A method and device for filtering pseudorange observations

Abstract

An embodiment of the present invention relates to a method and device for filtering pseudorange observations. The method includes: for any frequency point, when it is determined that there is no cycle slip phenomenon at epoch t, determining an initial ionospheric residual at epoch t and a first error of the initial ionospheric residual at epoch t; obtaining n fitted ionospheric residuals according to the n initial ionospheric residuals at n epochs and the time difference between any epoch and the first epoch among the n epochs; determining a second error of the fitted ionospheric residual at epoch t according to the n initial ionospheric residuals and the n fitted ionospheric residuals; judging whether the relationship between the second error and the first error satisfies a first preset condition, and if so, filtering the pseudorange observation at epoch t based on the fitted ionospheric residual at epoch t. Filtering the pseudorange observation at epoch t based on the more accurate fitted ionospheric residual at epoch t improves the accuracy of the pseudorange observation and the navigation and positioning accuracy.

Description

Technical Field

[0001] Embodiments of the present invention relate to the technical field of navigation and positioning, and in particular, to a method, apparatus, computing device, and computer-readable storage medium for filtering pseudorange observations. Background Art

[0002] With the continuous expansion of the navigation and positioning services of the Global Navigation Satellite System (GNSS), the application of GNSS technology in deformation monitoring, vehicle navigation, etc. has also been continuously deepened. When performing positioning and solution calculation at the GNSS receiver terminal, pseudorange observations received by the receiver are generally used for positioning. In order to improve the GNSS positioning accuracy, various error correction models are usually introduced to correct the received pseudorange observations, such as troposphere, ionosphere, satellite and receiver clock errors, hardware delays, solid tides, ocean tides, phase wrapping and other error correction models. At the same time, due to the complexity of the observation environment and the influence of the receiver tracking loop thermal noise, the pseudorange observations received by the receiver also contain errors such as multipath and observation noise, which cannot be corrected using specific models, greatly reducing the GNSS positioning accuracy.

[0003] In view of the fact that the accuracy of GNSS carrier phase observations is much higher than that of pseudorange observations, the Hatch filtering method is usually used to filter and smooth the pseudorange observations through the carrier phase observations, in order to remove the influence of multipath and observation noise of the pseudorange observations. However, the current Hatch filter filters and smooths the pseudorange observations through the carrier phase observations, introducing the influence of ionospheric residuals on the pseudorange observations, and as the epoch increases, the ionospheric residuals gradually accumulate, that is, ionospheric divergence, which is more obvious when the ionospheric disturbance is large. This greatly reduces the accuracy of filtering and smoothing the pseudorange observations, thereby reducing the navigation and positioning accuracy.

[0004] In summary, a method for filtering pseudorange observations is provided to achieve divergence-free filtering of pseudorange observations, improve the accuracy of pseudorange observations, and thus improve the navigation and positioning accuracy. Summary of the Invention

[0005] Embodiments of the present invention provide a method for filtering pseudorange observations to achieve divergence-free filtering of pseudorange observations, improve the accuracy of pseudorange observations, and thus improve the navigation and positioning accuracy.

[0006] In a first aspect, embodiments of the present invention provide a method for filtering pseudorange observations, including:

[0007] For any frequency point, when it is determined that there is no cycle slip phenomenon at epoch t, determine the initial ionospheric residual of the frequency point at epoch t, and determine the first error of the initial ionospheric residual at epoch t according to the observation noise and the error propagation law.

[0008] According to the n initial ionospheric residuals of the frequency point at n epochs and the time difference between any epoch and the first epoch among the n epochs, fit the n initial ionospheric residuals to obtain n fitted ionospheric residuals; the n fitted ionospheric residuals include the fitted ionospheric residual at epoch t; the n epochs are epoch t and n - 1 epochs before epoch t; the n epochs are n consecutive epochs without cycle slip phenomenon.

[0009] Determine the second error of the fitted ionospheric residual at epoch t according to the n initial ionospheric residuals and the n fitted ionospheric residuals.

[0010] Judge whether the relationship between the second error and the first error satisfies the first preset condition. If it is satisfied, filter the pseudorange observation value of the frequency point at epoch t based on the fitted ionospheric residual at epoch t.

[0011] For any frequency point, after determining the initial ionospheric residual at epoch t, determine the first error of the initial ionospheric residual according to the observation noise and the error propagation law. According to the n initial ionospheric residuals of the frequency point at n epochs and the time difference between any epoch and the first epoch among the n epochs, fit the n initial ionospheric residuals to obtain n fitted ionospheric residuals, and the n fitted ionospheric residuals include the fitted ionospheric residual at epoch t. The fitted ionospheric residual determined here is determined according to the change of the initial ionospheric residuals at n epochs, and may have higher accuracy than the initial ionospheric residual. Determine the second error of the fitted ionospheric residual at epoch t. If the relationship between the second error and the first error satisfies the first preset condition, it can be proved that the fitted ionospheric residual is more accurate. Therefore, filter the pseudorange observation value of the frequency point at epoch t based on the more accurate fitted ionospheric residual at epoch t to achieve non-divergent filtering, avoid filtering divergence caused by ionospheric residuals, improve the accuracy of pseudorange observation values, and thus improve the navigation and positioning accuracy.

[0012] Optionally, it further includes:

[0013] If it is determined that the relationship between the second error and the first error does not satisfy the first preset condition and satisfies the second preset condition, filter the pseudorange observation value of the frequency point at epoch t based on the initial ionospheric residual at epoch t.

[0014] It is possible that the relationship between the second error and the first error does not meet the first preset condition. However, if the relationship between the second error and the first error meets the second preset condition, that is, the accuracy of the initial ionospheric residual is still relatively high, then the pseudorange observation value of the frequency point at the t epoch is filtered based on the more accurate initial ionospheric residual at the t epoch, realizing non-divergent filtering, avoiding the filtering divergence caused by the ionospheric residual, improving the accuracy of the pseudorange observation value, and thus improving the navigation and positioning accuracy.

[0015] Optionally, for any frequency point, determining the initial ionospheric residual of the frequency point at the t epoch includes:

[0016] According to the carrier phase observation values of the i-th frequency point and the j-th frequency point at the t epoch, determining the first carrier phase dual-frequency geometry-free (GF) observation value at the t epoch;

[0017] According to the carrier phase observation values of the i-th frequency point and the j-th frequency point at the t-1 epoch, determining the second carrier phase dual-frequency GF observation value at the t-1 epoch;

[0018] For any one of the i-th frequency point or the j-th frequency point, according to the first carrier phase dual-frequency GF observation value and the second carrier phase dual-frequency GF observation value, determining the initial ionospheric residual of the frequency point at the t epoch.

[0019] Determining the first carrier phase dual-frequency GF observation value at the t epoch according to the carrier phase observation values of two frequency points at the t epoch; determining the second carrier phase dual-frequency GF observation value at the t-1 epoch according to the carrier phase observation values of two frequency points at the t-1 epoch; and determining the initial ionospheric residual of the frequency point at the t epoch according to the first carrier phase dual-frequency GF observation value and the second carrier phase dual-frequency GF observation value. Utilizing the characteristic that the accuracy of the carrier phase observation value is much higher than that of the code observation value, the initial ionospheric residual is determined through the carrier phase observation value, which is more accurate and the process is simple.

[0020] Optionally, determining that no cycle slip occurs at the t epoch is performed by the following method:

[0021] If the difference between the first carrier phase dual-frequency GF observation value and the second carrier phase dual-frequency GF observation value is less than the absolute value of the wavelength difference between the i-th frequency point and the j-th frequency point, it is determined that no cycle slip occurs at the t epoch.

[0022] The above method for determining the occurrence of no cycle slip uses the values used in determining the initial ionospheric residual: the first carrier phase dual-frequency GF observation value and the second carrier phase dual-frequency GF observation value. In this way, if it is determined that no cycle slip occurs, the initial ionosphere can be directly determined, improving the filtering efficiency.

[0023] Optionally, for any one of the i - frequency point or the j - frequency point, determining the initial ionospheric residual of the frequency point at the t - epoch according to the first carrier - phase dual - frequency GF observation value and the second carrier - phase dual - frequency GF observation value includes:

[0024] For the i - frequency point, substituting the first carrier - phase dual - frequency GF observation value and the second carrier - phase dual - frequency GF observation value into the ionospheric residual determination equation of the i - frequency point to obtain the initial ionospheric residual of the i - frequency point at the t - epoch; the ionospheric residual determination equation is:

[0025]

[0026] where, ΔI i (t) is the initial ionospheric residual of the i - frequency point at the t - epoch; ΔL i,j (t) is the first carrier - phase dual - frequency GF observation value; ΔL i,j (t - 1) is the second carrier - phase dual - frequency GF observation value; γ is used to characterize the conversion relationship between the i - frequency point and the j - frequency point.

[0027] For the i - frequency point, by taking the difference between the first carrier - phase dual - frequency GF observation value and the second carrier - phase dual - frequency GF observation value, the influence of the hardware delay of the pseudorange signal at the satellite and receiver ends and the fractional phase deviation at the satellite end can be eliminated. Also, since there is no cycle - slip phenomenon, the influence of the cycle - slip value can be further eliminated. Thus, the accuracy of the determined initial ionospheric residual is greatly improved.

[0028] Optionally, according to the n initial ionospheric residuals of the frequency point at n epochs and the time difference between any epoch and the first epoch among the n epochs, fitting the n initial ionospheric residuals to obtain n fitted ionospheric residuals, including:

[0029] Substituting the n initial ionospheric residuals of the frequency point at n epochs and the time difference between any epoch and the first epoch among the n epochs into the m - order polynomial observation equation; by solving the m - order polynomial observation equation, n fitted ionospheric residuals are obtained; n≥m + 2; the m - order polynomial observation equation is:

[0030] L = B·x; L is the matrix formed by the n initial ionospheric residuals; B is the matrix formed by the time difference between any epoch and the first epoch among the n epochs; x is the polynomial fitting coefficient.

[0031] Since the ionospheric residuals change little in the short term, an m-order polynomial fitting method is introduced to fit n initial ionospheres. To determine n fitted ionospheric residuals, including the fitted ionospheric residual at epoch t. The fitted ionospheric residual at epoch t determined here is obtained based on the changes in the initial ionospheric residuals of n epochs, which can improve the accuracy of the n fitted ionospheric residuals obtained by fitting.

[0032] Optionally, by solving the m-order polynomial observation equation, n fitted ionospheric residuals are obtained, including:

[0033] The least squares method is used to solve the m-order polynomial observation equation, and the polynomial fitting coefficient x is solved;

[0034] According to the matrix B formed by the polynomial fitting coefficient x and the time difference between any epoch and the first epoch among the n epochs, the n fitted ionospheric residuals are determined;

[0035] According to the n initial ionospheric residuals and the n fitted ionospheric residuals, the second error corresponding to the fitted ionospheric residual at epoch t is determined, including:

[0036] According to the n initial ionospheric residuals and the n fitted ionospheric residuals, the fitting error of the n fitted ionospheric residuals is determined;

[0037] According to the fitting error, the n, and the m, the second error corresponding to the fitted ionospheric residual at epoch t is determined.

[0038] The n fitted ionospheric residuals determined in the above manner take into account the changes in the initial ionospheric residuals. Therefore, it is more likely that the fitted ionospheric residuals are more accurate than the initial ionospheric residuals. The second error corresponding to the fitted ionospheric residuals of n epochs is also determined. Since the ionospheric residuals change little in the short term, the error corresponding to the fitted ionospheric residuals of n epochs determined in the above manner can be used as the second error corresponding to the fitted ionospheric residual at epoch t, reflecting the accuracy of the fitted ionospheric residual at epoch t.

[0039] Optionally, based on the fitted ionospheric residual at epoch t, filtering is performed on the pseudorange observation value of the frequency point at epoch t, including:

[0040] The original pseudorange observation value P i (t) of the i-th frequency point received by the receiver at epoch t, the current count w of the filter, and the smoothed pseudorange observation value of the i-th frequency point at epoch t - 1 The original carrier phase observation value L i (t) of the i-th frequency point received by the receiver at epoch t and the original carrier phase observation value L of the i-th frequency point received by the receiver at epoch t - 1i (t - 1), the final ionospheric residual ΔI i，终 Substitute (t) into the filtering formula, so as to determine the smoothed pseudorange observation value of the i - frequency point at epoch t; the filtering formula is:

[0041]

[0042] The above filtering method eliminates the influence of ionospheric residuals. Therefore, as the number of epochs increases, the situation where the filtered pseudorange observation value becomes increasingly inaccurate due to the accumulation of ionospheric residuals will not occur, realizing non - divergent filtering, avoiding the filtering divergence caused by ionospheric residuals, improving the accuracy of pseudorange observation values, and thus improving the navigation and positioning accuracy.

[0043] Optionally, it further includes:

[0044] If it is determined that cycle slips occur at epoch t, or the relationship between the second error and the first error does not satisfy the first preset condition and does not satisfy the second preset condition, then before filtering the pseudorange observation value at epoch t + 1, reset the current count of the filter to 1.

[0045] If cycle slips occur, reset the filter, thereby avoiding the accumulation of ionospheric residuals, ensuring the accuracy of the filtered pseudorange observation value, and thus improving the navigation and positioning accuracy.

[0046] In a second aspect, an embodiment of the present invention further provides a device for filtering pseudorange observation values, including:

[0047] A processing unit, configured to:

[0048] For any frequency point, when it is determined that no cycle slips occur at epoch t, determine the initial ionospheric residual of the frequency point at epoch t, and determine the first error of the initial ionospheric residual at epoch t according to the observation noise and the error propagation law;

[0049] Fit the n initial ionospheric residuals according to the n initial ionospheric residuals of the frequency point at n epochs and the time difference between any epoch and the first epoch among the n epochs, to obtain n fitted ionospheric residuals; the n fitted ionospheric residuals include the fitted ionospheric residual at epoch t; the n epochs are epoch t and n - 1 epochs before epoch t; the n epochs are consecutive n epochs without cycle slips;

[0050] Determine the second error of the fitted ionospheric residual at epoch t according to the n initial ionospheric residuals and the n fitted ionospheric residuals;

[0051] A filtering unit, configured to:

[0052] Determine whether the relationship between the second error and the first error satisfies a first preset condition. If it is satisfied, filter the pseudorange observation value of the frequency point at the t epoch based on the fitting ionospheric residual at the t epoch.

[0053] Optionally, the filtering unit is further configured to:

[0054] If it is determined that the relationship between the second error and the first error does not satisfy the first preset condition and satisfies a second preset condition, filter the pseudorange observation value of the frequency point at the t epoch based on the initial ionospheric residual at the t epoch.

[0055] Optionally, the processing unit is specifically configured to:

[0056] Determine the first carrier phase dual-frequency geometric-free (GF) observation value at the t epoch according to the carrier phase observation values of the i frequency point and the j frequency point at the t epoch;

[0057] Determine the second carrier phase dual-frequency GF observation value at the (t - 1) epoch according to the carrier phase observation values of the i frequency point and the j frequency point at the (t - 1) epoch;

[0058] For any one of the i frequency point or the j frequency point, determine the initial ionospheric residual of the frequency point at the t epoch according to the first carrier phase dual-frequency GF observation value and the second carrier phase dual-frequency GF observation value.

[0059] Optionally, the processing unit is specifically configured to:

[0060] If the difference between the first carrier phase dual-frequency GF observation value and the second carrier phase dual-frequency GF observation value is less than the absolute value of the wavelength difference between the i frequency point and the j frequency point, determine that no cycle slip occurs at the t epoch.

[0061] Optionally, the processing unit is specifically configured to:

[0062] For the i frequency point, substitute the first carrier phase dual-frequency GF observation value and the second carrier phase dual-frequency GF observation value into the ionospheric residual determination equation of the i frequency point to obtain the initial ionospheric residual of the i frequency point at the t epoch; the ionospheric residual determination equation is:

[0063]

[0064] where, ΔI i (t) is the initial ionospheric residual of the i frequency point at the t epoch; ΔL i,j (t) is the first carrier phase dual-frequency GF observation value; ΔL i,j(t - 1) is the second carrier phase dual-frequency GF observation value; γ is used to characterize the conversion relationship between the i frequency point and the j frequency point.

[0065] Optionally, the processing unit is specifically configured to:

[0066] Substitute the n initial ionospheric residuals at the n epochs of the frequency point and the time difference between any epoch and the first epoch among the n epochs into the m-order polynomial observation equation; by solving the m-order polynomial observation equation, n fitted ionospheric residuals are obtained; n ≥ m + 2; the m-order polynomial observation equation is:

[0067] L = B · x; L is the matrix formed by the n initial ionospheric residuals; B is the matrix formed by the time difference between any epoch and the first epoch among the n epochs; x is the polynomial fitting coefficient.

[0068] Optionally, the processing unit is specifically configured to:

[0069] Solve the m-order polynomial observation equation by using the least squares method to obtain the polynomial fitting coefficient x;

[0070] Determine the n fitted ionospheric residuals according to the matrix B formed by the polynomial fitting coefficient x and the time difference between any epoch and the first epoch among the n epochs;

[0071] The processing unit is specifically configured to:

[0072] Determine the fitting error of the n fitted ionospheric residuals according to the n initial ionospheric residuals and the n fitted ionospheric residuals;

[0073] Determine the second error corresponding to the fitted ionospheric residual at the t epoch according to the fitting error, the n, and the m.

[0074] Optionally, the filtering unit is specifically configured to:

[0075] Substitute the original pseudorange observation value P i (t) of the i frequency point at the t epoch received by the receiver, the current count w of the filter, and the smoothed pseudorange observation value of the i frequency point at the t - 1 epoch The original carrier phase observation value L i (t) of the i frequency point at the t epoch received by the receiver, the original carrier phase observation value L i (t - 1) of the i frequency point at the t - 1 epoch received by the receiver, and the final ionospheric residual ΔI i，终 (t) into the filtering formula, so as to determine the smoothed pseudorange observation value of the i frequency point at the t epoch; the filtering formula is:

[0076]

[0077] The above filtering method eliminates the influence of ionospheric residuals. Therefore, as the epoch increases, the filtered pseudorange observations will not become increasingly inaccurate due to the accumulation of ionospheric residuals, realizing non-divergent filtering, avoiding the filtering divergence caused by ionospheric residuals, improving the accuracy of pseudorange observations, and thus improving the navigation and positioning accuracy.

[0078] Optionally, the filtering unit is further configured to:

[0079] If it is determined that cycle slips occur in the t-th epoch, or the relationship between the second error and the first error does not satisfy the first preset condition and does not satisfy the second preset condition, then before filtering the pseudorange observation value of the (t + 1)-th epoch, reset the current count of the filter to 1.

[0080] If cycle slips occur, reset the filter, thereby avoiding the accumulation of ionospheric residuals, ensuring the accuracy of the filtered pseudorange observations, and thus improving the navigation and positioning accuracy.

[0081] In a third aspect, an embodiment of the present invention further provides a computing device, including:

[0082] A memory for storing a computer program;

[0083] A processor for calling the computer program stored in the memory and executing the method for filtering pseudorange observations listed in any of the above manners according to the obtained program.

[0084] In a fourth aspect, an embodiment of the present invention further provides a computer-readable storage medium storing a computer-executable program for causing a computer to execute the method for filtering pseudorange observations listed in any of the above manners. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0086] Figure 1 A schematic diagram of a system architecture provided by an embodiment of the present invention;

[0087] Figure 2 A schematic diagram of a method for filtering pseudorange observations provided by an embodiment of the present invention;

[0088] Figure 3Schematic diagram of a method for filtering pseudorange observations provided by an embodiment of the present invention;

[0089] Figure 4 Schematic diagram of a method for filtering pseudorange observations provided by an embodiment of the present invention;

[0090] Figure 5 Schematic structural diagram of a device for filtering pseudorange observations provided by an embodiment of the present invention;

[0091] Figure 6 Schematic structural diagram of a computer device provided by an embodiment of the present invention. Detailed implementation manners

[0092] To make the objectives, implementation manners and advantages of the present application clearer, the following will clearly and completely describe the exemplary implementation manners of the present application with reference to the accompanying drawings in the exemplary embodiments of the present application. Apparently, the described exemplary embodiments are only a part rather than all of the embodiments of the present application.

[0093] Based on the exemplary embodiments described in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope protected by the appended claims of the present application. In addition, although the disclosure in the present application is introduced according to exemplary one or several examples, it should be understood that each aspect of these disclosures can also constitute a complete implementation manner alone.

[0094] It should be noted that the brief description of the terms in the present application is only for the convenience of understanding the subsequent described implementation manners, rather than intending to limit the implementation manners of the present application. Unless otherwise specified, these terms should be understood according to their ordinary and general meanings.

[0095] The terms "first", "second", "third", etc. in the description, claims and above-mentioned drawings of the present application are used to distinguish similar or like objects or entities, and do not necessarily mean to limit a specific order or sequence, unless otherwise indicated. It should be understood that such terms can be interchanged under appropriate circumstances, for example, they can be implemented in an order other than those given in the illustration or description of the embodiments of the present application.

[0096] In addition, the terms "comprising" and "having" and any variations thereof are intended to cover but not exclude inclusion. For example, a product or device including a series of components does not necessarily have to be limited to those components clearly listed, but may include other components not clearly listed or inherent to these products or devices.

[0097] Figure 1An internal structure diagram of a receiver applicable to an embodiment of the present invention is exemplarily shown, including an antenna 100, a radio frequency module 200, a tracking channel 300, and a processor 400. The antenna 100 is used to receive an analog signal and transmit the received analog signal to the radio frequency module 200. The radio frequency module 200 processes the analog signal to obtain a digital signal. The digital signal includes carrier phase observations and pseudorange observations at multiple frequency points. The digital signal enters the processor 400 through the tracking channel 300 and a bus, and the processor 400 performs filtering and smoothing processing on the received digital signal.

[0098] Since the accuracy of the carrier phase observation is much higher than that of the pseudorange observation, the processor 400 usually uses the Hatch filtering method to filter and smooth the pseudorange observation through the carrier phase observation, in order to remove the influence of multipath and observation noise of the pseudorange observation. However, filtering and smoothing the pseudorange observation through the carrier phase observation introduces the influence of ionospheric residuals on the pseudorange observation, and as the epoch increases, the ionospheric residuals gradually accumulate, that is, ionospheric divergence, which is more obvious when the ionospheric disturbance is large. This greatly reduces the accuracy of filtering and smoothing the pseudorange observation, thereby reducing the navigation and positioning accuracy.

[0099] Based on this, an embodiment of the present invention provides a method for filtering the pseudorange observation, as Figure 2 shown, including:

[0100] Step 201, for any frequency point, when it is determined that there is no cycle slip phenomenon at the t-th epoch, determine the initial ionospheric residual of the frequency point at the t-th epoch, and determine the first error of the initial ionospheric residual according to the observation noise and the error propagation law.

[0101] The receiver can receive carrier phase observations and pseudorange observations at multiple frequency points. The embodiment of the present invention does not limit the number of frequency points. For example, dual-frequency, triple-frequency, etc.

[0102] For any frequency point, when it is determined that there is no cycle slip phenomenon at the t-th epoch, determine the initial ionospheric residual of the frequency point at the t-th epoch and the first error of the initial ionospheric residual. The embodiment of the present invention does not limit the method for determining the initial ionospheric residual and the method for determining the first error.

[0103] Step 202: Fit the n initial ionospheric residuals according to the n initial ionospheric residuals at n epochs corresponding to the frequency point and the time difference between any epoch and the first epoch among the n epochs, to obtain n fitted ionospheric residuals; the n fitted ionospheric residuals include the fitted ionospheric residual at epoch t; the n epochs are epoch t and n - 1 epochs before epoch t; the n epochs are consecutive n epochs without cycle slips occurring.

[0104] In step 201, the initial ionospheric residual at epoch t is determined. The initial ionospheric residuals at n - 1 epochs are obtained in the same way, where the n - 1 epochs refer to the n - 1 epochs before epoch t. Thus, the initial ionospheric residuals at n epochs are obtained. To ensure the accuracy of fitting, the n epochs are consecutive n epochs without cycle slips occurring.

[0105] Furthermore, obtain the time difference between any epoch and the first epoch among the n epochs, and fit the n initial ionospheric residuals according to the n initial ionospheric residuals and the time difference between any epoch and the first epoch among the n epochs, to obtain n fitted ionospheric residuals. The embodiments of the present invention do not limit the fitting method. For example, an m - order polynomial fitting method, a linear regression method, etc. can be used.

[0106] By fitting the initial ionospheric residuals at consecutive n epochs including epoch t, the initial ionospheric residual at epoch t can be further corrected by combining multiple initial ionospheric residuals before epoch t, so as to obtain the fitted ionospheric residual at epoch t. Of course, the accuracy of the fitted ionospheric residual at epoch t after further correction is generally much higher than that of the initial ionospheric residual, but there may also be a situation where the accuracy of the fitted ionospheric residual after further correction is lower.

[0107] Step 203: Determine the second error of the fitted ionospheric residual at epoch t according to the n initial ionospheric residuals and the n fitted ionospheric residuals.

[0108] Analyze the n initial ionospheric residuals and the n fitted ionospheric residuals to determine the second error of the fitted ionospheric residual at epoch t. The embodiments of the present invention do not limit the way of determining the second error.

[0109] Step 204: Judge whether the relationship between the second error and the first error satisfies a first preset condition. If so, filter the pseudorange observation value of the frequency point at epoch t based on the fitted ionospheric residual at epoch t.

[0110] For any frequency point, after determining the initial ionospheric residual at epoch t, according to the observation noise and the error propagation law, determine the first error of the initial ionospheric residual. According to the n initial ionospheric residuals at n epochs of the frequency point and the time difference between any epoch and the first epoch among the n epochs, fit the n initial ionospheric residuals to obtain n fitted ionospheric residuals, and the n fitted ionospheric residuals include the fitted ionospheric residual at epoch t. The fitted ionospheric residual determined here is determined according to the change of the initial ionospheric residuals at n epochs, and may have higher accuracy than the initial ionospheric residual. Determine the second error of the fitted ionospheric residual at epoch t. If the relationship between the second error and the first error satisfies the first preset condition, it can be proved that the fitted ionospheric residual is more accurate. Therefore, based on the more accurate fitted ionospheric residual at epoch t, filter the pseudorange observation value of the frequency point at epoch t to achieve non-divergent filtering, avoid the filtering divergence caused by the ionospheric residual, improve the accuracy of the pseudorange observation value, and thus improve the navigation and positioning accuracy.

[0111] Optionally, if it is determined that the relationship between the second error and the first error does not satisfy the first preset condition and satisfies the second preset condition, filter the pseudorange observation value of the frequency point at epoch t based on the initial ionospheric residual at epoch t.

[0112] It is possible that the relationship between the second error and the first error does not conform to the first preset condition. However, if the relationship between the second error and the first error satisfies the second preset condition, that is, the accuracy of the initial ionospheric residual is still relatively high, then filter the pseudorange observation value of the frequency point at epoch t based on the more accurate initial ionospheric residual at epoch t to achieve non-divergent filtering, avoid the filtering divergence caused by the ionospheric residual, improve the accuracy of the pseudorange observation value, and thus improve the navigation and positioning accuracy.

[0113] For example, the first preset condition is that the second error is less than the first error, and the second preset condition is that the second error is not less than the first error and the second error is less than 3 times the first error, as shown in Formula 1:

[0114]

[0115] Among them, is the first error, is the second error; ΔI i (t) is the initial ionospheric residual; is the fitted ionospheric residual; ΔI i，终 (t) is the final ionospheric residual.

[0116] The following explains the situations involved in Formula 1.

[0117] (1) If the second error is less than the first error, it is determined that the accuracy of the fitted ionospheric residual at epoch t is higher. Then, the fitted ionospheric residual at epoch t is used as the final ionospheric residual, and the pseudorange observation value of the frequency point at epoch t is filtered based on the final ionospheric residual.

[0118] (2) If the second error is not less than the first error and the second error is less than 3 times the first error, it is determined that the accuracy of the initial ionospheric residual at epoch t is higher. Then, the initial ionospheric residual at epoch t is used as the final ionospheric residual, and the pseudorange observation value of the frequency point at epoch t is filtered based on the final ionospheric residual.

[0119] (3) If the relationship between the second error and the first error does not meet the first preset condition and the second preset condition, it means that the accuracies of both the initial ionospheric residual and the fitted ionospheric residual are low and do not meet the requirements. Then, let the final ionospheric residual be equal to 0. The final ionospheric residual being equal to 0 means that in the subsequent process, only the carrier phase observation value is used to filter the pseudorange observation value. In this way, the accuracy of the smoothed pseudorange observation value obtained is relatively low because the influence of the ionospheric residual is not considered.

[0120] (4) If a cycle slip occurs at epoch t, the initial ionospheric residual cannot be calculated, and the fitted ionospheric residual cannot be calculated either. Therefore, the final ionospheric residual is also set to 0. This means that in the subsequent process, only the carrier phase observation value is used to filter the pseudorange observation value. In this way, the accuracy of the smoothed pseudorange observation value obtained is relatively low because the influence of the ionospheric residual is not considered.

[0121] Further, if the situation in (3) and / or (4) occurs and the final ionospheric residual is set to 0, then the smoothed pseudorange observation value of epoch t obtained is inaccurate. To avoid the inaccurate smoothed pseudorange observation value of epoch t from affecting the smoothing results of the pseudorange observation values of subsequent epochs such as epoch t + 1, epoch t + 2, etc., the current count of the filter needs to be reset. The specific reset operation will be explained in detail when introducing the filtering and smoothing method below.

[0122] Next, taking the i - frequency point as an example, the method for filtering and smoothing the pseudorange observation value of the i - frequency point at epoch t is introduced.

[0123] The original pseudorange observation value P i (t) of the i - frequency point at epoch t received by the receiver, the current count w of the filter, and the smoothed pseudorange observation value of the i - frequency point at epoch t - 1 The original carrier phase observation value L i (t) of the i - frequency point at epoch t received by the receiver, and the original carrier phase observation value L i(t - 1), the final ionospheric residual ΔI i，终 (t) is substituted into the filtering formula, so as to determine the smoothed pseudorange observation value of the i - frequency point at epoch t; the filtering formula is:

[0124]

[0125] Among them, the initial count of the filter is 1, and the current count w of the filter increases with the growth of epochs. However, when a cycle slip occurs at epoch t, and / or when the relationship between the second error and the first error does not meet the first preset condition and the second preset condition, the current count w of the next epoch of epoch t, that is, epoch t + 1, is reset to 1, that is, the filter is reset.

[0126] The specific reason is that when a cycle slip occurs at epoch t, the final ionospheric residual is 0. That is to say, in the process of obtaining the smoothed pseudorange observation value by filtering the original pseudorange observation value, the influence of the ionospheric residual is not eliminated, so the accuracy of the smoothed pseudorange observation value at epoch t is relatively low. It can also be seen from formula 2 that the smoothed pseudorange observation value of the current epoch is affected by the smoothed pseudorange observation value of the previous epoch. Therefore, if the accuracy of the smoothed pseudorange observation value at epoch t is relatively low, then when calculating the smoothed pseudorange observation value at epoch t + 1, if the smoothed pseudorange observation value at epoch t is still used, it will lead to a relatively low accuracy of the smoothed pseudorange observation value at epoch t + 1. By analogy, as the epochs continue to grow, the accumulation of the ionospheric residual becomes larger and larger, and the accuracy of the smoothed pseudorange observation value of each subsequent epoch becomes worse and worse.

[0127] Therefore, if a cycle slip occurs at epoch t, it is necessary to reset the current count of the filter and set w = 1 before calculating the smoothed pseudorange observation value at epoch t + 1. In this way, when calculating the smoothed pseudorange observation value at epoch t + 1, w = 1, which can avoid the influence of the smoothed pseudorange observation value at epoch t on the smoothed pseudorange observation value at epoch t + 1.

[0128] Based on the same principle, when the relationship between the second error and the first error does not meet the first preset condition and the second preset condition, and the final ionospheric residual is set to 0, the accuracy of the smoothed pseudorange observation value at epoch t is relatively low. Then, it is also necessary to reset the current count of the filter and set w = 1 before calculating the smoothed pseudorange observation value at epoch t + 1. In this way, when calculating the smoothed pseudorange observation value at epoch t + 1, w = 1, which can avoid the influence of the smoothed pseudorange observation value at epoch t on the smoothed pseudorange observation value at epoch t + 1.

[0129] The above filtering method utilizes the characteristic that the accuracy of carrier phase observations is much higher than that of code observations, and uses carrier phase observations to filter pseudorange observations. At the same time, the influence of ionospheric residuals is eliminated. Therefore, as the epoch increases, the filtered pseudorange observations will not become increasingly inaccurate due to the accumulation of ionospheric residuals, realizing non-divergent filtering, avoiding the filtering divergence caused by ionospheric residuals, improving the accuracy of pseudorange observations, and thus improving the navigation and positioning accuracy.

[0130] If a cycle slip occurs at epoch t or the accuracies of both the initial ionospheric residual and the fitted ionospheric residual are relatively low, the filter is reset when filtering at epoch t + 1, thereby avoiding the accumulation of ionospheric residuals, ensuring the accuracy of the filtered pseudorange observations, and thus improving the navigation and positioning accuracy.

[0131] Next, a method for determining the initial ionosphere at epoch t provided by an embodiment of the present invention will be introduced, as Figure 3 shown, including:

[0132] Step 301: Determine the first carrier phase dual-frequency geometry-free (GF) observation at epoch t according to the carrier phase observations of frequency i and the carrier phase observations of frequency j at epoch t.

[0133] At epoch t, the receiver can receive carrier phase observations of multiple different frequencies. According to the carrier phase observations of two of these frequencies, such as frequency i and frequency j, the first carrier phase dual-frequency GF observation at epoch t can be determined.

[0134] For example, subtract the carrier phase observation L i (t) of frequency i at epoch t from the carrier phase observation L j (t) of frequency j at epoch t to obtain the first carrier phase dual-frequency GF observation ΔL i,j (t) at epoch t.

[0135] Step 302: Determine the second carrier phase dual-frequency GF observation at epoch t - 1 according to the carrier phase observations of frequency i and the carrier phase observations of frequency j at epoch t - 1.

[0136] At epoch t - 1, the receiver can receive carrier phase observations of multiple different frequencies. According to the carrier phase observations of two of these frequencies, such as frequency i and frequency j, the second carrier phase dual-frequency GF observation at epoch t - 1 can be determined.

[0137] For example, subtract the carrier phase observation L i (t - 1) of frequency i at epoch t - 1 from the carrier phase observation L jTake the difference at epoch (t - 1) to obtain the dual-frequency GF observation value ΔL of the second carrier phase at epoch (t - 1). i,j (t - 1).

[0138] Step 303: For any one of the i-frequency point or the j-frequency point, determine the initial ionospheric residual of the frequency point at epoch t according to the first carrier phase dual-frequency GF observation value and the second carrier phase dual-frequency GF observation value.

[0139] Take the i-frequency point as an example for introduction.

[0140] For the i-frequency point, substitute the first carrier phase dual-frequency GF observation value and the second carrier phase dual-frequency GF observation value into the ionospheric residual determination equation of the i-frequency point to obtain the initial ionospheric residual of the i-frequency point at epoch t; the ionospheric residual determination equation is:

[0141]

[0142] where, ΔI i (t) is the initial ionospheric residual of the i-frequency point at epoch t; ΔL i,j (t) is the first carrier phase dual-frequency GF observation value; ΔL i,j (t - 1) is the second carrier phase dual-frequency GF observation value; γ is used to characterize the conversion relationship between the i-frequency point and the j-frequency point.

[0143] Determine the first carrier phase dual-frequency GF observation value at epoch t according to the carrier phase observation values of two frequency points at epoch t; determine the second carrier phase dual-frequency GF observation value at epoch (t - 1) according to the carrier phase observation values of two frequency points at epoch (t - 1); determine the initial ionospheric residual of the frequency point at epoch t according to the first carrier phase dual-frequency GF observation value and the second carrier phase dual-frequency GF observation value. Utilize the characteristic that the accuracy of the carrier phase observation value is much higher than that of the code observation value. Determine the initial ionospheric residual through the carrier phase observation value, which is more accurate and the process is simple.

[0144] The following details the derivation process of Formula 3.

[0145] The general observation equations of the pseudorange observation value and the carrier phase observation value can be expressed as:

[0146]

[0147] where, P k is the pseudorange observation value of the k-frequency point, L k is the carrier phase observation value of the k-frequency point; ρ is the geometric distance between the satellite and the station; c is the speed of light; δt r is the receiver clock error; δt s is the satellite clock error; is the hardware delay of the carrier phase observation value or the pseudorange observation value at the satellite end; τ r,k is the hardware delay of the carrier phase observation value or the pseudorange observation value at the receiver end; is the fractional phase deviation of the carrier phase observation value at the satellite end; b k,r is the fractional phase deviation of the carrier phase observation value at the receiver end; ε P is the observation noise of the pseudorange observation value; ε L is the observation noise of the carrier phase observation value; λ k is the carrier wavelength at the k frequency point, B k is the integer ambiguity; T ro is the tropospheric delay; I k is the first-order ionospheric delay at the k frequency point, specifically expressed as:

[0148]

[0149] Assume that at epoch t, the receiver receives the carrier phase observation values of two frequency points, such as the i frequency point and the j frequency point. According to Equation 4-2, by taking the difference between the carrier phase observation value of the i frequency point and the carrier phase observation value of the j frequency point, we can obtain:

[0150]

[0151] In the formula, ΔL i,j (t) is the first carrier phase dual-frequency GF observation value at epoch t. By taking the difference between the carrier phase observation values of the two frequency points, the satellite-station geometric distance ρ and the tropospheric delay T ro , the fractional phase deviation b i,r and b j,r of the carrier phase observation value at the receiver end are eliminated, leaving only the integer ambiguity B i and B j , the hardware delays τ r,i and τ r,j of the carrier phase observation value or the pseudorange observation value at the receiver end that are independent of distance and the hardware delays of the carrier phase observation value or the pseudorange observation value at the satellite end and the ionospheric inter-frequency deviation (1 - γ)I i and the observation error ε L′ of the dual-frequency GF combined observation value.

[0152] According to the observation noise ε L of the carrier phase observation value and the error propagation law, we can obtain

[0153] γ is the ionospheric combination coefficient, which is used to characterize the conversion relationship between the i frequency point and the j frequency point:

[0154]

[0155] According to the conversion relationship between the i frequency point and the j frequency point in Equation 4-5, the original inter-frequency ionospheric deviation I in Equation 4-4 i -I j can be expressed only by I i as (1 - γ)I i .

[0156] Of course, according to the conversion relationship between the i frequency point and the j frequency point in Equation 4-5, the original inter-frequency ionospheric deviation I in Equation 4-4 i -I j can also be expressed only by I j as

[0157] The dual-frequency GF observation value of the second carrier phase at epoch t - 1 can be obtained in the same way as in Equation 4-4:

[0158]

[0159] Let the dual-frequency GF observation value of the first carrier phase and the dual-frequency GF observation value of the second carrier phase be subtracted. Since the hardware delays at the satellite and receiver ends have good time stability (usually taken as a fixed value within a day), τ r,i , τ r,j , can be regarded as constant values. Therefore, they are eliminated after subtracting the two epochs before and after. Thus, the increment of the dual-frequency GF observation value of the carrier phase

[0160]

[0161] Among them, according to the error propagation law, the observation error corresponding to Equation 4-7 is:

[0162]

[0163] Among them, the cycle slip combination value S i,j is specifically:

[0164] S i,j = λ i ·(B i (t) - B i (t - 1)) - λ j ·(B j (t) - B j (t - 1))

[0165] = λi ·Z i -λ j ·Z j Equation 4-9

[0166] Z i and Z j are the cycle slip values at the i-th frequency point and the j-th frequency point respectively.

[0167] Then Equation 4-7 can be further expressed as:

[0168]

[0169] When there is no cycle slip at the t-th epoch, Z i = Z j = 0, then Equation 4-10 can be further expressed as:

[0170] ▽ΔL i,j (t) = ΔL i,j (t) - ΔL i,j (t - 1)

[0171] = -(1 - γ)(I i (t) - I i (t - 1)) Equation 4-11

[0172] Thus, the determination equation for the initial ionospheric residual at the i-th frequency point is:

[0173]

[0174] It can also be seen from Equation 4-10 that if there is a cycle slip at the t-th epoch, the initial ionospheric residual cannot be calculated, and thus the fitted ionospheric residual cannot be calculated. Then only the final ionospheric residual can be set to 0. In this way, the accuracy of the smoothed pseudorange observation value obtained only based on the carrier phase observation value is relatively low.

[0175] According to the error propagation law, the first error of the initial ionospheric residual ΔI i (t) can be directly obtained

[0176]

[0177] The observation noise ε of the carrier phase observation values of different receivers L is different. If the observation noise ε of the carrier phase observation value L is 1 mm, when using the carrier at the L1 (1575.42 MHz) and L2 (1227.60) frequency points, that is, the first error of the initial ionospheric residual is 3 mm.

[0178] It can be conceived that the initial ionospheric residual determination equation for frequency point j is different from that for frequency point i.

[0179] The above is only an example. The frequency points received by the receiver are not limited to frequency point i and frequency point j, and can be multiple frequency points. According to the carrier phase observations of any two frequency points received by the receiver, the initial ionospheric residual of any frequency point can be determined. The embodiments of the present invention do not limit this.

[0180] The embodiments of the present invention also provide a method for determining that no cycle slip occurs at epoch t, including:

[0181] If the difference between the first carrier phase dual-frequency GF observation value and the second carrier phase dual-frequency GF observation value is less than the absolute value of the wavelength difference between frequency point i and frequency point j, it is determined that no cycle slip occurs at epoch t.

[0182] The following details the derivation process of the above method for determining that no cycle slip occurs at epoch t.

[0183] According to Equation 4-10, it can be known that the increment ▽ΔL i,j (t) of the carrier phase dual-frequency GF observation value is mainly the increment (1-γ)(I i (t)-I i (t-1)) of the inter-frequency ionospheric deviation between epochs and the cycle slip value Z i and Z j . Also, since λ i ·Z i -λ j ·Z j >>-(1-γ)(I i (t)-I i (t-1)), the influence of the ionospheric residual can be ignored during cycle slip detection.

[0184] Equation 4-10 can then be expressed as:

[0185]

[0186] According to common sense, the minimum value of the cycle slip value Z i is 1, and the minimum value of Z j is 1. When the cycle slip Z i =Z j =1, Equation 4-10 can be expressed as:

[0187]

[0188] The following cycle slip detection formula can be obtained therefrom:

[0189]

[0190] The method for determining the absence of cycle slips described above uses the values used in determining the initial ionospheric residuals: the first carrier phase dual-frequency GF observation value and the second carrier phase dual-frequency GF observation value. Thus, if it is determined that no cycle slips occur, the initial ionosphere can be directly determined, improving the filtering efficiency.

[0191] Since the ionospheric residuals change little in the short term, the embodiment of the present invention introduces an m-order polynomial fitting method to fit the n initial ionospheres.

[0192] Assuming there are n epochs and the polynomial order is m, the following m-order polynomial observation equation can be established:

[0193] L = B·x Equation 6-1

[0194] Where L is the matrix formed by the n initial ionospheric residuals; B is the matrix formed by the time difference between any epoch and the first epoch among the n epochs; x is the polynomial fitting coefficient.

[0195] L = [ΔI i (t1) ΔI i (t2)... ΔI i (t n )] T ;

[0196]

[0197] x = [α1 α2... α n T ;

[0198] Where x is the unknown. To ensure the solvability of the m-order polynomial observation equation, let n ≥ m + 2.

[0199] Solving the above m-order polynomial observation equation by the least squares method, the polynomial fitting coefficient x is obtained:

[0200] x = (B T B) -1 B T L Equation 6-2

[0201] According to the polynomial fitting coefficient x and the matrix B formed by the time difference between any epoch and the first epoch among the n epochs, n fitted ionospheric residuals are determined

[0202]

[0203] Then, according to the n initial ionospheric residuals and the n fitted ionospheric residuals, the fitting error of the n fitted ionospheric residuals can be determined

[0204] v = B·x - L Formula 6-3

[0205] where the fitting error v = [v1 v2... v n T .

[0206] Determine the errors of the n fitting ionospheric residuals for n epochs according to the fitting error, the n, and the m:

[0207]

[0208] Since the ionospheric residuals change little in the short term, an m-order polynomial fitting method is introduced to fit the n initial ionospheres to determine the n fitting ionospheric residuals, including the fitting ionospheric residual at epoch t. The fitting ionospheric residual at epoch t determined here is obtained based on the changes in the initial ionospheric residuals of n epochs, which can improve the accuracy of the n fitting ionospheric residuals obtained by fitting.

[0209] The n fitting ionospheric residuals determined in the above manner take into account the changes in the initial ionospheric residuals. Therefore, it is more likely that the fitting ionospheric residuals are more accurate than the initial ionospheric residuals. Also determine the second error corresponding to the n fitting ionospheric residuals of n epochs. Since the ionospheric residuals change little in the short term, the error corresponding to the n fitting ionospheric residuals of n epochs determined in the above manner can be used as the second error corresponding to the fitting ionospheric residual at epoch t, reflecting the accuracy of the fitting ionospheric residual at epoch t.

[0210] The method for fitting the n initial ionospheric residuals is not limited to the m-order polynomial fitting method introduced above, and methods such as linear regression can also be used.

[0211] Linear regression method:

[0212] Linear regression, as the name implies, is to fit data points using a linear model. The common generalized linear model is as follows:

[0213] f(x) = w1x1 + w2x2 + … + w d x d + b

[0214] The above generalized vector model is expressed in vector form as follows:

[0215] f(x) = w T X + b

[0216] where f(x) is the matrix formed by the n initial ionospheric residuals; w is the matrix formed by the time difference between any epoch and the first epoch among the n epochs; X is the polynomial fitting coefficient.​

[0217] By the same method as the m-order polynomial fitting method, n fitting ionospheric residuals can be obtained, as well as the second error corresponding to the fitting ionospheric residuals at epoch t. The embodiments of the present invention will not elaborate on this.

[0218] In this way, the obtained first error and second error can be compared, and according to their relationship, it is determined whether to use the initial ionospheric residual at epoch t or the fitting ionospheric residual at epoch t to filter the pseudorange observation value of the i frequency point at the epoch t.

[0219] For the detailed filtering method, refer to the above description and will not be elaborated here.

[0220] To better explain the embodiments of the present invention, the above process of filtering the pseudorange observation value will be described in a specific implementation scenario as follows. Figure 4 As shown in the figure, it includes:

[0221] Step 401: Obtain the carrier phase observation value of the i frequency point at epoch t and the carrier phase observation value of the j frequency point at epoch t. Subtract the carrier phase observation value of the i frequency point at epoch t from the carrier phase observation value of the j frequency point at epoch t to obtain the first carrier phase dual-frequency GF observation value.

[0222] Step 402: Obtain the carrier phase observation value of the i frequency point at epoch t - 1 and the carrier phase observation value of the j frequency point at epoch t - 1. Subtract the carrier phase observation value of the i frequency point at epoch t - 1 from the carrier phase observation value of the j frequency point at epoch t - 1 to obtain the second carrier phase dual-frequency GF observation value.

[0223] Step 403: Determine whether the difference between the first carrier phase dual-frequency GF observation value and the second carrier phase dual-frequency GF observation value is less than the absolute value of the wavelength difference between the i frequency point and the j frequency point. If it is less, it is determined that there is no cycle slip phenomenon at epoch t, and step 404 is entered. If it is not less, it is determined that there is a cycle slip phenomenon at epoch t, and step 412 is entered.

[0224] Step 404: Substitute the first carrier phase dual-frequency GF observation value and the second carrier phase dual-frequency GF observation value into the ionospheric residual determination equation of the i frequency point to obtain the initial ionospheric residual of the i frequency point at the epoch t.

[0225] The ionospheric residual determination equation is:

[0226]

[0227] Among them, ΔI i (t) is the initial ionospheric residual of the i frequency point at the epoch t; ΔL i,j (t) is the first carrier phase dual-frequency GF observation value; ΔLi,j (t - 1) is the second carrier phase dual - frequency GF observation value; γ is used to characterize the conversion relationship between the i - frequency point and the j - frequency point.

[0228] Step 405: Determine the first error of the initial ionospheric residual at the t epoch according to the observation noise and the error propagation law.

[0229] Step 406: Obtain the consecutive n - 1 epochs before the t epoch, and use the same method to determine that no cycle slips occur in the n - 1 epochs.

[0230] Step 407: Obtain the n initial ionospheric residuals of the n epochs including the t epoch, and the time differences between any epoch and the first epoch among the n epochs, and fit the n initial ionospheric residuals to obtain n fitted ionospheric residuals. The n fitted ionospheric residuals include the fitted ionospheric residual at the t epoch.

[0231] The fitting method can be an m - order polynomial fitting method or a linear regression method, and the embodiments of the present invention do not limit this.

[0232] Step 408: Determine the second error of the fitted ionospheric residual at the t epoch according to the n initial ionospheric residuals and the n fitted ionospheric residuals.

[0233] Step 409: Judge whether the relationship between the second error and the first error satisfies the first preset condition. If it satisfies the first preset condition, enter Step 410; if it does not satisfy the first preset condition and satisfies the second preset condition, enter Step 411; if it does not satisfy the first preset condition and does not satisfy the second preset condition, enter Step 412.

[0234] Step 410: Based on the fitted ionospheric residual at the t epoch, the original carrier phase observation value at the t epoch, the original carrier phase observation value at the (t - 1) epoch, and the smoothed pseudorange observation value at the (t - 1) epoch, perform smoothed filtering on the pseudorange observation value of the i - frequency point at the t epoch.

[0235] Step 411: Based on the initial ionospheric residual at the t epoch, the original carrier phase observation value at the t epoch, the original carrier phase observation value at the (t - 1) epoch, and the smoothed pseudorange observation value at the (t - 1) epoch, perform smoothed filtering on the pseudorange observation value of the i - frequency point at the t epoch.

[0236] Step 412: Based on the original carrier phase observation value at the t epoch, the original carrier phase observation value at the (t - 1) epoch, and the smoothed pseudorange observation value at the (t - 1) epoch, perform smoothed filtering on the pseudorange observation value of the i - frequency point at the t epoch.

[0237] Step 413: After smoothing the pseudorange observation value of the i frequency point at the t epoch, before smoothing the pseudorange observation value at the t+1 epoch, reset the current count of the filter to 1.

[0238] Based on the same technical concept, Figure 5 Exemplarily, the structure of a device for filtering pseudorange observation values provided by an embodiment of the present invention is shown. This structure can execute the process of filtering pseudorange observation values.

[0239] As Figure 5 shown, the device specifically includes:

[0240] A processing unit 501, configured to:

[0241] For any frequency point, when it is determined that there is no cycle slip phenomenon at the t epoch, determine the initial ionospheric residual of the frequency point at the t epoch, and determine the first error of the initial ionospheric residual at the t epoch according to the observation noise and the error propagation law;

[0242] According to the n initial ionospheric residuals of the frequency point at n epochs and the time difference between any epoch and the first epoch among the n epochs, fit the n initial ionospheric residuals to obtain n fitted ionospheric residuals; the n fitted ionospheric residuals include the fitted ionospheric residual at the t epoch; the n epochs are the t epoch and n-1 epochs before the t epoch; the n epochs are consecutive n epochs without cycle slip phenomenon;

[0243] Determine the second error of the fitted ionospheric residual at the t epoch according to the n initial ionospheric residuals and the n fitted ionospheric residuals;

[0244] A filtering unit 502, configured to:

[0245] Judge whether the relationship between the second error and the first error satisfies a first preset condition. If so, filter the pseudorange observation value of the frequency point at the t epoch based on the fitted ionospheric residual at the t epoch.

[0246] For any frequency point, after determining the initial ionospheric residual at epoch t, according to the observation noise and the error propagation law, determine the first error of the initial ionospheric residual. According to the n initial ionospheric residuals at n epochs of the frequency point and the time difference between any epoch and the first epoch among the n epochs, fit the n initial ionospheric residuals to obtain n fitted ionospheric residuals, and the n fitted ionospheric residuals include the fitted ionospheric residual at epoch t. The fitted ionospheric residual determined here is determined according to the changes of the initial ionospheric residuals at n epochs, and may have higher accuracy than the initial ionospheric residual. Determine the second error of the fitted ionospheric residual at epoch t. If the relationship between the second error and the first error satisfies the first preset condition, it can be proved that the fitted ionospheric residual is more accurate. Therefore, based on the more accurate fitted ionospheric residual at epoch t, filter the pseudorange observation value of the frequency point at epoch t to achieve non-divergent filtering, avoid the filtering divergence caused by the ionospheric residual, improve the accuracy of the pseudorange observation value, and thus improve the navigation and positioning accuracy.

[0247] Optionally, the filtering unit 502 is further configured to:

[0248] If it is determined that the relationship between the second error and the first error does not satisfy the first preset condition and satisfies the second preset condition, then filter the pseudorange observation value of the frequency point at epoch t based on the initial ionospheric residual at epoch t.

[0249] It is possible that the relationship between the second error and the first error does not conform to the first preset condition. However, if the relationship between the second error and the first error satisfies the second preset condition, that is, the accuracy of the initial ionospheric residual is still relatively high, then filter the pseudorange observation value of the frequency point at epoch t based on the more accurate initial ionospheric residual at epoch t to achieve non-divergent filtering, avoid the filtering divergence caused by the ionospheric residual, improve the accuracy of the pseudorange observation value, and thus improve the navigation and positioning accuracy.

[0250] Optionally, the processing unit 501 is specifically configured to:

[0251] According to the carrier phase observation values of frequency point i and frequency point j at epoch t, determine the first carrier phase dual-frequency geometry-free GF observation value at epoch t;

[0252] According to the carrier phase observation values of frequency point i and frequency point j at epoch t-1, determine the second carrier phase dual-frequency GF observation value at epoch t-1;

[0253] For any one of frequency point i or frequency point j, according to the first carrier phase dual-frequency GF observation value and the second carrier phase dual-frequency GF observation value, determine the initial ionospheric residual of the frequency point at epoch t.

[0254] Determine the first carrier phase dual-frequency GF observation value at epoch t based on the carrier phase observation values of two frequency points at epoch t; determine the second carrier phase dual-frequency GF observation value at epoch t-1 based on the carrier phase observation values of two frequency points at epoch t-1; determine the initial ionospheric residual of the frequency point at epoch t according to the first carrier phase dual-frequency GF observation value and the second carrier phase dual-frequency GF observation value. Utilizing the characteristic that the accuracy of the carrier phase observation value is much higher than that of the code observation value, the initial ionospheric residual is determined through the carrier phase observation value, which is more accurate and the process is simple.

[0255] Optionally, the processing unit 501 is specifically configured to:

[0256] If the difference between the first carrier phase dual-frequency GF observation value and the second carrier phase dual-frequency GF observation value is less than the absolute value of the wavelength difference between the i-th frequency point and the j-th frequency point, it is determined that no cycle slip occurs at epoch t.

[0257] The above method for determining the absence of cycle slip uses the values used in determining the initial ionospheric residual: the first carrier phase dual-frequency GF observation value and the second carrier phase dual-frequency GF observation value. Thus, if it is determined that no cycle slip occurs, the initial ionosphere can be directly determined, improving the efficiency of filtering.

[0258] Optionally, the processing unit 501 is specifically configured to:

[0259] For the i-th frequency point, substitute the first carrier phase dual-frequency GF observation value and the second carrier phase dual-frequency GF observation value into the ionospheric residual determination equation of the i-th frequency point to obtain the initial ionospheric residual of the i-th frequency point at epoch t; the ionospheric residual determination equation is:

[0260]

[0261] where ΔI i (t) is the initial ionospheric residual of the i-th frequency point at epoch t; ΔL i,j (t) is the first carrier phase dual-frequency GF observation value; ΔL i,j (t-1) is the second carrier phase dual-frequency GF observation value; γ is used to characterize the conversion relationship between the i-th frequency point and the j-th frequency point.

[0262] For the i-th frequency point, by taking the difference between the first carrier phase dual-frequency GF observation value and the second carrier phase dual-frequency GF observation value, the influence of the hardware delay of the pseudorange signal at the satellite and receiver ends and the fractional phase deviation at the satellite end can be eliminated. Also, due to the absence of cycle slip, the influence of the cycle slip value can be further eliminated. Thus, the accuracy of the determined initial ionospheric residual is greatly improved.

[0263] Optionally, the processing unit 501 is specifically configured to:

[0264] Substitute the n initial ionospheric residuals at n epochs and the time difference between any epoch and the first epoch among the n epochs into the m-order polynomial observation equation; by solving the m-order polynomial observation equation, obtain n fitted ionospheric residuals; n≥m + 2; the m-order polynomial observation equation is:

[0265] L = B·x; L is the matrix formed by the n initial ionospheric residuals; B is the matrix formed by the time differences between any epoch and the first epoch among the n epochs; x is the polynomial fitting coefficient.

[0266] Since the ionospheric residuals change little in the short term, an m-order polynomial fitting method is introduced to fit the n initial ionospheres. To determine n fitted ionospheric residuals, including the fitted ionospheric residual at epoch t. The fitted ionospheric residual at epoch t determined here is obtained based on the changes in the initial ionospheric residuals at n epochs, which can improve the accuracy of the n fitted ionospheric residuals obtained by fitting.

[0267] Optionally, the processing unit 501 is specifically configured to:

[0268] Solve the m-order polynomial observation equation by using the least squares method to obtain the polynomial fitting coefficient x;

[0269] Determine the n fitted ionospheric residuals according to the matrix B formed by the polynomial fitting coefficient x and the time differences between any epoch and the first epoch among the n epochs;

[0270] The processing unit 501 is specifically configured to:

[0271] Determine the fitting error of the n fitted ionospheric residuals according to the n initial ionospheric residuals and the n fitted ionospheric residuals;

[0272] Determine the second error corresponding to the fitted ionospheric residual at epoch t according to the fitting error, the n, and the m.

[0273] The n fitted ionospheric residuals determined in the above manner take into account the changes in the initial ionospheric residuals. Therefore, it is more likely that the fitted ionospheric residuals are more accurate than the initial ionospheric residuals. Also, the second error corresponding to the fitted ionospheric residuals at n epochs is determined. Since the ionospheric residuals change little in the short term, the error corresponding to the n fitted ionospheric residuals determined in the above manner can be used as the second error corresponding to the fitted ionospheric residual at epoch t, reflecting the accuracy of the fitted ionospheric residual at epoch t.

[0274] Optionally, the filtering unit 502 is specifically configured to:

[0275] Substitute the original pseudorange observation value P of the i-th frequency point at the t-th epoch received by the receiver i (t), the current count w of the filter, and the smoothed pseudorange observation value of the i-th frequency point at the (t - 1)-th epoch The original carrier phase observation value L of the i-th frequency point at the t-th epoch received by the receiver i (t), the original carrier phase observation value L of the i-th frequency point at the (t - 1)-th epoch received by the receiver i (t - 1), and the final ionospheric residual ΔI i，终 (t) into the filtering formula, so as to determine the smoothed pseudorange observation value of the i-th frequency point at the t-th epoch; the filtering formula is:

[0276]

[0277] The above filtering method eliminates the influence of the ionospheric residual. Therefore, as the number of epochs increases, the situation that the filtered pseudorange observation value becomes more and more inaccurate due to the accumulation of the ionospheric residual will not occur, realizing non-divergent filtering, avoiding the filtering divergence caused by the ionospheric residual, improving the accuracy of the pseudorange observation value, and thus improving the navigation and positioning accuracy.

[0278] Optionally, the filtering unit 502 is further configured to:

[0279] If it is determined that a cycle slip occurs at the t-th epoch, or the relationship between the second error and the first error does not satisfy the first preset condition and does not satisfy the second preset condition, then before filtering the pseudorange observation value at the (t + 1)-th epoch, reset the current count of the filter to 1.

[0280] If a cycle slip occurs, reset the filter, thereby avoiding the accumulation of the ionospheric residual, ensuring the accuracy of the filtered pseudorange observation value, and thus improving the navigation and positioning accuracy.

[0281] Based on the same technical concept, an embodiment of the present application provides a computer device, as Figure 6 shown, including at least one processor 601 and a memory 602 connected to at least one processor. In the embodiment of the present application, the specific connection medium between the processor 601 and the memory 602 is not limited. Figure 6 Taking the example that the processor 601 and the memory 602 are connected through a bus. The bus can be divided into an address bus, a data bus, a control bus, etc.

[0282] In an embodiment of the present application, the memory 602 stores instructions executable by at least one processor 601. By executing the instructions stored in the memory 602, the at least one processor 601 can perform the steps of the method for filtering pseudorange observations described above.

[0283] Among them, the processor 601 is the control center of the computer device. It can connect various parts of the computer device through various interfaces and lines, and by running or executing the instructions stored in the memory 602 and calling the data stored in the memory 602, it can filter the pseudorange observations. Optionally, the processor 601 may include one or more processing units. The processor 601 may integrate an application processor and a modem processor. Among them, the application processor mainly processes the operating system, user interface, application programs, etc., and the modem processor mainly processes wireless communication. It can be understood that the above modem processor may not be integrated into the processor 601. In some embodiments, the processor 601 and the memory 602 may be implemented on the same chip. In some embodiments, they may also be separately implemented on independent chips.

[0284] The processor 601 may be a general-purpose processor, such as a central processing unit (CPU), a digital signal processor, an application specific integrated circuit (ASIC), a field programmable gate array, or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, and can implement or execute the various methods, steps, and logic block diagrams disclosed in the embodiments of the present application. The general-purpose processor may be a microprocessor or any conventional processor, etc. The steps of the method disclosed in combination with the embodiments of the present application can be directly embodied as being executed by a hardware processor, or executed by a combination of hardware and software modules in the processor.

[0285] The memory 602, as a non-volatile computer-readable storage medium, can be used to store non-volatile software programs, non-volatile computer-executable programs, and modules. The memory 602 can include at least one type of storage medium. For example, it can include flash memory, hard disks, multimedia cards, card-type memories, random access memory (RAM), static random access memory (SRAM), programmable read-only memory (PROM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), magnetic memories, magnetic disks, optical disks, and so on. The memory 602 is any other medium that can be used to carry or store the desired program code in the form of instructions or data structures and can be accessed by a computer, but is not limited thereto. The memory 602 in the embodiments of the present application can also be a circuit or any other device capable of implementing a storage function, for storing program instructions and / or data.

[0286] Based on the same technical concept, an embodiment of the present invention also provides a computer-readable storage medium. The computer-readable storage medium stores a computer-executable program, and the computer-executable program is used to cause a computer to execute the method for filtering pseudorange observations listed in any of the above manners.

[0287] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memories, CD-ROMs, optical memories, etc.) containing computer-usable program code.

[0288] The present application is described with reference to the flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of flows and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to the processors of general-purpose computers, special-purpose computers, embedded processors, or other programmable data processing devices to generate a machine, so that the instructions executed by the processors of the computer or other programmable data processing devices generate for implementing the processes Figure 1one or more processes and / or blocks Figure 1 means for the functions specified in one or more blocks

[0289] These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means that implement the functions in the process Figure 1 one or more processes and / or blocks Figure 1 specified in one or more blocks

[0290] These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, whereby the instructions executed on the computer or other programmable apparatus provide steps for implementing the functions in the process Figure 1 one or more processes and / or blocks Figure 1 specified in one or more blocks

[0291] It is apparent that those skilled in the art can make various modifications and variations to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalent technologies, the present application is also intended to include these modifications and variations

Claims

1. A method for filtering pseudorange observations, characterized in that, Including: For any frequency point, when it is determined that there is no cycle slip phenomenon in the t epoch, determine the initial ionospheric residual of the frequency point in the t epoch, and determine the first error of the initial ionospheric residual in the t epoch according to the observation noise and the error propagation law; According to the n initial ionospheric residuals of the frequency point in n epochs and the time difference between any epoch and the first epoch among the n epochs, fit the n initial ionospheric residuals to obtain n fitted ionospheric residuals; the n fitted ionospheric residuals include the fitted ionospheric residual in the t epoch; the n epochs are the t epoch and n - 1 epochs before the t epoch; the n epochs are n consecutive epochs without cycle slip phenomenon; Determine the second error of the fitted ionospheric residual in the t epoch according to the n initial ionospheric residuals and the n fitted ionospheric residuals; Judge whether the relationship between the second error and the first error satisfies a first preset condition. If it satisfies, filter the pseudorange observation value of the frequency point in the t epoch based on the fitted ionospheric residual in the t epoch; Wherein, for any frequency point, when it is determined that there is no cycle slip phenomenon in the t epoch, determining the initial ionospheric residual of the frequency point in the t epoch includes: According to the carrier phase observation values of the i frequency point and the j frequency point in the t epoch, determine the first carrier phase dual-frequency geometric-free GF observation value of the t epoch; According to the carrier phase observation values of the i frequency point and the j frequency point in the t - 1 epoch, determine the second carrier phase dual-frequency GF observation value of the t - 1 epoch; If the difference between the first carrier phase dual-frequency GF observation value and the second carrier phase dual-frequency GF observation value is less than the absolute value of the wavelength difference between the i frequency point and the j frequency point, determine that there is no cycle slip phenomenon in the t epoch; For the i frequency point, substitute the first carrier phase dual-frequency GF observation value and the second carrier phase dual-frequency GF observation value into the ionospheric residual determination equation of the i frequency point to obtain the initial ionospheric residual of the i frequency point in the t epoch; the ionospheric residual determination equation is: where, ΔI i (t) is the initial ionospheric residual of the i-th frequency point at the t-th epoch; ΔL i,j (t) is the dual-frequency GF observation value of the first carrier phase; ΔL i,j (t - 1) is the dual-frequency GF observation value of the second carrier phase; γ is used to characterize the conversion relationship between the i-th frequency point and the j-th frequency point.

2. The method according to claim 1, characterized in that Also including: If it is determined that the relationship between the second error and the first error does not satisfy the first preset condition and satisfies a second preset condition, filter the pseudorange observation value of the frequency point in the t epoch based on the initial ionospheric residual in the t epoch.

3. The method according to claim 1, wherein According to the n initial ionospheric residuals of the frequency point in n epochs and the time difference between any epoch and the first epoch among the n epochs, fitting the n initial ionospheric residuals to obtain n fitted ionospheric residuals includes: Substitute the n initial ionospheric residuals of the frequency point in n epochs and the time difference between any epoch and the first epoch among the n epochs into the m - order polynomial observation equation; by solving the m - order polynomial observation equation, obtain n fitted ionospheric residuals; n ≥ m + 2; the m - order polynomial observation equation is: L = B·x; where L is the matrix formed by the n initial ionospheric residuals; B is the matrix formed by the time differences between any epoch and the first epoch among the n epochs; and x is the polynomial fitting coefficient.

4. The method according to claim 3, wherein By solving the m - order polynomial observation equation, n fitted ionospheric residuals are obtained, including: Using the least - squares method to solve the m - order polynomial observation equation, and solving for the polynomial fitting coefficient x; Based on the polynomial fitting coefficient x and the matrix B formed by the time differences between any epoch and the first epoch among the n epochs, determining the n fitted ionospheric residuals; Determining the second error corresponding to the fitted ionospheric residuals at the t - epoch based on the n initial ionospheric residuals and the n fitted ionospheric residuals, including: Determining the fitting error of the n fitted ionospheric residuals based on the n initial ionospheric residuals and the n fitted ionospheric residuals; Determining the second error corresponding to the fitted ionospheric residuals at the t - epoch based on the fitting error, n, and m.

5. An apparatus for filtering pseudorange observations, characterized in that, Including: A processing unit, configured to: For any frequency point, when it is determined that there is no cycle slip phenomenon at the t - epoch, determining the initial ionospheric residual of the frequency point at the t - epoch, and based on the observation noise and the error propagation law, determining the first error of the initial ionospheric residual at the t - epoch; Fitting the n initial ionospheric residuals based on the n initial ionospheric residuals of the frequency point at n epochs and the time differences between any epoch and the first epoch among the n epochs, to obtain n fitted ionospheric residuals; the n fitted ionospheric residuals include the fitted ionospheric residual at the t - epoch; the n epochs are the t - epoch and n - 1 epochs before the t - epoch; the n epochs are n consecutive epochs without cycle slip phenomenon; Determining the second error of the fitted ionospheric residual at the t - epoch based on the n initial ionospheric residuals and the n fitted ionospheric residuals; A filtering unit, configured to: Judge whether the relationship between the second error and the first error satisfies a first preset condition. If so, filter the pseudorange observation value of the frequency point at the t - epoch based on the fitted ionospheric residual at the t - epoch; The processing unit is specifically configured to: Based on the carrier - phase observation values of the i - th frequency point and the j - th frequency point at the t - epoch, determining the first carrier - phase dual - frequency geometric - free (GF) observation value at the t - epoch; Based on the carrier - phase observation values of the i - th frequency point and the j - th frequency point at the (t - 1) - epoch, determining the second carrier - phase dual - frequency GF observation value at the (t - 1) - epoch; If the difference between the first carrier - phase dual - frequency GF observation value and the second carrier - phase dual - frequency GF observation value is less than the absolute value of the wavelength difference between the i - th frequency point and the j - th frequency point, determining that there is no cycle slip phenomenon at the t - epoch; For the i - th frequency point, substituting the first carrier - phase dual - frequency GF observation value and the second carrier - phase dual - frequency GF observation value into the ionospheric residual determination equation of the i - th frequency point, to obtain the initial ionospheric residual of the i - th frequency point at the t - epoch; the ionospheric residual determination equation is: where ΔIi(t) is the initial ionospheric residual of the i-th frequency point at the t-th epoch; ΔL i,j (t) is the dual-frequency GF observation value of the first carrier phase; ΔL i,j (t - 1) is the dual-frequency GF observation value of the second carrier phase; γ is used to characterize the conversion relationship between the i-th frequency point and the j-th frequency point.

6. A computing device, characterized in that, Including: A memory, used to store computer programs; A processor, configured to call the computer program stored in the memory and execute the method according to any one of claims 1 to 4 based on the obtained program.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer-executable program, and the computer-executable program is configured to cause a computer to execute the method according to any one of claims 1 to 4.

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