Satellite pseudorange deviation correction method and device based on elevation and azimuth angles

Abstract

This invention discloses a method and apparatus for satellite pseudorange bias correction based on elevation and azimuth angles. The specific method involves: estimating parameters for each non-geostationary satellite and each available frequency under the BeiDou Navigation Satellite System, with a node distance of 0.1°, and proposing a segmented SICB correction method. Based on the BeiDou satellite's annual cumulative day, the ED-SICB value at the i-th frequency between consecutive epochs is estimated. Assuming that for a single satellite, there are n sets of ED-SICBs at the i-th frequency between the required elevation angles ([Elek-0.03, Elek+0.03]) for all measurement days, their weighted average estimate is calculated. The calculations in the first two steps yield a series of ED-SICB estimates, rather than absolute SICB estimates, thus further calculating SICB estimates at different elevation angles. Under the condition that the sum of all SICBs is zero, a polynomial segment fitting algorithm is used to minimize the sum of the absolute values ​​of the residuals, eliminating pseudorange bias and significantly improving model accuracy.

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 apparatus for correcting pseudorange deviations at the satellite end based on elevation angle and azimuth angle. Background Technology

[0002] The BeiDou Navigation Satellite System suffers from satellite-induced code bias (SICB), which can cause code-phase mismatches at the meter level. Since SICB is related to elevation angle and frequency, several SICB correction models have been proposed to eliminate the system bias. However, most of these models are based on elevation angle and ignore the influence of azimuth angle, limiting the accuracy of their development, especially for medium Earth orbit satellites.

[0003] Traditional SICB correction models have two drawbacks: (1) they only consider the elevation angle to establish the SICB correction model; and (2) they use a simple numerical averaging method to obtain the multipath (MP) combination estimator.

[0004] The independent variables in SICB correction models typically only include the satellite elevation angle, neglecting other factors such as the azimuth angle, which is detrimental to accurate SICB compensation. Furthermore, simple numerical averaging and large node spacing (1° or 10°) may cause the loss of MP bias details, making it difficult to obtain the optimal SICB estimate. Due to these two shortcomings, the improved satellite end pseudorange bias (SICB) correction model requires further refinement. Summary of the Invention

[0005] To address these issues, this invention provides a satellite pseudorange deviation correction method and apparatus based on elevation and azimuth angles. By considering both elevation and azimuth angles, it avoids the problem that existing models only consider elevation angles while ignoring azimuth angles, which limits the accuracy of their development models.

[0006] To achieve the above objectives, the technical solution adopted by this invention is: a satellite pseudorange deviation correction method based on elevation angle and azimuth angle, comprising the following steps:

[0007] Step 1: For satellites of the BeiDou Navigation Satellite System with an annual accumulation of days, estimate the ED-SICB at the i-th frequency between consecutive epochs;

[0008] Step 2: Based on the fact that a satellite has n sets of EDSICBs at the i-th frequency among the required elevation angles for all measurement days, calculate the weighted average estimate of ED-SICBs;

[0009] Step 3: Calculate a series of ED-SICB estimates based on the weighted average estimate, and then calculate the ED-SICB estimate at the required elevation angle based on the ED-SICB estimate.

[0010] Step 4: Introduce zero-sum constraints to the ED-SICB estimate at the required elevation angle, and solve for the SICB response at the i-th frequency in the ED-SICB estimate at the required elevation angle.

[0011] Step 5: Based on the results of Step 4, the sum of the absolute values ​​of the residuals is minimized using the polynomial segment fitting method, the polynomial coefficients are calculated, and then the pseudorange deviation correction expression of the satellite end is obtained.

[0012] Step 6: Correct the pseudorange deviation of the satellite end using the aforementioned pseudorange deviation correction expression.

[0013] In step 1, the ED-SICB at the i-th frequency between consecutive epochs is:

[0014]

[0015] In the formula For ED-SICB, MP is the MP deviation, Ele k and Azi k These are the elevation angle and azimuth angle at epoch k, respectively.

[0016] In step 2, the weighted average estimator is calculated as follows:

[0017]

[0018] in, The signal-to-noise ratio (SNR) observation at epoch k+1, measured in dB-Hz, effectively represents signal quality.

[0019] In step 3, the estimated SICB values ​​at the required elevation angle are as follows:

[0020]

[0021] in, Given the mid-altitude angle at which the satellite passes, the SICB response at the i-th frequency for this epoch is: Recognizing the limited azimuth angle of IGSO satellites, the elevation angle was chosen to replace the azimuth angle, and the SICB of the mid-elevation angle through which the satellite passes was set as a constant.

[0022] In step 4, the sum of all applied corrections is zero, as detailed below:

[0023]

[0024] Where m is the total number of MP combinations for satellite s at the i-th frequency.

[0025] Set the elevation angle node separation to 0.1°.

[0026] In step 5, the pseudorange bias correction expression for the satellite end is as follows:

[0027]

[0028] In the formula The coefficients of the polynomial of the fitted function are . and denoted by integer orders of elevation and azimuth, respectively, and t represents the highest order of the fitted function. The value of t does not exceed 5.

[0029] A computer device is also provided, including a processor and a memory. 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. When the processor executes part or all of the executable program, it can implement the satellite pseudorange deviation correction method based on elevation angle and azimuth angle described in this invention.

[0030] A computer-readable storage medium is also provided, in which a computer program is stored. When the computer program is executed by a processor, it can implement the satellite pseudorange deviation correction method applicable to elevation angle and azimuth angle described in this invention.

[0031] Compared with the prior art, the present invention has at least the following beneficial effects:

[0032] This invention adopts a dual-element approach considering both elevation and azimuth angles, avoiding the problem of existing models that only consider elevation angles while ignoring azimuth angles, which limits the accuracy of their development models. It effectively improves the pseudorange bias at the satellite end of non-geostationary satellites, eliminating pseudorange bias. This invention performs parameter estimation for each non-geostationary satellite and each available frequency under the BeiDou Navigation Satellite System. The improved model determines the elevation angle threshold based on the statistics of multipath combinations to reduce the impact of code noise and multipath under low elevation angle conditions.

[0033] Furthermore, the Epoch-Difference (ED) method is introduced into the SICB model to remove time-invariant parameters (such as integer ambiguity); the Weighted Average (WA) method is used to obtain the optimal SICB estimate, making the SICB estimate more accurate; and a two-element correction model of SICB based on azimuth and elevation angles is established, which significantly improves the modeling accuracy.

[0034] Furthermore, this invention uses a node distance of 0.1° instead of the 1° or 10° used in previous studies, resulting in a smaller node spacing than existing models and richer model details. Attached Figure Description

[0035] Figure 1 This is a flowchart illustrating the satellite pseudorange deviation correction method based on elevation angle and azimuth angle according to the present invention. Detailed Implementation

[0036] 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.

[0037] To make the purpose, technical solution, and advantages of this application clearer, the following will be combined with Figure 1 The embodiments of this application are described in further detail, including the following steps:

[0038] Step 1: For BeiDou Navigation Satellite System (BDS) satellites with a day of year (doy), the Epoch Difference-Satellite-induced Code Bias (ED-SICB) between consecutive epochs at the i-th frequency can be estimated as follows:

[0039]

[0040] In the formula For ED-SICB, MP is the MP deviation, and Ele and Azi are the elevation and azimuth angles at epoch k, respectively.

[0041] Step 2, assuming that for a single satellite, there are n sets of ED-SICBs at the i-th frequency between the required elevation angles ([Elek-0.03, Elek+0.03]) for all measurement days, the weighted average estimate can be calculated as follows:

[0042]

[0043] in, The signal-to-noise ratio (SNR) observation at epoch k+1, measured in dB-Hz, effectively represents signal quality.

[0044] Step 3: Based on the above equations, a series of ED-SICB estimators can be obtained, rather than absolute SICB estimators. The required SICB estimator at the desired elevation angle can be determined as follows:

[0045]

[0046] in, Given the mid-altitude angle at which the satellite passes, the SICB response at the epoch (k0) at the i-th frequency is: The unit is meters. Recognizing the limited azimuth angle of IGSO satellites, this invention uses elevation angle instead of azimuth angle. Furthermore, since the ED-SICB value at mid-elevation angles is typically smaller than the SICB value at low or high elevation angles, the SICB value at mid-elevation angles is set as a constant.

[0047] Step 4: To obtain the absolute level of the SICB model, this invention follows the idea that the sum of all applied corrections is zero, i.e.:

[0048]

[0049] Where m is the total number of MP combinations for satellite s at the i-th frequency. Under the above constraints, the unique unknown parameter in step 3 can be solved. This allows for the establishment of an accurate SICB correction model.

[0050] Step 5: Due to the small distance between elevation nodes (<1°), using the Epoch-Difference (ED) method would increase measurement noise. To overcome this drawback, the Polynomial Segment Fitting (PSF) algorithm is used to minimize the sum of the absolute values ​​of the residuals, as shown below:

[0051]

[0052] In the formula The coefficients of the polynomial of the fitted function are . and denoted by integer orders for elevation and azimuth, respectively, and t represents the highest order of the fitted function. To limit the complexity of the fitted model, in this model, The value of t does not exceed 5. It is worth noting that the SICB-corrected model and the MP time series are opposite in sign.

[0053] This invention establishes the correction model as a function of elevation and azimuth angles; it introduces the ED method into the SICB model to remove time-invariant parameters (such as integer ambiguity); and it uses the weighted average (WA) method to obtain the optimal SICB estimate. Furthermore, this invention sets the elevation angle node separation to 0.1°, instead of the 1° or 10° used in previous studies. If the node spacing is too large, the accuracy of the SICB model will decrease, and MP time series details will be lost. Using 3α as a criterion, the difference between the actual buoy elevation angle and the required elevation angle should not exceed 0.03°.

[0054] To verify the effectiveness of the aforementioned SICB correction model for BeiDou coding measurements, experiments were conducted on BDS-2IGSO satellites numbered C10 and C13 at frequencies B1 and B3 based on real GNSS data. The root-mean-square error (RMSE) and coefficient of determination were used for verification. The RMSE is used to represent the fitting performance; the smaller the RMSE, the better the fitting performance. The closer the value is to 1.0, the better the fit. The specific results are shown in Table 1:

[0055]

[0056] Table 1 lists the fitting metrics of the SICB model for the selected IGSO satellites at frequencies B1 and B3. For the BDS-2 IGSO satellites (PRN: C10 and C13), the RMSE of the conventional model for B1 is between 0.039 and 0.11, lower than the RMSE for B3 (0.029–0.04 m). In contrast, the RMSE of the corrected model for C10 is improved by 63.6% (B1) and 17.2% (B3), respectively, and the RMSE for C13 is improved by 2.6% (B1) and 20% (B3), respectively. We can conclude that the improved SICB corrected model is more suitable for the BDS-2 IGSO satellites than the conventional model that ignores the influence of azimuth.

[0057] The present invention also provides a computer device, including a processor 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 when the processor executes part or all of the executable program, it can realize the satellite pseudorange deviation correction method based on elevation angle and azimuth angle described in the present invention.

[0058] A computer-readable storage medium storing a computer program, which, when executed by a processor, enables the implementation of the satellite pseudorange deviation correction method based on elevation and azimuth angles as described in this invention.

[0059] The computer device may be a laptop, tablet, desktop computer, mobile phone, or workstation.

[0060] 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).

[0061] 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.

[0062] 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).

[0063] 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 satellite pseudorange deviation correction method based on elevation angle and azimuth angle, characterized in that, Includes the following steps: Step 1: For satellites of the BeiDou Navigation Satellite System with a cumulative date, estimate the ED-SICB at the i-th frequency across consecutive epochs; the ED-SICB at the i-th frequency across consecutive epochs is: In the formula For ED-SICB, MP is the MP deviation, Ele k and Azi k These are the elevation angle and azimuth angle at epoch k, respectively; Step 2: Based on the fact that a satellite has n sets of ED-SICBs at the i-th frequency among the required elevation angles for all measurement days, calculate the weighted average estimate of the ED-SICBs. Step 3: Calculate a series of ED-SICB estimates based on the weighted average estimate, and then calculate the ED-SICB estimate at the required elevation angle based on the ED-SICB estimate. Step 4: Introduce zero-sum constraints to the ED-SICB estimate at the required elevation angle, and solve for the SICB response at the i-th frequency in the ED-SICB estimate at the required elevation angle. Step 5: Based on the results of Step 4, the sum of the absolute values ​​of the residuals is minimized using the polynomial segment fitting method, the polynomial coefficients are calculated, and then the pseudorange deviation correction expression of the satellite end is obtained. Step 6: Correct the pseudorange deviation of the satellite end using the aforementioned pseudorange deviation correction expression.

2. The satellite pseudorange deviation correction method based on elevation angle and azimuth angle according to claim 1, characterized in that, In step 2, the weighted average estimator is calculated as follows: in, The signal-to-noise ratio (SNR) observation at epoch k+1, measured in dB-Hz, effectively represents signal quality.

3. The satellite pseudorange deviation correction method based on elevation angle and azimuth angle according to claim 1, characterized in that, In step 3, the estimated SICB values ​​at the required satellite elevation angle are as follows: in, Given the mid-altitude angle at which the satellite passes, the SICB response at the i-th frequency for this epoch is: Recognizing the limited azimuth angle of IGSO satellites, the elevation angle was chosen to replace the azimuth angle, and the SICB at the mid-elevation angle was set as a constant.

4. The satellite pseudorange deviation correction method based on elevation angle and azimuth angle according to claim 1, characterized in that, In step 4, the sum of all applied corrections is zero, as detailed below: Where m is the total number of MP combinations for satellite s at the i-th frequency.

5. The satellite pseudorange deviation correction method based on elevation angle and azimuth angle according to claim 1, characterized in that, Set the elevation angle node separation to 0.1°.

6. The satellite pseudorange deviation correction method based on elevation angle and azimuth angle according to claim 1, characterized in that, In step 5, the pseudorange bias correction expression for the satellite end is as follows: In the formula The coefficients of the polynomial of the fitted function are . and denoted by integer orders of elevation and azimuth, respectively, and t represents the highest order of the fitted function. The value of t does not exceed 5.

7. 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 being able to implement the satellite end pseudorange deviation correction method based on elevation angle and azimuth angle as described in any one of claims 1-6.

8. 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 satellite pseudorange deviation correction method based on elevation angle and azimuth angle as described in any one of claims 1-6.

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