A pseudo-range measurement positioning method with random error correction

Abstract

The present invention designs a pseudo-range measurement and positioning method with random error correction. The method comprises the following steps: firstly, parsing a received observation file to obtain parameters required for positioning solution; and parsing a received ephemeris file to calculate the satellite positions of Beidou navigation; a receiver calculates the spatial coordinates of each navigation satellite using the orbital parameters in the ephemeris file; constructing a zero-phase filtering pseudo-range differential positioning equation based on the zero-phase filtering principle; linearizing the pseudo-range differential equation after random error correction to calculate the pseudo-range differential error equation; processing the pseudo-range differential error equation after random error correction based on a least squares estimation model to solve the observation station coordinates; eliminating the random error-incapable-to-correct mathematical model-based and occasional pulse interference in the pseudo-range observation value, and also eliminating random errors including other periodic interferences, filtering out high-frequency thermal noise in the observation noise, and applying the method to fields requiring precise positioning such as military, ports and autonomous driving to achieve sub-meter positioning.

Description

Technical Field

[0001] The present invention relates to the fields of communication technology and satellite navigation positioning, and in particular to a pseudo-range measurement positioning method with random error correction. Background Art

[0002] As one of the world's four major satellite navigation and positioning systems, the BeiDou Navigation Satellite System (BDS) has expanded from serving only China to serving the world, and has been successfully applied in numerous fields, including modern transportation, smart agriculture, national forestry management, marine fisheries, public security, disaster prevention and mitigation, power supply maintenance, and financial stability. Pseudorange positioning, a positioning technology within the BDS, has been widely researched and applied due to its simplicity, high speed, and lack of ambiguity. It estimates the position and clock bias of an observation station using only the ranging codes broadcast by navigation satellites. However, current global satellite navigation systems, including BDS, are subject to errors such as satellite orbits, satellite clock errors, space propagation, and the ground environment, which can lead to deviations in satellite positioning and low positioning accuracy. Therefore, correcting for these errors has always been a key technology for pseudorange positioning in BDS navigation, significantly impacting its application and industrial development. Summary of the Invention

[0003] Aiming at the influence of receiver clock error and random errors including noise in the process of Beidou navigation pseudo-range differential positioning, the present invention constructs a pseudo-range measurement positioning method with random error correction, which combines median average filtering, householder transformation and zero-phase filtering to eliminate the occasional pulse interference in the pseudo-range observation value that cannot be completely corrected by mathematical models, and also eliminates random errors including other periodic interferences. It eliminates the receiver clock error while suppressing the expansion of observation noise and filtering out high-frequency thermal noise in the observation noise. It considers the problem of low positioning accuracy caused by the traditional positioning solution method when all visible satellite observations are processed equally; it is applied to many application fields requiring precise positioning, such as military, ports and autonomous driving, to achieve sub-meter positioning requirements.

[0004] A pseudo-range measurement positioning method with random error correction specifically comprises the following steps:

[0005] Step 1: Parse the received observation file to obtain the parameters required for positioning solution;

[0006] Get the current observation time of the base station and observation station through the observation file , the number of visible satellites at the current observation time ; The number of satellites observed by the base station and the observation station at the same time is ,and ; Pseudorange observation values ​​of satellites visible to the base station and the observation station at the current moment ,in ;

[0007] Step 2: Analyze the received ephemeris file and calculate the satellite positions of Beidou navigation according to the Beidou navigation ICD standard; the receiver uses the orbital parameters in the ephemeris file to calculate the spatial coordinates of each navigation satellite ;

[0008] Step 3: Based on the pseudo-range differential positioning principle, derive the pseudo-range single difference positioning equation;

[0009] Step 3.1: Location of base station It is obtained from the observation file and is accurately known; if the m satellite is observed at the base station, that is, , using the pseudo-range observation values ​​obtained by parsing the base station observation file , satellite space coordinates calculated from the ephemeris file , get the pseudo-range observation value from the base station to satellite m:

[0010] (1)

[0011] Where, for The actual distance from satellite m to the base station at time, represents the base station receiver clock error, represents the satellite clock error, represents the speed of light, represents the ionospheric error, represents the tropospheric error, represents random errors including noise;

[0012] The pseudorange correction in differential positioning is the actual distance from the satellite to the base station. and pseudorange observations By making the difference, we can get the pseudorange correction from the base station to the m satellite by rearranging formula (1). :

[0013] (2)

[0014] Step 3.2: According to formula (1), replace b with o, which represents the pseudorange observation value from the observation station to satellite m, expressed as:

[0015] (3)

[0016] Where, for The actual distance from satellite m to the observation station at time, Represents the receiver clock error of the observation station; the pseudo-range observation value of the observation station Add pseudorange correction , the pseudo-range single difference positioning equation is derived, as shown in formula (4);

[0017] (4)

[0018] in, It represents the difference between the ionospheric error of the observing station and the ionospheric error of the observing station; represents the difference between the two tropospheric errors; It represents the difference between the two random errors;

[0019] Step 4: Based on the median average filtering principle and pseudorange householder transformation principle, an improved pseudorange single difference positioning equation is constructed based on step 3;

[0020] Step 4.1: From formula (4), when the distance between the base station and the observation station is within 100 km, we have Eliminate satellite clock errors, troposphere and ionosphere errors, and observe For satellites, there are A single-difference equation, specifically:

[0021] (5)

[0022] in, express The matrix of single-difference observations, express The matrix of the true distance values ​​from satellites to observation stations, represents the receiver clock error term, represents the matrix composed of random errors including noise generated by each satellite;

[0023] Step 4.2: In order to suppress the occasional pulse interference and other periodic interference in formula (5) and eliminate the sampling value deviation error, according to the median average filtering principle, the number of sampling points is set to , ,right Sort the elements in , remove a certain number of maximum and minimum values, and then find the average of all remaining elements, specifically:

[0024] =( +...+ (6)

[0025] in, express The first element in the matrix, express The second element in the matrix, i = 1, 2, ..., N; the pseudorange single difference matrix after median average filtering is expressed as:

[0026] (7)

[0027] Substituting formula (7) into formula (5), we obtain the pseudorange single-difference equation after median average filtering, which eliminates occasional pulse interference except noise:

[0028] (8)

[0029] in, represents the noise term of pseudorange to each observation satellite; ; The noise of each observation is Gaussian noise with zero mean and no correlation between them;

[0030] Step 4.3: In order to eliminate the receiver clock error, perform householder orthogonal transformation on formula (8). According to the householder transformation principle, we get:

[0031] (9)

[0032] (10)

[0033] (11)

[0034] in, represents the number of observed satellites, represents the Hounslow matrix, for The transpose of represents a unit column vector, express The transpose of , , after calculation, we get the Hounslow matrix express:

[0035] (12)

[0036] in, , for Transpose of; multiply both sides of Formula 8 by the matrix get:

[0037] (13)

[0038] From formula (13), it can be seen that only the first row of the matrix contains the receiver clock error term, and the rest The clock error of the item is 0, which achieves the purpose of eliminating the receiver clock error. At the same time, due to the matrix It is a symmetric positive definite matrix, so the characteristics of the noise term will not change, avoiding the problem of noise amplification in double-difference positioning;

[0039] The receiver clock error will not be included. The term is extracted to obtain the pseudo-range differential positioning equation after median average filtering and elimination of receiver clock error:

[0040] (14)

[0041] Step 5: Based on the zero-phase filtering principle, construct the zero-phase filtering pseudo-range differential positioning equation;

[0042] It can be seen from formula (14) that there is still observation noise in the pseudo-range differential observation value. In order to further improve the positioning accuracy and reduce the influence of observation noise on the pseudo-range observation value, considering that the zero-phase low-pass filter has the characteristics of a zero-phase system, that is, to obtain an accurate zero-phase distortion signal, and at the same time, when filtering the pseudo-range differential positioning data, no phase offset occurs, therefore, the pseudo-range observation equation in formula (14) is Perform noise filtering;

[0043] According to the zero-phase low-pass filter principle, first The sequence is filtered in order, specifically:

[0044] (15)

[0045] Next, the sequentially filtered The sequence is processed by reversing the data order, and we get:

[0046] (16)

[0047] in, is the sequence length of pseudorange observations, ; Reverse the formula (16) through the filter to perform an inverse order filtering process, and obtain:

[0048] (17)

[0049] Finally, the filtered result obtained by formula (17) is reversed again and output to obtain the pseudorange difference residual term after zero-phase low-pass filtering to remove high-frequency thermal noise, which is specifically:

[0050] (18)

[0051] Substitute formula (18) into formula (14), and let , the pseudo-range differential equation after eliminating the accidental random error, receiver clock error and random error correction including high-frequency thermal noise error is obtained, specifically:

[0052] (19)

[0053] Step 6: Linearize the pseudorange differential equation after random error correction and calculate the pseudorange differential error equation;

[0054] When using the least squares correlation estimation model for positioning estimation, the pseudorange observation equation must be linearized first. According to the formula, equation (19) is linearized to obtain:

[0055] (20)

[0056] in, The coordinates of the observation station to be found are represented by are the position coordinates of the observing satellite, is the initial pseudorange value of the pseudorange observation in formula (20);

[0057] Further simplifying, let , , , , , , and set the parameters and ,make , , the pseudo-range differential error equation after random error correction is obtained:

[0058] (twenty one)

[0059] in, represents the pseudorange observation matrix after random error correction, It represents the error of pseudo-range differential positioning after random error correction;

[0060] Step 7: Process the pseudo-range differential error equation after random error correction based on the least squares estimation model to solve the observation station coordinates;

[0061] According to the estimation principle of the least squares estimation model, the pseudorange differential error correction after random error correction is:

[0062] (twenty two)

[0063] The correction value obtained by formula (22) is between the initial point and the true point, and has passed a linearization. The initial point is updated using this correction value to obtain the coordinates of the observation station after the correction:

[0064] (twenty three)

[0065] Use the corrected observation station coordinates in formula (23) as the initial value and iterate. As the number of iterations increases, the linearization accuracy will become higher and higher. Users can customize the number of iterations as needed. , The value is a positive integer. The larger the value, the higher the positioning accuracy. After iterative updates, the receiver coordinates of the observation station are obtained as follows:

[0066] . (twenty four)

[0067] Beneficial technical effects of the present invention:

[0068] The proposed random error-corrected pseudorange measurement positioning method achieves decimeter-level positioning overall, with centimeter-level average error and standard deviation in the x, y, and z directions. This significantly improves positioning accuracy compared to pseudorange double-difference LS positioning, pseudorange double-difference WLS positioning, and pseudorange double-difference LS-KF positioning. This method can be applied to numerous applications requiring precise positioning, such as military, ports, and autonomous driving, achieving sub-meter positioning requirements. It is also suitable for use with satellite navigation receiving systems and devices. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 A flowchart showing the principle of a pseudo-range measurement positioning method with random error correction according to an embodiment of the present invention;

[0070] Figure 2 Comparison results of x-direction errors of four positioning methods according to the embodiment of the present invention;

[0071] Figure 3 Comparison results of the y-direction errors of the four positioning methods according to the embodiment of the present invention;

[0072] Figure 4 Comparison results of z-direction errors of four positioning methods according to embodiments of the present invention. DETAILED DESCRIPTION

[0073] The present invention will be further described below with reference to the accompanying drawings and embodiments;

[0074] A pseudo-range measurement positioning method with random error correction, as shown in the attached Figure 1 As shown, the specific steps include:

[0075] Step 1: Parse the received observation file to obtain the parameters required for positioning solution; the observation file is downloaded from the IGS data center;

[0076] Get the current observation time of the base station and observation station through the observation file , the number of visible satellites at the current observation time ; The number of satellites observed by the base station and the observation station at the same time is ,and ; Pseudorange observation values ​​of satellites visible to the base station and the observation station at the current moment ,in ;

[0077] Step 2: Analyze the received ephemeris file and calculate the satellite positions of Beidou navigation according to the Beidou navigation ICD standard; the receiver uses the orbital parameters in the ephemeris file to calculate the spatial coordinates of each navigation satellite ;

[0078] Step 3: Based on the pseudo-range differential positioning principle, derive the pseudo-range single difference positioning equation;

[0079] Step 3.1: Location of base station It is obtained from the observation file and is accurately known; if the m satellite is observed at the base station, that is, , using the pseudo-range observation values ​​obtained by parsing the base station observation file , satellite space coordinates calculated from the ephemeris file , get the pseudo-range observation value from the base station to satellite m:

[0080] (1)

[0081] Where, for The actual distance from satellite m to the base station at time, represents the base station receiver clock error, represents the satellite clock error, represents the speed of light, represents the ionospheric error, represents the tropospheric error, represents random errors including noise;

[0082] The pseudorange correction in differential positioning is the actual distance from the satellite to the base station. and pseudorange observations By making the difference, we can get the pseudorange correction from the base station to the m satellite by rearranging formula (1). :

[0083] (2)

[0084] Step 3.2: According to formula (1), replace b with o, which represents the pseudorange observation value from the observation station to satellite m, expressed as:

[0085] (3)

[0086] Where, for The actual distance from satellite m to the observation station at time, Represents the receiver clock error of the observation station; the pseudo-range observation value of the observation station Add pseudorange correction , the pseudo-range single difference positioning equation is derived, as shown in formula (4);

[0087] (4)

[0088] in, It represents the difference between the ionospheric error of the observing station and the ionospheric error of the observing station; represents the difference between the two tropospheric errors; It represents the difference between the two random errors;

[0089] Step 4: Based on the median average filtering principle and pseudorange householder transformation principle, an improved pseudorange single difference positioning equation is constructed based on step 3;

[0090] Step 4.1: From formula (4), when the distance between the base station and the observation station is within 100 km, we have Eliminate satellite clock errors, troposphere and ionosphere errors, and observe For satellites, there are A single-difference equation, specifically:

[0091] (5)

[0092] in, express The matrix of single-difference observations, express The matrix of the true distance values ​​from satellites to observation stations, represents the receiver clock error term, represents the matrix composed of random errors including noise generated by each satellite;

[0093] Step 4.2: In order to suppress the occasional pulse interference and other periodic interference in formula (5) and eliminate the sampling value deviation error, according to the median average filtering principle, the number of sampling points is set to , ,right Sort the elements in , remove a certain number of maximum and minimum values, and then find the average of all remaining elements, specifically:

[0094] =( +...+ (6)

[0095] in, express The first element in the matrix, express The second element in the matrix, i = 1, 2, ..., N; the pseudorange single difference matrix after median average filtering is expressed as:

[0096] (7)

[0097] Substituting formula (7) into formula (5), we obtain the pseudorange single-difference equation after median average filtering, which eliminates occasional pulse interference except noise:

[0098] (8)

[0099] in, represents the noise term of pseudorange to each observation satellite; ; The noise of each observation is Gaussian noise with zero mean and no correlation between them;

[0100] Step 4.3: In order to eliminate the receiver clock error, perform householder orthogonal transformation on formula (8). According to the householder transformation principle, we get:

[0101] (9)

[0102] (10)

[0103] (11)

[0104] in, represents the number of observed satellites, represents the Hounslow matrix, for The transpose of represents a unit column vector, express The transpose of , , after calculation, we get the Hounslow matrix express:

[0105] (12)

[0106] in, , for Transpose of; multiply both sides of formula (8) by the matrix get:

[0107] (13)

[0108] From formula (13), it can be seen that only the first row of the matrix contains the receiver clock error term, and the rest The clock error of the item is 0, which achieves the purpose of eliminating the receiver clock error. At the same time, due to the matrix It is a symmetric positive definite matrix, so the characteristics of the noise term will not change, avoiding the problem of noise amplification in double-difference positioning;

[0109] The receiver clock error will not be included. The term is extracted to obtain the pseudo-range differential positioning equation after median average filtering and elimination of receiver clock error:

[0110] (14)

[0111] Step 5: Based on the zero-phase filtering principle, construct the zero-phase filtering pseudo-range differential positioning equation;

[0112] It can be seen from formula (14) that there is still observation noise in the pseudo-range differential observation value. In order to further improve the positioning accuracy and reduce the influence of observation noise on the pseudo-range observation value, considering that the zero-phase low-pass filter has the characteristics of a zero-phase system, that is, to obtain an accurate zero-phase distortion signal, and at the same time, when filtering the pseudo-range differential positioning data, no phase offset occurs, therefore, the pseudo-range observation equation in formula (14) is Perform noise filtering;

[0113] According to the zero-phase low-pass filter principle, first The sequence is filtered in order, specifically:

[0114] (15)

[0115] Next, the sequentially filtered The sequence is processed by reversing the data order, and we get:

[0116] (16)

[0117] in, is the sequence length of pseudorange observations, ; Reverse the formula (16) through the filter to perform an inverse order filtering process, and obtain:

[0118] (17)

[0119] Finally, the filtered result obtained by formula (17) is reversed again and output to obtain the pseudorange difference residual term after zero-phase low-pass filtering to remove high-frequency thermal noise, which is specifically:

[0120] (18)

[0121] Substitute formula (18) into formula (14), and let , the pseudo-range differential equation after eliminating the accidental random error, receiver clock error and random error correction including high-frequency thermal noise error is obtained, specifically:

[0122] (19)

[0123] Step 6: Linearize the pseudorange differential equation after random error correction and calculate the pseudorange differential error equation;

[0124] When using the least squares correlation estimation model for positioning estimation, the pseudorange observation equation must be linearized first. According to the formula, equation (19) is linearized to obtain:

[0125] (20)

[0126] in, The coordinates of the observation station to be found are represented by are the position coordinates of the observing satellite, is the initial pseudorange value of the pseudorange observation in formula (20);

[0127] Further simplifying, let , , , , , , and set the parameters and ,make , , the pseudo-range differential error equation after random error correction is obtained:

[0128] (twenty one)

[0129] in, represents the pseudorange observation matrix after random error correction, It represents the error of pseudo-range differential positioning after random error correction;

[0130] Step 7: Process the pseudo-range differential error equation after random error correction based on the least squares estimation model to solve the observation station coordinates;

[0131] According to the estimation principle of the least squares estimation model, the pseudorange differential error correction after random error correction is:

[0132] (twenty two)

[0133] The correction value obtained by formula (22) is between the initial point and the true point, and has passed a linearization. The initial point is updated using this correction value to obtain the coordinates of the observation station after the correction:

[0134] (twenty three)

[0135] Use the corrected observation station coordinates in formula (23) as the initial value and iterate. As the number of iterations increases, the linearization accuracy will become higher and higher. Users can customize the number of iterations as needed. , The value is a positive integer. The larger the value, the higher the positioning accuracy. After iterative updates, the receiver coordinates of the observation station are obtained as follows:

[0136] . (twenty four)

[0137] The above method is tested and verified as follows:

[0138] The simulation platform MATLAB software is used to parse the real Beidou observation data files and ephemeris data files downloaded from the IGS website. The data required for setting the pseudorange positioning method based on random error correction are shown in Table 1.

[0139] Table 1 Simulation parameter design;

[0140]

[0141] In the experimental simulation, the observation station position coordinates provided in the Beidou navigation observation file are used as the actual position: x=-2364337.4414m, y=4870285.6211m, z=-3360809.6724m. In order to verify the superiority of the pseudorange positioning method based on random error correction, the positioning errors are compared with the widely used pseudorange double difference least squares positioning method (pseudorange double difference LS), pseudorange measurement double difference angle weighted positioning method (pseudorange double difference WLS) and pseudorange double difference Kalman filter positioning method (pseudorange double difference KF). In order to clearly observe the error value changes of each method, only 100 epoch data are randomly selected from the downloaded Beidou navigation observation files for ten consecutive days for positioning analysis. The comparison results of the x, y, and z direction errors of the four positioning methods are shown in the figure below. Figure 2 、 Figure 3 、 Figure 4 shown.

Claims

1. A pseudo-range measurement positioning method with random error correction, characterized in that: The specific steps include: Step 1: Parse the received observation file to obtain the parameters required for positioning solution; Get the current observation time of the base station and observation station through the observation file , the number of visible satellites at the current observation time ; The number of satellites observed by the base station and the observation station at the same time is ,and ; Pseudorange observation values ​​of satellites visible to the base station and observation station at the current moment ,in ; Step 2: Analyze the received ephemeris file and calculate the satellite positions of Beidou navigation according to the Beidou navigation ICD standard; the receiver uses the orbital parameters in the ephemeris file to calculate the spatial coordinates of each navigation satellite ; Step 3: Based on the pseudo-range differential positioning principle, derive the pseudo-range single difference positioning equation; Step 4: Based on the median average filtering principle and pseudorange householder transformation principle, an improved pseudorange single difference positioning equation is constructed based on step 3; Step 5: Based on the zero-phase filtering principle, a zero-phase filtering pseudo-range differential positioning equation is constructed based on step 4; Step 6: Linearize the pseudorange differential equation after random error correction and calculate the pseudorange differential error equation; Step 7: Process the pseudorange differential error equation after random error correction based on the least squares estimation model to solve the observation station coordinates.

2. The random error corrected pseudo-range measurement positioning method according to claim 1, characterized in that: Step 3 is as follows: Step 3.1: Location of base station It is obtained from the observation file and is accurately known; if the m satellite is observed at the base station, that is, , using the pseudo-range observation values ​​obtained by parsing the base station observation file , satellite space coordinates calculated from the ephemeris file , get the pseudo-range observation value from the base station to satellite m: （1）； Where, for The actual distance from satellite m to the base station at time, represents the base station receiver clock error, represents the satellite clock error, represents the speed of light, represents the ionospheric error, represents the tropospheric error, represents random errors including noise; The pseudorange correction in differential positioning is the actual distance from the satellite to the base station. and pseudorange observations By making the difference, we can get the pseudorange correction from the base station to the m satellite by rearranging formula (1). : （2）； Step 3.2: According to formula (1), replace b with o, which represents the pseudorange observation value from the observation station to satellite m, expressed as: （3）； Where, for The actual distance from satellite m to the observation station at time, Represents the receiver clock error of the observation station; the pseudo-range observation value of the observation station Add pseudorange correction , the pseudo-range single difference positioning equation is derived, as shown in formula (4); （4）； in, It represents the difference between the ionospheric error of the observation station and the ionospheric error of the base station; represents the difference between the two tropospheric errors; It represents the difference between the two random errors.

3. The random error corrected pseudo-range measurement positioning method according to claim 2, characterized in that: Step 4 is as follows: Step 4.1: From formula (4), when the distance between the base station and the observation station is within 100 km, we have Eliminate satellite clock error, tropospheric error, ionospheric error, for the observed For satellites, there are A single-difference equation, specifically: （5）； in, express The matrix of single-difference observations, express The matrix of the true distance values ​​from satellites to observation stations, represents the receiver clock error term, represents the matrix composed of random errors including noise generated by each satellite; Step 4.2: According to the median average filtering principle, set the number of sampling points to , ,right Sort the elements in , remove a certain number of maximum and minimum values, and then find the average of all remaining elements, specifically: (6)； in, express The first element in the matrix, express The second element in the matrix, i = 1, 2, ..., N; the pseudorange single difference matrix after median average filtering is expressed as: (7)； Substituting formula (7) into formula (5), we obtain the pseudorange single-difference equation after median average filtering, which eliminates occasional pulse interference except noise: （8）； in, represents the noise term of pseudorange to each observation satellite; ; The noise of each observation is Gaussian noise with zero mean and no correlation between them; Step 4.3: Perform householder orthogonal transformation on formula (8). According to the householder transformation principle, we get: (9)； （10）； （11）； in, represents the number of observed satellites, represents the Hounslow matrix, for The transpose of represents a unit column vector, express The transpose of , , after calculation, we get the Hounslow matrix express: （12）； in, , for Transpose of; multiply both sides of formula (8) by the matrix get: (13)； From formula (13), it can be seen that only the first row of the matrix contains the receiver clock error term, and the rest The clock error is 0, the matrix is a symmetric positive definite matrix; The receiver clock error will not be included. The term is extracted to obtain the pseudo-range differential positioning equation after median average filtering and elimination of receiver clock error: (14) 。 4. The random error corrected pseudo-range measurement positioning method according to claim 3, characterized in that: Step 5 is as follows: From step 4, formula (14), we can see that there is still observation noise in the pseudo-range difference observation value. Perform noise filtering; According to the zero-phase low-pass filter principle, first The sequence is filtered in order, specifically: （15）； Next, the sequentially filtered The sequence is processed by reversing the data order, and we get: （16）； in, is the sequence length of pseudorange observations, ; Reverse the formula (16) through the filter to perform an inverse order filtering process, and obtain: （17）； Finally, the filtered result obtained by formula (17) is reversed again and output to obtain the pseudorange difference residual term after zero-phase low-pass filtering to remove high-frequency thermal noise, which is specifically: （18）； Substitute formula (18) into formula (14), and let , the pseudo-range differential equation after eliminating the accidental random error, receiver clock error and random error correction including high-frequency thermal noise error is obtained, specifically: （19）。 5. The random error corrected pseudo-range measurement and positioning method according to claim 4, characterized in that: Step 6 is as follows: When using the least squares correlation estimation model for positioning estimation, the pseudorange observation equation must be linearized first. Formula (19) is linearized to obtain: （20）； in, The coordinates of the observation station to be found are represented by are the position coordinates of the observing satellite, is the initial pseudorange value of the pseudorange observation in formula (19); Further simplifying, let , , , , , , and set the parameters and ,make , , the pseudo-range differential error equation after random error correction is obtained: （21） ； in, represents the pseudorange observation matrix after random error correction, It represents the error of pseudo-range differential positioning after random error correction.

6. The random error corrected pseudo-range measurement positioning method according to claim 1, characterized in that: Step 7 is as follows: According to the estimation principle of the least squares estimation model, the pseudorange differential error correction after random error correction is: （22）； The correction value obtained by formula (22) is between the initial point and the true point, and has passed a linearization. The initial point is updated using this correction value to obtain the coordinates of the observation station after the correction: （23）； Use the corrected observation station coordinates in formula (23) as the initial value and iterate; the user can customize the number of iterations as needed , The value is a positive integer. The larger the value, the higher the positioning accuracy. After iterative updates, the receiver coordinates of the observation station are obtained as follows: （24）。

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