GNSS data processing method based on generalized least square filter

Abstract

A GNSS data processing method based on a generalized least square filter comprises the following steps that firstly, an observation model is constructed, and then the generalized least square filter is obtained based on the least square principle; firstly, a transformation matrix is defined in each epoch so as to determine the dynamic change of the dimensionality of the state parameters, and then a dynamic model is constructed according to the real time-varying characteristics of the state parameters; initializing filtering according to a parameter minimum product estimation value of a first epoch, transmitting a state estimation value of a previous epoch to a current epoch to obtain a predicted value of a state parameter, adjusting the predicted value through an observation model, and combining original observation data to obtain an estimation value of the current epoch; the method comprises the following steps: taking an estimated value of a current epoch as a basis of prediction of a next epoch, and updating an estimated value of a state parameter in each epoch according to original observation data and a dynamic model so as to obtain real-time positioning information. The method is accurate in positioning precision and does not need to depend on an initial state value.

Description

Technical Field

[0001] The invention relates to an improvement of a GNSS data processing technology, belongs to the field of GNSS data processing, and in particular to a GNSS data processing method based on a generalized least squares filter. Background Art

[0002] As a recursive algorithm widely used in GNSS data processing, Kalman filter plays a key role in positioning, navigation and timing. However, the standard Kalman filter faces some challenges in practical applications, especially when processing GNSS data. It usually assumes that all state parameters already have initial values ​​and corresponding dynamic models, but this assumption is often difficult to meet in reality. When the initial state information is insufficient, the performance of the Kalman filter will be affected, which may lead to a decrease in the accuracy of the positioning results.

[0003] The Chinese patent application with application number CN201711127678.6 and application date November 9, 2017 discloses that the present invention relates to a method for estimating generalized absolute code deviation of multi-frequency and multi-mode GNSS, redefines and classifies the current multi-frequency and multi-mode GNSS code deviation, and uses the original pseudo-range observation data of the multi-frequency and multi-mode GNSS observation network to respectively construct a geometric range-free observation equation and an ionosphere-free observation equation, and fully expresses each code deviation in the observation equation. According to the distinguishability of each deviation parameter in the design matrix, the deviation parameters are recombined in combination with the condition number of the matrix rank deficiency, and the code deviation and other parameters are estimated by least squares; by introducing the same observation reference as the existing clock error product, the relative code deviation parameter can be converted into the absolute code deviation parameter. The invention can provide a quasi-absolute code deviation value for the original observation value, and provide a simple and unified deviation correction method for navigation and positioning users. However, the above scheme does not solve the problem of insufficient positioning accuracy.

[0004] The information disclosed in this background technology section is only intended to increase the understanding of the overall background of this patent application, and should not be regarded as acknowledging or suggesting in any form that the information constitutes the prior art already known to ordinary technicians in this field. Summary of the invention

[0005] The purpose of the present invention is to overcome the problem of insufficient positioning accuracy in the prior art and to provide a GNSS data processing method based on a generalized least squares filter with accurate positioning accuracy.

[0006] To achieve the above objectives, the technical solution of the present invention is: a GNSS data processing method based on a generalized least squares filter, the GNSS data processing method based on a generalized least squares filter comprises the following steps:

[0007] The first step is to build an observation model based on the original GNSS observation data, and then obtain a generalized least squares filter in the Gauss-Markov form based on the least squares principle according to the observation model;

[0008] In the second step, the transformation matrix is ​​defined in each epoch to determine the dynamic changes of the state parameter dimensions, and then the dynamic model is constructed based on the real time-varying characteristics of the state parameters;

[0009] Step 3: Initialize the filter based on the minimum multiplication estimate of the parameters of the first epoch, then transfer the state estimate of the previous epoch to the current epoch according to the dynamic model to obtain the predicted value of the state parameter, adjust the predicted value through the observation model, and then combine it with the original GNSS observation data to obtain the estimated value of the current epoch;

[0010] The fourth step is to use the estimated value of the current epoch as the basis for the prediction of the next epoch. In each epoch, the estimated value of the state parameter is updated through a generalized least squares filter based on the original GNSS observation data and the dynamic model to obtain real-time positioning information.

[0011] In the first step, the observation model is as follows:

[0012] ;

[0013] in, and denote the expected operator and the discrete operator respectively, is the observation vector, is the design matrix, is the state vector, is the observation variance matrix.

[0014] In the second step, we first define the transformation matrix: define two transformation matrices at each epoch and ;

[0015] ;

[0016] and is a linear function of the state parameter and Formulate dynamic models:

[0017] .

[0018] In the third step, the filter is initialized according to the minimum multiplication estimate of the parameters of the first epoch, specifically: the minimum multiplication estimate of the parameters of the first epoch is calculated to initialize the filter, considering the estimate of the previous epoch As a pseudo observation value, the combined observation equation is:

[0019] ;in, represent The variance matrix of

[0020] Since the observation equation has no redundant observations, the predicted value is:

[0021] ;

[0022] Among them, the pseudo observation .

[0023] The predicted value As a pseudo observation, it is combined with the observation collected in the current epoch to construct the combined observation equation:

[0024] ;

[0025] Based on this, the normal equation is:

[0026] ;

[0027] The solution is:

[0028] Will Substitution have to:

[0029] ;

[0030] in, yes The right inverse of ;

[0031] matrix represents the gain matrix;

[0032] get and The filter value of:

[0033] ;

[0034] in, The parameters used to predict the next epoch, Parameters used to smooth the previous epoch.

[0035] The This breaks down into:

[0036] ;

[0037] Among them, the matrix Reversible, due to:

[0038] ;

[0039] definition for The null space basis matrix satisfies In addition, define for The right inverse of .

[0040] The observation equation is reconstructed as:

[0041] ;

[0042] in,

[0043] ;

[0044] By elimination of equations in the block system , we can get The filter value is:

[0045] ;

[0046] in,

[0047] .

[0048] According to the least squares principle, we can get The filter value is:

[0049]

[0050] in, yes and The covariance matrix of ;

[0051] but The filter value is:

[0052] .

[0053] Said The residual for:

[0054] ;

[0055] Reconstructing the equation:

[0056] ;

[0057] in, .

[0058] Said get The smoothing value of

[0059] ;

[0060] in, .

[0061] Compared with the prior art, the present invention has the following beneficial effects:

[0062] 1. In a GNSS data processing method based on a generalized least squares filter of the present invention, the generalized least squares filter can automatically estimate the initial value when a newly introduced parameter appears, and the established dynamic model is only for the linear function of the parameter, and does not require all parameters to have a dynamic model, thereby avoiding the error caused by improper description of the dynamic model, solving the problem of the dependence of the traditional Kalman filter on the initial state value, and improving the positioning accuracy. Therefore, the positioning accuracy of the present invention is accurate and does not need to rely on the initial state value.

[0063] 2. In a GNSS data processing method based on a generalized least squares filter of the present invention, the filter can adapt to the parameters introduced or reduced due to changes in satellite visibility, and allows the parameter dimension to change dynamically over time; this adaptive parameter management improves the flexibility of the filter and is applicable to a variety of GNSS application scenarios. At the same time, the least squares smoothing technology is introduced, which can not only improve the positioning accuracy during the filtering process, but also make the method applicable to near-real-time GNSS applications, especially in multi-epoch ambiguity resolution, showing a higher success rate and positioning accuracy. Therefore, the positioning accuracy is better and is applicable to a variety of scenarios.

[0064] 3. In a GNSS data processing method based on a generalized least squares filter of the present invention, by estimating only the parameters with a dynamic model, the generalized least squares filter reduces the number of parameters to be estimated, thereby improving the calculation efficiency. In addition, the normal equation simplification strategy further improves the calculation efficiency, which is about 23% to 32% higher than the traditional method. Therefore, the present invention has higher calculation efficiency and reduces the number of parameters to be estimated. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 It is a generalized least squares filter framework diagram of the present invention.

[0066] Figure 2 It is a 3D positioning error diagram of GPS-only simulated dynamic RTK positioning based on generalized least squares filter and Kalman filter in the present invention.

[0067] Figure 3 It is a 3D positioning error diagram of three-system simulated dynamic RTK positioning based on generalized least squares filter and Kalman filter in the present invention.

[0068] Figure 4 It is a diagram of ambiguity-fixed 3D positioning error and time consumption of three-system simulated dynamic RTK positioning based on generalized least squares filter and Kalman filter in the present invention.

[0069] Figure 5 It is the ambiguity fixed positioning error diagram of the three systems simulating dynamic RTK in the present invention.

[0070] Figure 6 It is a GPS-only simulated dynamic positioning error diagram based on the least squares smoothing strategy in the present invention.

[0071] Figure 7 It is the horizontal trajectory and 3D positioning error diagram of the dynamic RTK positioning of only GPS vehicle based on the generalized least squares filter and the Kalman filter under different initial value variances and system noises in the present invention.

[0072] Figure 8 It is a result diagram of the ambiguity floating point solution and the ambiguity fixed solution of the three-system vehicle dynamic RTK positioning based on the generalized least squares filter and the Kalman filter under different initial value variances and system noises in the present invention.

[0073] Fig. 9 It is the ambiguity fixed 3D trajectory and time consumption diagram of the three-system vehicle dynamic RTK positioning based on the large variance setting of the generalized least squares filter and the Kalman filter in the present invention.

[0074] Fig.10 It is the ambiguity fixed vertical trajectory of the three-system vehicle dynamic short baseline and ultra-short baseline RTK positioning in the present invention.

[0075] Fig.11 It is a three-system vehicle dynamic RTK positioning error diagram based on the least squares smoothing strategy with different smoothing windows in the present invention. DETAILED DESCRIPTION

[0076] The present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0077] See also Figures 1 to 11 , a GNSS data processing method based on a generalized least squares filter, the GNSS data processing method based on a generalized least squares filter comprising the following steps:

[0078] The first step is to build an observation model based on the original GNSS observation data, and then obtain a generalized least squares filter in the Gauss-Markov form based on the least squares principle according to the observation model;

[0079] In the second step, the transformation matrix is ​​defined in each epoch to determine the dynamic changes of the state parameter dimensions, and then the dynamic model is constructed based on the real time-varying characteristics of the state parameters;

[0080] Step 3: Initialize the filter based on the minimum multiplication estimate of the parameters of the first epoch, then transfer the state estimate of the previous epoch to the current epoch according to the dynamic model to obtain the predicted value of the state parameter, adjust the predicted value through the observation model, and then combine it with the original GNSS observation data to obtain the estimated value of the current epoch;

[0081] The fourth step is to use the estimated value of the current epoch as the basis for the prediction of the next epoch. In each epoch, the estimated value of the state parameter is updated through a generalized least squares filter based on the original GNSS observation data and the dynamic model to obtain real-time positioning information.

[0082] In the first step, the observation model is as follows:

[0083] ;

[0084] in, and denote the expected operator and the discrete operator respectively, is the observation vector, is the design matrix, is the state vector, is the observation variance matrix.

[0085] In the second step, we first define the transformation matrix: define two transformation matrices at each epoch and ;

[0086] ;

[0087] and is a linear function of the state parameter and Formulate dynamic models:

[0088] .

[0089] In the third step, the filter is initialized according to the minimum multiplication estimate of the parameters of the first epoch, specifically: the minimum multiplication estimate of the parameters of the first epoch is calculated to initialize the filter, considering the estimate of the previous epoch As a pseudo observation value, the combined observation equation is:

[0090] ;in, represent The variance matrix of

[0091] Since the observation equation has no redundant observations, the predicted value is:

[0092] ;

[0093] Among them, the pseudo observation .

[0094] The predicted value As a pseudo observation, it is combined with the observation collected in the current epoch to construct the combined observation equation:

[0095] ;

[0096] Based on this, the normal equation is:

[0097] ;

[0098] The solution is:

[0099] ;Will Substitution have to:

[0100] ;

[0101] in, yes The right inverse of ;

[0102] matrix represents the gain matrix;

[0103] get and The filter value of:

[0104] ;

[0105] in, The parameters used to predict the next epoch, Parameters used to smooth the previous epoch.

[0106] The This breaks down into:

[0107] ;

[0108] Among them, the matrix Reversible, due to:

[0109] ;

[0110] definition for The null space basis matrix satisfies In addition, define for The right inverse of .

[0111] The observation equation is reconstructed as:

[0112] ;

[0113] in,

[0114] ;

[0115] By elimination of equations in the block system , we can get The filter value is:

[0116] ;

[0117] in,

[0118] .

[0119] According to the least squares principle, we can get The filter value is:

[0120]

[0121] in, yes and The covariance matrix of ;

[0122] but The filter value is:

[0123] .

[0124] Said The residual for:

[0125] ;

[0126] Reconstructing the equation:

[0127] ;

[0128] in, .

[0129] Said get The smoothing value of

[0130] ;

[0131] in, .

[0132] The supplementary description of the present invention is as follows:

[0133] Traditional Kalman filters usually require all state parameters to have initial values ​​and dynamic models when recursively processing data. The present invention reconstructs the generalized Kalman filter and proposes a generalized least squares filter that can flexibly process GNSS data when parameters change over time. The filter not only eliminates the dependence on initial values, but also allows the parameters of the dynamic model to be adjusted as satellite visibility changes.

[0134] Embodiment 1:

[0135] A GNSS data processing method based on a generalized least squares filter, the GNSS data processing method based on a generalized least squares filter comprising the following steps:

[0136] The first step is to build an observation model based on the original GNSS observation data, and then obtain a generalized least squares filter in the Gauss-Markov form based on the least squares principle according to the observation model;

[0137] In the second step, the transformation matrix is ​​defined in each epoch to determine the dynamic changes of the state parameter dimensions, and then the dynamic model is constructed based on the real time-varying characteristics of the state parameters;

[0138] Step 3: Initialize the filter based on the minimum multiplication estimate of the parameters of the first epoch, then transfer the state estimate of the previous epoch to the current epoch according to the dynamic model to obtain the predicted value of the state parameter, adjust the predicted value through the observation model, and then combine it with the original GNSS observation data to obtain the estimated value of the current epoch;

[0139] The fourth step is to use the estimated value of the current epoch as the basis for the prediction of the next epoch. In each epoch, the estimated value of the state parameter is updated through a generalized least squares filter based on the original GNSS observation data and the dynamic model to obtain real-time positioning information.

[0140] Embodiment 2:

[0141] Embodiment 2 is substantially the same as Embodiment 1, except that:

[0142] In the first step, the observation model is as follows:

[0143] ;

[0144] in, and denote the expected operator and the discrete operator respectively, is the observation vector, is the design matrix, is the state vector, is the observation variance matrix.

[0145] In the second step, we first define the transformation matrix: define two transformation matrices at each epoch and ;

[0146] ;

[0147] and is a linear function of the state parameter and Formulate dynamic models:

[0148] .

[0149] In the third step, the filter is initialized according to the minimum multiplication estimate of the parameters of the first epoch, specifically: the minimum multiplication estimate of the parameters of the first epoch is calculated to initialize the filter, considering the estimate of the previous epoch As a pseudo observation value, the combined observation equation is:

[0150] ;in, represent The variance matrix of

[0151] Since the observation equation has no redundant observations, the predicted value is:

[0152] ;

[0153] Among them, the pseudo observation .

[0154] The predicted value As a pseudo observation, it is combined with the observation collected in the current epoch to construct the combined observation equation:

[0155] ;

[0156] Based on this, the normal equation is:

[0157] ;

[0158] The solution is:

[0159] Will Substitution have to:

[0160] ;

[0161] in, yes The right inverse of ;

[0162] matrix represents the gain matrix;

[0163] get and The filter value of:

[0164] ;

[0165] in, The parameters used to predict the next epoch, Parameters used to smooth the previous epoch.

[0166] The This breaks down into:

[0167] ;

[0168] Among them, the matrix Reversible, due to:

[0169] ;

[0170] definition for The null space basis matrix satisfies In addition, define for The right inverse of .

[0171] The observation equation is reconstructed as:

[0172] ;

[0173] in,

[0174] ;

[0175] By elimination of equations in the block system , we can get The filter value is:

[0176] ;

[0177] in,

[0178] .

[0179] According to the least squares principle, we can get The filter value is:

[0180]

[0181] in, yes and The covariance matrix of ;

[0182] but The filter value is:

[0183] .

[0184] Said The residual for:

[0185] ;

[0186] Reconstructing the equation:

[0187] ;

[0188] in, .

[0189] Said get The smoothing value of

[0190] ;

[0191] in, .

[0192] Embodiment 3:

[0193] Embodiment 3 is substantially the same as Embodiment 1, except that:

[0194] See also Figures 2 to 6 , a GNSS simulated dynamic RTK positioning experiment was carried out, and the generalized least squares filter (GLSF) and Kalman filter (KF) were used for comparative analysis. The experiment involved the comparison of the non-difference RTK positioning performance of a single system (GPS only) and multiple systems (GPS+BDS+Galileo).

[0195] First, a simulated dynamic RTK positioning experiment with only GPS is conducted, and the positioning performance under different system noise variance settings is compared using generalized least squares filter and Kalman filter. For parameters without dynamic association (such as position, ionospheric delay, receiver and satellite clock, etc.), the system noise needs to be set to a very large value in the Kalman filter to simulate the random changes of these parameters. In addition, when a new satellite appears or a cycle slip occurs, the initial value of the relevant parameters is set to zero and the variance is set to the maximum value.

[0196] Figure 2The 3D positioning error of GPS-only simulated dynamic RTK positioning under different variance settings is shown, for both ambiguity floating point and ambiguity fixed results. When the variance setting is small, especially when newly tracked satellites appear, the positioning error of ambiguity floating point and fixed exceeds 0.4 meters in some epochs. As the variance increases, the positioning error decreases and gradually approaches the result of the generalized least squares filter. This shows that the results of the Kalman filter can be used as a numerical approximation of the results of the generalized least squares filter. However, the Kalman filter is very sensitive to the selection of the system noise variance, and if it is not set properly, it may lead to suboptimal positioning results. Even in some cases, the error converges to the centimeter level, but the uncertainty of the empirical variance setting may cause the Kalman filter to show degraded positioning accuracy.

[0197] Figure 3 The 3D positioning error of multi-system positioning is shown, also for the results of ambiguity floating point and ambiguity fixed. Compared with GPS positioning alone, the introduction of multiple systems significantly enhances the robustness of the model. The positioning error of the Kalman filter under three systems is reduced to the centimeter level after convergence. However, in the early stage of positioning, due to the dependence on the system noise variance, the convergence speed of the Kalman filter is slow, especially when the variance is set small, the convergence time will be significantly extended. In addition, when a new satellite is tracked, the positioning error may increase if the initial value is not set properly. In contrast, the generalized least squares filter avoids empirical parameter settings and exhibits better performance.

[0198] Figure 4 The ambiguity-fixed 3D positioning error (upper figure) and time consumption (lower figure) of the generalized least squares filter and the Kalman filter in the large variance setting in the three-system simulated dynamic RTK positioning are shown. The results show that the two filters perform almost the same in terms of positioning error, but the calculation time of the generalized least squares filter is significantly less than that of the Kalman filter. This is because the generalized least squares filter improves the computational efficiency by eliminating the parameters without dynamic models in the normal equations, while the Kalman filter needs to estimate all parameters at each epoch.

[0199] Figure 5 The positioning error with fixed ambiguity in the three-system simulated dynamic RTK is further demonstrated, in which two treatments are performed on the "sky" component: no time correlation (blue) and time constant (red). The experimental results show that although the positioning errors of the north and east components are almost unaffected by the constraints of the "sky" component, the positioning accuracy is significantly improved after setting the "sky" component as a time constant, especially the error in the vertical direction is greatly reduced. The results show that for some application scenarios, the overall positioning performance can be improved by imposing constraints on a specific position component.

[0200] Figure 6The results of GPS-only simulated dynamic positioning errors based on the least squares smoothing strategy are shown for floating ambiguity (above) and fixed ambiguity (below); the convergence time can be significantly shortened by using smoothing windows of different lengths (e.g., 5, 10, 15, 20, and 25 epochs). In the case of floating ambiguity, the positioning error can converge quickly within 1 epoch when the smoothing window is 20 or 25 epochs; and in the case of fixed ambiguity, the ambiguity problem can be resolved within a single epoch even if the smoothing window is set to 5 epochs. This shows that the smoothing strategy has a significant effect on accelerating the convergence speed of RTK positioning, especially when the ambiguity is fixed, which can greatly improve the positioning performance.

[0201] Embodiment 4:

[0202] Embodiment 4 is substantially the same as Embodiment 1, except that:

[0203] See also Figures 7 to 11 , conducted a real-world vehicle dynamic RTK positioning experiment based on Kalman filter (KF) and generalized least squares filter (GLSF), including a comparative analysis of a single system (GPS only) and a triple system (GPS+BDS+Galileo);

[0204] Figure 7 The horizontal trajectory and positioning error of a GPS-only vehicle are shown, for the results of the ambiguity float and ambiguity fixed solutions respectively. In the first 1600 epochs, the positioning errors of the different filters are almost the same because the same seven satellites are continuously tracked. However, after 1600 epochs, since one of the satellites can only be tracked intermittently, the Kalman filter needs to re-initialize the relevant parameters of this satellite, resulting in an increase in the positioning error, which is several decimeters. Even though the ambiguity resolution can reduce the error to a few centimeters, the error can still exceed two decimeters when the satellite is re-tracked and the ambiguity resolution is wrong. In contrast, the generalized least squares filter avoids the problem of empirical initialization and variance setting, and its ambiguity float solution gradually converges to a few centimeters, and the ambiguity fixed solution reduces the error to a few centimeters after about 60 seconds.

[0205] Figure 8 The horizontal trajectory and positioning error of the three systems (GPS+BDS+Galileo) are shown. When the Kalman filter is used and the variance is set small, the positioning error exceeds 1 meter, which is significantly higher than the error of GPS alone. This is because the new addition of BDS and Galileo satellites during initialization causes frequent changes in satellite visibility, which affects the positioning performance. When the system noise variance increases, the positioning converges faster and gradually approaches the result of the generalized least squares filter. This also proves that as long as the variance is set large enough, the result of the Kalman filter can be used as a numerical approximation of the generalized least squares filter.

[0206] Fig. 9 The 3D trajectory and computational time of the vehicle dynamic RTK are compared. The experiment shows that when the variance of the Kalman filter is set to a large value, its positioning trajectory is almost the same as that of the generalized least squares filter. However, the generalized least squares filter is more efficient by eliminating the parameters of the non-dynamic model, and the computational time is reduced from 0.13 seconds to 0.088 seconds, which significantly improves the calculation speed.

[0207] Fig.10 The positioning results in the vertical direction are shown. In this experiment, the vehicle is located on the roof of a building, and the coordinate change of the "sky" component is small. It is modeled as a random process with a small random walk noise, and the positioning trajectories with and without vertical component constraints are compared. The experimental results show that when no constraints are imposed, the trajectory deviates from the reference trajectory at some epochs; after applying the random walk constraint of the vertical component, the trajectory is closer to the reference value, indicating that the positioning accuracy is improved. This demonstrates the flexibility of the generalized least squares filter, which can design dynamic models with specific parameters to improve positioning performance.

[0208] Fig.11 The positioning error based on the least squares smoothing strategy is shown, for the results of ambiguity floating point and ambiguity fixed solutions respectively. The experiment shows that in the case of ambiguity floating point solution, the positioning needs about 170 seconds to converge, while after using the smoothing strategy, the convergence time is significantly shortened. The larger the smoothing window, the faster the convergence speed. In the case of ambiguity fixed solution, positioning usually only takes tens of seconds to complete convergence. When the smoothing window reaches 15 epochs or more, the positioning error can be reduced to a few centimeters within the first epoch, and the positioning accuracy is significantly improved. This shows that the least squares smoothing strategy can improve the positioning accuracy in quasi-real-time applications, reflecting the flexibility of the data processing method based on the least squares method.

[0209] The above description is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiment. Any equivalent modifications or changes made by ordinary technicians in this field based on the contents disclosed by the present invention should be included in the protection scope recorded in the claims.

Claims

1. A GNSS data processing method based on a generalized least squares filter, characterized in that: The GNSS data processing method based on the generalized least squares filter comprises the following steps: The first step is to build an observation model based on the original GNSS observation data, and then obtain a generalized least squares filter in the Gauss-Markov form based on the least squares principle according to the observation model; In the second step, the transformation matrix is ​​defined in each epoch to determine the dynamic changes of the state parameter dimensions, and then the dynamic model is constructed based on the real time-varying characteristics of the state parameters; Step 3: Initialize the filter based on the minimum multiplication estimate of the parameters of the first epoch, then transfer the state estimate of the previous epoch to the current epoch according to the dynamic model to obtain the predicted value of the state parameter, adjust the predicted value through the observation model, and then combine it with the original GNSS observation data to obtain the estimated value of the current epoch; The fourth step is to use the estimated value of the current epoch as the basis for the prediction of the next epoch. In each epoch, the estimated value of the state parameter is updated through a generalized least squares filter based on the original GNSS observation data and the dynamic model to obtain real-time positioning information.

2. The GNSS data processing method based on generalized least squares filter according to claim 1, characterized in that: In the first step, the observation model is as follows: ； in, and denote the expected operator and the discrete operator respectively, is the observation vector, is the design matrix, is the state vector, is the observation variance matrix; The above equations are the basic function model and random model for GNSS data processing, as well as the classic Gauss-Markov model. Note that it takes into account the time-varying characteristics of the dimensions of the observation value vector and the unknown parameter vector, and is applicable to any GNSS data processing scenario.

3. The GNSS data processing method based on generalized least squares filter according to claim 1, characterized in that: In the second step, we first define the transformation matrix: define two transformation matrices at each epoch and ; ； The unknown parameters extracted from the two transformation matrices are used to establish dynamic models with the parameters of the previous epoch and the next epoch respectively; and is a linear function of the state parameter and Formulate dynamic models: ； To facilitate least squares derivation, the dynamic model is still written in the form of a Gauss-Markov model, that is, the dynamic model noise is set as a virtual observation value.

4. The GNSS data processing method based on generalized least squares filter according to claim 1, characterized in that: In the third step, the filter is initialized according to the minimum multiplication estimate of the parameters of the first epoch, specifically: the minimum multiplication estimate of the parameters of the first epoch is calculated to initialize the filter, considering the estimate of the previous epoch As a pseudo observation value, the combined observation equation is: ;in, represent The variance matrix of The above equation is still a classic Gauss-Markov model, which can be directly solved according to the least squares principle. Since there are no redundant observations in this observation equation, the predicted value is: ； Among them, the pseudo observation , from which the optimal prediction value of the current epoch and its covariance matrix can be obtained.

5. The GNSS data processing method based on generalized least squares filter according to claim 4, characterized in that: The predicted value As a pseudo observation, it is combined with the observation collected in the current epoch to construct the combined observation equation: ； It is in the form of a classic Gauss-Markov model, consisting of equations for the predicted values ​​and the observed values ​​at the current epoch, and the corresponding covariance matrix; Based on this, the normal equation is: ； The normal matrix in this equation is full rank and invertible, and the solution is: Put the Substitution Adjusting the equation accordingly, we get: ； in, yes The right inverse of ; matrix represents the gain matrix; get and The filter value of: ； in, The parameters used to predict the next epoch, Parameters used to smooth the previous epoch.

6. The GNSS data processing method based on generalized least squares filter according to claim 5, characterized in that: The This breaks down into: ； Among them, the matrix Reversible, since the matrix is ​​full rank and reversible, the decomposition does not lose any information, and because: ； Among them, the definition for The null space basis matrix satisfies In addition, define for The right inverse of .

7. The GNSS data processing method based on generalized least squares filter according to claim 6, characterized in that: The observation equation is reconstructed as: ； in, ； By elimination of equations in the block system , we can get The filter value is: ； in, ； Its form is consistent with the design matrix in the Gauss-Markov model. Therefore, the above equation obtains the filtering solution of the parameters based on the least squares principle.

8. The GNSS data processing method based on generalized least squares filter according to claim 7, characterized in that: According to the least squares principle, we can get The filter value is: ； in, yes and The covariance matrix of ; but The filter value is: ； It can be seen that the filtered value of the parameter can be obtained by first solving the filtered values ​​of some parameters.

9. The GNSS data processing method based on generalized least squares filter according to claim 8, characterized in that: Said The residual for: ； Reconstructing the equation: ； in, , is regarded as the gain matrix in the smoothing process.

10. The GNSS data processing method based on generalized least squares filter according to claim 9, characterized in that: Said get The smoothing value of ； in, , which is regarded as the gain matrix in the smoothing process. It can be seen that according to the principle of least squares conditional adjustment, after two smoothing, the optimal smoothing value of the previous epoch can be obtained from the optimal estimate of the current epoch. By this calculation, the smoothing value of any epoch window can be finally obtained.

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