GPS measurement gross error robust estimation method, device, equipment and medium
By constructing the observation model and error equation of the GPS baseline network, the standardized residuals are calculated and the downweight factor of the improved IGG-III solution is constructed, and the equivalent weights are used to replace the baseline vector prior weight matrix, the data accuracy problem caused by coarse deviation in GPS measurement is solved, and a higher data adjustment accuracy is achieved.
Patent Information
- Application Number
- CN202510423578.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-03
- Publication Date
- 2025-08-19
AI Technical Summary
During the GPS measurement process, there is a rough difference in the observed data, which affects the robustness of the parameter estimation of the least squares method and reduces the data accuracy.
By constructing the observation model and error equation of the GPS baseline network, the standardized residuals are calculated and the downweight factor of the improved IGG-III scheme is constructed, and the baseline vector prior weight matrix is used to replace the baseline vector prior weight matrix, and the number of corrections to be determined is resolved to filter the coarse error.
Effectively resist the impact of crude deviation on GPS baseline network observation data, improving the data adjustment accuracy.
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Figure CN120507771A_ABST
Abstract
Description
Technical Field
[0001] The present application relates to the field of GPS measurement technology, and in particular to a GPS measurement gross error robustness estimation method, device, equipment and medium. Background Art
[0002] During Global Positioning System (GPS) measurements, the accuracy of observation data is constrained by satellite data quality and the external environment, and the observed values inevitably contain some gross errors. When the observed values deviate from a normal distribution or are contaminated by significant outliers, the robustness of the least squares (LS) method in parameter estimation is significantly affected, which in turn weakens the accuracy of the parameter estimates. With the continuous advancement of technology and the increasing demand for data accuracy, the relevant parameter estimation method, namely the least squares method, can no longer meet the requirements for data accuracy. Summary of the Invention
[0003] The purpose of this application is to provide a GPS measurement gross error robustness estimation method, device, equipment and medium, which can improve the data adjustment accuracy of the GPS baseline network.
[0004] To achieve the above objectives, this application provides the following solutions:
[0005] In a first aspect, the present application provides a GPS measurement gross error robust estimation method, comprising:
[0006] Converting GPS baseline network related observations into independent observations; the GPS baseline network includes multiple undetermined points and multiple observation baselines; the independent observations are baseline vector observations;
[0007] Constructing an observation model and error equation of the GPS baseline network based on the independent observations;
[0008] Calculating the coordinate correction number of the point to be determined based on the observation model and the error equation;
[0009] Determine whether the coordinate correction number of the current point to be determined meets the set conditions;
[0010] If the set conditions are not met, the standardized residual is calculated based on the current baseline observation residual value and the cofactor matrix of the current baseline observation residual value;
[0011] constructing a weight reduction factor of the improved IGG-III scheme according to the standardized residual, and determining an equivalent weight according to the weight reduction factor;
[0012] The equivalent weight is used to replace the baseline vector prior weight matrix used in solving the coordinate correction number of the undetermined point, and the coordinate correction number of the current undetermined point is recalculated, and the step of returning to determine whether the coordinate correction number of the current undetermined point meets the set conditions is returned.
[0013] If the set conditions are met, the coordinate anti-error value of the pending point is calculated based on the current coordinate correction number of the pending point.
[0014] Optionally, the observation model of the GPS baseline network is expressed as:
[0015] Among them, L is the baseline vector observation value, V is the baseline observation residual value, is the coordinate anti-error value, B is the coefficient matrix, d is the error coefficient, n is the number of observation baselines, and t is the number of points to be determined;
[0016] The error equation of the GPS baseline network is expressed as:
[0017] in, is the coordinate correction number of the point to be determined; l is the intermediate parameter; ΔX sw The difference in the X direction between the first and last endpoints of the baseline vector; The initial value of the X-direction coordinate of the first endpoint of the observation baseline vector; The initial value of the X-direction coordinate of the tail endpoint of the observation baseline vector.
[0018] Optionally, calculating the coordinate correction value of the undetermined point according to the observation model and the error equation specifically includes:
[0019] According to the observation model and the error equation, the least squares principle is used to establish the normal equation; the normal equation is expressed as: Where P is the baseline vector prior weight matrix;
[0020] The coordinate correction number of the point to be determined is calculated according to the normal equation; the coordinate correction number of the point to be determined is expressed as:
[0021]
[0022] Optionally, the setting condition is: in, The coordinate correction number of the point to be determined.
[0023] Optionally, the formula for calculating the standardized residual based on the current baseline observation residual value and the cofactor matrix of the current baseline observation residual value is:
[0024]
[0025] Among them, v iis the standardized residual of the ith observation, V i is the current baseline observation residual value of the i-th observation, σ is the posterior unit weighted mean error, is the cofactor value of the current baseline observation residual value of the i-th observation.
[0026] Optionally, constructing a weight reduction factor of the improved IGG-III scheme according to the standardized residual, and determining the equivalent weight according to the weight reduction factor, specifically includes:
[0027] The down-weighting factor is expressed as:
[0028] The equivalent weight is expressed as:
[0029] Among them, ω(v i ) is the weighting factor of the standardized residual of the i-th observation, k0 and k1 are both constants, v i is the standardized residual of the i-th observation, p i is the prior weight of the i-th observation, is the equivalent weight of the i-th observation.
[0030] Optionally, the formula for calculating the coordinate anti-error value of the pending point based on the current coordinate correction number of the pending point is:
[0031]
[0032] in, is the coordinate anti-error value, X 0 is the initial value of the coordinates of the point to be determined, The coordinate correction number of the point to be determined.
[0033] In a second aspect, the present application provides a GPS measurement gross error robustness estimation device, the GPS measurement gross error robustness estimation device comprising:
[0034] A GPS baseline network related observation quantity conversion module is used to convert GPS baseline network related observation quantities into independent observation quantities; the GPS baseline network includes multiple undetermined points and multiple observation baselines; the independent observation quantities are baseline vector observation values;
[0035] An observation model and error equation construction module, configured to construct an observation model and error equation of the GPS baseline network based on the independent observations;
[0036] A module for calculating the coordinate correction number of the undetermined point, used for calculating the coordinate correction number of the undetermined point according to the observation model and the error equation;
[0037] The judgment module is used to judge whether the coordinate correction number of the current point to be determined meets the set conditions;
[0038] a standardized residual calculation module, configured to calculate the standardized residual based on the current baseline observation residual value and the cofactor matrix of the current baseline observation residual value if the output of the judgment module is no;
[0039] An equivalent weight determination module, configured to construct a weight reduction factor of the improved IGG-III scheme according to the standardized residual, and determine an equivalent weight according to the weight reduction factor;
[0040] A module for updating the coordinate correction number of the pending point is used to replace the baseline vector prior weight matrix used in solving the coordinate correction number of the pending point with the equivalent weight, re-solve the coordinate correction number of the current pending point, and return to the step of determining whether the coordinate correction number of the current pending point meets the set conditions;
[0041] The coordinate anti-error value calculation module is used to calculate the coordinate anti-error value of the undetermined point based on the current coordinate correction number of the undetermined point if the output of the judgment module is yes.
[0042] In a third aspect, the present application provides a computer device comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the GPS measurement gross error robustness estimation method described above.
[0043] In a fourth aspect, the present application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of any one of the above-mentioned GPS measurement gross error robustness estimation methods.
[0044] According to the specific embodiments provided in this application, this application discloses the following technical effects:
[0045] The present application provides a GPS measurement gross error robust estimation method, apparatus, equipment and medium. If the current coordinate correction number of the undetermined point does not meet the set conditions, a weight reduction factor of the improved IGG-III scheme is constructed according to the standardized residual, and an equivalent weight is determined according to the weight reduction factor; the equivalent weight is used to replace the baseline vector prior weight matrix, and the current coordinate correction number of the undetermined point is recalculated. The step of judging whether the current coordinate correction number of the undetermined point meets the set conditions is returned, and the coordinate correction number of the undetermined point meets the set conditions. The method can effectively filter the baseline observations containing gross errors through the equivalent weight, thereby resisting the influence of gross errors on the GPS baseline network observation data, and improving the data adjustment accuracy of the GPS baseline network. BRIEF DESCRIPTION OF THE DRAWINGS
[0046] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.
[0047] Figure 1 A flowchart of a GPS measurement gross error robustness estimation method provided in one embodiment of the present application;
[0048] Figure 2 A detailed flowchart of a GPS measurement gross error robustness estimation method provided in one embodiment of the present application;
[0049] Figure 3 A schematic diagram of the GPS baseline network structure provided in one embodiment of the present application;
[0050] Figure 4 A schematic diagram showing a comparison of mean errors in coordinate adjustment values obtained through experiments according to an embodiment of the present application;
[0051] Figure 5 A schematic diagram of the structure of a computer device provided in one embodiment of the present application. DETAILED DESCRIPTION
[0052] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.
[0053] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.
[0054] This application provides a GPS measurement gross error robustness estimation method, such as Figure 1 and Figure 2 As shown, the GPS measurement gross error robustness estimation method includes step 101-step.
[0055] Step 101: converting GPS baseline network related observations into independent observations; the GPS baseline network includes multiple undetermined points and multiple observation baselines; the independent observations are baseline vector observations.
[0056] Step 102: constructing the observation model and error equation of the GPS baseline network based on the independent observations.
[0057] Step 103: Calculate the coordinate correction value of the point to be determined based on the observation model and the error equation.
[0058] Step 104: Determine whether the coordinate correction value of the current point to be determined meets the set conditions.
[0059] If the answer in step 104 is no, step 105 is executed.
[0060] Step 105: Calculate the standardized residual according to the current baseline observation residual value and the cofactor matrix of the current baseline observation residual value.
[0061] Step 106: construct a weight reduction factor of the improved IGG-III scheme according to the standardized residual, and determine the equivalent weight according to the weight reduction factor.
[0062] Step 107: Use the equivalent weight to replace the baseline vector prior weight matrix used in solving the coordinate correction number of the undetermined point, recalculate the coordinate correction number of the current undetermined point, and return to the step of determining whether the coordinate correction number of the current undetermined point meets the set conditions.
[0063] If the answer in step 104 is yes, then step 108 is executed.
[0064] Step 108: If the set conditions are met, the coordinate anti-error value of the pending point is calculated based on the current coordinate correction value of the pending point.
[0065] The present application can effectively filter out baseline observations containing gross errors through equivalent weights, thereby resisting the influence of gross errors on GPS baseline network observation data and improving the data adjustment accuracy of the GPS baseline network.
[0066] Wherein, step 101 converts the GPS network related observations into independent observations, specifically including: using the Cholesky decomposition method to convert the baseline vector observations into the related observations.
[0067] Since the observations processed by the robust estimation method are independent observations, the GPS network related observations need to be converted into independent observations before entering the robust estimation.
[0068] The observation model of the GPS baseline network is expressed as: The GPS baseline network is referred to as the GPS network.
[0069] Among them, L is the baseline vector observation value, V is the baseline observation residual value, is the coordinate anti-error value, B is the coefficient matrix, d is the error coefficient, n is the number of observation baselines, and t is the number of points to be determined.
[0070] In an exemplary embodiment, Figure 3As shown in Figure 1, the GPS network consists of 6 undetermined points and 16 observation baselines, where points 1 and 8 are known reference points, and the coordinates of the 6 undetermined points all have initial values.
[0071] The baseline observation vector and its covariance matrix D are obtained through data processing software. Among them, the baseline vector prior weight matrix P is given by the formula or Calculated, σ0 is the set priori unit weight error value.
[0072] Based on this GPS network, random errors are added to the observed baseline vectors. Gross errors are added at each location in increments of 3σ0 to 12σ0, simulating a GPS network containing both random and gross errors. A least squares adjustment is then performed on the GPS network containing gross errors to obtain the least squares adjusted 3D coordinates of each pending point and the mean square error of the least squares adjusted coordinates.
[0073] In the GPS network, the baseline vector observation value L is expressed as (ΔX sw ,ΔY sw ,ΔZ sw ), where ΔX sw =X w -X s , ΔY sw =Y w -Y s , ΔZ sw =Z w -Z s .
[0074] Among them, X s is the X coordinate value of the first endpoint s on the observation baseline vector sw, X w is the X coordinate value of the end point w on the observation baseline vector sw, ΔX sw For X w With X s The difference, Y s is the Y coordinate value of the first endpoint s on the observation baseline vector sw, Y w is the Y coordinate value of the end point w on the observation baseline vector sw, ΔY sw Y w With Y s The difference, Z s is the Z coordinate value of the first endpoint s on the observation baseline vector sw, Z w is the Z coordinate value of the tail endpoint w on the observation baseline vector sw, ΔZ sw Z w With Z s Each observation baseline vector is an observation.
[0075] Taking the X-axis coordinate as an example, the adjustment value of the baseline vector observation value is specifically expressed as in is the residual value of the X direction of a baseline observation; the error equation of a certain observation baseline vector is specifically expressed as
[0076] in, For X w With X s The initial difference, is the X coordinate correction value of the end point w on the observation baseline vector sw, It is the correction value of the X coordinate value of the first endpoint s on the observed baseline vector sw.
[0077] Wherein, step 102 constructs the observation model and error equation of the GPS baseline network according to the indirect adjustment principle.
[0078] The error equation of the GPS baseline network is expressed as:
[0079] in, is the coordinate correction number of the point to be determined, and l is the intermediate parameter. Taking the X-axis coordinate as an example, ΔX sw is the difference in X direction between the first and last endpoints of the baseline vector. is the initial value of the X direction coordinate of the first endpoint of the observation baseline vector, The initial value of the X-direction coordinate of the tail endpoint of the observation baseline vector.
[0080] Since the error equation in Satisfy the adjustment criterion V T PV=min, and the derivative of the adjustment criterion can be obtained as B T PV = 0. Where P is the baseline vector prior weight matrix.
[0081] Wherein, step 103 specifically includes: according to the observation model and the error equation, using the least squares principle to establish a normal equation; the normal equation is expressed as:
[0082] The coordinate correction number of the point to be determined is calculated according to the normal equation; the coordinate correction number of the point to be determined is expressed as:
[0083]
[0084] Solve the cofactor matrix of the coordinates of the point to be determined Specifically:
[0085]
[0086] in, represents the cofactor of the jth undetermined point coordinates, 1≤j≤t; Represents the mutual correlation factor between the coordinates of the ath undetermined point and the coordinates of the bth undetermined point, 1≤a≤t, 1≤b≤t.
[0087] The setting conditions are: in, The coordinate correction number of the point to be determined.
[0088] This application uses the residual value obtained by least squares and the cofactor matrix to calculate the standardized residual based on the equivalent weight principle.
[0089] The formula for calculating the standardized residual based on the current baseline observation residual value and the cofactor matrix of the current baseline observation residual value is:
[0090] Among them, v i is the standardized residual of the ith observation, V i is the current baseline observation residual value of the i-th observation, σ is the posterior unit weighted mean error, is the cofactor value of the current baseline observation residual value of the i-th observation. The cofactor values of the residual values of each observation constitute the cofactor matrix Q of the residual value of the observation V .
[0091] Cofactor value of the residual value of the observation Specifically, it is expressed as the observation residual value cofactor matrix Q V The diagonal value of : in, is the cofactor matrix of the coordinates of the points to be determined.
[0092] The posterior unit weighted error σ is specifically expressed as
[0093] Among them, V is the observation residual value matrix, which is specifically expressed as
[0094] In subsequent iterative calculations, the above parameters are updated by using the latest equivalent weights to replace the original weight matrix and the latest coordinate correction numbers to replace the original coordinate correction numbers, thereby obtaining updated standardized residuals.
[0095] Wherein, step 106 specifically includes:
[0096] The down-weighting factor is expressed as:
[0097] The equivalent weight is expressed as:
[0098] Among them, ω(v i) is the weighting factor of the standardized residual of the i-th observation, k0 and k1 are both constants, k0 and k1 are determined according to the actual problem needs, the value range of k0 and k1 is 1.0-1.5, k0<k1, p i is the prior weight of the i-th observation, is the equivalent weight of the i-th observation.
[0099] The equivalent weight is divided into three sections: the first section is the normal section, which adopts the classic least squares estimation; the second section is the suspected section, and the weight reduction method is adopted in the k0 to k1 section. This application improves the weight reduction function in this section. The improved weight reduction function adopts a higher-order third-order function. The high-order function can achieve stricter filtering of gross errors, avoid introducing gross errors in the suspected section, and thus improve the adjustment accuracy of the GPS network; the third section is the elimination section, and the strong elimination method is adopted when the weight is greater than the threshold k1, and the weight is reduced to zero or close to zero.
[0100] In step 107, the baseline vector prior weight matrix used in solving the coordinate correction number of the undetermined point is replaced by the equivalent weight. Specifically, the baseline vector prior weight matrix in the equation of the equivalent weight replacement method is replaced by the formula after replacement: in, For equivalent rights.
[0101] The equivalent weight is used to replace the weight in the original normal equation to reduce or eliminate the gross error in the observed baseline vector, and the normal equation after the equivalent weight is replaced is solved to further calculate the three-dimensional coordinate anti-error value of the GPS network point to be determined.
[0102] The formula for calculating the coordinate anti-error value of the pending point based on the current coordinate correction number of the pending point is:
[0103] in, is the coordinate anti-difference value, specifically the three-dimensional coordinate anti-difference value, X 0 is the initial value of the coordinates of the point to be determined, The coordinate correction number of the point to be determined.
[0104] Figure 4 Add a gross error to the first observation baseline o1 position, Figure 4 Parts (a) to (f) are comparative diagrams of the GPS measurement gross error robustness estimation for the coordinates of the pending points N002, N003, N004, N005, N006, and N007 using the least squares estimation value and the method of this application, respectively. Figure 4 The vertical coordinate is the mean error (m) of the X-coordinate adjustment information, and the horizontal coordinate is the size of the gross error. Figure 4Analysis shows that the comparison of the mean error of the least squares estimate and the mean error of the robust estimate shows the following characteristics: as the gross error increases, the difference between the mean errors of the two parameter estimates continues to increase, and the mean error of the robust estimate remains smaller than the mean error of the least squares estimate. The mean error of the least squares estimate increases continuously with the increase of gross error, while the mean error of the robust estimate remains within a smaller range as the gross error increases. Therefore, it can be seen that the robust estimate method has a significant robustness effect, while the least squares estimate method does not have this effect. When the GPS network contains gross errors, the robust estimate method has higher adjustment accuracy than the least squares estimate method.
[0105] This application innovatively applies the improved IGG-III scheme to GPS network adjustment, and uses the improved IGG-III scheme to construct reasonable equivalent weights to replace prior weights. The equivalent weights can effectively filter GPS network baseline observations containing gross errors, thereby resisting the influence of gross errors on GPS network observation data, and solving the problem that the traditional least squares estimation method cannot resist the influence of gross errors of observations on three-dimensional coordinate estimation, thereby improving the accuracy of GPS network data adjustment.
[0106] Based on the same inventive concept, an embodiment of the present application further provides a GPS measurement gross error robust estimation device for implementing the GPS measurement gross error robust estimation method involved above. The implementation solution provided by the device is similar to the implementation solution described in the above method, so the specific limitations in one or more GPS measurement gross error robust estimation device embodiments provided below can be found in the limitations of the GPS measurement gross error robust estimation method above, and will not be repeated here.
[0107] In an exemplary embodiment, the present application provides a GPS measurement gross error robustness estimation device comprising:
[0108] The GPS baseline network related observation quantity conversion module is used to convert the GPS baseline network related observation quantities into independent observation quantities; the GPS baseline network includes multiple undetermined points and multiple observation baselines; the independent observation quantities are baseline vector observation values.
[0109] The observation model and error equation construction module is used to construct the observation model and error equation of the GPS baseline network according to the independent observation quantities.
[0110] The module for calculating the coordinate correction number of the point to be determined is used to calculate the coordinate correction number of the point to be determined based on the observation model and the error equation.
[0111] The judgment module is used to judge whether the coordinate correction number of the current point to be determined meets the set conditions.
[0112] The standardized residual calculation module is used to calculate the standardized residual according to the current baseline observation residual value and the cofactor matrix of the current baseline observation residual value if the output of the judgment module is no.
[0113] An equivalent weight determination module is used to construct a weight reduction factor of the improved IGG-III scheme based on the standardized residual and determine the equivalent weight based on the weight reduction factor.
[0114] The module for updating the coordinate correction number of the undetermined point is used to replace the baseline vector prior weight matrix used in solving the coordinate correction number of the undetermined point with the equivalent weight, recalculate the coordinate correction number of the current undetermined point, and return to the step of judging whether the coordinate correction number of the current undetermined point meets the set conditions.
[0115] The coordinate anti-error value calculation module is used to calculate the coordinate anti-error value of the undetermined point based on the current coordinate correction number of the undetermined point if the output of the judgment module is yes.
[0116] In an exemplary embodiment, a computer device is provided. The computer device may be a server or a terminal. The internal structure diagram thereof may be as follows: Figure 5 As shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, abbreviated as I / O) and a communication interface. The processor, the memory and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store GPS measurement gross error and anti-error estimation data. The input / output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a GPS measurement gross error and anti-error estimation method is implemented.
[0117] Those skilled in the art will understand that Figure 5 The structure shown in the figure is only a block diagram of a portion of the structure related to the solution of the present application and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have a different component arrangement. In an exemplary embodiment, a computer device is provided, including a memory and a processor, wherein a computer program is stored in the memory, and when the processor executes the computer program, the steps in the above-mentioned embodiments of the GPS measurement gross error robustness estimation method are implemented.
[0118] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program. When the computer program is executed by a processor, the steps in the above-mentioned GPS measurement gross error robust estimation method embodiments are implemented.
[0119] In an exemplary embodiment, a computer program product is provided, including a computer program. When the computer program is executed by a processor, the steps in the above-mentioned GPS measurement gross error robust estimation method embodiments are implemented.
[0120] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant regulations.
[0121] Those skilled in the art will understand that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, database or other media used in the embodiments provided in this application may include at least one of non-volatile and volatile memory. Non-volatile memory may include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory may include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM may be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).
[0122] The databases involved in the various embodiments provided herein may include at least one of a relational database and a non-relational database. Non-relational databases may include, but are not limited to, distributed databases based on blockchains. The processors involved in the various embodiments provided herein may be, but are not limited to, general-purpose processors, central processing units, graphics processing units, digital signal processors, data processing logic of programmable logic devices, and the like.
[0123] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0124] This document uses specific examples to illustrate the principles and implementation methods of this application. The description of the above examples is only intended to help understand the method and core concept of this application. At the same time, for those skilled in the art, based on the concept of this application, there may be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.
Claims
1. A GPS measurement gross error robust estimation method, characterized in that: The GPS measurement gross error robustness estimation method comprises: Converting GPS baseline network related observations into independent observations; the GPS baseline network includes multiple undetermined points and multiple observation baselines; the independent observations are baseline vector observations; Constructing an observation model and error equation of the GPS baseline network based on the independent observations; Calculating the coordinate correction number of the point to be determined based on the observation model and the error equation; Determine whether the coordinate correction number of the current point to be determined meets the set conditions; If the set conditions are not met, the standardized residual is calculated based on the current baseline observation residual value and the cofactor matrix of the current baseline observation residual value; constructing a weight reduction factor of the improved IGG-III scheme according to the standardized residual, and determining an equivalent weight according to the weight reduction factor; The equivalent weight is used to replace the baseline vector prior weight matrix used in solving the coordinate correction number of the undetermined point, and the coordinate correction number of the current undetermined point is recalculated, and the step of returning to determine whether the coordinate correction number of the current undetermined point meets the set conditions is returned. If the set conditions are met, the coordinate anti-error value of the pending point is calculated based on the current coordinate correction number of the pending point.
2. The GPS measurement gross error robust estimation method according to claim 1, wherein: The observation model of the GPS baseline network is expressed as: Among them, L is the baseline vector observation value, V is the baseline observation residual value, is the coordinate anti-error value, B is the coefficient matrix, d is the error coefficient, n is the number of observation baselines, and t is the number of points to be determined; The error equation of the GPS baseline network is expressed as: in, is the coordinate correction number of the point to be determined, l is the intermediate parameter, ΔX sw is the difference in X direction between the coordinates of the two ends of the baseline vector. is the initial value of the X direction coordinate of the first endpoint of the observation baseline vector, The initial value of the X-direction coordinate of the tail endpoint of the observation baseline vector.
3. The GPS measurement gross error robust estimation method according to claim 2, characterized in that: Calculating the coordinate correction number of the undetermined point according to the observation model and the error equation specifically includes: According to the observation model and the error equation, the least squares principle is used to establish the normal equation; the normal equation is expressed as: Where P is the baseline vector prior weight matrix, and T represents the transpose; The coordinate correction number of the point to be determined is calculated according to the normal equation; the coordinate correction number of the point to be determined is expressed as:
4. The GPS measurement gross error robust estimation method according to claim 1, wherein: The setting conditions are: in, is the coordinate correction number of the point to be determined, and norm() means calculating the matrix norm.
5. The GPS measurement gross error robust estimation method according to claim 1, characterized in that: The formula for calculating the standardized residual based on the current baseline observation residual value and the cofactor matrix of the current baseline observation residual value is: Among them, v i is the standardized residual of the i-th observation, V i is the current baseline observation residual value of the i-th observation, σ is the posterior unit weighted mean error, Q Vi is the cofactor value of the current baseline observation residual value of the i-th observation.
6. The GPS measurement gross error robust estimation method according to claim 1, characterized in that: The weight reduction factor of the improved IGG-III scheme is constructed according to the standardized residual, and the equivalent weight is determined according to the weight reduction factor, specifically including: The down-weighting factor is expressed as: The equivalent weight is expressed as: Among them, ω(v i ) is the weighting factor of the standardized residual of the i-th observation, k0 and k1 are both constants, v i is the standardized residual of the i-th observation, p i is the prior weight of the i-th observation, is the equivalent weight of the i-th observation.
7. The GPS measurement gross error robust estimation method according to claim 1, characterized in that: The formula for calculating the coordinate anti-error value of the pending point based on the current coordinate correction number of the pending point is: in, is the coordinate anti-error value, X 0 is the initial value of the coordinates of the point to be determined, The coordinate correction number of the point to be determined.
8. A GPS measurement gross error robustness estimation device, characterized in that: The GPS measurement gross error robustness estimation device comprises: A GPS baseline network related observation quantity conversion module is used to convert GPS baseline network related observation quantities into independent observation quantities; the GPS baseline network includes multiple undetermined points and multiple observation baselines; the independent observation quantities are baseline vector observation values; An observation model and error equation construction module, configured to construct an observation model and error equation of the GPS baseline network based on the independent observations; A module for calculating the coordinate correction number of the undetermined point, used for calculating the coordinate correction number of the undetermined point according to the observation model and the error equation; The judgment module is used to judge whether the coordinate correction number of the current point to be determined meets the set conditions; a standardized residual calculation module, configured to calculate the standardized residual based on the current baseline observation residual value and the cofactor matrix of the current baseline observation residual value if the output of the judgment module is no; An equivalent weight determination module, configured to construct a weight reduction factor of the improved IGG-III scheme according to the standardized residual, and determine an equivalent weight according to the weight reduction factor; A module for updating the coordinate correction number of the pending point is used to replace the baseline vector prior weight matrix used in solving the coordinate correction number of the pending point with the equivalent weight, re-solve the coordinate correction number of the current pending point, and return to the step of determining whether the coordinate correction number of the current pending point meets the set conditions; The coordinate anti-error value calculation module is used to calculate the coordinate anti-error value of the undetermined point based on the current coordinate correction number of the undetermined point if the output of the judgment module is yes.
9. A computer device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the GPS measurement gross error robustness estimation method according to any one of claims 1 to 7.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the GPS measurement gross error robustness estimation method according to any one of claims 1 to 7 is implemented.