Intersatellite ranging error modeling method for navigation satellites

Abstract

The invention provides a navigation satellite inter-satellite ranging error modeling method, and belongs to the field of navigation satellite inter-satellite ranging. Firstly, precision orbit determination and precision clock error estimation are carried out by utilizing inter-satellite link observation data, and an inter-satellite orbit determination residual error and a clock error estimation residual error are output; secondly, normalizing the residual error sequence into the same orbital period, and performing fitting by using a high-order polynomial attached with a semi-orbital period item; checking the overall effectiveness of the model and the significance of each coefficient of the model through F test and t test; and finally, outputting the ranging error model and the ranging error model of the one-way link after reverse normalization. According to the process, the ranging error modeling work of the one-way observation value of any link can be completed. According to the invention, the inter-satellite link observation model can be effectively improved, the observation value residual error of orbit estimation and clock error calculation is reduced, and the requirements of high-precision precise orbit determination and clock error estimation are met.

Description

Technical Field

[0001] The invention belongs to the field of navigation satellite inter-satellite ranging, and in particular relates to a navigation satellite inter-satellite ranging error modeling method. Background Art

[0002] The intersatellite link payload is one of the most important payloads in the satellite navigation system. It can realize intersatellite data communication and intersatellite measurement, ensure that the satellite can operate stably without ground support, and greatly enhance the satellite's autonomous survivability and service capabilities. At present, the navigation satellites equipped with intersatellite link payloads mainly include the US GPS (Global Positioning System) and China's BeiDou-3 satellite. Compared with the traditional L-band pseudorange and phase observations of navigation satellites, intersatellite observations are a new type of observation. Their error characteristics are different from those of traditional navigation observations, so there is no clear method to improve their errors. The GPS method is based on dual-frequency intersatellite observations, while BeiDou-3 satellites use intersatellite single-frequency observations. Therefore, the GPS method is not suitable for modeling the intersatellite ranging errors of BeiDou-3 satellites. In addition to the GPS and BeiDou-3 systems, there are no other satellite navigation systems equipped with intersatellite links that have been built.

[0003] Restricted by the working system of the intersatellite links, the BeiDou-3 system can form a large number of intersatellite links, but most of the links cannot be continuously established, and each establishment time is only 1 hour. In addition, intersatellite observations are not equally spaced, and each pair of satellites completes two observations in different 3s time slots. This feature of uneven sampling intervals and intermittent link establishment is not conducive to extracting systematic errors from observation errors. The difficulty in identifying trend changes in residuals is related to many different factors, such as the type of equipment in the intersatellite link, the changes in azimuth and nadir angles between the relative positions of satellites, etc., so it is impossible to simply use one or several factors for modeling.

[0004] In summary, due to the complexity of Beidou intersatellite observation, there is currently no suitable method for modeling the Beidou intersatellite ranging system errors. These unmodeled systematic errors will affect the accuracy of precise orbit determination and precise clock error estimation. Therefore, it is crucial to establish an effective error correction model and improve the existing intersatellite observation model. Summary of the invention

[0005] In order to solve the problem of systematic error introduced by different factors in inter-satellite link ranging, the present invention provides a navigation satellite inter-satellite ranging error modeling method according to the characteristics that Beidou satellite inter-satellite ranging error has strong periodicity, ranging between the two ranging parties is discontinuous, and ranging error is related to hardware. The method can reduce the inter-satellite observation value residual and improve the orbit and clock error estimation accuracy.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] In a first aspect, the present invention provides a navigation satellite inter-satellite ranging error modeling method, characterized by comprising:

[0008] The two-way observation data of the intersatellite link is used to perform precise satellite orbit determination and satellite precise clock error estimation, and the residual of the observation value without clock error information and the residual of the observation value without orbit information are output;

[0009] The reference time of the model is selected, and the sequences of the residuals of the observation value without clock error information and the residuals of the observation value without orbit information are segmented according to the orbital period. The residuals of the observation value without clock error information and the residuals of the observation value without orbit information of different orbital periods after segmentation are respectively superimposed into the same orbital period with the reference time as the starting time, and the error model of the observation value without clock error information and the error model of the observation value without orbit information are obtained by fitting a high-order polynomial with a half-orbital period term.

[0010] The F test and t test were used to check the overall effectiveness and significance of the model coefficients of the error model of observations without clock information and the error model of observations without orbit information.

[0011] The checked observation error model without clock information and the observation error model without orbit information are inversely combined to obtain a one-way link error model, which is used to calculate the ranging error of the link.

[0012] Optionally, the two-way observation data of the inter-satellite link is two-way observation data of the inter-satellite link of Beidou MEO (Medium Earth Orbit) satellite for no less than 7 days.

[0013] Optionally, the using of the bidirectional observation data of the intersatellite link to perform satellite precise orbit determination and satellite precise clock error estimation is specifically as follows:

[0014] Select the AB link formed by satellite A and satellite B;

[0015] The bidirectional observation data of the AB link at different times are normalized to the same reference time, and the normalized One-way distance measurement at time and for:

[0016] ;

[0017] ;

[0018] In the formula, and They are The coordinate positions of satellites A and B at this moment, and They are The satellite clock difference between satellites A and B at this moment, and are the intersatellite equipment reception delays of satellites A and B, and are the intersatellite equipment launch delays of satellites A and B, and represents the unmodeled residual ranging error in one-way ranging, and are other errors that can be corrected by the model; Indicates the situation where satellite B receives and satellite A transmits; subscript Indicates the situation where satellite A receives and satellite B transmits; represents the speed of light;

[0019] Will and By combining them, we can obtain the observation values ​​without clock information and without orbit information as follows:

[0020] ;

[0021] ;

[0022] In the formula, represents the observation value without clock error information, Indicates observations without orbit information;

[0023] Use clock-free information observations to perform precise satellite orbit determination and derive the residuals of clock-free information observations after solution. for:

[0024] ;

[0025] Use the non-orbital information observation value to estimate the satellite precise clock error and derive the residual of the non-orbital information observation value after solution for:

[0026] .

[0027] Optionally, the orbital period is determined based on an average angular velocity and an average angular velocity correction in a satellite broadcast ephemeris.

[0028] Optionally, the step of respectively superimposing the clock-free observation residuals and orbit-free observation residuals of different orbital periods after segmentation into the same orbital period starting at the reference time is implemented as follows:

[0029] Will The residual of the observation without clock information at time and the residual of the observation without orbit information Remove integer orbital period , get new The residual of the observation without clock information at time and the residual of the observation without orbit information :

[0030] ;

[0031] .

[0032] Optionally, the observation value error model without clock information and the observation value error model without orbit information are respectively:

[0033] ;

[0034] ;

[0035] In the formula, and Respectively The residuals of observations without clock information and observations without orbit information at the time, It is the time calculated from the observation time to the time within the modeling period; and represents the polynomial model coefficients, and represents the model coefficient of the period term; is the orbital period; is the reference moment of the model; is the degree of the polynomial.

[0036] Optionally, the overall validity of the clock-free observation error model and the orbit-free observation error model is checked by an F test, and the significance of the model coefficients is checked by a t test. The t test process includes:

[0037] S1: Use t-test to analyze the coefficients of the periodic term model and Conduct significance analysis to determine whether the coefficient is significant: if significant, pass the significance analysis; if not significant, remove the periodic term corresponding to the insignificant coefficient from the model and refit the model until it passes the significance analysis;

[0038] S2: Use t-test to compare the coefficients of the polynomial model in order from the highest order to the lowest order. and Conduct a significance analysis to determine whether the coefficient is significant: if it is significant, pass the significance analysis; if it is not significant, eliminate it and The order terms corresponding to the insignificant coefficients in the analysis are refitted until the significance analysis is passed.

[0039] Optionally, the unidirectional link error model is:

[0040] ;

[0041] ;

[0042] In the formula, and represents the one-way observation error of the AB link formed by satellite A and satellite B; Indicates the situation where satellite B receives and satellite A transmits; subscript Indicates the situation where satellite A receives and satellite B transmits.

[0043] In a second aspect, the present invention provides a computer-readable storage medium storing a computer program, wherein the computer program enables a computer to execute the navigation satellite inter-satellite ranging error modeling method as described in the first aspect.

[0044] In a third aspect, the present invention provides an electronic device comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the navigation satellite inter-satellite ranging error modeling method as described in the first aspect is implemented.

[0045] The beneficial effects of the present invention are as follows: the present invention fully takes into account the orbital periodicity of the ranging error of any link and the correlation of different hardware, increases the amount of data available for modeling by normalizing different periods to the same period, uses polynomials to describe constants, linear or nonlinear trends related to hardware delays, etc. within the same orbital period, and adds the identification modeling of half-orbital period trends, thereby establishing a ranging error correction model; in the process of model construction, the present invention also fully considers that the error influencing factors are related to the equipment hardware and the relative positions of the two satellites, adds a periodic term of half an orbital period, and thus improves the inter-satellite link observation model, reduces the observation value residuals of orbit estimation and clock error solution, and meets the requirements of high-precision precise orbit determination and clock error estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 The present invention is a flow chart of a navigation satellite inter-satellite ranging error modeling method.

[0047] Figure 2 It is a comparison chart of orbit determination residuals of C21_C28 link before and after model fitting.

[0048] Figure 3 This is a comparison of the link orbit determination residuals related to the C28 satellite before and after model fitting.

[0049] Figure 4 This is a comparison chart of the link clock error estimation residuals related to the C28 satellite before and after model fitting. DETAILED DESCRIPTION

[0050] The technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application.

[0051] In one embodiment, the present invention proposes a navigation satellite inter-satellite ranging error modeling method, the process of which is as follows: Figure 1 As shown. First, the intersatellite link observation data is used to perform precise orbit determination and precise clock error estimation, and the intersatellite orbit determination residuals and clock error estimation residuals are output; secondly, the residual sequence is normalized to the same orbital period, and a high-order polynomial with a half-orbital period term is used for fitting; then, the F test and t test are used to check the overall effectiveness of the model and the significance of each model coefficient; finally, the ranging error model and the ranging error model of the one-way link after inverse normalization are output. According to this process, the ranging error modeling work of the one-way observation value of any link can be completed. The specific steps are as follows:

[0052] S1: Obtain the two-way observation data of the Beidou intersatellite link for a period of time (generally not less than 7 days).

[0053] In this embodiment, 7 days of Beidou MEO satellite intersatellite link observation data are selected.

[0054] S2: Select one of the links in order.

[0055] In this embodiment, the AB link formed by satellite A and satellite B is selected.

[0056] S3: The original round-trip observation data of two satellites in the same link at different times are normalized to the same reference time.

[0057] In this embodiment, naturalization to One-way distance measurement at time and It can be expressed as:

[0058] ;

[0059] ;

[0060] In the formula, and They are The coordinate positions of satellites A and B at this moment, and They are The satellite clock difference between satellites A and B at this moment, and are the intersatellite equipment reception delays of satellites A and B, and are the intersatellite equipment launch delays of satellites A and B, and represents the unmodeled residual ranging error (residual) in one-way ranging, and includes the antenna phase center, the earth's rotation and other errors that can be accurately corrected by the model; Indicates the situation where satellite B receives and satellite A transmits; subscript Indicates the situation where satellite A receives and satellite B transmits; Represents the speed of light.

[0061] S4: Combine the two-way observations normalized to the same reference time to obtain observations without clock error information and observations without orbit information.

[0062] In this embodiment, the observation value without clock information and the observation value without orbit information are expressed as:

[0063] ;

[0064] .

[0065] S5: Use the clock-free information observation value to perform precise satellite orbit determination and derive the residual of the solved clock-free information observation value.

[0066] In this embodiment, the simplified dynamics method is used for orbit determination, and the residual of the observation value without clock error information can be calculated according to the following formula:

[0067] .

[0068] S6: Use the observations without orbit information to estimate the satellite's precise clock error and derive the residuals of the solved observations without orbit information.

[0069] In this embodiment, the residual of the observation value without orbit information can be calculated according to the following formula:

[0070] .

[0071] S7: Select the reference time of the model, segment the residual sequence of observation values ​​without clock error and orbit information according to the orbital period, and superimpose the residuals of different periods after segmentation into the same orbital period with the reference time as the starting time.

[0072] In this embodiment, the orbital period It can be determined based on the average angular velocity and average angular velocity correction in the satellite broadcast ephemeris. is an integer. Select As the reference time, Time residual removal Integer number of cycles , you can get a new moment The corresponding residual is:

[0073] ;

[0074] ;

[0075] In the formula, as well as It indicates that the residual sequence is periodic.

[0076] S8: Use a high-order polynomial with periodic terms to fit the trend changes in the residual sequence that is approximated to the same orbital period.

[0077] In this embodiment, a high-order polynomial with a periodic term is used to fit the residual of the observation value without clock error information (ranging error): and the residual of the observation without orbit information (ranging error) , can be calculated according to the following formula:

[0078] ;

[0079] ;

[0080] In the formula, and Respectively The residuals of observations without clock information and observations without orbit information at the time, It is the time calculated from the observation time to the time within the modeling period; and represents the polynomial model coefficients, and represents the model coefficient of the period term; is the orbital period; is the reference moment of the model; is the degree of the polynomial.

[0081] S9: Test the variance of the modeling residuals through the F test to determine the validity of the model in S8. If the F test can be passed, it proves that the model has a significant fitting effect on the residuals. Otherwise, it is considered that the model cannot be used to describe the residuals of this link, and return to S2 to model the next link.

[0082] S10: The model coefficients of S8 were analyzed for significance by t-test. The specific process is as follows:

[0083] 1) Use t-test to test the coefficients of the periodic term model in the S8 model and Perform significance analysis to determine the significance of the periodic term and whether the parameter is a necessary parameter of the model; if there is no periodic term, jump directly to 2). If the parameter is not significant, remove the periodic term corresponding to the parameter from the model in S8 and repeat S8.

[0084] 2) Using t-test, the coefficients of the polynomial model of S8 were analyzed in the order from the highest order term to the lowest order term. and Perform significance analysis in turn to determine whether the parameter is a necessary parameter for the model. If the parameter is not significant, then remove it. and The insignificant model parameters correspond to the terms of order, and S8 is repeated.

[0085] 3) Iterate the loop S8 to S10 until the model and all model coefficients pass the check.

[0086] S11: The obtained error model of the observation value without clock information and the error model of the observation value without orbit information are reversely combined to obtain the final error model of the round-trip one-way observation of each link.

[0087] This embodiment is based on and Calculate the ranging error model for a unidirectional link:

[0088] ;

[0089] .

[0090] S12: According to steps S2-S11, the ranging error models of all links are completed, and the ranging errors of the links are calculated.

[0091] The improvement effect of the ranging error model can be verified from the precise orbit determination residuals and clock error estimation residuals. Take the C28 satellite with obvious ranging deviation as an example: Figure 2 It is the comparison of orbit determination residuals of C21_C28 link before and after model fitting, and the residual trend is well fitted; Figure 3 The comparison of the RMS (Root Mean Square) of orbit determination residuals of 19 links related to the C28 satellite before and after model fitting is shown in Figure 1. The average RMS of the residuals before fitting is about 6.9 cm, and after fitting is about 3.2 cm. Figure 4 It is a comparison of the clock error estimation residuals of 19 links related to the C28 satellite before and after the model fitting. The residual before fitting is about 4.1 cm, and after fitting is about 2.3 cm, which shows that the model can better describe the residual trend. The clock error accuracy of C28 is improved by about 16.7%. The improvement effect of the method in this embodiment is obvious.

[0092] In another embodiment, the present invention provides a computer-readable storage medium storing a computer program, wherein the computer program enables a computer to execute a navigation satellite inter-satellite ranging error modeling method of the aforementioned embodiment.

[0093] In another embodiment, the present invention proposes an electronic device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, a navigation satellite inter-satellite ranging error modeling method of the aforementioned embodiment is implemented.

[0094] In the embodiments disclosed in the present application, the computer storage medium may be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, device, or apparatus. The computer storage medium may include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, or equipment, or any suitable combination of the foregoing. More specific examples of computer storage media may include electrical connections based on one or more lines, portable computer disks, hard disks, random access memories (RAM), read-only memories (ROM), erasable programmable read-only memories (EPROM or flash memory), optical fibers, portable compact disk read-only memories (CDROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0095] Those of ordinary skill in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed in this application can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.

[0096] The above are only preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, some improvements and modifications without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims

1. A navigation satellite inter-satellite ranging error modeling method, characterized in that: include: The two-way observation data of the intersatellite link is used to perform precise satellite orbit determination and satellite precise clock error estimation, and the residual of the observation value without clock error information and the residual of the observation value without orbit information are output; The reference time of the model is selected, and the sequences of the residuals of the observation value without clock error information and the residuals of the observation value without orbit information are segmented according to the orbital period. The residuals of the observation value without clock error information and the residuals of the observation value without orbit information of different orbital periods after segmentation are respectively superimposed into the same orbital period with the reference time as the starting time, and the error model of the observation value without clock error information and the error model of the observation value without orbit information are obtained by fitting a high-order polynomial with a half-orbital period term. The F test and t test were used to check the overall effectiveness and significance of the model coefficients of the error model of observations without clock information and the error model of observations without orbit information. The checked observation error model without clock information and the observation error model without orbit information are inversely combined to obtain a one-way link error model, which is used to calculate the ranging error of the link.

2. The navigation satellite inter-satellite ranging error modeling method according to claim 1, characterized in that: The two-way observation data of the intersatellite link is no less than 7 days of two-way observation data of the Beidou MEO satellite intersatellite link.

3. The navigation satellite inter-satellite ranging error modeling method according to claim 1, characterized in that: The use of the bidirectional observation data of the intersatellite link to perform satellite precise orbit determination and satellite precise clock error estimation is specifically as follows: Select the AB link formed by satellite A and satellite B; The bidirectional observation data of the AB link at different times are normalized to the same reference time, and the normalized One-way distance measurement at time and for: ； ； In the formula, and They are The coordinate positions of satellites A and B at this moment, and They are The satellite clock difference between satellites A and B at this moment, and are the intersatellite equipment reception delays of satellites A and B, and are the intersatellite equipment launch delays of satellites A and B, and represents the unmodeled residual ranging error in one-way ranging, and are other errors that can be corrected by the model; Indicates the situation where satellite B receives and satellite A transmits; subscript Indicates the situation where satellite A receives and satellite B transmits; represents the speed of light; Will and By combining them, we can obtain the observation values ​​without clock information and without orbit information as follows: ； ； In the formula, represents the observation value without clock error information, Indicates observations without orbit information; Use clock-free information observations to perform precise satellite orbit determination and derive the residuals of clock-free information observations after solution. for: ； Use the non-orbital information observation value to estimate the satellite precise clock error and derive the residual of the non-orbital information observation value after solution for: 。 4. The navigation satellite inter-satellite ranging error modeling method according to claim 1, characterized in that: The orbital period is determined based on the average angular velocity and the average angular velocity correction in the satellite broadcast ephemeris.

5. The navigation satellite inter-satellite ranging error modeling method according to claim 1, characterized in that: The clock-free observation residuals and orbit-free observation residuals of different orbital periods after segmentation are respectively superimposed into the same orbital period with the reference time as the starting time, which is achieved by the following method: Will The residual of the observation without clock information at time and the residual of the observation without orbit information Remove integer orbital period , get new The residual of the observation without clock information at time and the residual of the observation without orbit information : ； 。 6. The navigation satellite inter-satellite ranging error modeling method according to claim 1, characterized in that: The observation value error model without clock information and the observation value error model without orbit information are respectively: ； ； In the formula, and Respectively The residuals of observations without clock information and observations without orbit information at the time, It is the time calculated from the observation time to the time within the modeling period; and represents the polynomial model coefficients, and represents the model coefficient of the period term; is the orbital period; is the reference moment of the model; is the degree of the polynomial.

7. A navigation satellite inter-satellite ranging error modeling method as claimed in claim 6, characterized in that: The overall effectiveness of the clock-free observation error model and the orbit-free observation error model is checked by an F test, and the significance of the model coefficients is checked by a t test. The t test process includes: S1: Use t-test to analyze the coefficients of the periodic term model and Conduct significance analysis to determine whether the coefficient is significant: if significant, pass the significance analysis; if not significant, remove the periodic term corresponding to the insignificant coefficient from the model and refit the model until it passes the significance analysis; S2: Use t-test to compare the coefficients of the polynomial model in order from the highest order to the lowest order. and Conduct a significance analysis to determine whether the coefficient is significant: if it is significant, pass the significance analysis; if it is not significant, eliminate it and The order terms corresponding to the insignificant coefficients in the analysis are refitted until the significance analysis is passed.

8. A navigation satellite inter-satellite ranging error modeling method as claimed in claim 6, characterized in that: The unidirectional link error model is: ； ； In the formula, and represents the one-way observation error of the AB link formed by satellite A and satellite B; Indicates the situation where satellite B receives and satellite A transmits; subscript Indicates the situation where satellite A receives and satellite B transmits.

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