A Method for Modeling the Inter-Satellite Ranging Error of Navigation Satellites

Abstract

The present invention proposes a method for modeling the ranging error between navigation satellites, belonging to the field of ranging between navigation satellites. First, precise orbit determination and precise clock error estimation are performed using the inter-satellite link observation data, and the inter-satellite orbit determination residuals and clock error estimation residuals are output. Secondly, the residual sequences are normalized to the same orbital period, and a high-order polynomial with a semi-orbital period term is used for fitting. Subsequently, through the F-test and t-test, the overall effectiveness of the model and the significance of each coefficient of the model are checked. Finally, the ranging error model and the ranging error model of the reverse-normalized one-way link are output. According to this process, the ranging error modeling work of the one-way observation value of any link can be completed. The present invention can effectively improve the inter-satellite link observation model, reduce the observation value residuals of orbit estimation and clock error solution, and meet the requirements of high-precision precise orbit determination and clock error estimation.

Description

Technical Field

[0001] The present invention belongs to the field of inter-satellite ranging of navigation satellites, and particularly relates to a method for modeling inter-satellite ranging errors of navigation satellites. Background Art

[0002] The inter-satellite link payload is one of the extremely important payloads that make up a satellite navigation system. It can achieve inter-satellite data communication and inter-satellite measurement, ensuring that the satellite can operate stably without ground support, greatly enhancing the satellite's autonomous survival ability and service ability. Currently, the navigation satellites equipped with inter-satellite link payloads mainly include the GPS (Global Positioning System) of the United States and the Beidou-3 satellites of China. Compared with the traditional L-band pseudo-range and phase observations of navigation satellites, the inter-satellite observations are a new type of observation, and their error characteristics are different from those of traditional navigation observation data. Therefore, there is no clear method for improving their errors. The method of GPS is based on dual-frequency inter-satellite observations, while the Beidou-3 satellites use single-frequency inter-satellite observations. Therefore, the method of GPS is not applicable to the modeling of inter-satellite ranging errors of Beidou-3 satellites. In addition to the GPS and Beidou-3 systems, there are no other established satellite navigation systems equipped with inter-satellite links.

[0003] Restricted by the working mechanism of the inter-satellite link, the Beidou-3 system can form a relatively large number of inter-satellite links, but most of the links cannot continuously establish links, and the link establishment time is only 1 hour each time. In addition, the inter-satellite observations are non-equidistant, and each pair of satellites completes two opposite observations in different 3s time slots. This characteristic of uneven sampling intervals and intermittent link establishment is not conducive to extracting systematic errors from the observation errors. The trend changes in the residuals are difficult to identify and are related to various different factors, such as the types of inter-satellite link devices, the changes in the azimuth and nadir angles between the relative positions of the satellites, etc. Therefore, it is impossible to simply use a certain factor or several factors for modeling.

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

[0005] In order to solve the problem of systematic errors introduced by different factors in inter-satellite link ranging, in view of the characteristics of strong periodicity of inter-satellite ranging errors of Beidou satellites, discontinuous ranging between the two ranging parties, and the fact that the ranging errors are hardware-related, the present invention provides a method for modeling inter-satellite ranging errors of navigation satellites, which can reduce the residuals of inter-satellite observations and improve the accuracy of orbit and clock bias estimation.

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

[0007] In a first aspect, the present invention provides a method for modeling the ranging error between navigation satellites, which is characterized by including:

[0008] Using the two-way observation data of the inter-satellite link to perform precise orbit determination of the satellite and estimate the precise clock offset of the satellite, and outputting the observation value residuals without clock offset information and the observation value residuals without orbit information;

[0009] Selecting the reference time of the model, segmenting the sequences of the observation value residuals without clock offset information and the observation value residuals without orbit information according to the orbit period respectively, superimposing the segmented observation value residuals without clock offset information and the observation value residuals without orbit information of different orbit periods into the same orbit period starting from the reference time, and using a high-order polynomial with a semi-orbit period term to fit to obtain the observation value error model without clock offset information and the observation value error model without orbit information;

[0010] Through F-test and t-test, checking the overall effectiveness of the observation value error model without clock offset information and the observation value error model without orbit information and the significance of the model coefficients;

[0011] Performing reverse combination on the observation value error model without clock offset information and the observation value error model without orbit information that pass the inspection to obtain a one-way link error model for calculating the ranging error of the link.

[0012] Optionally, the two-way observation data of the inter-satellite link is the two-way observation data of the Beidou MEO (Medium Earth Orbit) satellite inter-satellite link for not less than 7 days.

[0013] Optionally, the using the two-way observation data of the inter-satellite link to perform precise orbit determination of the satellite and estimate the precise clock offset of the satellite is specifically:

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

[0015] Normalizing the two-way observation data of the AB link at different times to the same reference time to obtain the one-way ranging at and as:

[0016] ;

[0017] ;

[0018] In the formula, and are respectively the coordinate positions of satellite A and B at and are respectively The satellite clock biases of satellites A and B at a certain moment, and are the receiving time delays of the inter-satellite devices of satellites A and B respectively, and are the transmitting time delays of the inter-satellite devices of satellites A and B respectively, and represent the unmodeled residual ranging errors in one-way ranging, and are other errors that can be corrected by the model; the subscript represents the case where satellite B receives and satellite A transmits; the subscript represents the case where satellite A receives and satellite B transmits; represents the speed of light;

[0019] Combining and respectively obtains the clock-bias-free information observation value and the orbit-information-free observation value as:

[0020] ;

[0021] ;

[0022] In the formula, represents the clock-bias-free information observation value, represents the orbit-information-free observation value;

[0023] Using the clock-bias-free information observation value for precise satellite orbit determination, the residual of the clock-bias-free information observation value after solution is:

[0024] ;

[0025] Using the orbit-information-free observation value for precise satellite clock bias estimation, the residual of the orbit-information-free observation value after solution is:

[0026] .

[0027] Optionally, the orbital period is determined according to the average angular velocity and the average angular velocity correction in the satellite broadcast ephemeris.

[0028] Optionally, the residuals of the clock-bias-free information observation values and the residuals of the orbit-information-free observation values with different orbital periods after segmentation are respectively superimposed into the same orbital period starting from the reference moment, and are realized by the following method:

[0029] Combining the residual of the clock-bias-free information observation value at the moment and the residual of the orbit-information-free observation value Remove an integer orbital period , to obtain a new observation value residual of clock - error - free information at a moment and observation value residual of orbit - information - free :

[0030] ;

[0031] .

[0032] Optionally, the clock - error - free information observation value error model and the orbit - information - free observation value error model are respectively:

[0033] ;

[0034] ;

[0035] In the formula, and respectively represent the observation value residual of clock - error - free information and the observation value residual of orbit - information - free at a moment, is the moment reduced from the observation moment to the modeling period; and represent the polynomial model coefficients, and represent the periodic term model coefficients; is the orbital period; is the reference moment of the model; is the order of the polynomial.

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

[0037] S1: Use the t - test to perform a significance analysis on the periodic term model coefficients and to determine whether the coefficients are significant: If significant, then pass the significance analysis; If not significant, then remove the periodic term corresponding to the non - significant coefficient from the model and refit the model until passing the significance analysis;

[0038] S2: In the order from the highest order to the lowest order, use the t - test to perform a significance analysis on the polynomial model coefficients and to determine whether the coefficients are significant: If significant, then pass the significance analysis; If not significant, then remove and For the order terms corresponding to the coefficients that are not significant in the middle, refit the model until it passes the significance analysis.

[0039] Optionally, the one-way link error model is:

[0040] ;

[0041] ;

[0042] In the formula, and represent the one-way observation errors of the AB link formed by satellite A and satellite B; the subscript represents the situation where satellite B receives and satellite A transmits; the subscript represents 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, and the computer program causes 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, including: a memory, a processor, and a computer program stored on the memory and executable on the processor, and when the processor executes the computer program, it implements the navigation satellite inter-satellite ranging error modeling method as described in the first aspect.

[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. By normalizing different periods to the same period, the amount of available data for modeling is increased. Within the same orbital period, polynomials are used to describe constants, linear or non-linear trends related to hardware delays, etc., and the identification and modeling of the semi-orbital period trend are added, thereby establishing a ranging error correction model; in the process of constructing the model, the present invention also fully considers that the error influencing factors are related to the device hardware and the relative positions of two satellites, adds a periodic term of half an orbital period, and further improves the inter-satellite link observation model, reduces the observation value residuals of orbit estimation and clock bias solution, and meets the requirements of high-precision precise orbit determination and clock bias estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 is a flowchart of a navigation satellite inter-satellite ranging error modeling method.

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

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

[0049] Figure 4 It is a comparison chart of the residual of the link clock error related to satellite C28 before and after model fitting. Specific implementation mode

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

[0051] In one embodiment, the present invention proposes a method for modeling the ranging error between navigation satellites, and its process is as Figure 1 shown. First, use the inter-satellite link observation data for precise orbit determination and precise clock error estimation, and output the inter-satellite orbit determination residual and clock error estimation residual; secondly, normalize the residual sequence to the same orbit period, and use a high-order polynomial with a semi-orbit period term for fitting; then, through the F-test and t-test, check the overall effectiveness of the model and the significance of each coefficient of the model; finally, output the ranging error model and the ranging error model of the reverse-normalized one-way link. 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 inter-satellite link for a period of time (generally not less than 7 days).

[0053] In this embodiment, 7-day observation data of the Beidou MEO satellite inter-satellite link is selected.

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

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

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

[0057] In this embodiment, normalize to The one-way ranging at time and can be expressed as:

[0058] ;

[0059] ;

[0060] In the formula, and are respectively The coordinate positions of satellite A and B at time and are respectively The satellite clock errors of satellite A and B at time and They are the receiving time delays of the inter-satellite devices of satellites A and B respectively, and They are the transmitting time delays of the inter-satellite devices of satellites A and B respectively, and represent the unmodeled residual ranging error (residual) in one-way ranging, and are the errors that include the antenna phase center, the earth's rotation, etc. and can be accurately corrected through models; the subscript represents the case where satellite B receives and satellite A transmits; the subscript represents the case 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 the clock-error-free observation values and the orbit-information-free observation values.

[0062] In this embodiment, the clock-error-free observation values and the orbit-information-free observation values are expressed as:

[0063] ;

[0064] .

[0065] S5: Use the clock-error-free observation values to perform precise orbit determination of the satellite, and derive the residuals of the clock-error-free observation values after solution.

[0066] In this embodiment, the simplified dynamics method is used for orbit determination, and the residuals of the clock-error-free observation values can be calculated according to the following formula:

[0067] .

[0068] S6: Use the orbit-information-free observation values to perform precise clock bias estimation of the satellite, and derive the residuals of the orbit-information-free observation values after solution.

[0069] In this embodiment, the residuals of the orbit-information-free observation values can be calculated according to the following formula:

[0070] .

[0071] S7: Select the reference time of the model, segment the sequences of the residuals of the clock-error-free and orbit-information-free observation values according to the orbit period, and superimpose the residuals of different periods after segmentation onto the same orbit period starting from the reference time.

[0072] In this embodiment, the orbit period can be determined according to the mean angular velocity and the mean angular velocity correction amount in the satellite broadcast ephemeris, is an integer. Select as the reference time, and Remove the time residual by an integer number of cycles to obtain a new time and the corresponding residual:

[0073] ;

[0074] ;

[0075] In the formula, and indicate that the residual sequence has periodicity.

[0076] S8: Use a high-order polynomial with a periodic term to fit and approximate the trend change in the residual sequence reduced to the same orbital period.

[0077] In this embodiment, use a high-order polynomial with a periodic term to fit the residual of the clock-free information observation (ranging error) and the residual of the orbit-free information observation (ranging error) , which can be calculated according to the following formula:

[0078] ;

[0079] ;

[0080] In the formula, and respectively represent the residual of the clock-free information observation and the residual of the orbit-free information observation at time which is the time reduced from the observation time to the modeling period; and represent the polynomial model coefficients, and represent the periodic term model coefficients; is the orbital period; is the reference time of the model; is the order of the polynomial.

[0081] S9: Test the variance of the modeling residual through the F-test to determine the effectiveness of the model in S8. If the F-test can be passed, it proves that the fitting effect of the model on the residual is significant, otherwise it is considered that the residual of this link cannot be described by the model, and return to S2 to model the next link.

[0082] S10: Conduct a significance analysis of the model coefficients in S8 through the t-test. The specific process is as follows:

[0083] 1) Use the t-test for the periodic term model coefficients and Perform significance analysis to determine the significance of the periodic terms and identify whether the parameters are necessary parameters for the model. Among them, if there are no periodic terms, directly jump to 2). If the parameters are not significant, remove the periodic terms corresponding to the parameters from the model in S8 and re-perform S8.

[0084] 2) In the order from the highest-order term to the lowest-order term, use the t-test to perform significance analysis on the polynomial model coefficients of S8 and sequentially to determine whether the parameters are necessary parameters for the model. If the parameters are not significant, remove and the terms corresponding to the insignificant model parameters in the order of the corresponding orders and re-perform S8.

[0085] 3) Iteratively loop through S8 to S10 until the model and all model coefficients pass the verification.

[0086] S11: Reverse-combine the obtained clock-error-free observation error model and orbit-information-free observation error model to obtain the final error model for the round-trip one-way observation of each link.

[0087] This embodiment is based on and to deduce the ranging error model of the one-way link:

[0088] ;

[0089] .

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

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

[0093] In another embodiment, the present invention provides an electronic device, including: a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, a method for modeling the ranging error between navigation satellites in the foregoing embodiment is implemented.

[0094] In the embodiments disclosed in the present application, the computer storage medium may be a tangible medium that can contain or store a program for use by or in connection with an instruction execution system, apparatus, or device. The computer storage medium may include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of the computer storage medium would include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (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 the examples described in connection with the embodiments disclosed in the present application can be implemented in electronic hardware or in a combination of computer software and electronic hardware. Whether these functions are executed in hardware or software depends on the specific application and design constraints of the technical solution. Skilled artisans may use different methods for each specific application to implement the described functions, but such implementation should not be considered to exceed the scope of the present application.

[0096] The above are only the preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions falling within the concept of the present invention belong to the protection scope of the present invention. It should be noted that for those of ordinary skill in the art, several improvements and refinements made without departing from the principle of the present invention should be regarded as within 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 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 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 information and the error model of the observation value without orbit information are obtained by high-order polynomial fitting with half-orbital period terms; the error model of the observation value without clock information and the error model of the observation value without orbit information are respectively: In the formula, Δ orb (t′0) and Δ clk (t′0) represents the residual of the observation without clock information and the residual of the observation without orbit information at time t′0, respectively. t′0 is the time calculated from the observation time to the modeling period; a i and b i represents the polynomial model coefficient, c i and d i represents the model coefficient of the periodic term; T is the orbital period; t ref is the reference moment of the model; m is the order of the polynomial; 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 one-way ranging P normalized to time t0 is obtained. BA (t0) and P AB (t0) is: In the formula, and are the coordinate positions of satellites A and B at time t0, dt A (t0) and dt B (t0) are the satellite clock errors of satellites A and B at time t0, and are the intersatellite equipment reception delays of satellites A and B, and are the intersatellite equipment transmission delays of satellites A and B, and b BA and b AB represents the unmodeled residual ranging error in one-way ranging, ε BA and ε AB are other errors that can be corrected by the model; the subscript BA indicates the case where satellite B receives and satellite A transmits; the subscript AB indicates the case where satellite A receives and satellite B transmits; c indicates the speed of light; P BA (t0) and P AB (t0) are combined to obtain the observation value without clock error information and the observation value without orbit information: In the formula, represents the observation value without clock error information, Indicates observations without orbit information; The clock-free information observations are used to perform precise satellite orbit determination, and the residual error Δ of the clock-free information observations after solution is derived. orb for: The satellite precise clock error is estimated by using the observation value without orbit information, and the residual error Δ of the observation value without orbit information after solution is derived. clk 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: The residual Δ of the observation value without clock error information at time t0 orb (t0) and the residual error Δ of the observation without orbit information clk (t0) Remove k integer orbital periods T and obtain the new clock-free observation residual Δ at time t′0 orb (t′0) and the residual error Δ of the observation without orbit information clk (t′0): Δ orb (t0)=Δ orb (t′0+kT)=Δ orb (t′0); Δ clk (t0)=Δ clk (t′0+kT)=Δ clk (t′0)。 6. The navigation satellite inter-satellite ranging error modeling method according to claim 1, 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 periodic term model coefficient c i and d i 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: From the highest order to the lowest order, use the t-test to test the coefficients a of the polynomial model. i and b i 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 a i and b i The order terms corresponding to the insignificant coefficients in the analysis are refitted until the significance analysis is passed.

7. A navigation satellite inter-satellite ranging error modeling method as claimed in claim 5, characterized in that: The unidirectional link error model is: In the formula, Δb BA (t0) and Δb AB (t0) represents the one-way observation error of the AB link formed by satellite A and satellite B; the subscript BA represents the case where satellite B receives and satellite A transmits; the subscript AB represents the case where satellite A receives and satellite B transmits.

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