Pseudo-range observation refinement method and device suitable for BDS non-geostationary orbit satellite

Abstract

This invention discloses a method and device for refining pseudorange observations for BDS non-geostationary orbit satellites. The specific method includes: analyzing the SCB characteristics of BDS non-geostationary orbit satellites using multipath combination analysis; eliminating the influence of time-invariant parameters in MP combination based on epoch difference, establishing an ED-SCB sequence for each satellite and frequency, and using the averaging method to achieve the best estimate of the ED-SCB for the equation; for satellite a at the i-th frequency, assuming the ED-SCB at the mid-elevation angle is θ, calculating the absolute value of the elevation angle E1; establishing an SCB correction model using a polynomial piecewise fitting algorithm, with the principle of minimizing the sum of the absolute values ​​of the residuals; deriving the DSC filter variance based on the CSC filtering principle, using the DSC variance function described by the error propagation law, and determining the smoothing window based on the principle of minimizing variance; to suppress Doppler cumulative integration error, introducing a balance factor to adjust the weights of DSC and the original pseudorange, establishing an RDSC variance equation based on the error propagation law, and establishing a dynamic weight adjustment model for RDSC based on the principle of minimizing variance.

Description

Technical Field

[0001] This invention belongs to the field of data preprocessing for the BeiDou Navigation Satellite System, specifically relating to a method and equipment for refining pseudorange observations for BDS non-geostationary orbit satellites. Background Technology

[0002] Global Navigation Satellite System (GNSS) provides users with navigation, positioning, and timing services, with navigation primarily based on code-based pseudorange. The quality of the code-based pseudorange signal directly determines the overall navigation performance of the satellite system. Typically, a high-precision phase observation measurement method (Carrier-Smoothed Code, CSC) is used to refine the pseudorange's random noise. However, in complex GNSS operating environments, cycle slips are difficult to avoid, leading to frequent interruptions of the CSC filter and affecting the accuracy and reliability of navigation and positioning. Doppler, a high-precision observation independent of carrier phase and unaffected by cycle slips, can be used to refine the random noise of pseudorange observations.

[0003] The accuracy of pseudorange observations is limited not only by the level of random noise but also by systematic errors. Existing research indicates that the pseudorange observations of the BeiDou system exhibit a systematic bias originating from the space satellites, which can cause pseudorange-phase discrepancies to reach the meter level; this is known as Satellite Code Bias (SCB). Since SCB at the user end is closely related to the satellite elevation angle, some scholars have established SCB correction models based on the satellite elevation angle. However, these models are based on satellite orbit types, neglecting the differences between satellites. To more accurately correct SCB errors, some scholars have established SCB correction models for each non-geostationary orbit satellite.

[0004] However, many models only establish different groups based on orbit type, ignoring the deviation differences between different satellites. To solve this problem, some researchers have established separate correction models for each Inclined Geosynchronous Orbit (IGSO) and Medium Earth Orbit (MEO) satellite by differentiating the MP combinations between epochs; or they have established an improved SCB piecewise correction model for each BDS non-GEO satellite and each frequency as a function of altitude, and reduced the altitude node separation to 1° to improve the accuracy of the model.

[0005] Furthermore, DSC exhibits good noise levels and high positioning accuracy in challenging environments, especially at high sampling frequencies. However, as the sampling interval increases, the accuracy of DSC decreases due to a significant increase in the integral accumulation error of Doppler observations. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention provides a satellite-end pseudorange deviation correction method suitable for BDS non-geostationary orbit satellites. In order to eliminate the differences in mathematical models and calculations, a balance factor is introduced to refine the original code and DSC, and the pure Doppler-assisted smoothing code is improved, which helps to improve the reliability of SPP and the accuracy of DSC.

[0007] To achieve the above objectives, the technical solution adopted by this invention is: a method for refining pseudorange observations applicable to BDS non-geostationary orbit satellites, comprising the following steps:

[0008] S1, introduce multipath combination equations to analyze satellite-end pseudorange bias in BDS satellite raw pseudorange observations;

[0009] S2, introducing the epoch difference method to eliminate the invariant terms of the multipath combination equation, yields the ED-SCB for the first epoch between consecutive epochs. The equations for each frequency are used to obtain the optimal estimate of ED-SCB by applying the averaging method to the equations.

[0010] S3, introduce zero-sum constraints, and calculate the absolute value of the pseudorange deviation at the satellite end based on the optimal estimate of ED-SCB;

[0011] S4. Based on the principle of minimizing the sum of the absolute values ​​of the residuals, a polynomial piecewise fitting algorithm is used to establish a correction model for the absolute value of the pseudorange deviation at the satellite end.

[0012] S5. Calculate the variance function of Doppler smoothed pseudorange observations based on the error propagation law. With the principle of minimizing variance, determine the size of the smoothing window based on the first derivative of the variance function. Obtain Doppler smoothed pseudorange observations by referring to the phase smoothing pseudorange algorithm.

[0013] S6 introduces a balance factor to adjust the weights of the Doppler smoothed pseudorange observations and the original pseudorange observations described in S5, and obtains the refined Doppler smoothed pseudorange observations.

[0014] In S1, the formula for multi-path combination is:

[0015] (1)

[0016] (2)

[0017] in Indicates the carrier frequency. Indicates a linear factor. and These are pseudorange and phase observations, respectively. It is a combination of multiple paths. and These represent pseudorange and phase multipath effects, respectively. and These represent the pseudorange and phase observation noise, respectively. This refers to phase ambiguity, which includes stable hardware delays at both the satellite and receiver ends. This represents the sum of user-side multipath and observation noise.

[0018] In S2, ED-SCB represents the first epoch between consecutive epochs. The equation for each frequency is:

[0019] (3)

[0020] in, Indicates BDS satellite, Indicates accumulated days over a year. It is the calendar The corresponding satellite elevation angle, It refers to ED-SCB;

[0021] The averaging method is used to achieve the optimal estimate of ED-SCB for the equation:

[0022] (4)

[0023] in, It is the total number of ED-SCB estimators for the satellite at the required satellite elevation angle.

[0024] In S3, the elevation angle The corresponding absolute code deviation is calculated using the following formula:

[0025] (5)

[0026] Adding unknown parameters to the zero-sum constraint determination (5) (Corresponding epoch) The calculation formula is as follows:

[0027] (6)

[0028] in It is a satellite The total number of SCB valuations.

[0029] In S4, based on the principle of summing the absolute values ​​of the residuals, the satellite pseudorange bias correction model is established using piecewise polynomials as follows:

[0030] (7)

[0031] in These are the coefficients of the piecewise polynomial mentioned above. .

[0032] In S5, the Doppler smooth pseudorange observation is expressed as:

[0033] (8)

[0034] Where: the subscript is the epoch. It is the carrier phase wavelength. This represents the original pseudorange measurement, in meters.

[0035] The above equation yields the DSC variance function based on the error propagation law:

[0036] (9)

[0037] in: Let Variance be the variance of DSC. and These represent the noise levels of pseudorange and Doppler observations, respectively.

[0038] In S6, the refined RDSC is:

[0039]

[0040] (10)

[0041] The variance of RDSC can be derived from the above formula as follows:

[0042] (11)

[0043] Let be the variance of RDSC. and These represent the noise levels of pseudorange and Doppler observations, respectively.

[0044] Compared with the prior art, the present invention has at least the following beneficial effects:

[0045] Based on multipath (MP) combination, the characteristics of SCB are analyzed to determine the high correlation between SCB and satellite elevation angle. Using the principle of minimizing the sum of absolute residuals, a piecewise polynomial fitting algorithm is employed to establish an SCB correction model based on satellite elevation angle for each frequency of non-Geostationary orbit satellite. During the establishment of this SCB correction model, the influence of time-invariant parameters such as integer ambiguity is eliminated through epoch-difference (ED), and the optimal ED-SCB estimate is obtained using the mean method. A zero-sum constraint is introduced to obtain the absolute value of SCB. Referring to the CSC filtering algorithm, a DSC filtering equation is established, based on error propagation... The present invention determines the DSC variance equation based on the law of error propagation and establishes the optimal smoothing window based on the principle of minimum variance. To suppress the cumulative error of Doppler integral, a smoothing factor is introduced to adjust the weights of DSC and the original pseudorange, and the DSC variance is determined based on the error propagation law. A dynamic adjustment model of DSC is established based on the principle of minimum variance. The present invention uses a piecewise polynomial correction model to weaken the influence of pseudorange bias at the satellite end and smooths pseudorange random noise based on Doppler, which can effectively improve the accuracy of pseudorange observations of BDS non-Geostationary satellites. The present invention can be effectively applied to the refinement of pseudorange observations of BDS non-Geostationary satellites in complex environments, ensuring the performance and reliability of navigation services based on pseudorange observations. Attached Figure Description

[0046] Figure 1 This is a flowchart illustrating the method described in this invention. Detailed Implementation

[0047] In the following description, many technical details are presented to help the reader better understand this application. However, those skilled in the art will understand that the technical solutions claimed in this application can be implemented even without these technical details and various variations and modifications based on the following embodiments.

[0048] To make the objectives, technical solutions, and advantages of this application clearer, the embodiments of this application will be described in further detail below, including:

[0049] Step 1: Use MP combined analysis to analyze the SCB of BDS non-Geostationary satellites, the formula is as follows:

[0050] (1)

[0051] in Indicates the carrier frequency. Indicates a linear factor. and These are the observations of the code and the phase, respectively. It is a combination of multiple paths. This refers to the ambiguity of the carrier phase involving constant satellite and receiver hardware delays. This refers to the sum of multipath and observation noise. It is the SCB in BDS satellite coded observations.

[0052] Step 2: Use the epoch difference method to eliminate the time-invariant parameter in the above formula ( ), obtain the relative value of SCB (ED-SCB):

[0053] (2)

[0054] in, Indicates BDS satellite, Indicates accumulated days over a year. yes The satellite altitude of the era, It refers to ED-SCB.

[0055] Using the averaging method to achieve the best estimate of ED-SCB, we get:

[0056] (3)

[0057] in, The satellite is at the required altitude angle ( The total number of ED-SCB valuations.

[0058] Step 3: For the first i satellites at various frequencies Assuming at a mid-altitude angle ( ) of ED-SCB is Introducing a zero-sum constraint, the absolute value of SCB is calculated based on the optimal estimate of ED-SCB, yielding:

[0059] (4)

[0060] in It is a satellite The total number of SCB valuations.

[0061] Adding unknown parameters to the zero-sum constraint determination (5) The calculation formula is as follows:

[0062] (5)

[0063] in It is a satellite The total number of SCB valuations.

[0064] Step 4: A polynomial piecewise fitting algorithm was used to establish the SCB correction model by minimizing the sum of the absolute values ​​of the residuals.

[0065] (6)

[0066] in The coefficients represent the above fourth-degree polynomials.

[0067] Step 5: Referring to the DSC filtering algorithm (phase-smooth pseudorange algorithm), the Doppler smoothed pseudorange observation is used, and the calculation formula is as follows:

[0068] (7)

[0069] Where: the subscript is the epoch index. It is the carrier phase wavelength. These are the observed values ​​of the code, in meters.

[0070] The above equation yields the DSC variance function based on the error propagation law:

[0071] (8)

[0072] in: Let Variance be the variance of DSC. and These represent the noise levels of pseudorange and Doppler observations, respectively.

[0073] Step 6: Based on the result obtained in Step 5, refine the DSC by adding a balancing factor to obtain the refined RDSC:

[0074]

[0075] (9)

[0076] Calculate the RDSC variance based on the law of error propagation:

[0077] (10)

[0078] The present invention also provides a computer device, including but not limited to one or more processors and a memory, wherein the memory is used to store a computer executable program, the processor reads part or all of the computer executable program from the memory and executes it, and the processor can implement the pseudorange observation refinement method applicable to BDS non-geostationary orbit satellites described in the present invention when executing part or all of the computer executable program.

[0079] A computer-readable storage medium storing a computer program, which, when executed by a processor, enables the implementation of the pseudorange observation refinement method described in this invention, applicable to BDS non-geostationary orbit satellites based on DSC filters.

[0080] The computer device may be a laptop, tablet, desktop computer, mobile phone, or workstation.

[0081] The processor can be a central processing unit (CPU), a digital signal processor (DSP), an application-specific integrated circuit (ASIC), or an off-the-shelf programmable gate array (FPGA).

[0082] The memory described in this invention can be an internal storage unit of a laptop, tablet, desktop computer, mobile phone, or workstation, such as memory or hard disk; or it can be an external storage unit, such as a portable hard disk or flash memory card.

[0083] Computer-readable storage media can include computer storage media and communication media. Computer storage media includes volatile and non-volatile, removable and non-removable media implemented using any method or technology for storing information such as computer-readable instructions, data structures, program modules, or other data. Computer-readable storage media can include: read-only memory (ROM), random access memory (RAM), solid-state drives (SSDs), or optical discs, etc. Random access memory can include resistive random access memory (ReRAM) and dynamic random access memory (DRAM).

[0084] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of the claims of the present invention.

Claims

1. A method for refining pseudorange observations applicable to BDS non-geostationary orbit satellites, characterized in that, Includes the following steps: S1, introduces a multipath combination equation to describe the satellite-end pseudorange bias in the raw pseudorange observations of BDS satellites; S2, introducing the epoch difference method to eliminate the invariant terms of the multipath combination equation, yields the ED-SCB for the first epoch between consecutive epochs. The equations for each frequency are used to obtain the optimal estimate of ED-SCB by applying the averaging method to the equations. S3, introduce zero-sum constraints, and calculate the absolute value of the pseudorange deviation at the satellite end based on the optimal estimate of ED-SCB; S4. Based on the principle of minimizing the sum of the absolute values ​​of the residuals, a polynomial piecewise fitting algorithm is used to establish a correction model for the absolute value of the pseudorange deviation at the satellite end. Based on the correction model for the absolute value of the pseudorange deviation at the satellite end, systematic noise in the pseudorange observation system is eliminated. S5. Calculate the variance function of Doppler smoothed pseudorange observations based on the error propagation law. With the principle of minimizing variance, determine the size of the smoothing window based on the first derivative of the variance function. Obtain Doppler smoothed pseudorange observations by referring to the phase smoothing pseudorange algorithm. S6 introduces a balance factor to adjust the weights of the Doppler smoothed pseudorange observations obtained in S5 and the original pseudorange observations obtained in S4, thus obtaining the refined Doppler smoothed pseudorange observations.

2. The method for refining pseudorange observations for BDS non-geostationary orbit satellites according to claim 1, characterized in that, In S1, the formula for multi-path combination is: (1) (2) in Indicates the carrier frequency. Indicates a linear factor. and These are pseudorange and phase observations, respectively. It is a combination of multiple paths. and These represent pseudorange and phase multipath effects, respectively. and These represent the pseudorange and phase observation noise, respectively. This refers to phase ambiguity, which includes stable hardware delays at both the satellite and receiver ends. This represents the sum of multipath and observation noise at the user end.

3. The method for refining pseudorange observations for BDS non-geostationary orbit satellites according to claim 1, characterized in that, In S2, ED-SCB represents the first epoch between consecutive epochs. The equation for each frequency is: (3) in, Indicates BDS satellite, Indicates accumulated days over a year. yes Satellite elevation angle at epoch, It refers to ED-SCB; The averaging method is used to achieve the optimal estimate of ED-SCB for the equation: (4) in, It is the total number of satellite ED-SCB estimates at the required satellite elevation angle.

4. The method for refining pseudorange observations for BDS non-geostationary orbit satellites according to claim 1, characterized in that, In S3, the elevation angle The corresponding absolute code deviation is calculated using the following formula: (5) Adding unknown parameters to the zero-sum constraint determination (5) The corresponding epoch is The calculation formula is as follows: (6) in It is a satellite The total number of SCB valuations.

5. The method for refining pseudorange observations for BDS non-geostationary orbit satellites according to claim 1, characterized in that, In S4, based on the principle of summing the absolute values ​​of the residuals, the satellite pseudorange bias correction model is established using piecewise polynomials as follows: (7) in These are the coefficients of the piecewise polynomial mentioned above. .

6. The method for refining pseudorange observations for BDS non-geostationary orbit satellites according to claim 1, characterized in that, In S5, the Doppler smooth pseudorange observation is expressed as: (8) Where: the subscript is the epoch. It is the carrier phase wavelength. These are the observed values ​​of the code; The above equation yields the DSC variance function based on the error propagation law: (9) in: Let Variance be the variance of DSC. and These represent the noise levels of pseudorange and Doppler observations, respectively.

7. The method for refining pseudorange observations for BDS non-geostationary orbit satellites according to claim 1, characterized in that, In S6, the refined RDSC is: (10) The subscript is the epoch. It is the carrier phase wavelength. These are the observed values ​​of the code. For Doppler observations, As the balancing factor, the variance of RDSC is derived from the above formula as follows: (11) Let be the variance of RDSC. and These represent the noise levels of pseudorange and Doppler observations, respectively.

8. A computer device, characterized in that, It includes a processor and a memory, the memory being used to store a computer-executable program, the processor reading part or all of the computer-executable program from the memory and executing it, and the processor executing part or all of the computed executable program is able to implement the pseudorange observation refinement method applicable to BDS non-geostationary orbit satellites as described in any one of claims 1-7.

9. A computer-readable storage medium, characterized in that, A computer-readable storage medium stores a computer program that, when executed by a processor, enables the pseudorange observation refinement method for BDS non-geostationary orbit satellites as described in any one of claims 1-7.

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