or a combination thereof, and the programming language includes an object-oriented programming language such as Java, Smalltalk, C++, and also includes a conventional procedural programming language such as "C" language or similar programming language. The program code can be executed completely on the user's computer, partially on the user's computer, as an independent software package, partially on the user's computer and partially on a remote computer, or completely on a remote computer or server. In the case of a remote computer, the remote computer can be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or can be connected to an external computer (for example, utilizing an Internet service provider to connect through the Internet).

[0094] The above description is merely a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as a preferred embodiment as above, it is not intended to limit the present invention. Any person skilled in the art can make some changes or modifications to equivalent embodiments using the technical contents disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention are still within the scope of the technical solution of the present invention.

Claims

1. A method for ephemeris broadcasting and time synchronization based on BeiDou pseudolite deformation monitoring, characterized in that: The following steps are involved: S1: Obtain the ground receiver coordinates and pseudo-satellite coordinates, simplify the positioning equation through the pseudo-range observation values ​​of the real satellite, and send ranging signals to the satellite in both directions through the pseudo-satellite; S2: Performing Taylor expansion on the geometric distance of the positioning equation to establish a linearized positioning equation, solving the clock error correction in the positioning equation through robust iteration; iteratively updating the weights using the pseudorange measurement noise variance, and outputting the optimal clock error estimate; S3: Analyze the ephemeris parameters of the BeiDou GEO satellite, calculate the position of the satellite in the orbital plane, and adapt the coordinates to the Earth-centered Earth-fixed coordinate system through coordinate rotation. Establish an affine transformation relationship between the actual coordinates of the pseudolite and the GEO satellite coordinates, solve the rotation scaling matrix and translation vector in the affine transformation relationship, fit the pseudolite virtual orbit parameters based on the mapping relationship, and generate ephemeris data that conforms to the BeiDou message format; S4: The master base station calibrates the local clock using BeiDou timing signals and periodically synchronizes time with pseudolites to compensate for clock deviations.

2. The method according to claim 1, characterized in that The simplified positioning equation is: Among them, ρ i is the pseudorange, (X i ,Y i ,Z i ) is the satellite coordinate or pseudo-satellite coordinate, (X r ,Y r ,Z r ) is the receiver coordinate, c is the speed of light, δt r represents the clock error, is the parameter to be estimated, ε i is the observation noise and other error terms.

3. The method according to claim 1, characterized in that The linearized positioning equation is constructed by using the coordinates and pseudo-range observations of the satellite and pseudo-satellite. The geometric distance of the simplified positioning equation is Taylor expanded, and the high-order terms are ignored to obtain the linearized error equation. The calculation formula is: Among them, Δx, Δy, Δz are the receiver position corrections, Δ(δt r ) is the clock error correction, e i is the linearized residual, is the direction cosine matrix element, and the specific calculation is:

4. The method according to claim 1, wherein The robust iterative method is: The observation equation is combined into a matrix form: y = Hx + e, where y is the pseudorange residual vector, H is the design matrix, including direction cosine and clock error coefficients, and x = [Δx, Δy, Δz, Δ(δt r )] T , is the parameter vector to be estimated, e is the noise vector; By using the least squares criterion, the goal is to minimize the weighted residual sum of squares: Where W is the weight matrix, and the initial state is set as a diagonal matrix based on the satellite's altitude angle; Decompose the design matrix H into an orthogonal matrix Q and an upper triangular matrix R, H = QR; According to the above calculation process, the matrix form of the observation equation is converted into: Q T y=Rx+Q T and, And solve the parameter vector to be estimated by back substitution method, x=R -1 Q T y; the clock error correction is the last element of the parameter vector to be estimated; The weight matrix is ​​updated iteratively, and an optimal clock error estimate is output after convergence.

5. The method according to claim 1, wherein The objective constraint for solving the affine transformation relationship is to minimize the residual sum of squares, and the calculation formula is: Solve the rotation and scaling matrix and translation vector using the least squares method, and the solution is: R=(P T P) -1 P T Q, in, is the center of mass coordinate, Q i is the actual coordinate of the pseudo-satellite, P i are the GEO satellite ECEF coordinates.

6. The method according to claim 1, characterized in that The accuracy verification index of the rotation scaling matrix and translation vector in the affine transformation relationship is the root mean square error. If the root mean square error is greater than the preset accuracy verification threshold, resampling is performed until convergence. The calculation formula is: Among them, RMSE is the root mean square error, Q i is the actual coordinate of the pseudo-satellite, R is the rotation and scaling matrix, P i is the ECEF coordinate of the GEO satellite, and t is the translation vector.

7. The method according to claim 1, characterized in that The virtual orbit parameter fitting adopts an 18-parameter model and is smoothed by cubic spline interpolation.

8. The method according to claim 1, characterized in that The time synchronization protocol includes the generation and transmission of timestamps, the estimation and compensation of clock deviations, and the monitoring and feedback of synchronization status.

9. The method according to claim 1, characterized in that The main base station calibrates its local clock through the Beidou timing signal and periodically sends time synchronization instructions to the pseudo-satellite. After receiving the instructions, the pseudo-satellite records the local clock reading at the time of reception and immediately replies with a confirmation message, attaching the local clock reading at the time of reply.

10. The method according to claim 9, characterized in that The master base station estimates the clock deviation of the pseudo-satellite based on the timestamp of the round-trip message and compensates for it through the clock deviation correction in the pseudo-range observation value; the status monitoring of the time synchronization includes triggering an alarm mechanism when multiple synchronization failures occur continuously or the deviation exceeds a threshold, and recording an abnormal log.

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