A Real-time Adjustment Method for the Random Walk Variance of BDS PPP Ionospheric Delay

Abstract

The present invention provides a real-time adjustment method for the random walk variance of the BDS PPP ionospheric delay, which relates to the technical field of GNSS satellite navigation and positioning. This method constructs a random walk form of the ionospheric delay, utilizes the parameter correlation between the epoch-to-epoch ionospheric delay EDI change value and the true ionospheric delay in the short term, weakens the noise in the ionospheric observations, calculates the power spectral density PSD of the ionospheric delay, and then combines the relationship between the PSD and the random walk variance to adjust the variance constraint value in real time, thereby effectively shortening the integer ambiguity fixing time and improving the positioning accuracy. The present invention realizes the real-time adjustment based on the random model of the BDS ionospheric parameters, effectively improves the positioning accuracy, and has strong practical application value.

Description

Technical Field

[0001] The present invention belongs to the technical field of GNSS satellite navigation and positioning, and particularly relates to a method for real-time adjustment of the variance of the BDS PPP ionospheric delay random walk. Background Art

[0002] With the completion of the BeiDou Navigation Satellite System (BDS), the application scenarios of the BDS Precise Point Positioning (PPP) technology are becoming more and more extensive, and the requirements for positioning accuracy are also getting higher and higher. Ionospheric delay is one of the most significant error sources in the Global Navigation Satellite System (GNSS). In traditional GNSS high-precision positioning, the Ionospheric-free (IF) combination model is often used to eliminate the ionospheric delay error. However, the IF model will cause the amplification of the observation noise when eliminating the ionospheric parameters, it is difficult to utilize the spatio-temporal variation characteristics of the ionospheric delay itself, and it is difficult to model when processing single-frequency or multi-frequency data. Currently, the widely used global ionospheric models and several large-scale long-period average empirical models globally cannot reflect the actual spatio-temporal characteristics of the ionosphere. In the ionospheric observations obtained from the measured dual-frequency observation data, it includes ionospheric delay and observation noise, and the change of the observation noise at a small epoch difference interval is much larger than the ionospheric delay, resulting in the ionospheric delay being unable to be accurately extracted. Therefore, the key to obtaining the true ionospheric delay is to weaken the observation noise, analyze the correlation of the ionospheric delay parameters in the short term according to the change value of the epoch-differenced ionosphere (EDI), and perform denoising processing on the obtained ionospheric observations to obtain the true ionospheric delay. The variance of the true ionosphere can be used to adjust the ionospheric delay in real time. By adjusting the variance constraint value in real time, the fixed time of the integer ambiguity can be effectively shortened, and the positioning accuracy can be improved. Therefore, a reasonable method is needed to determine the Power Spectral Density (PSD) of the ionospheric delay in the non-combination observation model to achieve the purpose of real-time adjustment of the variance of the ionospheric delay random walk, so as to meet the positioning requirements of higher-precision BDS PPP. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a method for real-time determining the variance of the random walk process of the ionospheric delay of each satellite through denoising the ionospheric delay observation data in view of the above-mentioned deficiencies of the prior art.

[0004] The technical solution adopted by the present invention is as follows:

[0005] A real-time adjustment method for the random walk variance of BDS PPP ionospheric delay, specifically including the following steps:

[0006] Step 1: Obtain observation data, including BDS observation data, precise orbits and clock differences, and differential code bias products, to provide data preparation for obtaining ionospheric observation values;

[0007] Step 2: According to the change value of the epoch-differenced ionosphere (EDI), analyze the correlation of ionospheric delay parameters in the short term, denoise the obtained ionospheric observation values, obtain the PSD of the ionosphere based on the ionospheric delay power spectral density (PSD) estimation method, and obtain the random walk variance of the ionospheric delay of each satellite in real time;

[0008] Step 3: Adjust the ionospheric random model according to the obtained random walk variance of the ionospheric delay. Based on the newly established ionospheric random model, use the non-combination observation values and to solve the positioning parameters.

[0009] Among them, the specific process of Step 1 is as follows:

[0010] Step 1.1: Query the day of year (DOY) of the observation data used in the experiment through the IGS data center of Wuhan University;

[0011] Step 1.2: Download the observation data through the official website of NASA, including BDS observation data, precise orbits and clock differences, and differential code bias products.

[0012] The specific process of Step 2 is as follows:

[0013] Step 2.1: Establish a non-combination PPP observation model, and its formula can be expressed as:

[0014]

[0015] In the formula and respectively represent the pseudorange observation value and the carrier phase observation value, and the two form non-combination observation values; n represents the nth frequency, r and s respectively represent the receiver label and the pseudo-random noise code (prn) number of the satellite; represents the direction cosine; x represents the coordinate increment, with the unit of meter; represents the receiver clock difference, with the unit of meter; γ n ionospheric mapping factor λ1 represents the first frequency wavelength, λ n represents the wavelength of the nth frequency; is expressed as the non-combined ionospheric observation value, with the unit of meter; is expressed as the projection function corresponding to the zenith tropospheric wet delay, which can be obtained through the Global Mapping Function (GMF); Z r,w is expressed as the zenith tropospheric wet delay, with the unit of meter; is expressed as the integer carrier phase ambiguity, with the unit of cycle; is the sum of the observation noise and multipath of the pseudorange; is the sum of the observation noise and multipath on the phase observation value.

[0016] Step 2.2: Parameterize the ionospheric delay in the form of a random walk, and its formula can be expressed as:

[0017]

[0018] In the formula is white noise with a mean and variance of zero, i is the time of the current observation, is the variance of the ionospheric delay random walk, is a normal distribution with an expectation of 0 and a variance of . This variance can be obtained from the key parameters of the random walk that do not change with the observation sampling frequency, and its formula can be expressed as:

[0019]

[0020] In the formula, where Δt is the time interval between two periods, is the key parameter of the random walk that does not change with the observation sampling frequency.

[0021] Step 2.3: Use the carrier phase observation values of the mth and nth frequencies to perform non-combined parameter solution;

[0022] Step 2.4: Perform epoch-by-epoch difference solution on the non-combined ionospheric observation value to obtain EDI;

[0023] Step 2.5: Calculate the estimated value of the EDI variance;

[0024] Step 2.6: Utilize the relationship between the ionospheric PSD and the variance of the ionospheric delay random walk to finally obtain the variance of the ionospheric delay random walk for real-time adjustment.

[0025] The specific process of Step 3 is as follows:

[0026] Step 3.1: Obtain the variance of the ionospheric delay random walk;

[0027] According to the relationship between the PSD and the ionospheric random walk variance the specific values of the random walk variance for each difference interval can be obtained, and the formula is expressed as follows:

[0028]

[0029] Step 3.2: Adjust the ionospheric random model according to the obtained ionospheric delay random walk variance, and solve the positioning parameters;

[0030] Since the above-mentioned ionospheric delay random walk variance is obtained, the parametric random model changes as follows, and its formula can be expressed as:

[0031]

[0032] Combined with the above model, when using the Kalman filter to solve the positioning parameters including ionospheric delay parameters epoch by epoch, the variance of the change of ionospheric delay parameters between epochs is solved in real time.

[0033] The beneficial effects of adopting the above technical solution are as follows: A real-time adjustment method for the ionospheric delay random walk variance of BDS PPP provided by the present invention realizes the real-time adjustment of the ionospheric parameter random model based on BDS, effectively improves the positioning accuracy, and has strong practical application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 is a flowchart of the present invention;

[0035] Figure 2 is a schematic diagram of the approximate power spectral density (APSD) obtained by EDI with different sampling intervals (1S and 60S) of the present invention;

[0036] Figure 3 is a schematic diagram of the comparison of the positioning accuracy between the proposed scheme of the present invention and the traditional PSD empirical model. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0037] The following combines the drawings and embodiments to further describe in detail the specific embodiments of the present invention. The following embodiments are used to illustrate the present invention, but are not used to limit the application scope of the present invention.

[0038] In this embodiment, a real-time adjustment method for the ionospheric delay random walk variance of BDS PPP, as Figure 1 shown, includes the following steps:

[0039] Step 1: Obtain observation data, including BDS observation data, precise orbits and clock biases, and differential code bias products, to prepare data for calculating ionospheric delay parameters. The specific steps are as follows:

[0040] Step 1.1: Query through the IGS data center of Wuhan University that the day of year (DOY) of the observation data used in the experiment is from the 135th to the 144th day of 2020;

[0041] Step 1.2: Download from the official website of NASA for a total of 10 days from DOY135 - 144 in 2020, including BDS and GPS observation data, precise orbits and clock biases, and differential code bias products;

[0042] In the embodiment of the present invention, data from 12 multi - GNSS experiment stations (MEGX) evenly distributed globally is used; the precise satellite orbit and clock bias products used for non - combined PPP solution are provided by the German Research Centre for Geosciences (GFZ).

[0043] Step 2: Analyze the correlation of ionospheric delay parameters in the short term according to the epoch - differenced ionosphere (EDI) change value, denoise the obtained ionospheric observations, obtain the PSD of the ionosphere based on the ionospheric delay PSD estimation method proposed by the present invention, and obtain the ionospheric delay random walk variance of each satellite in real time. The specific steps are as follows:

[0044] Step 2.1: Establish a non - combined PPP observation model, and its formula can be expressed as:

[0045]

[0046] In the formula and respectively represent the pseudorange observation value and the carrier - phase observation value, n represents the nth frequency, r and s respectively represent the receiver label and the pseudo - random noise code (prn) number of the satellite; represents the direction cosine; x represents the coordinate increment, with the unit of meter; represents the receiver clock bias, with the unit of meter; γ n Ionospheric mapping factor λ1 represents the wavelength of the first frequency, λ n represents the wavelength of the nth frequency; represents the non - combined ionospheric observation value, with the unit of meter; represents the projection function corresponding to the zenith tropospheric wet delay, which can be obtained through the Global Mapping Function (GMF); Zr,w Denoted as the zenith tropospheric wet delay, with the unit of meter; Denoted as the integer carrier phase ambiguity, with the unit of cycle; Is the sum of the observation noise and multipath of the pseudorange; Is the sum of the observation noise and multipath on the phase observation value;

[0047] Step 2.2: Parameterize the ionospheric delay in the form of a random walk, and its formula can be expressed as:

[0048]

[0049] In the formula is white noise with a mean and variance of zero, i is the time of the current observation, is the variance of the ionospheric delay, is a normal distribution with an expectation of 0 and a variance of . This variance can be obtained from the key parameters of the random walk that do not change with the observation sampling frequency, and its formula can be expressed as:

[0050]

[0051] In the formula, where Δt is the time interval between two periods, is the key parameter of the random walk that does not change with the observation sampling frequency;

[0052] Step 2.3: Since the noise of the pseudorange observation value is too large to reflect the short-term ionospheric change characteristics, it is more reasonable to use the phase observation value to calculate the ionospheric change amount. Assume that the carrier phase observation values of the mth and nth frequencies are used, then the ionospheric delay combination can be expressed as:

[0053]

[0054] In the formula, L m (i) and L n (i) are the phase observation values of different frequencies at epoch i, B m (i) and B n (i) are the receiver hardware delays of the phase, f1 is the first frequency of the observation value, f m 、f n are the mth and nth frequencies respectively, I is the ionospheric delay, N is the integer ambiguity of the phase observation value, and are the noises of the phase observation value;

[0055] Step 2.4. Perform epoch-differencing on the non-combined ionospheric observations to solve for EDI. There are also multipath effects caused by the surrounding environment of the station, antenna phase center offset, and ionospheric higher-order term delays. These are all related to the signal frequency and can cause deviations in the ionospheric observation results. These deviations are very small and change slowly over time. Therefore, these errors can be ignored. In the absence of cycle slips and gross errors, epoch-differencing can eliminate the influence of ambiguity parameters and hardware delays. The formula is expressed as:

[0056]

[0057] where \(I(i,i + \Delta i)\) is the difference in ionospheric delays between the \(i\)-th and \((i+\Delta i)\)-th epochs, is the noise of the combined observations between the \(i\)-th and \((i+\Delta i)\)-th epochs;

[0058] Based on the denoised ionospheric observations, EDI is solved. The formula is expressed as:

[0059]

[0060] Step 2.5. Calculate the estimate of the EDI variance. For convenience of representation, the above formula is simplified as:

[0061]

[0062] Then the corresponding variance is simplified as:

[0063]

[0064] In the formula, is the variance of the EDI observations, \(D(I)\) is the variance of the ionospheric delay, is the variance of the observation noise;

[0065] For a total of \(s\) observations, the estimate of the EDI observation variance is as follows:

[0066]

[0067] Step 2.6. Denoise the ionospheric observations. According to the calculated variance of the EDI observations, obtain the approximate power spectral density APSD. Using the relationship between PSD and variance, finally obtain the ionospheric delay random walk variance for real-time adjustment.

[0068] Similar to the relationship between the ionospheric delay PSD and the ionospheric random walk variance The APSD can be obtained based on EDI. The formula is expressed as follows:

[0069]

[0070]

[0071] Considering the indicated EDI variance form, the relationship between ionospheric variations and observation noise can be expressed by the following formula and separated as:

[0072]

[0073] Among them, the APSD is calculated from the EDI observations and varies with the sampling frequency. The ionospheric variations and observation noise have different manifestations. The ionospheric variations have the characteristics of a random walk process, while the observation noise appears as white noise. It is not difficult to find that if the differential interval of EDI observations is increased, the contribution of the observation noise to the APSD will decrease. In addition, if the APSDs of multiple different differential intervals are calculated, the ionospheric delay PSD and the variance of the observation noise can be easily separated.

[0074] Step 3: Adjust the ionospheric stochastic model according to the obtained random walk variance. Based on the newly established ionospheric stochastic model, use the non-combination observations to solve the positioning parameters.

[0075] Step 3.1: Obtain the random walk variance of the ionospheric delay;

[0076] According to the relationship between the PSD and the ionospheric random walk variance the specific values of the random walk variance at each differential interval can be obtained, and the formula is expressed as follows:

[0077]

[0078] Step 3.2: Adjust the ionospheric stochastic model according to the obtained random walk variance of the ionospheric delay and solve the positioning parameters;

[0079] Since the random walk variance of the ionospheric delay is obtained above, the parametric stochastic model changes as follows, and its formula can be expressed as:

[0080]

[0081] Combined with the above model, when using the Kalman filter to solve the positioning parameters containing ionospheric delay parameters epoch by epoch, the variance of the ionospheric delay parameter variation between epochs is solved in real time to improve the estimation accuracy of the ionospheric delay parameters, thereby improving the positioning performance.

[0082] By comparing the accuracy with the traditional empirical method of ionospheric PSD, the superiority of the method proposed by the present invention is verified. Combining the manifestations of the EDI variance listed in Step 2.5 and Step 2.6, in order to analyze the different effects of ionospheric delay and observation noise, the observation data of the HKWS station in Hong Kong, China on May 15, 2022 is used. The receiver model is LEICA GR50, the antenna type is: LEIAR25.R4, and the sampling frequency is 1HZ; different differential intervals are used to analyze the APSD, and the analysis results are as Figure 2 shown, indicating that the APSD of different satellites basically degrades with the increase of the differential interval. The influence of observation noise is inversely proportional to the differential interval. If the APSD is calculated with a smaller differential interval, the main component is observation noise rather than the change of ionospheric delay. If the time interval is too large, it may not be able to reflect the short-term ionospheric changes.

[0083] Scheme 1: The PSD in the ionospheric random walk is set to 0.04 [m / sqrt(s)]; Scheme 2: The PSD is estimated by the method of the present invention. The positioning results of the two schemes are as Figure 3 shown. In the convergence stage, the two schemes perform basically the same in three directions; after convergence, the positioning error curves of the two schemes basically coincide in the E and N directions, but in the U direction, Scheme 2 has a significant improvement compared with Scheme 1. It can be shown that the real-time adjustment method of the BDS PPP ionospheric delay random walk variance proposed by the present invention can effectively improve the positioning accuracy and has more practical value compared with setting the empirical value of PSD in Scheme 1.

[0084] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope defined by the claims of the present invention.

Claims

1. A real-time adjustment method for the random walk variance of BDS PPP ionospheric delay, characterized in that , including the following steps: Step 1: Obtain observation data, including BDS observation data, precise orbits and clock errors, and differential code bias products, to provide data preparation for obtaining ionospheric observation values; Step 1.1: Query the year-day-of-year of the observation data used in the experiment through the IGS data center of Wuhan University; Step 1.2: Download the observation data through the NASA website, including BDS observation data, precise orbits and clock errors, and differential code bias products; Step 2: Analyze the correlation of ionospheric delay parameters in the short term according to the change value of the inter-epoch ionospheric delay EDI, denoise the obtained ionospheric observation values, obtain the PSD of the ionosphere based on the ionospheric delay power spectral density estimation method, and obtain the ionospheric delay random walk variance of each satellite in real time; Step 2.1: Establish a non-combined PPP observation model, and its formula can be expressed as: In the formula and represent the pseudorange observation value and the carrier phase observation value respectively, and the two form a non-combined observation value; n represents the nth frequency, and r and s represent the receiver label and the pseudorandom noise code number of the satellite respectively; represents the direction cosine; x represents the coordinate increment, with the unit of meter; represents the receiver clock error, with the unit of meter; γ n ionospheric mapping factor λ1 represents the wavelength of the first frequency, and λ n represents the wavelength of the nth frequency; is expressed as the non-combined ionospheric observation value, with the unit of meter; represents the projection function corresponding to the zenith tropospheric wet delay, which can be obtained through the global projection function; Z r,w is expressed as the zenith tropospheric wet delay, with the unit of meter; is expressed as the integer carrier phase ambiguity, with the unit of cycle; is the sum of the observation noise and multipath of the pseudorange; is the sum of the observation noise and multipath on the phase observation value; Step 2.2: Parameterize the ionospheric delay in the form of a random walk; Step 2.3: Use the carrier phase observation values of the mth and nth frequencies to perform non-combined parameter solution; Step 2.

4. Perform epoch-differencing on the non-combined ionospheric observations to solve for the EDI; Step 2.5: Calculate the estimated value of the EDI variance; Step 2.6: Utilize the relationship between the ionospheric PSD and the ionospheric delay random walk variance to finally obtain the ionospheric delay random walk variance for real-time adjustment; Step 3: Adjust the ionospheric stochastic model according to the obtained ionospheric delay random walk variance. Based on the newly established ionospheric stochastic model, use the non-combination observations and to solve the positioning parameters.

2. A real-time adjustment method for the random walk variance of the BDS PPP ionospheric delay according to claim 1, characterized in that , the specific content of Step 2.2 is as follows: Parameterize the ionospheric delay in the form of a random walk, and its formula can be expressed as: where is white noise with zero mean and variance, i is the time of the current observation, is the variance of the ionospheric delay random walk, has an expectation of 0 and a variance of and follows a normal distribution; this variance can be obtained from the key parameters of the random walk that do not change with the observation sampling frequency, and its formula can be expressed as: where Δt is the time interval between two periods, is the key parameter of random walk that does not change with the observation sampling frequency.

3. A real-time adjustment method for the variance of the random walk of the BDS PPP ionospheric delay according to claim 2, characterized in that , the specific content of Step 2.3 is as follows: Since the noise of the pseudorange observation value is too large to reflect the ionospheric variation characteristics in the short term, it is more reasonable to use the phase observation value to calculate the ionospheric variation amount; assuming that the carrier phase observation values of the mth and nth frequencies are used, the ionospheric delay combination can be expressed as: Where L m (i) and L n (i) are phase observation values of different frequencies at epoch i, B m (i) and B n (i) are receiver hardware delays of the phase, f1 is the first frequency of the observation value, f m and f n are the m-th and n-th frequencies respectively, I is the ionospheric delay, N is the integer ambiguity of the phase observation value, and are the noises of the phase observation value.

4. A real-time adjustment method for the variance of the BDS PPP ionospheric delay random walk according to claim 3, characterized in that , the specific content of Step 2.4 is as follows: Perform inter-epoch difference solution on the non-combined ionospheric observation values to obtain EDI; there are also multipath effects caused by the surrounding environment of the station, antenna phase center offset, and ionospheric higher-order term delay, all of which are related to the signal frequency and will cause deviations in the ionospheric observation results; these deviations are very small and change slowly over time, so these errors can be ignored; In the absence of cycle slips and gross errors, the effects of ambiguity parameters and hardware delays can be eliminated by inter-epoch differencing, and the formula is expressed as: where I(i, i + Δi) is the difference in ionospheric delay between the i-th and (i + Δi)-th epochs, is the combined observation value noise between the i-th and (i + Δi)-th epochs; Solve EDI based on the denoised ionospheric observation values, and its formula is expressed as:

5. A real-time adjustment method for the BDS PPP ionospheric delay random walk variance according to claim 4, characterized in that , the specific content of Step 2.5 is as follows: Calculate the estimated value of the EDI variance; for the convenience of representation, simplify the above formula to: Furthermore, the corresponding variance is simplified to: In the formula, is the variance of the EDI observation value, and D(I) is the variance of the ionospheric delay, is the variance of the observation value noise; For a total of s observation values, the variance estimated value of the EDI observation value is as follows:

6. A real-time adjustment method for the random walk variance of BDS PPP ionospheric delay according to claim 5, characterized in that , the specific content of Step 2.6 is as follows: Denoise the ionospheric observations, obtain the approximate power spectral density APSD based on the calculated EDI variance, and utilize the relationship between the PSD and the ionospheric random walk variance Finally, obtain the ionospheric delay random walk variance for real-time adjustment; Relationship between Ionospheric Delay PSD and Ionospheric Random Walk Variance The APSD can be obtained based on EDI, and the formula is as follows: Considering the indicated form of the EDI variance, the relationship between ionospheric variation and observation noise can be expressed by the following formula and separated as: Among them, APSD is calculated from the observation results of EDI and varies with the sampling frequency. The ionospheric variation and the observation noise have different manifestations. The ionospheric variation has the characteristics of a random walk process, while the observation noise shows white noise. If the differential interval of EDI observation is increased, the contribution of the observation noise to APSD will decrease. In addition, if the APSDs of multiple different differential intervals are calculated, the ionospheric delay PSD and the variance of the observation noise can be easily separated.

7. A real-time adjustment method for the random walk variance of the BDS PPP ionospheric delay according to claim 6, characterized in that , the specific content of step 3 is as follows: Step 3.1: Obtain the random walk variance of the ionospheric delay; According to the relationship between PSD and the ionospheric random walk variance the specific values of the random walk variance at each difference interval can be obtained, and the formula is expressed as follows: Step 3.2: Adjust the ionospheric random model according to the obtained random walk variance of the ionospheric delay and perform the solution of the positioning parameters; Since the random walk variance of the ionospheric delay is obtained above, the parameterized random model changes as follows, and its formula can be expressed as: Combined with the above model, when using the Kalman filter to perform epoch-by-epoch solution of the positioning parameters including the ionospheric delay parameters, the variance of the epoch-by-epoch change of the ionospheric delay parameters is solved in real time.

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