Star-based enhanced satellite clock error correction processing method and system based on Fourier series

Abstract

The invention discloses a Fourier series-based satellite clock correction correction processing method and system, and relates to a satellite navigation wide-area difference technology, and the method comprises the steps: observing the carrier phase observed quantity of a GNSS satellite j through a monitoring station i, and smoothing the pseudo-range observed quantity; eliminating ionospheric delay of the smoothed pseudo-range observed quantity to obtain a pseudo-range observed quantity after the ionospheric delay is eliminated; calculating an ephemeris position and a satellite clock skew of a GNSS satellite j, calculating an inter-station-satellite distance, and eliminating the inter-station-satellite distance and the satellite clock skew from the pseudo-range observed quantity after the ionospheric delay is eliminated to obtain a pseudo-range residual error; a satellite orbit error in the pseudo-range residual error is eliminated through an inter-station single-difference method; according to the method, the state model of the satellite clock error is established by using the Fourier series, the state model is solved to obtain the satellite clock error correction, and the precision of the GNSS satellite orbit clock error difference correction can be improved.

Description

Technical Field

[0001] The present application relates to the field of satellite navigation wide-area differential technology, and in particular to a Fourier series-based satellite-based enhanced satellite clock correction number processing method and system. Background Art

[0002] The clock error of the Global Navigation Satellite System (GNSS) satellite is mainly caused by the distribution and coordinate error of the monitoring stations in the ground control part, the accuracy of the observations obtained by the monitoring stations tracking the satellites, the stability of the satellite clocks, etc. The Satellite Based Augmentation System (SBAS) estimates the satellite clock error and generates the corresponding satellite clock correction number to reduce the impact of the satellite clock error on the user's positioning accuracy.

[0003] Since the frequency of the satellite clock is affected by the periodic changes in the satellite's speed and the earth's gravity, the change in the satellite clock error has a certain periodicity. When the satellite moves from the apogee to the perigee, the speed gradually increases and the distance from the earth gets closer and closer, which makes the clock frequency gradually slow down, resulting in a gradual decrease in the clock error; while when the satellite moves from the perigee to the apogee, the speed gradually decreases and the distance from the earth gets farther and farther, which makes the clock frequency gradually increase, resulting in a gradual increase in the clock error.

[0004] The existing publicly available methods for calculating satellite-based augmentation satellite clock corrections all use the least squares method or the Kalman filtering method based on the acceleration model. They fail to establish a motion model based on the characteristics of the satellite clock error. They simply use the least squares method or the Kalman filtering method based on the acceleration model for calculation. The calculated satellite clock corrections cannot effectively reflect the true characteristics of the satellite clock error. Summary of the invention

[0005] The embodiment of the present application provides a method and system for processing satellite-based enhanced satellite clock correction numbers based on Fourier series. A dynamic change model of satellite clock error is established using Fourier series. The calculated satellite clock correction number can more realistically reflect the satellite clock error and improve the accuracy of GNSS satellite orbit clock difference correction numbers.

[0006] The embodiment of the present application provides a method for processing satellite clock correction numbers based on Fourier series for satellite-based augmentation, including:

[0007] Among the monitoring stations that observe GNSS satellite j, select the monitoring station with an elevation angle greater than the altitude cutoff angle;

[0008] The pseudo-range observations are smoothed using the carrier phase observations of GNSS satellite j observed by monitoring station i;

[0009] Eliminating the ionospheric delay of the smoothed pseudo-range observations to obtain the pseudo-range observations after the ionospheric delay is eliminated;

[0010] The ephemeris position and satellite clock bias of GNSS satellite j are calculated using the orbital parameters and clock parameters broadcast by the navigation message, and the station-satellite distance is calculated in combination with the position of monitoring station i. The station-satellite distance and satellite clock bias are eliminated from the pseudorange observation after eliminating the ionospheric delay to obtain the pseudorange residual.

[0011] The satellite clock error in the pseudorange residual is eliminated by the inter-station single difference method;

[0012] A state model of satellite clock error is established using Fourier series, and the state model is solved to obtain satellite clock corrections.

[0013] Optionally, the pseudorange observation is smoothed using the carrier phase observation of GNSS satellite j observed by monitoring station i, including:

[0014] Transform the carrier observations:

[0015]

[0016] in, f1 is the frequency of carrier L1, f5 is the frequency of carrier L5; and are the carrier phase observations at the L1 and L5 frequency points at time t respectively;

[0017] use To smooth the noise in the pseudorange observations:

[0018]

[0019] Among them, L k Indicates L1 or L5 frequency point, is the pseudo-range observation value of the corresponding frequency point, is the pseudorange observation after smoothing of the corresponding frequency point, and τ is the smoothing time.

[0020] Optionally, eliminating ionospheric delay from the smoothed pseudorange observation, and obtaining the pseudorange observation after eliminating ionospheric delay includes:

[0021] The pseudorange observation after eliminating the ionospheric delay satisfies:

[0022]

[0023] in, This is the pseudorange observation after eliminating the ionospheric delay.

[0024] Optionally, the orbit parameters and clock parameters broadcast by the navigation message are used to calculate the ephemeris position and satellite clock bias of GNSS satellite j, and the inter-station distance is calculated in combination with the position of monitoring station i to satisfy:

[0025]

[0026] in, represents the ephemeris position and satellite clock bias of GNSS satellite j represents the location of monitoring station i, Represents the ephemeris distance.

[0027] Optionally, the station-satellite distance and the satellite clock bias are eliminated from the pseudorange observation after eliminating the ionospheric delay to obtain a pseudorange residual satisfying:

[0028]

[0029] Among them, ΔR j (t) = [Δx j (t) Δy j (t) Δz j (t)] T is the orbit error of GNSS satellite j in the X, Y, and Z directions in the Earth-centered Earth-fixed coordinate system, is the unit direction vector from monitoring station i to GNSS satellite j, ΔB j (t) is the clock error of GNSS satellite j, is the residual error, is the variance.

[0030] Optionally, eliminating the clock error in the pseudorange residual by the inter-station single difference method includes:

[0031] Pseudorange residual Each value of Subtracting, we get:

[0032]

[0033] in, is the residual error, and the variance is

[0034] Convert equation (7) into the corresponding matrix form:

[0035]

[0036] in, V o j The covariance matrix of

[0037] The satellite orbit error can be estimated using the weighted least squares method. and correction accuracy

[0038]

[0039] Substitute equation (9) into equation (6):

[0040]

[0041] The corresponding matrix form is:

[0042]

[0043] in, V c j The covariance matrix of

[0044] Optionally, the state model of the satellite clock error is established using Fourier series including:

[0045] The Fourier series that expands the satellite clock error into a trigonometric function satisfies:

[0046]

[0047] Among them, a0 is the DC component; a1cos(ωt)+b1sin(ωt) is the fundamental component; a n cos(nωt)+b n sin(nωt) is the high-order harmonic component (n=2,3,4,…); a n is the amplitude of each cosine component; b n is the amplitude of each sinusoidal component; ω is the fundamental angular frequency;

[0048] The state model of the satellite clock error obtained after processing satisfies:

[0049] X c (t n )=Φ c (t n -t n-1 )X c (t n-1 )+W c (t n-1 ) (twenty one)

[0050] Among them, t n is a time series, W c (t n ) is noise, and its covariance matrix is ​​Qc (t n )=diag([10 -7 10 -7 10 -7 ]).

[0051] Optionally, solving the state model to obtain satellite clock corrections includes:

[0052] According to formula (12), the observation equation of satellite clock error can be obtained:

[0053] Z c (t n )=H c (t n )X c (t n )+V c (t n ) (twenty two)

[0054] in, Its covariance matrix

[0055] Using equations (21) and (22), the satellite clock correction can be solved by Kalman filtering:

[0056]

[0057] P c (t n |t n-1 )=Φ c (t n -t n-1 ) c (t n-1 )Φ c T (t n -t n-1 )+Q c (t n-1 ) (twenty four)

[0058]

[0059] P c (t n )=[IK c (t n )H c (t n )]P c (t n |t n-1 ) (27)

[0060] Where I is the identity matrix;

[0061] Satellite clock correction for:

[0062]

[0063] Among them, X c,1,1 (t n ) is X c (t n )'s first row and first column.

[0064] In an embodiment of the present application, a Fourier series-based satellite-based augmented satellite clock correction number processing system is also proposed, including a processor and a memory, wherein a computer program is stored in the memory, and when the computer program is executed by the processor, the steps of the aforementioned Fourier series-based satellite-based augmented satellite clock correction number processing method are implemented.

[0065] The method of the embodiment of the present application uses Fourier series to establish a dynamic change model of satellite clock error. The calculated satellite clock error correction number can more realistically reflect the satellite clock error and improve the accuracy of the GNSS satellite orbit clock error differential correction number.

[0066] The above description is only an overview of the technical solution of the present application. In order to more clearly understand the technical means of the present application, it can be implemented in accordance with the contents of the specification. In order to make the above and other purposes, features and advantages of the present application more obvious and easy to understand, the specific implementation methods of the present application are listed below. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Various other advantages and benefits will become apparent to those of ordinary skill in the art by reading the detailed description of the preferred embodiments below. The accompanying drawings are only for the purpose of illustrating the preferred embodiments and are not to be considered as limiting the present application. Also, the same reference symbols are used throughout the accompanying drawings to represent the same components. In the accompanying drawings:

[0068] Figure 1 The basic process flow of the Fourier series-based satellite-based augmented satellite clock correction number processing method of the embodiment of the present application is schematically illustrated. DETAILED DESCRIPTION

[0069] The exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the present disclosure to those skilled in the art.

[0070] The present application embodiment provides a method for processing satellite clock correction numbers based on Fourier series. Figure 1 As shown, the following steps are included:

[0071] In step S101 , among the monitoring stations that observe the GNSS satellite j, the monitoring stations whose elevation angles are greater than the altitude cutoff angle are selected. For example, in some examples, the number of the monitoring stations is M.

[0072] In step S102, the pseudorange observations are smoothed using the carrier phase observations of the GNSS satellite j observed by the monitoring station i.

[0073] In step S103, the ionospheric delay is eliminated from the smoothed pseudorange observation quantity to obtain the pseudorange observation quantity after the ionospheric delay is eliminated.

[0074] In step S104, the orbital parameters and clock parameters broadcast by the navigation message are used to calculate the ephemeris position and satellite clock bias of the GNSS satellite j, and the station-satellite distance is calculated in combination with the position of the monitoring station i. The station-satellite distance and the satellite clock bias are eliminated from the pseudorange observation after eliminating the ionospheric delay to obtain the pseudorange residual.

[0075] In step S105, the clock error in the pseudorange residual is eliminated by the inter-station single difference method. In a specific example, the satellite orbit error can be solved by the least square method.

[0076] In step S106, a state model of the satellite clock error is established using Fourier series, and the state model is solved to obtain the satellite clock correction number.

[0077] In some embodiments, the pseudorange observation is smoothed using the carrier phase observation of the GNSS satellite j observed by the monitoring station i, including: transforming the carrier phase observation:

[0078]

[0079] in, f1 is the frequency of carrier L1, f5 is the frequency of carrier L5; and are the carrier phase observations at the L1 and L5 frequency points at time t respectively;

[0080] because The integer ambiguity of the two moments before and after is basically the same. In the embodiment of the present application, To smooth the noise in the pseudorange observations:

[0081]

[0082] Among them, L k Indicates L1 or L5 frequency point, is the pseudo-range observation value of the corresponding frequency point, is the pseudorange observation after smoothing of the corresponding frequency point, and τ is the smoothing time.

[0083] In some embodiments, eliminating ionospheric delay from the smoothed pseudorange observations, and obtaining the pseudorange observations after eliminating ionospheric delay includes:

[0084] The pseudorange observation after eliminating the ionospheric delay satisfies:

[0085]

[0086] in, This is the pseudorange observation after eliminating the ionospheric delay.

[0087] In some embodiments, the orbital parameters and clock parameters broadcast by the navigation message are used to calculate the ephemeris position and satellite clock bias of the GNSS satellite j, and the inter-station distance is calculated in combination with the position of the monitoring station i to satisfy:

[0088]

[0089] in, represents the ephemeris position and satellite clock bias of GNSS satellite j represents the location of monitoring station i, Represents the ephemeris distance.

[0090] In some embodiments, the station-satellite distance and the satellite clock bias are eliminated from the pseudorange observation after the ionospheric delay is eliminated to obtain the pseudorange residual satisfy:

[0091]

[0092] Among them, ΔR j (t) = [Δx j (t) Δy j (t) Δz j (t)] T is the orbit error of GNSS satellite j in the X, Y, and Z directions in the Earth-centered Earth-fixed coordinate system (the error between the satellite ephemeris position and the true position), is the unit direction vector from monitoring station i to GNSS satellite j, ΔB j (t) is the clock error of GNSS satellite j (the residual error after correction using the satellite clock bias in the navigation message), is the residual error, is the variance.

[0093] In some embodiments, the clock error in the pseudorange residual is eliminated by using an inter-station single difference method. Specifically, after eliminating the ionosphere, the satellite clock error is eliminated by using an inter-station single difference method, as shown in formula (7), which specifically includes:

[0094] Pseudorange residual Each value of Subtracting, we get:

[0095]

[0096] in, is the residual error, and the variance is

[0097] Convert equation (7) into the corresponding matrix form:

[0098]

[0099] in, The covariance matrix of

[0100] The satellite orbit error is solved by least squares, and then the solved satellite orbit error is substituted into equation (6), and the satellite clock error is solved by Fourier series transform and Kalman filter.

[0101] The satellite orbit error can be estimated using the weighted least squares method. and correction accuracy

[0102]

[0103] Substitute equation (9) into equation (6):

[0104]

[0105] The corresponding matrix form is:

[0106]

[0107] in, V c j The covariance matrix of

[0108] In some embodiments, establishing a state model of satellite clock errors using Fourier series includes:

[0109] The Fourier series that expands the satellite clock error into a trigonometric function satisfies:

[0110]

[0111] Among them, a0 is the DC component; a1cos(ωt)+b1sin(ωt) is the fundamental component; a n cos(nωt)+b n sin(nωt) is the high-order harmonic component (n=2,3,4,…); a n is the amplitude of each cosine component; b n is the amplitude of each sinusoidal component; ω is the fundamental angular frequency.

[0112] Ignoring the influence of higher-order terms, simplifying equation (13), we can obtain ΔB j (t) can be approximately expressed as:

[0113] ΔB j (t)≈a0+a1cos(ωt)+b1sin(ωt) (14)

[0114] By taking the first and second order derivatives of equation (14) with respect to t, we can obtain:

[0115]

[0116] Let ΔB at time t = 0 j (0) and Substituting into equation (14), equation (15) and equation (16) respectively, we can obtain:

[0117]

[0118] Substituting a0, a1 and b1 into equation (14), equation (15) and equation (16) respectively, we can obtain:

[0119] X c (t) = Φ c (t)X c (0) (20)

[0120] in,

[0121] Using formula (20), the state model of satellite clock error can be obtained:

[0122] X c (t n )=Φ c (t n -t n-1 )X c (t n-1 )+W c (t n-1 ) (twenty one)

[0123] Among them, tn is a time series, W c (t n ) is noise, and its covariance matrix is ​​Q c (t n )=diag([10 -7 10 -7 10 -7 ]).

[0124] In some embodiments, solving the state model to obtain satellite clock corrections includes:

[0125] According to formula (12), the observation equation of satellite clock error can be obtained:

[0126] Z c (t n )=H c (t n )X c (t n )+V c (t n ) (twenty two)

[0127] in, Its covariance matrix

[0128] Using equations (21) and (22), the satellite clock correction can be solved by Kalman filtering:

[0129]

[0130] P c (t n |t n-1 )=Φ c (t n -t n-1 ) c (t n-1 )Φ c T (t n -t n-1 )+Q c (t n-1 ) (twenty four)

[0131]

[0132] P c (t n )=[IK c (t n )H c (t n )]P c (t n|t n-1 ) (27)

[0133] Where I is the identity matrix;

[0134] Satellite clock correction for:

[0135]

[0136] Among them, X c,1,1 (t n ) is X c (t n )'s first row and first column.

[0137] The method of the embodiment of the present application uses Fourier series to describe the satellite clock error, and uses Fourier series to establish a state equation, and solves the satellite clock correction number through the Kalman filter method. The method of the embodiment of the present application solves the problem that there is no effective equation to describe the satellite clock error. The solved satellite clock correction number can effectively reflect the characteristics of the satellite clock error. The method of the present application is easy to implement in engineering.

[0138] In an embodiment of the present application, a Fourier series-based satellite-based augmented satellite clock correction number processing system is also proposed, including a processor and a memory, wherein a computer program is stored in the memory, and when the computer program is executed by the processor, the steps of the aforementioned Fourier series-based satellite-based augmented satellite clock correction number processing method are implemented.

[0139] It should be noted that in the various embodiments of the present application, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also includes other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the sentence "includes a ..." does not exclude the presence of other identical elements in the process, method, article or device including the element.

[0140] The serial numbers of the above-mentioned embodiments of the present application are for description only and do not represent the advantages or disadvantages of the embodiments.

[0141] Through the description of the above implementation methods, those skilled in the art can clearly understand that the above-mentioned embodiment methods can be implemented by means of software plus a necessary general hardware platform, and of course by hardware, but in many cases the former is a better implementation method. Based on such an understanding, the technical solution of the present application, or the part that contributes to the prior art, can be embodied in the form of a software product, which is stored in a storage medium (such as ROM / RAM, a magnetic disk, or an optical disk), and includes a number of instructions for a terminal (which can be a mobile phone, a computer, a server, an air conditioner, or a network device, etc.) to execute the methods described in each embodiment of the present application.

[0142] The embodiments of the present application are described above in conjunction with the accompanying drawings, but the present application is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the guidance of the present application, ordinary technicians in this field can also make many forms without departing from the purpose of the present application and the scope of protection of the claims, all of which are within the protection of the present application.

Claims

1. A Fourier series-based satellite-based augmentation satellite clock correction number processing method, characterized in that: include: Among the monitoring stations that observe GNSS satellite j, select the monitoring station with an elevation angle greater than the altitude cutoff angle; The pseudo-range observations are smoothed using the carrier phase observations of GNSS satellite j observed by monitoring station i; Eliminating the ionospheric delay of the smoothed pseudo-range observations to obtain the pseudo-range observations after the ionospheric delay is eliminated; The ephemeris position and satellite clock bias of GNSS satellite j are calculated using the orbital parameters and clock parameters broadcast by the navigation message, and the station-satellite distance is calculated in combination with the position of monitoring station i. The station-satellite distance and satellite clock bias are eliminated from the pseudorange observation after eliminating the ionospheric delay to obtain the pseudorange residual. The clock error in the pseudorange residual is eliminated by using the inter-station single difference method; A state model of satellite clock error is established using Fourier series, and the state model is solved to obtain satellite clock corrections.

2. The Fourier series-based satellite-based augmented satellite clock correction number processing method according to claim 1, characterized in that: The pseudorange observations are smoothed using the carrier phase observations of GNSS satellite j observed by monitoring station i, including: Transform the carrier observations: in, f1 is the frequency of carrier L1, f5 is the frequency of carrier L5; and are the carrier phase observations at the L1 and L5 frequency points at time t respectively; use To smooth the noise in the pseudorange observations: Among them, L k Indicates L1 or L5 frequency point, is the pseudo-range observation value of the corresponding frequency point, is the pseudorange observation after smoothing of the corresponding frequency point, and τ is the smoothing time.

3. The Fourier series-based satellite-based augmented satellite clock correction number processing method according to claim 2, characterized in that: The ionospheric delay is eliminated for the smoothed pseudo-range observations. The pseudo-range observations after the ionospheric delay is eliminated include: The pseudorange observation after eliminating the ionospheric delay satisfies: in, This is the pseudorange observation after eliminating the ionospheric delay.

4. The method for processing satellite clock corrections based on Fourier series according to claim 3, characterized in that: The orbital parameters and clock parameters broadcast by the navigation message are used to calculate the ephemeris position and satellite clock bias of GNSS satellite j, and the inter-station distance is calculated in combination with the position of monitoring station i to satisfy: in, represents the ephemeris position of GNSS satellite j, represents the satellite clock bias, represents the location of monitoring station i, Indicates the distance between stations and satellites.

5. The method for processing satellite clock corrections based on Fourier series according to claim 4, characterized in that: Eliminate the station-satellite distance and satellite clock bias from the pseudorange observation after eliminating the ionospheric delay to obtain the pseudorange residual satisfying: Among them, ΔR j (t) = [Δx j (t) Δy j (t) Δz j (t)] T is the orbit error of GNSS satellite j in the X, Y, and Z directions in the Earth-centered Earth-fixed coordinate system, is the unit direction vector from monitoring station i to GNSS satellite j, ΔB j (t) is the clock error of GNSS satellite j, is the residual error, is the variance.

6. The Fourier series-based satellite-based augmented satellite clock correction number processing method according to claim 5, characterized in that: Eliminating the clock error in the pseudorange residual by the inter-station single difference method includes: Pseudorange residual Each value of Subtracting, we get: in, is the residual error, and the variance is Convert equation (7) into the corresponding matrix form: in, The covariance matrix of The satellite orbit error can be estimated using the weighted least squares method. and correction accuracy Substitute equation (9) into equation (6): The corresponding matrix form is: in, The covariance matrix of 7. The Fourier series-based satellite-based augmented satellite clock correction number processing method according to claim 6, characterized in that: The state model of satellite clock error established using Fourier series includes: The Fourier series that expands the satellite clock error into a trigonometric function satisfies: Among them, a0 is the DC component; a1cos(ωt)+b1sin(ωt) is the fundamental component; a n cos(nωt)+b n sin(nωt) is the high-order harmonic component (n=2,3,4,…); a n is the amplitude of each cosine component; b n is the amplitude of each sinusoidal component; ω is the fundamental angular frequency; The state model of the satellite clock error obtained after processing satisfies: X c (t n )=Φ c (t n -t n-1 )X c (t n-1 )+W c (t n-1 ) (21) Among them, t n is a time series, W c (t n ) is noise, and its covariance matrix is ​​Q c (t n )=diag([10 -7 10 -7 10 -7 ]).

8. The Fourier series-based satellite-based augmented satellite clock correction number processing method according to claim 7, characterized in that: Solving the state model to obtain satellite clock corrections includes: According to formula (12), the observation equation of satellite clock error can be obtained: Z c (t n )=H c (t n )X c (t n )+V c (t n ) (22) in, Its covariance matrix Using equations (21) and (22), the satellite clock correction can be solved by Kalman filtering: P c (t n |t n-1 )=Φ c (t n -t n-1 )P c (t n-1 )Φ c T (t n -t n-1 )+Q c (t n-1 ) (24) P c (t n )=[I-K c (t n )H c (t n )]P c (t n |t n-1 ) (27) Where I is the identity matrix; Satellite clock correction for: Among them, X c,1,1 (t n ) is X c (t n )'s first row and first column.

9. A Fourier series-based satellite-based augmented satellite clock correction processing system, characterized in that: The method comprises a processor and a memory, wherein a computer program is stored in the memory, and when the computer program is executed by the processor, the steps of the Fourier series-based satellite-based enhanced satellite clock correction number processing method as described in any one of claims 1 to 8 are implemented.

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