A multipath correction method based on signal-to-noise ratio reflected signal and adaptive weighting

Abstract

This invention discloses a multipath correction method based on signal-to-noise ratio (SNR) reflected signals and adaptive weighting, comprising the following steps: S1, extensively collecting raw GPS observations in environments without multipath propagation; S2, data preprocessing; S3, constructing a detection model; S4, collecting raw GPS observations for the observation day, obtaining the first and second detection measurements for the observation day through step S2, wherein the first and second detection measurements for the observation day are combined with the first and second detection models respectively to perform multipath detection on frequencies L1 and L2, and outputting the first and second detection results; S5, combining the first and second detection results to correct satellites with multipath errors, and saving and outputting the corrected results, which can effectively overcome the problems of low detection accuracy caused by ignoring the influence of direct SNR signals and noise, and low multipath correction accuracy caused by using a single SNR weighted model.

Description

Technical Field

[0001] This invention relates to the field of high-precision navigation and positioning technology applications in global navigation satellite systems, specifically to a signal-to-noise ratio (SNR) multipath error correction method based on SNR reflected signals and an adaptive weighting strategy. Background Technology

[0002] The Global Positioning System (GPS) provides real-time, continuous positioning services. To achieve high-precision and real-time positioning accuracy and speed, effective elimination or correction of errors is necessary. Currently, common error sources have been effectively corrected or eliminated; for example, ionospheric and tropospheric errors can be eliminated using empirical models or differential techniques, and orbital errors can be corrected using precise ephemeris. However, multipath errors vary significantly with the environment, making them difficult to eliminate or correct effectively, and thus one of the main errors currently hindering high-precision navigation and positioning. Furthermore, data analysis shows that multipath can cause carrier phase errors at the centimeter or decimeter level, while errors in pseudorange observations can reach tens or even hundreds of meters. Therefore, proposing a real-time, efficient, and accurate multipath error correction method to effectively eliminate multipath error interference from pseudorange and carrier phase observations, thereby improving navigation and positioning accuracy and speed, is one of the urgent problems to be solved in the field of high-precision navigation and positioning applications using GPS.

[0003] Currently, methods for GPS multipath error correction can be mainly divided into two categories. The first category involves hardware-level correction, such as designing multi-array antennas to suppress multipath errors during signal reception, or designing vector tracking loops to suppress multipath errors during signal processing. However, this type of algorithm requires hardware upgrades, which is costly, difficult, and unsuitable for low-cost receivers. The second category is based on post-processing algorithms for multipath error correction, which can be further divided into three types: The first type is a multipath error correction method based on time-domain stellar filtering. This method utilizes the repeating period characteristics of GPS satellites to model the multipath error of the static receiver on the reference day (i.e., the day before the observation day), and then uses broadcast ephemeris or correlation analysis to calculate the satellite repeating period deviation to correct the multipath error of the observations. Although this algorithm has good real-time performance, it is greatly affected by satellite orbital maneuvers, and at low sampling rates, it cannot determine the precise time deviation, which also leads to reduced accuracy. The second type is a multipath error correction method based on spatial elevation angle and azimuth angle model search. This method leverages the spatial invariance of multipath error in a static environment to model the receiver's multipath error in the spatial domain using elevation and azimuth angles. While this method offers high accuracy, the large amount of subsequent search results leads to low computational efficiency, and it is also highly dependent on the model's resolution.

[0004] Furthermore, utilizing the direct correlation between multipath error and signal-to-noise ratio (SNR) for multipath error detection and correction can effectively overcome problems such as satellite maneuvering, low data sampling rates, and large algorithm search requirements. However, existing SNR-based methods mainly use SNR observations directly for detection, ignoring the influence of direct signals and noise. Noise in multipath environments is often severe, leading to low accuracy in multipath error detection. In addition, existing methods neglect the correlation between elevation angle and multipath error when correcting multipath errors, resulting in reduced correction accuracy. All of these factors severely impact the detection and correction of multipath errors. Summary of the Invention

[0005] This invention proposes a multipath correction method based on signal-to-noise ratio reflected signals and adaptive weighting, which can effectively overcome the problems of low detection accuracy caused by ignoring the influence of signal-to-noise ratio direct signals and noise, and low multipath correction accuracy caused by using a single signal-to-noise ratio weighting model.

[0006] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows:

[0007] A multipath correction method based on signal-to-noise ratio reflected signal and adaptive weighting includes the following steps:

[0008] S1. Collect a wide range of raw GPS observations in environments without multipath, including raw signal-to-noise ratio, raw pseudorange, and raw carrier, and calculate the corresponding elevation angle, azimuth angle, and epoch time interval.

[0009] S2, Data Preprocessing

[0010] S2-1. Use a Hermite polynomial curve fitting algorithm to eliminate direct signal-to-noise ratio signals;

[0011] S2-2. A wavelet transform algorithm based on root mean square error constraint is used to filter out high-frequency noise, thereby obtaining a signal-to-noise ratio reflection signal that has removed the influence of direct signal and high-frequency noise, i.e., the first probe measurement.

[0012] S2-3. Using a linear-to-periodic model, a periodic signal-to-noise ratio reflected signal is obtained;

[0013] S2-4. Perform inter-epoch difference calculation on the periodic signal-to-noise ratio reflected signal to obtain the second probe measurement.

[0014] S3. Constructing a detection model

[0015] The establishment of the first detection model involves dividing the data by satellite and frequency, and storing the first detection measurements in the form of a database on the local computer according to the elevation and azimuth information, thus forming the first detection model.

[0016] The second detection model was established by dividing the data into satellites and frequencies, and storing the second detection measurements in the form of a database on the local computer according to the elevation and azimuth information, thus forming the second detection model.

[0017] S4. Collect the raw GPS observation values ​​of the observation day. After step S2, obtain the first and second probe measurements of the observation day. The first and second probe measurements of the observation day are combined with the first and second probe models to perform multipath detection on the L1 and L2 frequencies respectively, and output the first and second probe results.

[0018] S5, combining the first and second detection results, corrects satellites with multipath errors, and saves and outputs the corrected results.

[0019] Preferably, the method for eliminating the direct signal-to-noise ratio signal in step S2-1 is as follows:

[0020] S2-1-1 Establishing a Hermite polynomial curve fitting algorithm n The expression for a polynomial curve of order 1 is as follows:

[0021] Hermite orthogonal polynomials are represented as:

[0022] (1)

[0023] In the formula, n Indicates the order, H n ( x ) for Hermite n An orthogonal polynomial of order 1, where exp represents the exponentiation operation. d To represent the differential,

[0024] Hermite polynomials in x The condition for orthogonality on (-∞, +∞) is:

[0025] (2)

[0026] In the formula, ! represents the factorial operation. m and n Both represent the order and have the same length. π Since is a constant, the recurrence formula for this polynomial is expressed as:

[0027] (3)

[0028] In the formula, n The order is represented by the above formula, which can be used to obtain the Hermite orthogonal polynomial expression for the corresponding order.

[0029] S2-1-2. Establish a fitting model for the Hermite polynomial, specifically expressed as follows: The Hermite polynomial curve fitting formula is expressed as:

[0030] (4)

[0031] In the formula, f p ( x )for x The fitted value at time 10:00. H n ( x )yes n Hermite orthogonal polynomial of order 1 a n These are the weight coefficients of the Hermite orthogonal polynomial;

[0032] S2-1-3, Using the fitting coefficients a n and n The fitted value at the corresponding time step is obtained by using the Hermite polynomial curve of order 1. f p ( x Subtracting the fitted value from the original signal-to-noise ratio (SNR) observations yields the observations free from the influence of the direct signal, expressed as:

[0033] (5)

[0034] In the formula, f o-p ( x This refers to the signal-to-noise ratio reflected signal after removing the influence of the direct signal-to-noise ratio.

[0035] Preferably, the method for filtering high-frequency noise in step S2-2 is as follows;

[0036] S2-2-1. Decompose the signal-to-noise ratio reflection signal obtained after step S2-1 by wavelet transform to obtain the wavelet coefficients to be denoised.

[0037] S2-2-2. Denoising the wavelet coefficients after decomposition is performed by selecting the optimal denoising threshold and decomposition level using a threshold and hierarchical strategy based on root mean square constraints.

[0038] The wavelet coefficients are denoised using a threshold denoising formula, specifically expressed as follows:

[0039] (6)

[0040] In the formula, W j,t Represents the original wavelet coefficients. Represents the wavelet coefficients after denoising. α for sign(˙) represents the sign function. j Indicates a decomposition layer. t λ represents a sequence node, and λ represents the threshold.

[0041] S2-2-3. The denoised wavelet coefficients are reconstructed using inverse wavelet transform to obtain the denoised signal-to-noise ratio reflection signal. The reconstruction process is as follows:

[0042] (7)

[0043] In the formula, f o-p-n ( x This is the denoised signal. j Indicates the number of decomposition layers. The wavelet transform scaling function is... It is the wavelet mother function of wavelet transform. After denoising using wavelet transform based on root mean square constraints, an accurate signal-to-noise ratio reflection signal is obtained, i.e. f o-p-n ( x This is the first probe measurement.

[0044] Preferably, step S2-2-2 further includes the following step:

[0045] To improve denoising accuracy, the root mean square (RMS) of the signal is first calculated, then the RMS is used to constrain the denoising threshold, and adaptive layering is performed. The RMS calculation process is as follows:

[0046] (8)

[0047] In the formula, Rms Represents the root mean square of the signal. N Indicates the total length of the signal. x This represents the value of each signal.

[0048] Therefore, in the expression for wavelet coefficient denoising... l The calculation formula can be expressed as:

[0049] (9)

[0050] In the formula, median(˙) represents taking the middle value of the sequence. N Indicates signal length. Rms Represents the root mean square of the signal.

[0051] In addition, the decomposition layer j It also needs to be based on Rms The size is set adaptively.

[0052] Preferably, the expression for the linear-to-periodic model in step S2-3 is as follows:

[0053] (10)

[0054] In the formula, f o-p-n ( x The signal obtained in step S2-2-3 that contains only the signal-to-noise ratio of the reflected signal is expressed in dB-Hz. f c ( x The signal-to-noise ratio reflected signal, in volts / volts, is obtained after the linear-to-periodic model.

[0055] Preferably, the method for detection using the first detection model in step S4 is as follows:

[0056] S4-1. Based on the satellite number, frequency, elevation angle, and azimuth angle information recorded in the first probe measurement on the observation day, search for the corresponding signal-to-noise ratio (SNR) reflection signal in the first probe model. If the error range between the elevation angle and azimuth angle in the probe model and the elevation angle and azimuth angle at the epoch of the current observation day is within 0.5 degrees, then the SNR reflection signal in the first probe model can be used as the reference value for the current probe. If the difference between the elevation angle and azimuth angle and the elevation angle and azimuth angle in the first probe model is greater than 0.5 degrees, then the corresponding SNR reflection signal is calculated using the Lagrange interpolation method and used as the reference value for the current probe.

[0057] S4-2. Compare the first detection result with the signal-to-noise ratio reflection signal reference value obtained in step S4-1. If the difference between the two results is greater than 1 dB-Hz, the first detection result has a multipath error and is marked; otherwise, it is not marked.

[0058] S4-3. Combine the signal-to-noise ratio reflection signals of two frequencies, namely L1 and L2, to detect multipath error. If both frequencies are marked, then the epoch is considered to have multipath error and the epoch is marked; otherwise, it is not marked.

[0059] Preferably, the expression for the Lagrange interpolation method in step S4-1 is as follows:

[0060] (11)

[0061] In the formula, e Indicates the satellite's elevation angle. i and p The sequence number represents a known quantity in the first detection model. e kThis represents the currently calculated elevation angle. Indicates the elevation angle as e The corresponding signal-to-noise ratio of the reflected signal at that time, due to e i , e p , e k and X ( e i Since all of these are known quantities, the elevation angle can be calculated as follows: e k The signal-to-noise ratio of the reflected signal is the reference value at that time.

[0062] Preferably, the method for detection using the second detection model in step S4 is as follows:

[0063] S4-4. Based on the satellite number, frequency, elevation angle, and azimuth angle information recorded in the second probe measurement on the observation day, search for the corresponding periodic signal-to-noise ratio (SNR) reflection signal epoch difference value in the second probe model. If the error range between the elevation angle and azimuth angle in the probe model and the elevation angle and azimuth angle at the current epoch of the observation day is within 0.5 degrees, then the periodic SNR reflection signal epoch difference value in the second probe model can be used as the reference value for the current probe. However, if the difference between the elevation angle and azimuth angle and the elevation angle and azimuth angle in the second probe model is greater than 0.5 degrees, then the corresponding periodic SNR reflection signal epoch difference value is calculated using the Lagrange interpolation method and used as the reference value for the current probe.

[0064] S4-5. Compare the second detection result with the epoch difference reference value of the periodic signal-to-noise ratio reflected signal obtained in step S4-4. If the difference is greater than 1 Volts / Volts, the second detection result has a multipath error and is marked; otherwise, it is not marked.

[0065] S4-6. Combine the signal-to-noise ratio reflection signals of two frequencies, namely L1 and L2, to detect multipath error. If both frequencies are marked, then the epoch is considered to have multipath error and the epoch is marked; otherwise, it is not marked.

[0066] Preferably, in step S5, based on the detection results of step S4, if both the first and second detection results are marked, then the epoch of the observation day has a multipath error, and an adaptive weighting strategy based on correlation analysis is used to correct the multipath error; otherwise, it is considered that there is no multipath and no correction is performed.

[0067] Preferably, in step S5, the correction method is as follows:

[0068] S5-1. Extracting single-frequency pseudorange multipath error using the code phase method.

[0069] (12)

[0070] In the formula, CP This represents the phase combination of a single-frequency pseudorange code. P These are pseudorange observations. For carrier phase observations, P and These are known quantities, obtained directly from the original observations. For frequency wavelength, for CP The mean of the quantity, i Represents a sequence. CM This represents the pseudorange multipath error obtained after mean sliding;

[0071] S5-2. The correlation between pseudorange multipath error and signal-to-noise ratio reflected signal, as well as the correlation between pseudorange multipath error and elevation angle, are calculated using three correlation analysis methods: Pearson correlation analysis, Spearman correlation analysis, and Kendall correlation analysis. The mean values ​​of the three results are then calculated to obtain the correlation analysis results.

[0072] S5-3. Using the correlation analysis results, adaptively determine the optimal weighting strategy to correct multipath errors. If the correlation between the signal-to-noise ratio (SNR) reflected signal and the multipath error is greater than the correlation between the elevation angle and the multipath error, then use the SNR reflected signal weighting model to correct the multipath error. The specific weighting model is expressed as follows:

[0073] (13)

[0074] In the formula, f o-p-n ( x i ) indicates the first i The signal-to-noise ratio of the reflected signal at each epoch s This indicates the precision of the epoch, used for weighted processing of that epoch.

[0075] If the correlation between the signal-to-noise ratio reflected signal and the multipath error is less than the correlation between the elevation angle and the multipath error, then an elevation angle-weighted model is used to correct the multipath error. The specific weighted model is expressed as follows:

[0076] (14)

[0077] In the formula, e ( i ) indicates the first i The satellite elevation angle of each epoch. sThis indicates the precision of the epoch and is used for weighted processing of that epoch.

[0078] This invention has the following characteristics and beneficial effects:

[0079] By employing the above technical solution and the method described in this invention, multipath errors of GPS satellites are detected using the epoch-time difference between the signal-to-noise ratio (SNR) reflected signal and the periodic SNR reflected signal. An adaptive weighting strategy based on correlation analysis is then used to correct the multipath errors. Compared to existing methods, this approach solves problems such as low detection accuracy or detection failure caused by ignoring the influence of direct SNR signals and noise, and also addresses the low multipath correction accuracy caused by using a fixed single weighting strategy. Furthermore, joint detection using the epoch-time difference between the SNR reflected signals of dual-frequency GPS signals and the periodic SNR reflected signal ensures detection success rate and stability, thus meeting the requirements for high-precision, high-real-time, and high-stability multipath error detection and correction. Considering the low detection accuracy caused by the original direct SNR signal, the Hermite polynomial curve fitting method is used to eliminate the direct signal in the original SNR observations, reducing its influence. A wavelet transform algorithm based on root mean square error constraints is used to filter out high-frequency random noise and extract high-precision SNR reflected signals, ensuring detection accuracy. A linear-to-periodic model is used to periodize the linear signal-to-noise ratio (SNR) reflected signal, resulting in a periodic SNR reflected signal. Then, inter-epoch subtraction is performed on the periodized SNR reflected signal to obtain a second probe measurement. Using two probe measurements simultaneously ensures detection accuracy and stability. A Lagrange interpolation algorithm is employed to calculate non-sampling point data, overcoming issues such as low data sampling rates. A code phase combination method is used to calculate pseudorange multipath error, and three correlation analysis methods are used to analyze the correlation between multipath error, SNR reflected signal, and elevation angle. An adaptive weighting strategy is used to correct multipath error, overcoming the low accuracy of fixed weighting strategies and ensuring the success rate and accuracy of multipath error detection and correction. Attached Figure Description

[0080] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0081] Figure 1 This is a multipath error detection model based on signal-to-noise ratio reflected signals in this embodiment of the invention;

[0082] Figure 2This is a flowchart of a multipath correction method based on signal-to-noise ratio reflected signals and an adaptive weighting strategy in an embodiment of the present invention. Detailed Implementation

[0083] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0084] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0085] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0086] This invention provides a multipath correction method based on signal-to-noise ratio reflected signals and adaptive weighting, such as... Figure 1 and Figure 2 As shown, it includes the following steps:

[0087] S1. Extensively collect raw GPS observations under multipath-free conditions. These raw GPS observations include the raw signal-to-noise ratio, raw pseudorange, and raw carrier wave, and calculate the corresponding elevation angle, azimuth angle, and epoch time interval. Understandably, a standard geodetic receiver is used to continuously collect raw GPS observations under conditions without multipath error (i.e., good observation conditions and no signal obstruction), providing support for subsequent establishment of multipath detection models and correction algorithms.

[0088] S2. Data Preprocessing: To address the impact of direct signal-to-noise ratio (SNR) signals, a Hermite polynomial curve fitting method is used to eliminate direct signals from the original SNR observations, ensuring a high data quality rate. To mitigate the impact of noise, a wavelet transform algorithm based on root mean square error constraints is used to filter out high-frequency random noise and extract a high-precision SNR reflection signal as the first probe measurement to detect multipath errors. Secondly, a linear-to-periodic model is used to convert the linear SNR reflection signal into a periodic signal, and the difference is calculated between epochs as the second probe measurement, further improving the detection accuracy and precision of multipath errors.

[0089] Specifically:

[0090] S2-1. The Hermite polynomial curve fitting algorithm is used to eliminate the signal-to-noise ratio direct signal.

[0091] S2-1-1 Establishing a Hermite polynomial curve fitting algorithm n The expression for a polynomial curve of order 1 is as follows:

[0092] Hermite orthogonal polynomials are represented as:

[0093] (15)

[0094] In the formula, n Indicates the order, H n ( x ) for Hermite n An orthogonal polynomial of order 1, where exp represents the exponentiation operation. d To represent a differential, for example, the above expression can be expressed as: (The expression is incomplete and requires further context to be fully translated.) x beg n The first derivative.

[0095] Hermite polynomials in x The condition for orthogonality on (-∞, +∞) is:

[0096] (16)

[0097] In the formula, ! represents factorial operation, which is common knowledge in the field of mathematics. m and n Both letters represent the order and have the same length. The reason for using two letters here is mainly to distinguish different orders in orthogonal multiplication. π Since is a constant, the recurrence formula for this polynomial is expressed as:

[0098] (17)

[0099] In the formula, nThe order is represented by the above formula, which can be used to obtain the Hermite orthogonal polynomial expression for the corresponding order.

[0100] S2-1-2. Establish a fitting model for the Hermite polynomial, specifically expressed as follows: The Hermite polynomial curve fitting formula is expressed as:

[0101] (18)

[0102] In the formula, f p ( x )for x The fitted value at time 10:00. H n ( x )yes n Hermite orthogonal polynomial of order 1 a n These are the weight coefficients of the Hermite orthogonal polynomial.

[0103] As one can imagine, the weighting coefficients a n The solution can be obtained using the least squares algorithm, and the solution process is as follows:

[0104] Assumption f o ( x ) represents x The original sampled value at time point S1, that is, the original signal-to-noise ratio observation value obtained in step S1. If f p ( x It can achieve an overall approximation of the actual sampled value at any given time. f o ( x If the result is the same, then the squared error is minimized, and it can be expressed as:

[0105] (19)

[0106] In the formula, M Indicates the total length of the data. k This represents a data sequence. Wherein, f o ( x ) represents x The sampled value at time 1 is a known quantity. That is, the original signal-to-noise ratio observation value obtained in the first step. H n ( x )yes n The Hermite orthogonal polynomial of order 1 can be obtained from formulas (15-17) and is also a known quantity. Therefore, the coefficients of the above formula can be obtained by the least squares algorithm. an Since the least squares algorithm is a commonly used algorithm, it will not be described in detail here.

[0107] S2-1-3, Using the fitting coefficients a n and n The fitted value at the corresponding time step is obtained by using the Hermite polynomial curve of order 1. f p ( x Subtracting the fitted value from the original signal-to-noise ratio (SNR) observations yields the observations free from the influence of the direct signal, expressed as:

[0108] (20)

[0109] In the formula, f o-p ( x This refers to the signal-to-noise ratio reflected signal after removing the influence of the direct signal-to-noise ratio.

[0110] S2-2. A wavelet transform algorithm based on root mean square error constraint is used to filter out high-frequency noise, thereby obtaining a signal-to-noise ratio reflection signal that has removed the influence of direct signal and high-frequency noise, which is the first probe measurement.

[0111] S2-2-1. The signal-to-noise ratio reflection signal obtained after step S2-1 is decomposed by wavelet transform to obtain the wavelet coefficients to be denoised.

[0112] Specifically, its wavelet transform decomposition process is represented as follows:

[0113] (twenty one)

[0114] In the formula, The orthogonal scaling function of the wavelet transform is represented by . is the wavelet function of the wavelet transform. t For continuous time variable sequences, n It represents a discrete-time variable sequence. It represents the signal from the previous level, and the original signal during initial calculation. The wavelet transform scaling function is... It is the wavelet mother function of the wavelet transform, and the two satisfy the following relationship:

[0115]

[0116] Assumption and If it is established, then... The following recursive relationship can be obtained at this time:

[0117] (twenty two)

[0118] The above equation represents the wavelet decomposition of the signal. It should be noted that the original signal, after wavelet transform, can only be decomposed into one low-frequency and one high-frequency signal each time. To improve denoising accuracy, the low-frequency signal needs to be re-decomposed, thus requiring iteration.

[0119] S2-2-2. Denoising the wavelet coefficients after decomposition is performed by selecting the optimal denoising threshold and decomposition level using a threshold and hierarchical strategy based on root mean square constraints.

[0120] The wavelet coefficients are denoised using a threshold denoising formula, specifically expressed as follows:

[0121] (twenty three)

[0122] In the formula, W j,t Represents the original wavelet coefficients. Represents the wavelet coefficients after denoising. α for sign(˙) represents the sign function. j Indicates a decomposition layer. t Let λ represent a continuous time variable sequence, and let λ represent the threshold.

[0123] Furthermore, to improve denoising accuracy, the root mean square (RMS) of the signal is first calculated, then the RMS is used to constrain the denoising threshold, and adaptive layering is performed. The RMS calculation process is as follows:

[0124] (twenty four)

[0125] In the formula, Rms Represents the root mean square of the signal. N Indicates the total length of the signal. x This represents the value of each signal.

[0126] Therefore, in the expression for wavelet coefficient denoising... l The calculation formula can be expressed as:

[0127] (25)

[0128] In the formula, median(˙) represents taking the middle value of the sequence. N Indicates signal length. Rms The root mean square (RMS) of the signal is represented by the above-mentioned RMS constraint strategy, which can effectively improve the denoising effect.

[0129] In addition, the decomposition layer j It also needs to be based on Rms The size is adaptively set. In this embodiment, the calculation is performed under good observation conditions. Rms This is set as the reference value. If the currently processed signal... Rms If the value and the reference value remain within a 10% fluctuation range, then a 3-level decomposition is set, i.e. j =3. If the current signal Rms If the value is 10%-50% greater than the reference value, then j Set to 4 layers. If it exceeds 50%, then... j Set to 5 layers. Similarly, if it's less than 10%-50%, then... j Set to 2 layers. If it is less than 50%, then... j Set to level 1. This improves wavelet decomposition efficiency and denoising accuracy.

[0130] S2-2-3. The denoised wavelet coefficients are reconstructed using inverse wavelet transform to obtain the denoised signal-to-noise ratio reflection signal. The reconstruction process is as follows:

[0131] (26)

[0132] In the formula, f o-p-n ( x This is the denoised signal. j Indicates the number of decomposition layers. The wavelet transform scaling function is... It is the wavelet mother function of wavelet transform. After denoising using wavelet transform based on root mean square constraints, an accurate signal-to-noise ratio reflection signal is obtained, i.e. f o-p-n ( x This is the first probe measurement.

[0133] S2-3. Using a linear-to-periodic model, a periodic signal-to-noise ratio reflected signal is obtained;

[0134] The expression for the linear-to-period model is as follows:

[0135] (27)

[0136] In the formula, f o-p-n ( x The signal obtained in step S2-2-3 that contains only the signal-to-noise ratio of the reflected signal is expressed in dB-Hz. f c ( x The signal-to-noise ratio reflected signal, in volts / volts, is obtained after the linear-to-periodic model.

[0137] S2-4. Perform inter-epoch difference calculation on the periodic signal-to-noise ratio reflection signal to obtain the second probe measurement.

[0138] The calculation formula is as follows:

[0139] (28)

[0140] In the formula, f c ( x () is a periodic signal-to-noise ratio reflected signal. i Represents a signal sequence. f d ( x The difference between two adjacent epochs is represented by ). It should be noted that since this difference algorithm is backward difference, that is, the difference is calculated by subtracting the previous epoch from the current epoch. For the first epoch, since there are no previous epoch values ​​to be differenced, the first epoch is not recorded, and the recording starts directly from the second epoch.

[0141] S3. Constructing a detection model

[0142] The establishment of the first detection model involves dividing the data by satellite and frequency, and storing the first detection measurements in the form of a database on the local computer according to the elevation and azimuth information, thus forming the first detection model.

[0143] The second detection model was established by dividing the data into satellites and frequencies, and storing the second detection measurements in the form of a database on the local computer according to the elevation and azimuth information, thus forming the second detection model.

[0144] It should be noted that elevation angle and azimuth angle are basic knowledge in this field and will not be discussed in detail here.

[0145] S4. Collect the original GPS observation values ​​of the observation day. After step S2, obtain the first and second probe measurements of the observation day. The first and second probe measurements of the observation day are combined with the first and second probe models to perform multipath detection on the L1 and L2 frequencies respectively, and output the first and second probe results.

[0146] The specific detection method of the first detection model is as follows:

[0147] S4-1. Based on the satellite number, frequency, elevation angle, and azimuth angle information recorded in the first probe measurement on the observation day, search for the corresponding signal-to-noise ratio (SNR) reflection signal in the first probe model. If the error range between the elevation angle and azimuth angle in the probe model and the elevation angle and azimuth angle at the epoch of the current observation day is within 0.5 degrees, then the SNR reflection signal in the first probe model can be used as the reference value for the current probe. If the difference between the elevation angle and azimuth angle and the elevation angle and azimuth angle in the first probe model is greater than 0.5 degrees, then the corresponding SNR reflection signal is calculated using the Lagrange interpolation method and used as the reference value for the current probe.

[0148] The expression for Lagrange interpolation is as follows:

[0149] (29)

[0150] In the formula, e Indicates the satellite's elevation angle. i and p The sequence number represents a known quantity in the first detection model. e k This represents the currently calculated elevation angle. Indicates the elevation angle as e The corresponding signal-to-noise ratio of the reflected signal at that time, due to e i , e p , e k and X ( e i Since all of these are known quantities, the elevation angle can be calculated as follows: e k The signal-to-noise ratio of the reflected signal is the reference value at that time.

[0151] In this example, the meaning of the above formula can be interpreted as follows: Suppose we calculate the elevation angle and signal-to-noise ratio (SNR) of the current probe epoch as (25 degrees, 30 dB-Hz), but the closest values ​​in the probe model database are (24 degrees, 28 dB-Hz) and (26 degrees, 32 dB-Hz). In this case, we need to use the Lagrange interpolation method to find the SNR reference value of the probe model when the elevation angle is 25 degrees, so as to probe the current epoch.

[0152] S4-2. Compare the first detection result with the signal-to-noise ratio reflection signal reference value obtained in step S4-1. If the difference between the two results is greater than 1 dB-Hz, the first detection result has a multipath error and is marked; otherwise, it is not marked.

[0153] S4-3. Combine the signal-to-noise ratio reflection signals of two frequencies, namely L1 and L2, to detect multipath error. If both frequencies are marked, then the epoch is considered to have multipath error and the epoch is marked; otherwise, it is not marked.

[0154] It should be noted that L1 and L2 are common knowledge in the GPS field, so they will not be specifically described in this embodiment.

[0155] The specific method for detection using the second detection model is as follows:

[0156] S4-4. Based on the satellite number, frequency, elevation angle, and azimuth angle information recorded in the second probe measurement on the observation day, search for the corresponding periodic signal-to-noise ratio (SNR) reflection signal epoch difference value in the second probe model. If the error range between the elevation angle and azimuth angle in the probe model and the elevation angle and azimuth angle at the current epoch of the observation day is within 0.5 degrees, then the periodic SNR reflection signal epoch difference value in the second probe model can be used as the reference value for the current probe. However, if the difference between the elevation angle and azimuth angle and the elevation angle and azimuth angle in the second probe model is greater than 0.5 degrees, then the corresponding periodic SNR reflection signal epoch difference value is calculated using the Lagrange interpolation method and used as the reference value for the current probe.

[0157] S4-5. Compare the second detection result with the epoch difference reference value of the periodic signal-to-noise ratio reflected signal obtained in step S4-4. If the difference is greater than 1 Volts / Volts, the second detection result has a multipath error and is marked; otherwise, it is not marked.

[0158] S4-6. Combine the signal-to-noise ratio reflection signals of two frequencies, namely L1 and L2, to detect multipath error. If both frequencies are marked, then the epoch is considered to have multipath error and the epoch is marked; otherwise, it is not marked.

[0159] S5 combines the first and second detection results to correct the satellites with multipath errors, and then maintains and outputs the corrected results.

[0160] Specifically, based on the detection results of step S4, if both the first and second detection results are marked, then the epoch of the observation day has a multipath error. An adaptive weighting strategy based on correlation analysis is used to correct the multipath error; otherwise, it is assumed that there is no multipath and no correction is performed.

[0161] Furthermore, the correction method is as follows:

[0162] S5-1. Extracting single-frequency pseudorange multipath error using the code phase method.

[0163] (30)

[0164] In the formula, CP This represents the phase combination of a single-frequency pseudorange code. P These are pseudorange observations. For carrier phase observations, P and These are known quantities, obtained directly from the original observations. The wavelength is a common knowledge in this field; for example, the wavelength of the L1 frequency of GPS satellites is 19.0 cm. for CP The mean of the quantity, i Represents a sequence. CM This represents the pseudorange multipath error obtained after mean sliding;

[0165] S5-2. The correlation between pseudorange multipath error and signal-to-noise ratio reflected signal, as well as the correlation between pseudorange multipath error and elevation angle, are calculated using three correlation analysis methods: Pearson correlation analysis, Spearman correlation analysis, and Kendall correlation analysis. The average of the three results is then calculated to obtain the correlation analysis results.

[0166] Specifically, Pearson correlation analysis. The formula for calculating the correlation coefficient is:

[0167] (31)

[0168] In the formula, r This is the correlation coefficient that needs to be calculated. X and Y This represents two quantities used to solve for correlation, such as the multipath error and signal-to-noise ratio reflected signal in this case, or the multipath error and the corresponding elevation angle. and They are X and Y The average of two quantities. n express X and Y The lengths of the two are equal, and are both represented as... n . i The index represents the sequence number. The Pearson correlation coefficient can be calculated using the above formula, ranging from -1 to 1. A value of 1 indicates a perfect positive correlation, meaning the two sequences are identical. A value of -1 indicates a perfect negative correlation, meaning the vectors are completely opposite. A value of 0 indicates no correlation.

[0169] The second method: Spearman correlation analysis. The formula for calculating the correlation coefficient is:

[0170] (32)

[0171] In the formula, r This is the Spearman correlation coefficient that needs to be calculated. X and Y Let represent two quantities for solving the correlation problem. Rank(˙) means to calculate the rank, which is common knowledge in the field of linear algebra. n express X and Y The lengths of the two are equal, and are both represented as... nThe Spearman correlation coefficient can be calculated using the above formula, ranging from -1 to 1. A value of 1 indicates a perfect positive correlation, meaning the two sequences are identical. A value of -1 indicates a perfect negative correlation, meaning the vectors are completely opposite. A value of 0 indicates no correlation.

[0172] The third method: Kendall correlation analysis. The formula for calculating the correlation coefficient is:

[0173] (33)

[0174] Calculated by the following formula

[0175] (34)

[0176] In the formula, r This is the correlation coefficient that needs to be calculated. X and Y These represent the two quantities used to solve for correlation. n express X and Y The lengths of the two are equal, and are both represented as... n . i and j The index represents the sequence number. The Kendall correlation coefficient can be calculated using the above formula, ranging from -1 to 1. A value of 1 indicates a perfect positive correlation, meaning the two sequences are identical. A value of -1 indicates a perfect negative correlation, meaning the vectors are completely opposite. A value of 0 indicates no correlation.

[0177] Calculate the mean values ​​of the three correlation coefficients for multipath error and signal-to-noise ratio (SNR) reflected signal, and the mean values ​​of the three correlation coefficients for multipath error and elevation angle. Obtain the correlation analysis results, i.e., which variable (SNR reflected signal and elevation angle) has the strongest correlation with multipath error.

[0178] S5-3. Using the correlation analysis results, adaptively determine the optimal weighting strategy to correct multipath errors. If the correlation between the signal-to-noise ratio (SNR) reflected signal and the multipath error is greater than the correlation between the elevation angle and the multipath error, then use the SNR reflected signal weighting model to correct the multipath error. The specific weighting model is expressed as follows:

[0179] (35)

[0180] In the formula, f o-p-n ( x i ) indicates the first i The signal-to-noise ratio of the reflected signal at each epoch s This indicates the precision of the epoch, used for weighted processing of that epoch, and is common knowledge in this field.

[0181] If the correlation between the signal-to-noise ratio reflected signal and the multipath error is less than the correlation between the elevation angle and the multipath error, then an elevation angle-weighted model is used to correct the multipath error. The specific weighted model is expressed as follows:

[0182] (36)

[0183] In the formula, e ( i ) indicates the first i The satellite elevation angle of each epoch. s This indicates the precision of the epoch, used for weighted processing of that epoch, and is common knowledge in this field.

[0184] After processing by the above multipath error detection and correction algorithm, the problems of low detection accuracy or method failure caused by ignoring the influence of direct signal and noise in existing signal-to-noise ratio-based methods can be effectively solved. It can also solve the problem of low correction accuracy based on fixed single weighting strategy, thus providing a guarantee for timely, accurate and efficient multipath error detection and correction.

[0185] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions, and variations can be made to these embodiments, including components, without departing from the principles and spirit of the present invention, and these variations still fall within the protection scope of the present invention.

Claims

1. A method of multipath correction based on signal-to-noise ratio reflection signals and adaptive weighting, characterized by, It comprises the following steps: S1, collecting GPS original observation values in a non-multipath environment, the GPS original observation values comprising original signal-to-noise ratio, original pseudorange and original carrier, and calculating corresponding elevation angle, azimuth angle and epoch time interval; S2, data preprocessing S2-1, eliminating direct signal of signal-to-noise ratio by using Hermite polynomial curve fitting algorithm; S2-2, filtering high-frequency noise by using wavelet transform algorithm based on root mean square error constraint, thereby obtaining signal-to-noise ratio reflection signal free from the influence of direct signal and high-frequency noise, i.e. first detection quantity; S2-3, obtaining periodized signal-to-noise ratio reflection signal by using linear-to-periodic model; S2-4, obtaining second detection quantity by epoch-to-epoch difference of the periodized signal-to-noise ratio reflection signal; S3, constructing detection model The first detection model is constructed by storing the first detection quantity in the form of database into a local computer according to elevation angle, azimuth angle information and by satellite and frequency; The second detection model is constructed by storing the second detection quantity in the form of database into a local computer according to elevation angle, azimuth angle information and by satellite and frequency; S4, collecting GPS original observation values of an observation day, obtaining first detection quantity and second detection quantity of the observation day by step S2, and performing multipath detection on L1 and L2 frequencies by combining the first detection model and the second detection model with the first detection quantity and the second detection quantity respectively, and outputting first detection result and second detection result; S5, correcting satellites with multipath error by combining the first detection result and the second detection result, and keeping and outputting the result after multipath error correction, In step S5, according to the detection result of step S4, if both the first detection result and the second detection result have a mark, it is considered that there is multipath error in the epoch of the observation day, and the multipath error is corrected by using an adaptive weighting strategy based on correlation analysis, otherwise it is considered that there is no multipath and no correction is performed; in step S5, the correction method is as follows: S5-1, extracting single-frequency pseudorange multipath error by using code phase method where CP represents the single-frequency pseudorange code-phase combination, P is the pseudorange observation, is the carrier phase observation, P and are known quantities, obtained directly from the raw observations, and λ is the frequency wavelength, is the mean of the CP quantities, i represents the sequence, and CM represents the pseudorange multipath error after smoothing by the mean. S5-2, calculating the correlation of pseudorange multipath error and signal-to-noise ratio reflection signal and the correlation of pseudorange multipath error and elevation angle by using Pearson correlation analysis method, Spearman correlation analysis method and Kendall correlation analysis method respectively, and obtaining correlation analysis result by averaging the three results respectively; S5-3, correcting multipath error by using the correlation analysis result to adaptively determine the best weighting strategy, if the correlation of signal-to-noise ratio reflection signal and multipath error is greater than the correlation of elevation angle and multipath error, the multipath error is corrected by using signal-to-noise ratio reflection signal weighting model, and the specific weighting model is represented as: In the formula, f o-p-n (x i ) represents the signal-to-noise ratio of the reflection signal of the i th epoch, and σ represents the precision at the time of the epoch, which is used for weighting processing of the epoch, if the correlation of signal-to-noise ratio reflection signal and multipath error is less than the correlation of elevation angle and multipath error, the multipath is corrected by using elevation angle weighting model, and the specific weighting model is represented as: Wherein, e(i) represents the satellite elevation angle of the i-th epoch, and sigma represents the accuracy at the time of the epoch, which is used for weighting processing of the epoch.

2. The method of claim 1, wherein, The method for eliminating the signal-to-noise ratio direct signal in the step S2-1 is as follows: S2-1-1, an n-order polynomial curve expression of the Hermite polynomial curve fitting algorithm is established, and is specifically expressed as follows: The Hermite orthogonal polynomial is expressed as: where n represents the order, H n (x) is the nth order orthogonal polynomial of Hermite, exp represents the exponential operation, d represents differentiation, The Hermite polynomial satisfies the orthogonal condition on x∈(-∞, +∞) and is expressed as: Wherein,! represents the factorial operation, m and n represent the order, and the length is the same, and π is a constant, and the recursive formula of the polynomial is expressed as: Wherein, n represents the order, and the Hermite orthogonal polynomial expression of the corresponding order can be obtained through the above formula; S2-1-2, a fitting model of the Hermite polynomial is established, and is specifically expressed as follows: the Hermite polynomial curve fitting formula is expressed as: where f p (x) is the fitted value at time x, H n (x) is the nth order Hermite orthogonal polynomial, a n is the weight coefficient of the Hermite orthogonal polynomial S2-1-3, using the fitting coefficient a n and the n-order Hermite polynomial curve to obtain the fitting value of the corresponding moment, and obtain the fitting value f of the corresponding moment p (x), subtract the fitting value from the original signal-to-noise ratio observation value, that is, the observation value after removing the influence of the signal-to-noise ratio direct signal, which is represented as: where f o-p (x) is the signal-to-noise ratio of the reflected signal without the influence of the signal-to-noise ratio of the direct signal.

3. The method of claim 2, wherein the method is based on a signal-to-noise ratio reflection signal and an adaptive weighting. In the step S2-2, the method for filtering out high-frequency noise is as follows: S2-2-1, the signal-to-noise ratio reflection signal obtained after the step S2-1 is decomposed through wavelet transform to obtain the wavelet coefficient to be denoised; S2-2-2, the optimal denoising threshold and the decomposition layer number are selected by using the threshold value based on the root mean square constraint and the hierarchical strategy to denoise the decomposed wavelet coefficient, The wavelet coefficient is denoised by using the threshold denoising formula, and is specifically expressed as: wherein W j,t denotes the original wavelet coefficients, denotes the wavelet coefficients after denoising, and α is sign(˙) denotes the sign function, j denotes the decomposition layer, t denotes the sequence node, and λ denotes the threshold value; S2-2-3, the wavelet coefficient after denoising is reconstructed by using the wavelet inverse transform to obtain the signal-to-noise ratio reflection signal after denoising, and the reconstruction process is expressed as follows: In the formula, f o-p-n (x) is the signal after denoising, j represents the number of decomposition layers, a(n) is a wavelet transform scale function, b(n) is a wavelet transform mother function, and after denoising based on the root mean square constraint, an accurate signal-to-noise ratio reflection signal f o-p-n (x) is the first detection quantity.

4. The method of claim 3, wherein, The step S2-2-2 further includes the following steps: In order to improve the denoising accuracy, the root mean square of the signal is calculated first, and then the root mean square is used to constrain the denoising threshold and perform adaptive hierarchical processing, and the root mean square calculation process of the signal is expressed as follows: Wherein, Rms represents the root mean square of the signal, N represents the total length of the signal, and x represents the value of each signal, Therefore, the calculation formula of λ in the expression of the wavelet coefficient denoising can be expressed as: Wherein, median(˙) represents the median value of the sequence, N represents the signal length, and Rms represents the root mean square of the signal, In addition, the decomposition layer j also needs to be adaptively set according to the size of Rms.

5. The method of claim 3, wherein the method is based on a signal-to-noise ratio reflection signal and an adaptive weighting. The expression of the linear-to-periodic model in the step S2-3 is as follows: where f o-p-n (x) is the signal containing only the reflected signal signal-to-noise ratio in dB-Hz, f c (x) is the periodic signal-to-noise ratio reflected signal in volts / volts after linear conversion to periodic model.

6. The method of claim 5, wherein the method is based on a signal-to-noise ratio reflection signal and an adaptive weighting. The method for detecting by using the first detection model in the step S4 is specifically as follows: S4-1, the corresponding signal-to-noise ratio reflection signal is searched from the first detection model according to the satellite number, frequency, elevation angle and azimuth angle information recorded in the first detection quantity of the observation day, if the elevation angle and azimuth angle error range of the epoch time of the current observation day in the first detection model is within 0.5 degrees, it is considered that the signal-to-noise ratio reflection signal in the first detection model can be used as the reference value of the current detection, and when the elevation angle and azimuth angle difference range of the first detection model is greater than 0.5 degrees, the corresponding signal-to-noise ratio reflection signal is calculated by using the Lagrange interpolation method as the reference value of the current detection. S4-2, compare the first detection quantity with the signal-to-noise ratio reflection signal reference value obtained in step S4-1, if the difference between the comparison results is greater than 1dB-Hz, the first detection result has multipath error, and is marked, otherwise, it is not marked; S4-3, combine the signal-to-noise ratio reflection signals of two frequencies, i.e. L1 and L2 frequencies, to detect the multipath error, if both frequencies are marked, it is considered that the epoch has multipath error, and the epoch is marked, otherwise, it is not marked.

7. The method of claim 6, wherein the method is based on a signal-to-noise ratio reflection signal and an adaptive weighting. The expression of the Lagrange interpolation method in step S4-1 is as follows: where e represents the satellite elevation angle, i and p represent the serial number, which are known quantities in the first detection model, e k represents the current calculated elevation angle, X(e) represents the signal-to-noise ratio of the reflected signal corresponding to the elevation angle e, since e i p k and X(e i ) are all known quantities, so the signal-to-noise ratio reference value of the reflected signal when the elevation angle is e k can be obtained.​​ 8. The method of claim 6, wherein the method is based on a signal-to-noise ratio reflection signal and an adaptive weighting. The method of detecting by the second detection model in step S4 is as follows: S4-4, search the corresponding periodic signal-to-noise ratio reflection signal epoch difference value from the second detection model according to the satellite number, frequency, elevation angle and azimuth angle information recorded in the second detection quantity of the observation day, if the elevation angle and azimuth angle error range of the current epoch time of the observation day in the second detection model is within 0.5 degrees, it is considered that the periodic signal-to-noise ratio reflection signal epoch difference value in the second detection model can be used as the reference value of the current detection, and when the difference between the elevation angle and azimuth angle and the elevation angle and azimuth angle in the second detection model is greater than 0.5 degrees, the corresponding periodic signal-to-noise ratio reflection signal epoch difference value is calculated by the Lagrange interpolation method as the reference value of the current detection; S4-5, compare the second detection quantity with the periodic signal-to-noise ratio reflection signal epoch difference value reference value obtained in step S4-4, if the difference between the comparison results is greater than 1Volts / Volts, the second detection result has multipath error, and is marked, otherwise, it is not marked; S4-6, combine the signal-to-noise ratio reflection signals of two frequencies, i.e. L1 and L2 frequencies, to detect the multipath error, if both frequencies are marked, it is considered that the epoch has multipath error, and the epoch is marked, otherwise, it is not marked.

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