CN117346786A - Data processing method for global optimization algorithm and GNSS receiver - Google Patents
Data processing method for global optimization algorithm and GNSS receiver Download PDFInfo
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Classifications
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/20—Instruments for performing navigational calculations
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
- G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
- G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
- G01C21/165—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation combined with non-inertial navigation instruments
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/13—Receivers
- G01S19/35—Constructional details or hardware or software details of the signal processing chain
- G01S19/37—Hardware or software details of the signal processing chain
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
- G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/42—Determining position
- G01S19/48—Determining position by combining or switching between position solutions derived from the satellite radio beacon positioning system and position solutions derived from a further system
- G01S19/49—Determining position by combining or switching between position solutions derived from the satellite radio beacon positioning system and position solutions derived from a further system whereby the further system is an inertial position system, e.g. loosely-coupled
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
Abstract
The invention discloses a data processing method for a global optimization algorithm and a GNSS receiver, wherein the data processing method comprises the following steps: collecting GNSS observation data and differential data of a sliding window and IMU sampling data; constructing a sequential least square problem by using all GNSS observation data, differential data and IMU sampling data in a sliding window; and acquiring precision data of all moments in the sliding window by sequentially solving covariance matrixes of the sequential least square problem. The method is used for solving the covariance quick estimation problem of the PPK algorithm based on global optimization, so that the algorithm based on optimization can provide precision factor information for users in an efficient manner as the traditional filtering-based method. And moreover, a user can easily realize centimeter-level accurate target point measurement in a shielding environment.
Description
Technical Field
The invention relates to a data processing method for a global optimization algorithm and a GNSS receiver.
Background
In recent years, tilt measurement based on an inertial measurement unit has been increasingly popularized and applied. Through an inertial directional positioning navigation system (INS) built in the GNSS receiver, attitude data of the GNSS receiver are output in real time, and then a direction angle, an inclined angle and an inclined direction angle of the centering rod in an inclined state are calculated, and the coordinates of the ground point at the bottom of the inclined centering rod can be calculated by combining the acquired coordinates of the antenna phase center of the GNSS receiver.
The GNSS/INS integrated navigation post-processing algorithm (PPK) can provide high-precision position and posture information for users in various use scenes, and is widely applied to carrier true value acquisition, photogrammetry, laser scanning and other applications. Traditionally, almost all GNSS/INS integrated navigation post-processing commercial software uses filtering+smoothing (EKF filtering+rts smoothing) to make algorithmic solutions, such as Novatel Inertial Explorer, trimble CenterPoint RTX, etc. In recent years, with the development of optimization technology, more and more scientific research cases apply optimization to a GNSS/INS integrated navigation post-processing algorithm, and better effects are achieved compared with the former.
However, optimization-based methods often require global optimization using GNSS and INS measurements at all times, which makes the covariance of the estimated parameters of the method difficult to calculate quickly, i.e., the time required to solve the globally optimized covariance is several orders of magnitude higher than the time required to solve the global optimization problem itself.
In the prior art, a great deal of time is consumed for solving the covariance of the global optimization, so that the operation efficiency is greatly reduced.
Disclosure of Invention
The invention aims to overcome the defect that a large amount of time is consumed for solving the covariance of global optimization in the prior art, so that the operation efficiency is greatly reduced, and provides a data processing method and a GNSS receiver for solving the covariance quick estimation problem of a PPK algorithm based on global optimization, which can provide precision factor information for a user in an efficient manner as in the traditional filtering-based method.
The invention solves the technical problems by the following technical scheme:
a data processing method for a global optimization algorithm, the data processing method comprising:
collecting GNSS observation data and differential data of a sliding window and IMU sampling data;
constructing a sequential least square problem by using all GNSS observation data, differential data and IMU sampling data in a sliding window;
and acquiring precision data of all moments in the sliding window by sequentially solving covariance matrixes of the sequential least square problem.
Preferably, the data processing method includes:
constructing a sequential least square problem by using all GNSS observation data, differential data and IMU sampling data in a sliding window;
acquiring forward covariance values at all moments by sequentially solving covariance matrices of the sequential least square problem;
reversely constructing a sequential least square problem by utilizing all GNSS observation data, differential data and IMU sampling data in a sliding window;
obtaining reverse covariance values at all moments by sequentially solving covariance matrices of the reverse constructed sequential least squares problem;
and acquiring precision data of all moments in the sliding window according to the forward covariance value and the reverse covariance value.
Preferably, the obtaining the accuracy data of all the moments in the sliding window according to the first covariance value and the second covariance value includes:
and combining the numerical value of the second half time of the forward covariance value with the numerical value of the first half time of the reverse covariance value to obtain precision data of all the time in the sliding window.
Preferably, the data processing method includes:
collecting GNSS observation data and differential data of the sliding window and IMU sampling data, wherein the sliding window comprises a measurement starting point, a measurement end point and a position to be measured, and the position to be measured is positioned between the measurement starting point and the measurement end point;
the nonlinear least square problem constructed by utilizing all GNSS observation data and differential data in a sliding window and IMU sampling data;
and estimating a positioning solution of the position to be detected by using the nonlinear least square problem.
Preferably, the data processing method includes:
and matching the GNSS observation value of each moment in the sliding window with one precision data according to time.
Preferably, the nonlinear least squares problem is:
wherein χ is the parameter to be estimated, z r And z I GNSS observation data and IMU sampling data, h r And h I Nonlinear measurement equations for the GNSS observations and IMU samples, respectively.
Preferably, the sequential least squares problem is:
wherein χ is a parameter to be estimated in the sliding window, z r And z I GNSS observation data and IMU sampling data, h r And h I Nonlinear measurement equations of GNSS observation data and IMU sampling data, respectively, k being GNSS measurement epoch, z M,k-1 To marginalize false observations, J M,k-1 A Jacobian matrix corresponding to the marginalized pseudo-observation value;
the sequential least squares problem of reverse construction is:
wherein χ is a parameter to be estimated in the sliding window, z r And z I GNSS observation data and IMU sampling data, h r And h I Nonlinear measurement equations of GNSS observation data and IMU sampling data, respectively, k being GNSS measurement epoch, z M,k+1 To marginalize false observations, J M,k+1 And the Jacobian matrix corresponding to the marginalized pseudo observed value is obtained.
Preferably, the forward covariance value is:
the reverse covariance value is:
for a GNSS measurement epoch, the forward covariance value and the reverse covariance value are combined into
Covariance sequence of all moments in sliding windowAs the precision data.
The invention also provides a data processing system which is characterized by comprising a GNSS receiver and a processing module, wherein the data processing system is used for realizing the data processing method.
The invention also provides a GNSS receiver which is characterized by comprising a processing unit, wherein the processing unit is used for realizing the data processing method.
On the basis of conforming to the common knowledge in the field, the above preferred conditions can be arbitrarily combined to obtain the preferred examples of the invention.
The invention has the positive progress effects that:
the method is used for solving the covariance quick estimation problem of the PPK algorithm based on global optimization, so that the algorithm based on optimization can provide precision factor information for users in an efficient manner as the traditional filtering-based method. And moreover, a user can easily realize centimeter-level accurate target point measurement in a shielding environment.
The problem of covariance calculation difficulty of a global optimization-based PPK algorithm belongs to a large technical problem which restricts the commercial use of the algorithm. The problem is solved, so that the related PPK software provides a pose solution with higher precision for a user compared with the traditional PPK, and simultaneously provides available precision factor information for the user with similar operation burden as the precision factor estimation algorithm of the traditional PPK software.
Drawings
Fig. 1 is a flowchart of a data processing method according to embodiment 1 of the present invention.
Fig. 2 is another flowchart of the data processing method of embodiment 1 of the present invention.
Detailed Description
The invention is further illustrated by means of the following examples, which are not intended to limit the scope of the invention.
Example 1
Referring to fig. 1, the present embodiment provides a GNSS receiver for a global optimization algorithm, specifically a GNSS receiver facing the global optimization PPK algorithm.
The GNSS receiver comprises an inertial measurement unit for implementing a tilt measurement function.
The GNSS receiver comprises an acquisition module 11, a processing module 12 and a positioning module 13.
The acquisition module is used for acquiring GNSS observation data and differential data of the sliding window and IMU sampling data;
the processing module is used for constructing a sequential least square problem by utilizing all GNSS observation data and differential data in the sliding window and IMU sampling data;
the processing module is further used for obtaining precision data of all moments in the sliding window through a covariance matrix of the sequential least square problem.
The GNSS observations and differential data are position, velocity, and time information collected by a Global Navigation Satellite System (GNSS) receiver. Such data is typically stored in a particular format, such as RINEX (Receiver Independent Exchange Format) or NMEA (National Marine Electronics Association).
The IMU sample data refers to data of an inertial navigation system (Inertial Navigation System). Inertial navigation systems are a technique for determining the position, velocity and direction of an object by measuring and integrating accelerometer and gyroscope data. The IMU sample data includes measurements of accelerometers and gyroscopes, which in this embodiment are used to represent the attitude of the GNSS receiver.
In the description and claims of this application, the terms "comprises" and "comprising," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of method steps or modules is not necessarily limited to those steps or modules that are expressly listed or inherent to such process, method, article, or apparatus.
It should be noted that the terms "first," "second," and the like in the description and in the claims of the present application are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order. It will be appreciated that the data may be interchanged where appropriate.
Further, the acquisition module is used for:
constructing a sequential least square problem by using all GNSS observation data, differential data and IMU sampling data in a sliding window;
acquiring forward covariance values at all moments by sequentially solving covariance matrices of the sequential least square problem;
reversely constructing a sequential least square problem by utilizing all GNSS observation data, differential data and IMU sampling data in a sliding window;
obtaining reverse covariance values at all moments by sequentially solving covariance matrices of the reverse constructed sequential least squares problem;
and acquiring precision data of all moments in the sliding window according to the forward covariance value and the reverse covariance value.
Covariance is an important means for the algorithm software to tell the user that the accuracy of different locations in the whole piece of data is good or bad.
Specifically, the acquisition module is used for:
and combining the numerical value of the second half time of the forward covariance value with the numerical value of the first half time of the reverse covariance value to obtain precision data of all the time in the sliding window.
The acquisition module is used for:
collecting GNSS observation data and differential data of the sliding window and IMU sampling data, wherein the sliding window comprises a measurement starting point, a measurement end point and a position to be measured, and the position to be measured is positioned between the measurement starting point and the measurement end point;
the nonlinear least square problem constructed by utilizing all GNSS observation data and differential data in a sliding window and IMU sampling data;
and estimating a positioning solution of the position to be detected by using the nonlinear least square problem.
The "extension measurement" technique proposed in this embodiment is implemented by a near real-time GNSS/INS integrated navigation post-processing technique.
The technology requires a user to move the equipment to a point to be measured in a severe signal environment from an open sky environment, click to start measurement, stop for a few seconds (1-5 s) at the point to be measured, and move the equipment to the open sky environment again. After the measurement operation is finished, the device automatically performs near real-time post-processing on the whole data, and high-precision coordinates of the measurement points are calculated.
In conventional direct measurement, the measurement accuracy at a point depends on the RTK fixed solution accuracy when the device is at that point; in the extension measurement, the forward and backward motion constraint based on inertial navigation is further added to the measurement of a certain point, so that the coordinate precision acquired in the open sky can be extended to a severe signal scene, and the measurement precision of the severe signal scene is improved.
If the traditional measurement means are used, the process of switching (open, shielding and open) the user motion scene leads out different measurement precision, namely centimeter, decimeter and centimeter, and the continuous centimeter precision can be optimized by the extension measurement technology.
Because the accuracy of the GNSS/INS integrated navigation post-processing algorithm in the shielding environment can be improved by 5-10 times compared with that of the real-time processing algorithm, after the extended measurement technology is used, a user can stay in the shielding environment for tens of seconds, which is far higher than that of the few seconds described in the background technology, and the measurement operation (in the shielding environment in extremely short time) can be spanned from unrealistic to easy to realize.
In other embodiments, a data processing system may be provided, where the data processing system includes a GNSS receiver and an external processing module, and the processing module may be a mobile phone, a tablet computer, a notebook computer, etc., and the data processing system is used to implement the data processing method.
The global optimization technology uses all GNSS and INS measurement information in the whole track of a user to construct the following nonlinear least square problem:
wherein χ is the parameter to be estimated, z r And z I GNSS observation data and IMU sampling data, h r And h I Nonlinear measurement equations for the GNSS observations and IMU samples, respectively.
Wherein χ is a parameter to be estimatedIncluding parameters such as position, speed, attitude and the like at each moment in the window, z r And z I Measured values of GNSS and INS, respectively, h r And h I Nonlinear measurement equations for GNSS and INS, respectively.
The problem may be solved using a nonlinear optimization algorithm. Because of the sparsity of the jacobian matrix in the solving process, the solving of the optimization problem can be often performed by using a sparse matrix inversion method, and the time consumption is relatively low.
However, if one wants to estimate the covariance of all parameters in this optimization problem, then using sparse matrix solution tends to fail the solution because of the numerical stability problem, so in most cases such problems tend to be solved only by dense matrix inversion algorithms, which increases their computational effort by several orders of magnitude.
The invention separates the problem description of covariance estimation from the problem description of parameter estimation. And acquiring a positioning solution of the position to be detected by utilizing a nonlinear least square problem, acquiring precision data by utilizing a sequential least square problem, and matching the GNSS observation value at each moment in the sliding window with one piece of precision data according to time.
Specifically, the sequential least squares problem is:
wherein χ is a parameter to be estimated in the sliding window, z r And z I GNSS observation data and IMU sampling data, h r And h I Nonlinear measurement equations of GNSS observation data and IMU sampling data, respectively, k being GNSS measurement epoch, z M,k-1 To marginalize false observations, J M,k-1 A Jacobian matrix corresponding to the marginalized pseudo-observation value;
k is a certain GNSS measurement epoch, z M,k-1 For marginalizing pseudo-observations, it characterizes all the measured information from time 1 to time k-1, J M,k-1 Jacobian matrix corresponding to the marginalized pseudo-observationThe linearization point is calculated from the estimated valueGiven.
From the first moment, the covariance matrix of the problem is solved sequentially until the last moment, and the covariance values of all the moments can be obtainedThe covariance value is a forward estimated covariance value and is not a globally optimized covariance value.
Next, reverse building the sequential least squares problem:
the sequential least squares problem of reverse construction is:
wherein χ is a parameter to be estimated in the sliding window, z r And z I GNSS observation data and IMU sampling data, h r And h I Nonlinear measurement equations of GNSS observation data and IMU sampling data, respectively, k being GNSS measurement epoch, z M,k+1 To marginalize false observations, J M,k+1 And the Jacobian matrix corresponding to the marginalized pseudo observed value is obtained.
Wherein k-1 and k+1 are varied. The sequential problem starts from the end of the time sequence until the end of the first moment.
Also, a series of inverse estimated covariance values can be obtained
Combining the forward and backward covariances:
the globally optimized covariance sequence can be obtained
Specifically, the forward covariance value is:
the reverse covariance value is:
for a GNSS measurement epoch, the forward covariance value and the reverse covariance value are combined into
Covariance sequence of all moments in sliding windowAs the precision data.
The method solves the problem that the covariance calculation of the PPK algorithm based on global optimization is difficult, and belongs to a large technical problem for restricting the commercial use of the algorithm. The problem is solved, so that the related PPK software provides a pose solution with higher precision for a user compared with the traditional PPK, and simultaneously provides available precision factor information for the user with similar operation burden as the precision factor estimation algorithm of the traditional PPK software.
Referring to fig. 1, with the GNSS receiver described above, this embodiment further provides a data processing method, including:
step 100, acquiring GNSS observation data and differential data of a sliding window and IMU sampling data;
step 101, constructing a sequential least square problem by using all GNSS observation data and differential data in a sliding window and IMU sampling data;
and 102, acquiring precision data of all moments in a sliding window through a covariance matrix of the sequential least square problem.
The step 101 specifically includes:
step 1011, constructing a sequential least square problem by using all GNSS observation data and differential data in a sliding window and IMU sampling data;
step 1012, obtaining forward covariance values at all moments by sequentially solving covariance matrices of the sequential least squares problem;
step 1013, reversely constructing a sequential least square problem by using all GNSS observation data and differential data in the sliding window and IMU sampling data;
step 1014, obtaining reverse covariance values at all moments by sequentially solving covariance matrices of the reverse constructed sequential least squares problem;
step 102 is to obtain accuracy data of all moments in the sliding window according to the forward covariance value and the reverse covariance value.
Step 102 specifically comprises:
and combining the numerical value of the second half time of the forward covariance value with the numerical value of the first half time of the reverse covariance value to obtain precision data of all the time in the sliding window.
In step 100, acquiring GNSS observation data and differential data of the sliding window and IMU sampling data, where the sliding window includes a measurement start point, a measurement end point, and a position to be measured, and the position to be measured is located between the measurement start point and the measurement end point;
referring to fig. 2, the data processing method further includes:
step 200, constructing a nonlinear least square problem by utilizing all GNSS observation data and differential data in a sliding window and IMU sampling data;
step 201, estimating a positioning solution of the position to be measured by using the nonlinear least square problem.
Step 102 further comprises:
step 103, matching the GNSS observation value of each moment in the sliding window with one precision data according to time.
Specifically, the nonlinear least squares problem is:
wherein χ is the parameter to be estimated, z r And z I GNSS observation data and IMU sampling data, h r And h I Nonlinear measurement equations for the GNSS observations and IMU samples, respectively.
Specifically, the sequential least squares problem is:
wherein χ is a parameter to be estimated in the sliding window, z r And z I GNSS observation data and IMU sampling data, h r And h I Nonlinear measurement equations of GNSS observation data and IMU sampling data, respectively, k being GNSS measurement epoch, z M,k-1 To marginalize false observations, J M,k-1 A Jacobian matrix corresponding to the marginalized pseudo-observation value;
the sequential least squares problem of reverse construction is:
wherein χ is a parameter to be estimated in the sliding window, z r And z I GNSS observation data and IMU sampling data, h r And h I Nonlinear measurement equations of GNSS observation data and IMU sampling data, respectively, k being GNSS measurement epoch, z M,k+1 To marginalize false observations, J M,k+1 And the Jacobian matrix corresponding to the marginalized pseudo observed value is obtained.
Specifically, the forward covariance value is:
the reverse covariance value is:
for a GNSS measurement epoch, the forward covariance value and the reverse covariance value are combined into
Covariance sequence of all moments in sliding windowAs the precision data.
While specific embodiments of the invention have been described above, it will be appreciated by those skilled in the art that these are by way of example only, and the scope of the invention is defined by the appended claims. Various changes and modifications to these embodiments may be made by those skilled in the art without departing from the principles and spirit of the invention, but such changes and modifications fall within the scope of the invention.
Claims (10)
1. A data processing method for a global optimization algorithm, the data processing method comprising:
collecting GNSS observation data and differential data of a sliding window and IMU sampling data;
constructing a sequential least square problem by using all GNSS observation data, differential data and IMU sampling data in a sliding window;
and acquiring precision data of all moments in the sliding window by sequentially solving covariance matrixes of the sequential least square problem.
2. The data processing method according to claim 1, wherein the data processing method comprises:
constructing a sequential least square problem by using all GNSS observation data, differential data and IMU sampling data in a sliding window;
acquiring forward covariance values at all moments by sequentially solving covariance matrices of the sequential least square problem;
reversely constructing a sequential least square problem by utilizing all GNSS observation data, differential data and IMU sampling data in a sliding window;
obtaining reverse covariance values at all moments by sequentially solving covariance matrices of the reverse constructed sequential least squares problem;
and acquiring precision data of all moments in the sliding window according to the forward covariance value and the reverse covariance value.
3. The method for processing data according to claim 2, wherein the obtaining precision data of all time instants in the sliding window according to the first covariance value and the second covariance value includes:
and combining the numerical value of the second half time of the forward covariance value with the numerical value of the first half time of the reverse covariance value to obtain precision data of all the time in the sliding window.
4. A data processing method according to claim 3, wherein the data processing method comprises:
collecting GNSS observation data and differential data of the sliding window and IMU sampling data, wherein the sliding window comprises a measurement starting point, a measurement end point and a position to be measured, and the position to be measured is positioned between the measurement starting point and the measurement end point;
the nonlinear least square problem constructed by utilizing all GNSS observation data and differential data in a sliding window and IMU sampling data;
and estimating a positioning solution of the position to be detected by using the nonlinear least square problem.
5. The data processing method according to claim 4, wherein the data processing method comprises:
and matching the GNSS observation value of each moment in the sliding window with one precision data according to time.
6. The data processing method of claim 4, wherein the nonlinear least squares problem is:
wherein χ is the parameter to be estimated, z r And z I GNSS observation data and IMU sampling data, h r And h I Nonlinear measurement equations for the GNSS observations and IMU samples, respectively.
7. The data processing method of claim 4, wherein the sequential least squares problem is:
wherein χ is a parameter to be estimated in the sliding window, z r And z I GNSS observation data and IMU sampling data, h r And h I Nonlinear measurement equations of GNSS observation data and IMU sampling data, respectively, k being GNSS measurement epoch, z M,k-1 To marginalize false observations, J M,k-1 A Jacobian matrix corresponding to the marginalized pseudo-observation value;
the sequential least squares problem of reverse construction is:
wherein χ is a parameter to be estimated in the sliding window, z r And z I GNSS observation data and IMU sampling data, h r And h I Nonlinear measurement equations of GNSS observation data and IMU sampling data, respectively, k being GNSS measurement epoch, z M，k+1 To marginalize false observations, J M，k+1 And the Jacobian matrix corresponding to the marginalized pseudo observed value is obtained.
8. The data processing method of claim 7, wherein the forward covariance value is:
the reverse covariance value is:
for a GNSS measurement epoch, the forward covariance value and the reverse covariance value are combined into
Covariance sequence of all moments in sliding windowAs the precision data.
9. A data processing system comprising a GNSS receiver and a processing module for implementing the data processing method according to any of the claims 1 to 8.
10. A GNSS receiver comprising a processing unit for implementing the data processing method according to any of the claims 1 to 8.
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