A method for post-processing of Beidou positioning data based on EMD algorithm

Abstract

The application provides a method for post-processing Beidou positioning data based on an EMD algorithm, comprising the following steps: step one, preprocessing original Beidou static positioning data with a 24-hour span; step two, obtaining a new data sequence of the original Beidou static positioning data by extending the preprocessed original Beidou static positioning data, and performing end effect correction processing on the original Beidou static positioning data with a next 24-hour span based on the new data sequence. According to the periodic characteristics of the original Beidou static positioning data and the slow overall trend change characteristics, the data is extended by connecting the head and tail of the data itself; after sufficient extended data is obtained, MPCI-EMD decomposition is directly performed, so that the data distortion occurs in the extended data part and does not affect the interval where the target data is located, thereby eliminating the data distortion problem caused by splitting.

Description

Technical Field

[0001] This invention relates to the field of BeiDou positioning technology, specifically to a method for post-processing BeiDou positioning data based on the EMD algorithm. Background Technology

[0002] Current methods for eliminating multipath in static receivers in the BeiDou positioning system include modifying the antenna using methods such as stellar filtering or radomes to eliminate multipath in static receivers.

[0003] The most widely used method in existing technologies is sidereal filtering. Sidereal filtering is based on the periodicity of satellite orbits around the Earth and the relatively stable signal environment of a static receiver. It analyzes satellite ephemeris data, calculates the low-frequency components of each satellite, and finally sums and differentially analyzes the low-frequency components according to the receiver's satellite search results to eliminate multipath propagation. However, sidereal filtering has the following drawbacks: it is computationally complex, requiring individual analysis and calculation for all received satellites; and it cannot be post-processed, requiring calculations only during the computational step.

[0004] The method of using fairings is not practical due to its large size and cost, and is generally not considered unless there is a specific need. Summary of the Invention

[0005] This invention provides a method for post-processing BeiDou positioning data based on the EMD algorithm, comprising the following steps:

[0006] Step 1: Preprocess the raw BeiDou static positioning data spanning 24 hours.

[0007] Step 2: By expanding the preprocessed original BeiDou static positioning data, a new data sequence of the original BeiDou static positioning data is obtained, and based on the new data sequence, endpoint effect correction processing is performed on the original BeiDou static positioning data for the next 24-hour span.

[0008] Optionally, the method for preprocessing the raw BeiDou static positioning data spanning 24 hours in step one is as follows:

[0009] Step 1: Divide the raw BeiDou static positioning data spanning 24 hours into 5760 epochs;

[0010] Step 2: Remove outlier data from the original BeiDou static positioning data using a slope recognition algorithm;

[0011] Step 3: Based on the standard that the original BeiDou static positioning data spans 24 hours and has 5760 epochs, complete the original BeiDou static positioning data after Step 2; and fit the missing data in the original BeiDou static data using a monotonic piecewise interpolation algorithm.

[0012] Optionally, in step two, the method for expanding the original BeiDou static positioning data after preprocessing in step one is as follows:

[0013] By leveraging the characteristics of satellite static positioning data, the original BeiDou static positioning data is expanded using a 24-hour cycle, with the first and last data points of the original BeiDou static positioning data being expanded to three days' worth of data, resulting in a new data sequence of the original BeiDou static positioning data.

[0014] Optionally, in step two, the method for performing endpoint effect correction processing on the original BeiDou static positioning data for the next 24-hour span based on the new data sequence is as follows:

[0015] The new data sequence was split in 16 steps using the MPCI-EMD algorithm to obtain 16 sets of IMF sequences;

[0016] The 16 IMF sequences were arranged in descending order of frequency from highest to lowest.

[0017] The 10th to 16th IMF sequences from the 16 IMF sequences were extracted as empirical low-frequency component data for endpoint effect correction of the raw BeiDou static positioning data for the next 24-hour span.

[0018] Optionally, the process of splitting the new data sequence into 16 steps using the MPCI-EMD algorithm is as follows:

[0019] A. Suppose the time series x(t) of the original BeiDou static positioning data consists of the following:

[0020] x(t) = T(t) + mul(t) + h(t)

[0021] Where: t is the epoch; T(t) is the trend term data used to reflect the degree of positive real displacement. Under static monitoring environment, the trend term of Beidou generally changes displacement in units of 24 hours, which is extremely low frequency; mul(t) is the low frequency component, which generally changes in a sidereal day period; h(t) is the high frequency component, which includes thermal noise, observation noise and pulse interference, etc.

[0022] B. Based on the EMD algorithm theory, the fluctuations at each frequency level are decomposed through modal analysis to obtain the corresponding IMF sequence. The steps are as follows:

[0023] ① Perform local extremum analysis on the time series x(t) to obtain the local maximum value sequence x. max and local minimum sequence x min :

[0024] {xmin x max}=f(x(t)), t∈[t a , t b ]

[0025] Where: f(x(t)) represents the endpoint effect treatment applied to the time series x(t), x min ≤x(t)≤x max , t a t represents the starting epoch of the original BeiDou static positioning data. b This is the end era of the original BeiDou static positioning data;

[0026] ② Using the MPCI algorithm to analyze the local maximum sequence x max and local minimum sequence x min Find the upper envelope sequence. up and lower envelope sequence low :

[0027] envelope low =MPCI({x min})

[0028] envelope up =MPCI({x max});

[0029] ③ Based on the upper envelope sequence up and lower envelope sequence low Find the mean sequence m of the low-frequency component mul(t) of the original BeiDou static positioning data. 1k (t) and the mean sequence h of the high-frequency component h(t). 1k (t):

[0030] m 1k (t)=(envelope up +envelope low ) / 2

[0031] h 1k (t)=x(t)-m 1k (t)

[0032] Where: m 1k (t) represents the mean of the envelope in the kth iteration, where k = 1, 2, ..., N, and N is the total number of envelope values.

[0033] ④ Repeat steps ①-③ to continuously remove low-frequency components mul(t), and finally extract the highest frequency component in the current BeiDou static positioning data, until the stopping criterion satisfies k reaching a specific number S, to obtain the highest frequency fluctuation IMF1(t) in the time series:

[0034] IMT1(t)=h 1s (t)

[0035] Where: h 1s (t) represents the high-frequency component decomposed by the first step of EMD after S repeated filtering;

[0036] ⑥ Subtract the highest frequency fluctuation IMF1(t) from the time series x(t) to obtain the residual series r1(t). The residual series r1(t) contains the second highest frequency component and the low frequency component. Further decompose the residual series r1(t). When the stopping criterion satisfies k reaching a specific number S, the data sequences of each frequency band can be obtained, which are specifically represented as follows:

[0037]

[0038] IMF1(t)=h 1s (t)

[0039] T(t) = r n (t)

[0040] Where: r n (t) represents the final residual sequence.

[0041] Optionally, the specific process of arranging the 16 IMF sequences in descending order of frequency is as follows:

[0042] The 16 IMF sequences were split into two parts based on frequency:

[0043]

[0044]

[0045] Substitute the two parts of the 16 IMF sequences according to their frequency into...

[0046] x(t)=T(t)+mul(t)+h(t) where:

[0047]

[0048] According to the above formula, the original BeiDou static positioning data x1(t) and x2(t) of two consecutive days have the following relationship:

[0049] mul1(t)≈mul2(t)

[0050] Where: mul1(t) is the low-frequency component of the first day of two consecutive days, and mul2(t) is the low-frequency component of the second day of two consecutive days;

[0051] Obtain multipath eliminated sequences

[0052]

[0053]

[0054]

[0055] in: This is an assumed low-frequency component in the data for that day, with a value of mul1(t); r 2，n (t) represents the true trend component of the data for that day; Δmul2(t) is the multipath corrected residual, which is considered as noise; These are high-frequency residual components.

[0056] Optionally, the specific method for endpoint effect correction of the raw BeiDou static positioning data for the next 24-hour span is as follows:

[0057] (i) The original BeiDou static positioning data spanning one day is segmented. When there is not much missing data in the original BeiDou static positioning data spanning one day, the insufficient part is supplemented by the MPCI interpolation algorithm.

[0058] (II) The supplemented original BeiDou static positioning data is denoted as a one-dimensional vector X. day :

[0059] X day = [x1, x2, ... x 5760 ]

[0060] Where: x1, x2…x 5760 These represent the first to the 5760th epochs, respectively.

[0061] (III) Transform the one-dimensional vector X day Split into X f and X b Two parts:

[0062] X f = [x1, x2, ... x 2880 ]

[0063] X b =[x 2881 x 2882 , ...x 5760 ]

[0064] Where f stands for forward and b stands for backward.

[0065] (iv) Through X f and X b By stitching together the original BeiDou static positioning data, the augmented data X is obtained. Ex X Ex The expression is as follows:

[0066]

[0067]

[0068]

[0069] in: For splicing, To spell from left to X day , To spell from right to X day ;

[0070] (v) Obtain the extended data X Ex Endpoint effect correction was performed using the original BeiDou static positioning data for that day.

[0071] Compared with the prior art, the present invention has the following beneficial effects:

[0072] This invention expands the original BeiDou static positioning data by connecting the first and last parts of the data based on the periodic characteristics and the slow overall trend of change. After obtaining sufficient expanded data, MPCI-EMD decomposition is performed directly, so that data distortion occurs within the expanded data part without affecting the interval where the target data is located, thereby eliminating the data distortion problem caused by splitting.

[0073] In addition to the objectives, features and advantages described above, the present invention has other objectives, features and advantages. Detailed Implementation

[0074] Example:

[0075] This invention provides a method for post-processing BeiDou positioning data based on the EMD algorithm, comprising the following steps:

[0076] Step 1: Data Preprocessing

[0077] Step 1: Divide the raw BeiDou static positioning data spanning 24 hours into 5760 epochs (i.e., divide the raw BeiDou static positioning data into 1 epochs with each 15-second interval).

[0078] Step 2: Remove outlier data from the original BeiDou static positioning data using the slope recognition algorithm (i.e., after removing outlier data from the original 5760 epochs of BeiDou static positioning data, the data is reduced to less than 5760 epochs).

[0079] Step 3: Based on the standard that the original BeiDou static positioning data spanning 24 hours has 5760 epochs, complete the original BeiDou static positioning data after Step 2; and fit the missing data in the original BeiDou static data (i.e., the outlier data that was removed) using a monotonic piecewise interpolation algorithm (i.e., MPCI algorithm).

[0080] Step 2: Endpoint effect correction:

[0081] Step 1) Based on the characteristics of satellite static positioning data, the original BeiDou static positioning data is expanded by adding the first and last data of the original BeiDou static positioning data based on the current 24-hour span (the expansion of the first and last data is usually enough to add three days' worth of data), to obtain a new data sequence of the original BeiDou static positioning data.

[0082] Step 2) The obtained new data sequence is split into 16 steps using the MPCI-EMD algorithm to obtain 16 groups of IMF sequences; the physical characteristics corresponding to the 16 groups of IMF sequences are noise signals;

[0083] Step 3) Arrange the 16 IMF sequences in descending order of frequency from high to low;

[0084] Step 4) Extract the 10th to 16th IMF sequences from the 16 IMF sequences as empirical low-frequency component data for multipath interference correction (i.e., endpoint effect correction) of the raw BeiDou static positioning data for the next 24-hour span.

[0085] In step 2, the procedure for removing outlier data from the original BeiDou static positioning data using the slope recognition algorithm is as follows:

[0086]

[0087]

[0088] The above is pseudocode. ii, jj, and kk are all data addresses, pointing to different array contents of the data; max and min are the arrays storing local maximum and minimum extrema, respectively; max_index and min_index are the addresses of the local maximum and minimum extrema in the original data array, respectively.

[0089] In step 2), the process of splitting the new data sequence into 16 steps using the MPCI-EMD algorithm is as follows:

[0090] A. Suppose the time series x(t) of the original BeiDou static positioning data consists of the following:

[0091] x(t)=T(t)+mul(t)+h(t) (1)

[0092] Where: t is the epoch; T(t) is the trend term data used to reflect the degree of positive displacement. In the static monitoring environment of BeiDou, the trend term generally changes displacement in units of 24 hours, which is extremely low frequency; mul(t) is the low frequency component, which generally changes in a sidereal day period; h(t) is the high frequency component, which includes thermal noise, observation noise and pulse interference, etc.

[0093] B. Based on the EMD algorithm theory, the fluctuations at each frequency level are decomposed through modal analysis to obtain the corresponding IMF sequence. The steps are as follows:

[0094] ① Perform local extremum analysis on the time series x(t) to obtain the local maximum value sequence x. max and local minimum sequence x min :

[0095] {x min x max}=f(x(t)), t∈[t a , t b (2)

[0096] Where: f(x(t)) represents the endpoint effect treatment applied to the time series x(t), x min ≤x(t)≤x max , t a t represents the starting epoch of the original BeiDou static positioning data. b This is the end era of the original BeiDou static positioning data.

[0097] ② The local maximum sequence x is obtained by using the MPCI (Monotone Piecewise Cubic Interpolation; the MPCI algorithm is a method of calculation using monotonically piecewise spline interpolation) algorithm. max and local minimum sequence x min Find the upper envelope sequence. up and lower envelope sequence low :

[0098] envelope low =MPCI({x min}) (3)

[0099] envelope up =MPCI({xmax}) (4).

[0100] ③ Based on the upper envelope sequence up and lower envelope sequence low Find the mean sequence m of the low-frequency component mul(t) of the original BeiDou static positioning data. 1k (t) and the mean sequence h of the high-frequency component h(t). 1k (t):

[0101] m 1k (t)=(envelope up +envelope low ) / 2 (5)

[0102] h 1k (t)=x(t)-m 1k (t) (6)

[0103] Where: mul(t) is the mean of the envelope in the kth iteration, k = 1, 2, ..., N, and N is the total number of envelope values.

[0104] ④ Repeat steps ①-③ to continuously remove low-frequency components mul(t), and finally extract the highest frequency component in the current BeiDou static positioning data, until the stopping criterion satisfies k reaching a specific number S, to obtain the highest frequency fluctuation IMF1(t) in the time series:

[0105] IMF1(t)=h 1s (t) (7)

[0106] Where: h 1s (t) represents the high-frequency component obtained by the first step of EMD splitting after S repeated filtering.

[0107] ⑥ Subtract the highest frequency fluctuation IMF1(t) from the time series x(t) to obtain the residual series r1(t). The residual series r1(t) contains the second highest frequency component and the low frequency component. Further decompose the residual series r1(t). When the stopping criterion satisfies k reaching a specific number S, the data sequences of each frequency band can be obtained, which are specifically represented as follows:

[0108]

[0109] IMF1(t)=h 1s (t) (9)

[0110] T(t) = r n (t) (10)

[0111] Where: r n (t) represents the final residual sequence.

[0112] The specific process of arranging the 16 groups of IMF sequences in descending order of frequency from high to low in step 3) is as follows:

[0113] I. Taking the 16-step split as an example, the 16 groups of IMF sequences are divided into two parts according to their frequency: Equation (11) and Equation (12).

[0114]

[0115]

[0116] Therefore, Equation 1 can be replaced with the following form:

[0117]

[0118] Tests revealed the following relationship between the raw BeiDou static positioning data (i.e., the raw BeiDou static positioning data within two adjacent 24-hour spans) x1(t) and x2(t):

[0119] mul1(t)≈mul2(t) (14)

[0120] Where: mul1(t) is the low-frequency component of the first day of the two consecutive days, and mul2(t) is the low-frequency component of the second day of the two consecutive days.

[0121] Therefore, the following operations can be performed to obtain the sequence that eliminates multipaths.

[0122]

[0123]

[0124]

[0125] in: This is an assumed low-frequency component in the data for that day, with a value of mul1(t); r 2，n (t) represents the true trend component of the data for that day; Δmul2(t) is the multipath corrected residual, which is considered as noise; These are high-frequency residual components.

[0126] Preferably, to eliminate the influence of actual displacement, the data used to calculate the data error variance is: Right now

[0127] II. The MPCI algorithm is used to derive the new data sequence obtained from step I. The specific process is as follows:

[0128] The function p(x) for each subinterval is expressed as follows:

[0129] p(x)=f i H1(x)+f i+1 H2(x)+d i H3(x)+d i+1 H4(x) (19)

[0130] f i =p(x i (20)

[0131] d j =p′(x j ), j = (i, i+1) (21)

[0132] Where: f i The function for each subinterval in x i The value at H k (x) is a common spline Hermite equation;

[0133] Based on this, for sub-interval I i =[x i x i+1 ]I i =[x i x i+1 ], has the following function:

[0134]

[0135]

[0136]

[0137]

[0138] h i =x i+1 -x i (25)

[0139] φ(t)=3t 2 -2t 3 (26)

[0140] ψ(t)=t 3 -t 2 (27)

[0141] The first derivative d with respect to each point j j = i, i+1 is obtained through the three-point difference formula. If the point is located at the beginning, end or turning point, the first derivative of the point is set to zero.

[0142] Monotonic piecewise spline interpolation follows these principles: within each subinterval, let Δ i =(f i+1 -f i ) / h i The first derivatives at the endpoints of this subinterval have the following requirements:

[0143] sgn(d i ) = sgn(d i+1 )=sgn(Δ i (28)

[0144] And when sgn(Δ i )≠sgn(Δ i+1 ), that is, point x i+1 When x is an extreme point, i+1 The corresponding d i+1 Set it to 0.

[0145] For general Δ i ≠0, for p(x) at x = x i Expand:

[0146]

[0147] The first and second derivatives are:

[0148]

[0149]

[0150] And let α i =d i / Δ i ,β i =d i+1 / Δ i Therefore, we have Lemma 1: When α i +β i When -2≤0 and the equation is satisfied, the local monotonicity is satisfied.

[0151] There is also a special extreme point x of p′(x). * :

[0152]

[0153] Substituting into equation (28) above, we get:

[0154]

[0155] For x * We will discuss two cases, namely (i) and (ii)x* ∈(x i x i+1 (i) can be expressed as 2α i +β i -3≤0, x * ≤x i and α i +2β i -3≤0, x * ≥x i+1 For case (ii), the following inequality holds:

[0156]

[0157] In summary, we can derive the following Lemma 2:

[0158] α i +β i When -2 > 0 and the expression satisfies this condition, the local monotonicity is satisfied if and only if at least one of the following three conditions is met:

[0159] 2α i +β i -3≤0 (35)

[0160] α i +2β i -3≤0 (36)

[0161] θ(α i ,β i )≥0 (37)

[0162] A region can be obtained by Lemma 1 and Lemma 2. For simplified calculation, a region is generally taken. A subregion l (subregion l is a circle with a radius of 3); the above are all for values ​​of (α, β) ≥ 0, while for (α, β) < 0, the above intervals can be symmetrical about the origin.

[0163] In step 4), the specific method for correcting the endpoint effect of the raw BeiDou static positioning data for the next 24-hour span is as follows:

[0164] (i) The original BeiDou static positioning data spanning one day is segmented (since the epoch interval is 15s and one day is 86400s, the data for one day is 5760 epochs). When there are not many missing data in the original BeiDou static positioning data spanning one day (i.e., 24-hour span), the insufficient part is supplemented by the MPCI interpolation algorithm.

[0165] (II) The supplemented original BeiDou static positioning data is denoted as a one-dimensional vector X. day :

[0166] X day = [x1, x2, ... x 5760 (38)

[0167] Where: x1, x2…x 5760 These are the first to the 5760th epochs.

[0168] (III) Transform the one-dimensional vector X day Split into X f and X b Two parts:

[0169] X f = [x1, x2, ... x 2880 (39)

[0170] X b =[x 2881 x 2882 , ...x 5760 (40)

[0171] Where f stands for forward and b stands for backward.

[0172] (iv) Through X f and X b By stitching together the original BeiDou static positioning data, the augmented data X is obtained. Ex X Ex The expression is as follows:

[0173]

[0174]

[0175]

[0176] in: For splicing, To spell from left to X day , To spell from right to X day .

[0177] (v) Obtain the extended data X Ex Endpoint effect correction was performed using the original BeiDou static positioning data for that day.

[0178] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for post-processing Beidou positioning data based on an EMD algorithm, characterized in that, The method comprises the following steps: Step one, preprocessing the original Beidou static positioning data of 24 hours span, Step two, obtaining a new data sequence of the original Beidou static positioning data by extending the original Beidou static positioning data after preprocessing, and correcting the end effect of the original Beidou static positioning data of the next 24 hours span based on the new data sequence; The method for correcting the end effect of the original Beidou static positioning data of the next 24 hours span based on the new data sequence is specifically as follows: The obtained new data sequence is split into 16 groups of IMF sequences through the MPCI-EMD algorithm; The 16 groups of IMF sequences are arranged in descending order from high to low frequency; The 10th to 16th groups of IMF sequences in the 16 groups of IMF sequences are extracted as empirical low-frequency component data for correcting the end effect of the original Beidou static positioning data of the next 24 hours span.

2. The method for post-processing Beidou positioning data based on the EMD algorithm according to claim 1, characterized in that, In the step one, the method for preprocessing the original Beidou static positioning data of 24 hours span is specifically as follows: Step 1, dividing the original Beidou static positioning data of 24 hours span into 5760 epochs; Step 2, removing outlier data in the original Beidou static positioning data through a slope identification algorithm; Step 3, completing the original Beidou static positioning data after step 2 according to the standard of 5760 epochs of the original Beidou static positioning data of 24 hours span, and fitting the missing data in the original Beidou static data through a monotonic piecewise interpolation algorithm.

3. The method for post-processing Beidou positioning data based on the EMD algorithm according to claim 2, characterized in that, In the step two, the method for extending the original Beidou static positioning data after preprocessing in step one is specifically as follows: According to the characteristics of satellite static positioning data, the original Beidou static positioning data is extended based on the first and last data of the original Beidou static positioning data of the current 24 hours span, to obtain a new data sequence of the original Beidou static positioning data.

4. The method for post-processing Beidou positioning data based on EMD algorithm according to claim 1, characterized in that, The process of splitting the new data sequence through the MPCI-EMD algorithm for 16 steps is specifically as follows: A, the composition of the time sequence x(t) of the original Beidou static positioning data is as follows: x(t) = T(t) + mul(t) + h(t) where t is an epoch; T(t) is a trend item data for reflecting the degree of positive displacement, the trend item changes displacement in 24 hours under the static monitoring environment of Beidou, and belongs to extremely low frequency; mul(t) is a low-frequency component, which changes in a sidereal day; h(t) is a high-frequency component, which includes thermal noise, observation noise and impulse interference; B, according to the EMD algorithm theory, the wave of each frequency is split through modal analysis to obtain the corresponding IMF sequence, and the steps are as follows: ①, Local extremum analysis is performed on the time series x(t) to obtain a local maximum value sequence x max and a local minimum value sequence x min : {x min , x max} = f(x(t)), t e [t a , t b ] Wherein: f(x(t)) is the end effect processing of time series x(t), x min ≤x(t)≤x max , t a is the starting epoch of the original Beidou static positioning data, t b is the end epoch of the original Beidou static positioning data; ii. The local maximum sequence x max and the local minimum sequence x min are obtained by the monotone piecewise interpolation MPCI algorithm up and the lower envelope sequence envelope low : envelope low = MPCI({x min}) envelope up = MPCI({x max}) ; III. According to the upper envelope sequence envelope up and the lower envelope sequence envelope low The mean sequence m of the low-frequency component mul(t) of the original Beidou static positioning data is obtained 1k (t) and the mean sequence h of the high-frequency component h(t) 1k (t): m 1k (t) = (envelope up +envelope low ) / 2 h 1k (t) = x(t) - m 1k (t) wherein: m 1k (t) is the kth envelope mean, k = 1, 2,... N, N is the total number of envelope values; ④, repeat steps ①-③ to continuously remove the low-frequency component mul(t), finally extract the highest frequency component in the current Beidou static positioning data, and until the stopping criterion is met and k reaches a certain number S, the highest frequency wave IMF1(t) in the time sequence is obtained: IMF1(t) = h 1s (t) wherein: h 1s (t) is the high frequency component of the first step EMD decomposition repeated S times ⑥ Subtract the highest frequency fluctuation IMF1(t) from the time series x(t) to obtain the residual series r1(t). The residual series r1(t) contains the second highest frequency component and the low frequency component. Further decompose the residual series r1(t). When the stopping criterion satisfies k reaching a specific number S, the data sequences of each frequency band can be obtained, which are specifically represented as follows: IMF1(t) = h 1s (t) T(t) = r n (t) where: r n (t) is the last residual sequence.

5. The method for post-processing Beidou positioning data based on the EMD algorithm according to claim 4, characterized in that, The specific process of arranging the 16 IMF sequences in descending order of frequency is as follows: The 16 IMF sequences were split into two parts based on frequency: Substituting the two parts of the 16 IMF sequences, separated by frequency, into the equation x(t) = T(t) + mul(t) + h(t), we get: According to the above formula, the original BeiDou static positioning data x1(t) and x2(t) of two consecutive days have the following relationship: mul1(t)≈mul2(t) Where: mul1(t) is the low-frequency component of the first day of two consecutive days, and mul2(t) is the low-frequency component of the second day of two consecutive days; Obtaining a sequence that eliminates multipath where: is the assumed low frequency component of the current day data, with value mul1(t); r 2，n (t) is the true trend component of the current day data; Δmul2(t) is the multipath correction residual, treated as noise; is the high frequency residual component.

6. The method for post-processing Beidou positioning data based on the EMD algorithm according to claim 4, characterized in that, The specific method for endpoint effect correction of the raw BeiDou static positioning data for the next 24-hour span is as follows: (i) The original BeiDou static positioning data spanning one day is segmented. When there is not much missing data in the original BeiDou static positioning data spanning one day, the insufficient part is supplemented by the MPCI interpolation algorithm. (ii) the supplemented original Beidou static positioning data is denoted as a one-dimensional vector X day : X day = [x1, x2,... x 5760 ] wherein: x1, x2...x 5760 are the 1st to 5760th epochs, respectively; (Three), splitting the one-dimensional vector X day into two parts: X f and X b ​ X f = [x1, x2,..., x 2880 ] X b = [x 2881 , x 2882 ,... x 5760 ] Where: f stands for forward and b stands for backward; (IV) by X f and X b splicing the original Beidou static positioning data to obtain the expanded data X Ex , X Ex is expressed as follows: wherein: is spliced, is left spliced to X day , is right spliced to X day ; (V), the obtained extension data X Ex The endpoint effect correction is made to the original Beidou static positioning data of the day.

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