A method for improving positioning accuracy using GNSS non-line-of-sight signals

Abstract

This invention discloses a method for improving positioning accuracy using GNSS non-line-of-sight (NLS) signals. The method includes the following steps: prior value calculation based on a weighted model of the NLS signal; NLS signal reflection delay correction; NLS signal design matrix correction; and joint positioning solution using the line-of-sight signal and the corrected NLS signal. Compared with existing technologies, this invention significantly improves the positioning accuracy of GNSS observations in high-density urban areas. It proposes an analytical expression for reflection delay correction even with prior position errors, and suggests that in addition to traditional reflection delay correction, the correction of the design matrix for NLS signals should also be performed simultaneously. This approach truly improves the accuracy and stability of the solution, even when the prior value contains errors, making it more suitable for practical scenarios, especially for upgrading from street-level to lane-level positioning.

Description

Technical Field

[0001] This invention relates to the field of global satellite positioning technology, specifically a method for improving positioning accuracy using GNSS non-line-of-sight signals. Background Technology

[0002] Currently, satellite positioning methods identify and discard or downweight non-line-of-sight (NLS) signals in GNSS observations. While this avoids contaminating the positioning solution with NLS errors, it also significantly reduces the number of effective satellites, failing to guarantee a good spatial distribution of satellites and limiting improvements in cross-street and vertical positioning accuracy. In recent years, international efforts have begun to explore using corrected NLS signals in conjunction with line-of-sight signals to increase redundant observations and further improve positioning accuracy. However, current methods still rely on precise prior coordinates of the station or precise prior relative positions of the station and adjacent buildings for NLS reflection delay correction. If the prior positions are incorrect, these methods are less effective and may even reduce accuracy. Since actual prior station positions always contain errors, these methods are difficult to apply in practice. Summary of the Invention

[0003] The purpose of this invention is to address the shortcomings of existing technologies by providing a method for improving positioning accuracy using GNSS non-line-of-sight (NLS) signals. This method employs prior values ​​for NLS signal reflection delay correction and design matrix correction, then combines the corrected NLS and LS signals for joint positioning, significantly improving the positioning accuracy of GNSS observations in high-density urban areas, particularly from street-level to lane-level positioning. The method theoretically derives a rigorous analytical expression for error correction when prior positions are inaccurate. It proposes that NLS signal correction, in addition to traditional delay correction, also requires simultaneous design matrix correction to truly improve the accuracy and stability of the solution, even when prior values ​​contain errors. Even based on inaccurate prior positions, it can effectively improve positioning accuracy in urban and canyon environments. The method is simple, effective, and highly accurate, making it particularly suitable for precise positioning in real-world scenarios.

[0004] The specific technical solution to achieve the purpose of this invention is: a method for improving positioning accuracy using GNSS non-line-of-sight signals, characterized by using prior values ​​to correct the reflection delay of non-line-of-sight signals and designing a matrix, and then jointly positioning the corrected non-line-of-sight signals with line-of-sight signals to improve positioning accuracy. This method includes the following specific steps:

[0005] Step 1: Prior value calculation based on the non-line-of-sight signal weighted model. The prior value calculation process is described in pseudorange least squares mode as follows:

[0006] Step 1-1: The pseudorange observation equation is expressed by the following equation (1):

[0007]

[0008] In the formula: the superscript i represents the satellite pseudo-random noise code; the subscript k represents the receiver serial number; r represents the geometric distance between the satellite and the station; c represents the speed of light in a vacuum; dt k dt i These represent receiver and satellite clock errors, respectively; I represents ionospheric error; T represents tropospheric error; N represents non-line-of-sight signal error; and ε represents unmodeled error.

[0009] Step 1-2: After linearizing the above equation (1), it can be expressed as the following equation (2):

[0010] omc=GΔx+ε (2).

[0011] In the formula: omc is the difference between the observed value and the estimated value; Δx is the correction number of the unknown parameter vector; G is the design matrix.

[0012] Steps 1-3: The influence of non-line-of-sight signals is reduced by weighting. The weight matrix W of each satellite observation is defined by the following equation (3):

[0013]

[0014] Where n is the number of satellite observations; σ i It is the standard deviation of satellite signals;

[0015] The standard deviation of the satellite signal σ i Defined by the following equation (4):

[0016]

[0017] In the formula, CN0 i denoted as the signal-to-noise ratio of satellite i; c0 is the variance coefficient; m is the signal variance amplification factor. By using a larger value of m for non-line-of-sight signals, the weighting of non-line-of-sight signals is reduced.

[0018] Steps 1-4: Calculate the correction Δx of the unknown parameter vector using the following (5):

[0019] Δx=(G T WG) -1 G T Womc (5).

[0020] The superscript T is the transpose operator.

[0021] Steps 1-5: Update the unknown parameter estimate using the following equation (6).

[0022]

[0023] Where x0 is the initial value of the unknown parameter.

[0024] Steps 1-6: Determine if Δx converges. If Δx does not converge, then... As the new x0, repeat steps 1-2 to 1-5; if Δx has converged, then This refers to the prior value result that needs to be calculated in this step.

[0025] Step 2: Correction of non-line-of-sight signal reflection delay

[0026] Step 2-1: Perform map matching on the prior location value results from Step 1. Find the street arc corresponding to the prior location in the previously collected urban road data, and then find the reflective walls on both sides of the street by combining the urban 3D map containing urban building 3D information. Define the azimuth angle of the arc less than π as the street direction, and define the wall on the left side of the street as the left reflective wall and the wall on the right side as the right reflective wall.

[0027] Step 2-2: Calculate the distance W from the prior value to the left reflecting wall surface. L and the distance W to the right-side reflective wall R .

[0028] Step 2-3: Calculate the non-line-of-sight signal reflection delay error N using the following equation (7):

[0029]

[0030] Where e is the satellite elevation angle; β is the difference between the satellite azimuth angle and the street azimuth angle, and β needs to be normalized to the range [0, 2π]; a is the reflection delay error direction coefficient, which is 1 when the satellite and the prior value are on the same side of the reflector wall, and -1 when the satellite and the prior value are on opposite sides of the reflector wall.

[0031] Steps 2-4: Calculate the error N of satellite i. i From the corresponding row of equation (2) above, omc i By subtracting from the midpoint, reflection delay correction for non-line-of-sight signals is achieved, resulting in the row corresponding to the difference between the corrected observed and estimated values ​​(omc). i The process is expressed by the following equation (8):

[0032] (omc i )′=omc i -N i (8).

[0033] Step 3: Design matrix correction for non-line-of-sight signals

[0034] Step 3-1: Calculate the rotation matrix for the transformation from Earth-centered Earth-fixed rectangular coordinates to wall-centered rectangular coordinates and the rotation matrix for the transformation from wall-centered rectangular coordinates to Earth-centered Earth-fixed rectangular coordinates, respectively. The wall-centered rectangular coordinate system is a right-handed coordinate system, with the origin at the foot of the perpendicular from the prior value to the reflecting wall surface, the normal of the wall surface as the X-axis, and the orientation of the wall surface as the Y-axis. The positive direction of the X-axis is defined by the upward right-handed system of the Z-axis. The transformation matrix from Earth-centered Earth-fixed rectangular coordinates to wall-centered rectangular coordinates is expressed by the following equation (9):

[0035]

[0036] The transformation matrix from the wall core rectangular coordinates to the Earth core solid rectangular coordinates is expressed by the following equation (10):

[0037]

[0038] Where B and L are the latitude and longitude of any point on the wall, respectively; α is the heading angle of the street.

[0039] Step 3-2: Change the row corresponding to the non-line-of-sight signal of the design matrix G in the above equation (2) to the following equation (11) (G i )′:

[0040]

[0041] Where x0, y0, and z0 are the coordinate elements of the initial value coordinate vector x0; x i y i , z i is the coordinate of satellite i; r is the geometric distance between the satellite and the receiver; S is the multi-system bias coefficient, which is a 1×(sn-1) vector; sn is the number of all satellite systems involved in the solution; I is the identity matrix; M is the direction cosine correction matrix defined by the following equation (12):

[0042]

[0043] Step 4: Joint positioning solution using line-of-sight signals and corrected non-line-of-sight signals

[0044] Step 4-1: OMC of combined line-of-sight satellite signals i And the non-line-of-sight satellite signal after step 2 correction (omc) i The updated difference matrix omc is formed between the observed and estimated values. corr Joint line-of-sight satellite signal design matrix G i and the non-line-of-sight satellite signal design matrix row (G) after step 3 correction i The updated design matrix G is formed by )′. corrThe unknown vector correction value Δx′ is obtained by the following equation (13):

[0045]

[0046] Among them, the standard deviation σ of the line-of-sight and non-line-of-sight signals in the weight matrix W i Using the same signal variance amplification factor m; C is the constraint matrix defined by the following equation (14):

[0047]

[0048] in: and These are the prior variances of the three-dimensional coordinates and the receiver clock bias, respectively.

[0049] Step 4-2: Use the following equation (15) to modify the prior boolean of step 1. Update to obtain the final location result.

[0050]

[0051] Compared with existing technologies, this invention significantly improves the positioning accuracy of GNSS observations in high-density urban areas. It rigorously derives the analytical expression for reflection delay correction when prior position errors exist. It proposes that in addition to traditional delay correction, correction of non-line-of-sight signals also requires correction of the design matrix to truly improve the accuracy and stability of the solution when prior values ​​contain errors. In particular, the improvement from street-level positioning to lane-level positioning is more suitable for practical scenarios and has good application prospects. Attached Figure Description

[0052] Figure 1 This is a flowchart of the present invention;

[0053] Figure 2 The positioning deviations of a single GPS system across streets, along streets, and vertically are calculated using four methods. Detailed Implementation

[0054] This invention rigorously derives the analytical expression for reflection delay correction when prior position errors exist. It proposes that, in addition to traditional delay correction, the correction of non-line-of-sight signals should also include correction of the design matrix. Only then can the accuracy and stability of the solution be truly improved, even when prior values ​​contain errors. Joint positioning using corrected non-line-of-sight and line-of-sight signals can significantly improve the positioning accuracy of GNSS observations in high-density urban areas, particularly from street-level positioning to lane-level positioning.

[0055] See Figure 1This invention uses prior values ​​to correct the reflection delay of non-line-of-sight signals and to design a matrix. The corrected non-line-of-sight signals are then combined with line-of-sight signals for joint positioning to improve positioning accuracy. The method includes the following specific steps:

[0056] Step 1: Prior value calculation based on the non-line-of-sight signal weighted model. The prior value calculation process is described in pseudorange least squares mode as follows:

[0057] Step 1-1: The pseudorange observation equation is expressed by the following equation (1):

[0058]

[0059] In the formula: the superscript i represents the satellite pseudo-random noise code; the subscript k represents the receiver serial number; r represents the geometric distance between the satellite and the station; c represents the speed of light in a vacuum; dt k dt i These represent receiver and satellite clock errors, respectively; I represents ionospheric error; T represents tropospheric error; N represents non-line-of-sight signal error; and ε represents unmodeled error.

[0060] Step 1-2: After linearizing the above equation (1), it can be expressed as the following equation (2):

[0061] omc=GΔx+ε (2).

[0062] In the formula: omc is the difference between the observed value and the estimated value; Δx is the correction number of the unknown parameter vector; G is the design matrix.

[0063] Taking a single GPS system as an example: omc is expressed by the following equation (2-1):

[0064]

[0065] in, Let be the pseudorange value of satellite i after passing through the ionosphere, troposphere, and satellite clock error correction; let x0 be the initial coordinate vector of the receiver [x0, y0, z0]. T The superscript T indicates the transpose operator; r(x0) i dt represents the initial distance between the receiver and satellite i; k，0 Let Δx be the initial value of the receiver clock bias; Δx is the correction of the unknown parameter number vector, which is expressed in the form of the following equation (2-2) in the case of a single GPS system:

[0066] Δx=[δx,δy,δz,δdt k ] T (2-2).

[0067] Among them, δx, δy, δz and δdt kThese correspond to the three-dimensional coordinates of x, y, and z in geocentric rectangular coordinates and the corrections for receiver clock bias, respectively.

[0068] G is the design matrix defined by the following equation (2-3):

[0069]

[0070] Where, x i y i , z i is the coordinate of satellite i; n is the number of satellite observations.

[0071] Steps 1-3: The influence of non-line-of-sight signals is reduced by weighting. The weight matrix W of each satellite observation is defined by the following equation (3):

[0072]

[0073] Where n is the number of satellite observations; σ i It is the standard deviation of satellite signals.

[0074] The standard deviation of the satellite signal σ i Defined by the following equation (4):

[0075]

[0076] In the formula, CN0 i denoted as the signal-to-noise ratio of satellite i; c0 is the variance coefficient; m is the signal variance amplification factor. By using a larger value of m for non-line-of-sight signals, the weighting of non-line-of-sight signals is reduced.

[0077] Steps 1-4: Calculate the correction Δx of the unknown parameter vector using the following (5):

[0078] Δx=(G T WG) -1 G T Womc (5).

[0079] Steps 1-5: Update the unknown parameter estimates using the following (6)

[0080]

[0081] Steps 1-6: Determine if Δx converges. If Δx does not converge, then... As the new x0, repeat steps 1-2 to 1-5; if Δx has converged, then This refers to the prior value result that needs to be calculated in this step.

[0082] Step 2: Correction of non-line-of-sight signal reflection delay

[0083] Step 2-1: Perform map matching on the prior location value results from Step 1. Find the street arc corresponding to the prior location in the previously collected urban road data, and then find the reflective walls on both sides of the street by combining the urban 3D map containing urban building 3D information. Define the azimuth angle of the arc less than π as the street direction, and define the wall on the left side of the street as the left reflective wall and the wall on the right side as the right reflective wall.

[0084] Step 2-2: Calculate the distance W from the prior value to the left reflecting wall surface. L and the distance W to the right-side reflective wall R ;

[0085] Step 2-3: Calculate the non-line-of-sight signal reflection delay error N using the following equation (7):

[0086]

[0087] Where e is the satellite elevation angle; β is the difference between the satellite azimuth and the street azimuth in the range [0, 2π]; a is the reflection delay error direction coefficient, which is 1 when the satellite and the prior value are on the same side of the reflector wall, and -1 when the satellite and the prior value are on opposite sides of the reflector wall.

[0088] Steps 2-4: Calculate the error N of satellite i. i From the corresponding row of equation (2) above, omc i By subtracting from the midpoint, reflection delay correction for non-line-of-sight signals is achieved, resulting in the row corresponding to the difference between the corrected observed and estimated values ​​(omc). i The correction process is expressed by the following equation (8):

[0089] (omc i )′=omc i -N i (8).

[0090] Step 3: Design matrix correction for non-line-of-sight signals

[0091] Step 3-1: Calculate the rotation matrix for the transformation from Earth-centered and Earth-based rectangular coordinates to wall-centered rectangular coordinates, and the rotation matrix for the transformation from wall-centered rectangular coordinates to Earth-centered and Earth-based rectangular coordinates. The wall-centered rectangular coordinate system is a right-handed coordinate system, with the origin at the foot of the perpendicular from the prior value to the reflecting wall surface. The normal to the wall surface is the X-axis, and the orientation of the wall surface is the Y-axis. The positive direction of the X-axis is defined by the upward right-handed system of the Z-axis.

[0092] The transformation matrix from the Earth's core rectangular coordinates to the wall's core rectangular coordinates is expressed by the following equation (9):

[0093]

[0094] The transformation matrix from the wall core rectangular coordinates to the Earth core solid rectangular coordinates is expressed by the following equation (10):

[0095]

[0096] Where B and L are the geographical latitude and longitude of any point on the wall, respectively; α is the heading angle of the street.

[0097] Step 3-2: Change the row corresponding to the non-line-of-sight signal in the design matrix G of formula (2) from the following formula (11) to (G i )′:

[0098]

[0099] Where S is the multi-system bias coefficient, which is a 1×(sn-1) vector; sn is the number of all satellite systems involved in the solution; I is the identity matrix; and M is the direction cosine correction matrix defined by the following equation (12):

[0100]

[0101] Specifically, the row corresponding to the design matrix after correction for a single GPS system (G i )′ is expressed by the following equation (12-1):

[0102]

[0103] Step 4: Joint positioning solution using line-of-sight signals and corrected non-line-of-sight signals

[0104] Step 4-1: OMC of combined line-of-sight satellite signals i And the non-line-of-sight satellite signal after step 2 correction (omc) i The updated difference matrix omc is formed between the observed and estimated values. corr Joint line-of-sight satellite signal design matrix G i and the non-line-of-sight satellite signal design matrix row (G) after step 3 correction i The updated design matrix G is formed by )′. corr The unknown vector correction value Δx′ is obtained by the following equation (13):

[0105]

[0106] Among them, the standard deviation σ of the line-of-sight and non-line-of-sight signals in the weight matrix W i Using the same signal variance amplification factor m; C is the constraint matrix defined by the following equation (14):

[0107]

[0108] In the formula: and These are the prior variances of the three-dimensional coordinates and the receiver clock bias, respectively.

[0109] Step 4-2: Use formula (15) to process the prior knowledge obtained in step 1. Update to obtain the final location result.

[0110]

[0111] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. Obviously, the examples listed are only for explaining the present invention and are not intended to limit the scope of the invention.

[0112] Example 1

[0113] An observation experiment was conducted using a mobile phone in front of a well-known restaurant in a certain city. The heights of the buildings on either side were 34 meters and 27 meters, respectively. The observation duration was 42 minutes, and the sampling frequency was 1Hz. The reference value was the real-time dynamic differential fixed value obtained by the Zhongwei ZG20 receiver.

[0114] See Figure 2 The results of single-system pseudorange positioning for the four methods are compared (the figure shows the deviation results for 60 seconds).

[0115] Method 1 is a standard single-point positioning based on the signal-to-noise ratio weighting model, which means that regardless of whether it is a line-of-sight signal or a non-line-of-sight signal, the signal variance amplification factor m in formula (4) is always 1.

[0116] Method 2 is a standard single-point positioning based on the non-line-of-sight signal weighting model. In formula (4) of this method, the line-of-sight signal variance amplification factor m is 1, and the non-line-of-sight signal variance amplification factor m is 15.

[0117] Method 3 first calculates the prior value based on Method 2, then modifies the reflection delay according to step 2, only modifying the reflection delay without modifying the design matrix, and finally performs positioning by combining the line-of-sight signal and the non-line-of-sight signal with only the reflection delay corrected. During positioning, the variance amplification factor m of both signals is set to 1.

[0118] Method 4 is the method of this invention. First, the prior value is calculated based on Method 2. Then, the reflection delay and design matrix are modified according to steps 2 and 3. Finally, the positioning is performed by combining the line-of-sight signal and the two corrected non-line-of-sight signals. During positioning, the variance amplification factor m of the two signals is taken as 1. In the fourth step, the empirical values ​​of the diagonal variance in formula (14) are selected as 400, 400, 400, and 2500, respectively.

[0119] When implementing the above four methods, the value of c0 in formula (4) is 1.1 × 10 4 m 2 The root mean square errors of the four methods' single GPS system solutions compared to the reference values ​​for cross-street, along-street, and vertical directions are detailed in Table 1 below.

[0120] Table 1. Root mean square errors of single GPS system solutions for street crossing, street along, and vertical directions using four methods (unit: m)

[0121]

[0122] Since the average number of line-of-sight signals received by the observation point is 2 satellites, Method 2 reduces the weighting of the elements of the weight matrix corresponding to the non-line-of-sight signal satellites by 1 / 15, resulting in a reduction in effective redundant observations, even approaching an ill-conditioned state. Its horizontal positioning results are actually worse than Method 1, which does not perform any processing on the non-line-of-sight signals. Although Method 3 performs reflection delay correction, the prior position error causes errors in the reflection delay correction, which are amplified by the design matrix, leading to a significant decrease in the accuracy of the positioning solution in the cross-street direction. Meanwhile, the accuracy of the method in this invention is significantly superior to other methods overall, especially in the cross-street and vertical directions. Compared to the solution of Method 3, the accuracy of the solution in this invention is improved by 69.55% and 36.64% in the cross-street and vertical directions, respectively.

[0123] The above is merely a further description of the present invention and is not intended to limit the scope of this patent. Any equivalent implementation of the present invention should be included within the scope of the claims of this patent.

Claims

1. A method for improving positioning accuracy using GNSS non-line-of-sight signals, characterized in that, The method employs prior values ​​to correct the reflection delay of non-line-of-sight signals and a design matrix. The corrected non-line-of-sight signals are then combined with line-of-sight signals for joint positioning to improve positioning accuracy. The specific steps of this method are as follows: Step 1: Prior value calculation based on the non-line-of-sight signal weighting model Step 1-1: Calculate the pseudorange observation equation using the following equation (1): where the superscript i is the satellite pseudo-random noise code number; the subscript k is the receiver number; r is the geometric range between the satellite and the station; c is the speed of light in a vacuum; dt k , dt i are the receiver and satellite clock errors, respectively; I is the ionospheric error; T is the tropospheric error; N is the non-line-of-sight signal error; and ε is the unmodeled error; Step 1-2: After linearizing the pseudorange observation equation in equation (1) above, it can be expressed as equation (2) below: omc=GΔx+ε (2); In the formula: omc is the difference between the observed value and the estimated value; Δx is the correction value of the unknown parameter vector; G is the design matrix; Steps 1-3: The influence of non-line-of-sight signals is reduced by weighting. The weight matrix W of each satellite observation is defined by the following equation (3): Where n is the number of satellite observations; σ i It is the standard deviation of satellite signals; The satellite signal standard deviation σ i Defined by the following equation (4): In the formula, CN0 i is the signal-to-noise ratio of satellite i; c0 is the variance coefficient; m is the signal variance amplification factor; Steps 1-4: Calculate the correction value Δx of the unknown parameter vector using the following equation (5): Δx=(G T WG) -1 G T Womc (5); Where the superscript T is the transpose operator; Steps 1-5: Update the estimated values ​​of the unknown parameters using the following equation (6). Where x0 is the initial value of the unknown parameter. Steps 1-6: Determine if Δx converges. If Δx does not converge, then... As the new x0, repeat steps 1-2 to 1-5; if Δx has converged, then The result is the prior value calculated; Step 2: Correction of non-line-of-sight signal reflection delay Step 2-1: Perform map matching on the prior location value from Step 1. Find the street arc corresponding to the prior location in the previously collected urban road data. Combine the city 3D map containing urban building 3D information to find the reflective walls on both sides of the street. Define the azimuth angle of the arc less than π as the street direction. Define the wall on the left side of the street as the left reflective wall and the wall on the right side as the right reflective wall. Step 2-2: Calculate the distance W from the prior value to the left reflecting wall surface. L and the distance W to the right-side reflective wall R ; Step 2-3: Calculate the non-line-of-sight signal reflection delay error N using the following equation (7): Where e is the satellite elevation angle; β is the difference between the satellite azimuth and the street azimuth between [0, 2π]; a is the reflection delay error direction coefficient, which is 1 when the satellite and the prior value are on the same side of the reflector wall, and -1 when the satellite and the prior value are on opposite sides of the reflector wall. Steps 2-4: Calculate the error N of satellite i. i From the corresponding row of equation (2) above, omc i By subtracting from the midpoint, reflection delay correction for non-line-of-sight signals is achieved, resulting in the row corresponding to the difference between the observed and estimated non-line-of-sight signal values ​​after correction (omc). i The process is expressed by the following equation (8): (omc i )′=omc i -N i (8); Step 3: Design matrix correction for non-line-of-sight signals Step 3-1: Calculate the rotation matrix for transforming from Earth-centered rectangular coordinates to wall-centered rectangular coordinates and the rotation matrix for transforming from wall-centered rectangular coordinates to Earth-centered rectangular coordinates. The wall-centered rectangular coordinate system is a right-handed coordinate system, with the origin being the foot of the perpendicular from the prior value to the reflecting wall surface. The normal of the wall surface is the X-axis, and the orientation of the wall surface is the Y-axis. The positive direction of the X-axis is defined by the upward right-handed system of the Z-axis. The transformation matrix from the Earth's core rectangular coordinates to the wall's core rectangular coordinates is expressed by the following equation (9): The transformation matrix from the wall core rectangular coordinates to the Earth core solid rectangular coordinates is expressed by the following equation (10): Where B and L are the geographical latitude and longitude of any point on the wall, respectively; α is the heading angle of the street; Step 3-2: Change the row corresponding to the non-line-of-sight signal in the design matrix G from the following equation (11) to (G i )′: Where x0, y0, and z0 are the coordinate elements of the initial value coordinate vector x0; x i y i , z i is the coordinate of satellite i; r is the geometric distance between the satellite and the receiver; S is the multi-system bias coefficient represented by a 1×(sn-1) vector; sn is the number of all satellite systems involved in the solution; I is the identity matrix; M is the direction cosine correction matrix defined by the following equation (12): Step 4: Joint positioning solution of line-of-sight signal and modified non-line-of-sight signal Step 4-1: OMC of combined line-of-sight satellite signals i And the non-line-of-sight satellite signal after step 2 correction (omc) i The updated difference matrix omc is formed between the observed and estimated values. corr Joint line-of-sight satellite signal design matrix G i and the non-line-of-sight satellite signal design matrix row (G) after step 3 correction i The updated design matrix G is formed by )′. corr The unknown vector correction value Δx′ is obtained by the following equation (13): Among them, the standard deviation σ of the line-of-sight and non-line-of-sight signals in the weight matrix W i Using the same signal variance amplification factor m; C is the constraint matrix defined by the following equation (14): In the formula: and These are the prior variances of the three-dimensional coordinates and the receiver clock bias, respectively. Step 4-2: Use the following equation (15) to evaluate the prior value from step 1. Update to obtain the final location result.

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