CN113449263A - Multi-path error correction method, system and equipment based on sparsity-promoted regularization - Google Patents

Multi-path error correction method, system and equipment based on sparsity-promoted regularization Download PDF

Info

Publication number
CN113449263A
CN113449263A CN202010225275.0A CN202010225275A CN113449263A CN 113449263 A CN113449263 A CN 113449263A CN 202010225275 A CN202010225275 A CN 202010225275A CN 113449263 A CN113449263 A CN 113449263A
Authority
CN
China
Prior art keywords
error
coefficient
regularization
determining
model
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202010225275.0A
Other languages
Chinese (zh)
Inventor
李灯熬
赵菊敏
马晓丽
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Taiyuan University of Technology
Original Assignee
Taiyuan University of Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Taiyuan University of Technology filed Critical Taiyuan University of Technology
Priority to CN202010225275.0A priority Critical patent/CN113449263A/en
Publication of CN113449263A publication Critical patent/CN113449263A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • 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
    • 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
    • G01S19/40—Correcting position, velocity or attitude
    • 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
    • G01S19/43—Determining position using carrier phase measurements, e.g. kinematic positioning; using long or short baseline interferometry
    • G01S19/44—Carrier phase ambiguity resolution; Floating ambiguity; LAMBDA [Least-squares AMBiguity Decorrelation Adjustment] method
    • 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
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • 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
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00—Road transport of goods or passengers
    • Y02T10/10—Internal combustion engine [ICE] based vehicles
    • Y02T10/40—Engine management systems

Abstract

The invention provides a multi-path error correction method, a system and equipment based on sparsity-promoted regularization, wherein the method comprises the following steps of initializing satellite data received in the previous period; determining a baseline vector based on the initialized satellite data; substituting the integer ambiguity and the baseline vector into a double-difference equation one by one, and performing model expansion on each coefficient of the candidate set; and optimizing satellite data received in the previous period based on the expanded coefficient model, determining error statistical data, and determining a regularization coefficient based on the error information amount. Sparse methods are applied during the model construction process to facilitate the regularization process. The method can optimize the analysis process, can solve the differential error item appearing in the multipath problem, further combine the initial modeling objective equation, substitute the determined optimization parameter, and regularly update the measured value to achieve the effects of reducing the multipath error and improving the positioning accuracy.

Description

Multi-path error correction method, system and equipment based on sparsity-promoted regularization
Technical Field
The application relates to the technical field of satellite navigation and positioning, in particular to a multi-path error correction method, a system and equipment for promoting regularization based on sparsity.
Background
The global Positioning system gps (global Positioning system) is a satellite navigation Positioning system developed based on a wireless communication technology and a navigation satellite technology. At present, the GPS is widely applied to various navigation and positioning fields of vehicles, aircrafts, ships and the like. With the wider application range of the GPS, the GPS gradually enters the daily life of people, and users have made higher demands on the positioning and navigation performance of receivers. As a spread spectrum ranging system, tropospheric errors, ionospheric errors, satellite orbit errors, and multipath errors remain the main sources of error affecting GPS positioning performance. The first three errors belong to systematic errors, and can be eliminated through modeling and difference, so that the influence of the systematic errors on the positioning errors is reduced to a satisfactory degree. Multipath signal errors belong to accidental errors, are related to media of reflecting objects around a receiver antenna and distance, change along with the environment, and are difficult to inhibit through means such as modeling, so that the multipath inhibition technology is always a hot point for research in the field of satellite navigation. Especially in recent years, much research has been conducted on empirical multipath error modeling and mitigation. Modeling and determining repetition periods are two key aspects of the star filtering technique. Moreover, double difference techniques are commonly used in GNSS applications because they can eliminate or reduce significant errors, such as ionospheric and tropospheric delays, satellite orbit and clock errors, especially for short baselines. Even with double difference techniques, poor cancellation usually occurs, so there are still errors that cannot be modeled. Although hardware-based techniques may reduce multipath errors in the received signal, it is not possible for the receiver to completely avoid multipath errors regardless of the type of hardware.
Disclosure of Invention
To solve the above problems, the present invention provides a method, system and apparatus for multipath error correction based on sparsity-facilitated regularization, which overcomes the above technical problems.
To achieve the above object, the present application provides a method of multipath error correction that facilitates regularization based on sparsity, the method comprising: initializing satellite data received in the previous period; determining a baseline vector based on the initialized satellite data; substituting the integer ambiguity and the baseline vector into a double-difference equation one by one, and performing model expansion on each coefficient of the candidate set; optimizing the satellite data received in the previous period based on the expanded coefficient model, determining error statistical data, and determining a regularization coefficient based on the error information amount, wherein the error statistical data is characterized by a model expansion strategy corresponding to the coefficient and an overall modeling error of a super coefficient.
Optionally, the initializing process of the satellite data received in the previous cycle includes: determining a multipath error corresponding to the satellite signal received in the previous period based on a preset measurement model of the satellite; and based on the multipath error, sparsely correcting the satellite signal received in the previous period.
Optionally, determining a baseline vector based on the initialized satellite data includes: constructing a Gaussian elimination equation solver by means of a special tri-diagonal matrix algorithm; and performing iterative recursion of a forward recursion and a least square method, and extending the baseline vector equation to a preset matrix transformation space for analysis.
Optionally, the preset matrix transformation space includes: a coefficient matrix space; moreover, the coefficient matrix space includes:
Figure RE-GDA0002472599050000021
optionally, substituting the integer ambiguity and the baseline vector into a double difference equation one by one, and performing model extension on each coefficient of the candidate set, including: based on a Thomas algorithm and a Cholesky rank-one updating algorithm, respectively serving as the core of first-order and second-order differential iteration, executing a model extension process on each coefficient of a candidate set; wherein, the Cholesky rank-one updating algorithm is formula decomposed:
Figure RE-GDA0002472599050000022
after the factorization decomposition process, a normalized residual error formula is defined:
Figure RE-GDA0002472599050000023
and performing model extension on each coefficient of the candidate set based on the normalized residual error formula.
Optionally, optimizing the satellite data received in the previous cycle based on the expanded coefficient model, determining error statistical data, and determining a regularization coefficient based on the error information amount, where the regularization coefficient includes:
optimizing original measurement data by using a bootstrap estimation method;
determining the error information amount by a preset method:
Figure RE-GDA0002472599050000024
Figure RE-GDA0002472599050000031
these error statistics represent the overall modeling error with different modeling strategies (first or second derivative regularization) and super coefficients, the resulting regularization coefficients are represented as:
Figure RE-GDA0002472599050000032
Figure RE-GDA0002472599050000033
optionally, the optimizing of the raw measurement data by using a bootstrap estimation method includes:
obtaining a corresponding multipath error based on a preset satellite measurement model;
based on the multipath error, performing minimization operation through a joint formula, and extracting multipath signals to optimize original measurement data;
wherein the preset satellite measurement model comprises:
Figure RE-GDA0002472599050000034
wherein the subscript k represents the time period,
Figure RE-GDA0002472599050000035
representing a carrier phase measurement residual for use as an observation; m iskRepresenting multipath errors, considered as a reconstructed signal; η k is the equivalent noise representing all other unmodeled errors;
the joint formula includes:
Figure RE-GDA0002472599050000036
Figure RE-GDA0002472599050000037
in a second aspect of the present application, a multipath error correction system for promoting regularization based on sparsity is provided, comprising: the initialization module is used for initializing satellite data received in the previous period; the baseline vector module is used for determining a baseline vector based on the initialized satellite data; the model expansion module is used for substituting the integer ambiguity and the baseline vector into a double difference equation one by one and executing model expansion on each coefficient of the candidate set; and the regularization module is used for optimizing the satellite data received in the previous period based on the expanded coefficient model, determining error statistical data and determining a regularization coefficient based on the error information quantity, wherein the error statistical data are represented by a model expansion strategy corresponding to the coefficient and an overall modeling error of a super-coefficient.
In a third aspect of the present application, an electronic device is provided, which comprises a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor executes the program to implement the method described above.
In a fourth aspect of the application, a non-transitory computer-readable storage medium is provided, which stores computer instructions for causing the computer to perform the above-mentioned method.
According to the multi-path error correction method, system and equipment for promoting regularization based on sparsity, a regularization process is promoted by using a sparse method in a model construction process. In the ideal situation of the algorithm and the technology planned to be adopted in the period, the satellite receiving signal data can be effectively extracted and processed by using a proper algorithm for further research, the analysis process can be optimized, the differential error item appearing in the multipath problem can be solved, the determined optimization parameters are substituted by combining the initial modeling objective equation, and the measured value is regularly updated to achieve the effects of reducing the multipath error and improving the positioning accuracy.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the invention and, together with the description, serve to explain the invention and not to limit the invention.
In the drawings:
FIG. 1 is a block diagram of a modeling process in an embodiment of the invention;
fig. 2 is a schematic flow chart of a multipath error correction method based on sparsity-promoted regularization in the embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. The following description of at least one exemplary embodiment is merely illustrative in nature and is in no way intended to limit the invention, its application, or uses. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular is intended to include the plural unless the context clearly dictates otherwise, and further it is to be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of the stated features, steps, operations, devices, components and/or combinations thereof.
The relative arrangement of the components and steps, the numerical expressions and numerical values set forth in these embodiments do not limit the scope of the present invention unless specifically stated otherwise. Meanwhile, it should be understood that the sizes of the respective portions shown in the drawings are not drawn in an actual proportional relationship for the convenience of description. Techniques, methods, and apparatus known to those of ordinary skill in the relevant art may not be discussed in detail but are intended to be part of the specification where appropriate. In all examples shown and discussed herein, any particular value should be construed as merely illustrative, and not limiting. Thus, other examples of the exemplary embodiments may have different values. It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, further discussion thereof is not required in subsequent figures.
As shown in fig. 1, the present invention proposes a new sidereal filtering method based on sparsity-facilitated regularization to mitigate multipath errors in static short baseline GNSS applications. The key idea is to emphasize that the L1 specification is used to extract multipath signals from noisy carrier phase residuals. Consider two regularization schemes with first and second order differences. For each solution, an efficient numerical algorithm was developed to find the solution by using the Thomas algorithm and Cholesky rank-one update algorithm as the core of the first and second order differential iterations, respectively. The whole process contemplates the use of baseline equations to evaluate the characteristics of multipath effects and the performance of the proposed method. Compared with the traditional modeling method, the method can effectively improve the precision of the carrier phase measurement residual error. Namely: the invention mainly utilizes sparse regularization to correct the coefficients lambda and mu in the modeling process,
specifically, multipath mitigation based on double difference star filtering requires the following steps. First, the dataset of the previous session is processed in static mode and the final baseline vector is estimated after resolving the ambiguity. Second, the integer ambiguities and baseline vectors are substituted back into the double difference equation one by one. We can obtain the corresponding residual in double-differenced multipath and the noise per satellite. Thirdly, we can establish the residual error obtained by double-difference positioning after double-difference multi-mode and denoise by using the proposed method. Finally, the extracted multipath model is applied to the next period data with time shift. So combining the above, we use the residual correlation method to calculate the multipath repetition time following the double difference mode of operation without loss of generality.
In order to facilitate understanding of the embodiments of the present invention, the method flow of the present invention is described in detail by several specific embodiments.
As shown in fig. 2, an embodiment of the present invention provides a method for correcting a multipath error based on sparsity-promoted regularization, which is applied to a terminal device, and the method includes:
s101, initializing satellite data received in a previous period;
step S102, determining a baseline vector based on the initialized satellite data;
step S103, substituting the integer ambiguity and the baseline vector into a double-difference equation one by one, and performing model extension on each coefficient of the candidate set;
and S104, optimizing the satellite data received in the previous period based on the expanded coefficient model, determining error statistical data, and determining a regularization coefficient based on the error information amount.
And the error statistical data are represented by a model extension strategy corresponding to the coefficient and an overall modeling error of the super-coefficient.
Through the steps S101 to S104, in the present embodiment, a sparse method is implemented in the model building process to promote the regularization process. In the ideal situation of the algorithm and the technology planned to be adopted in the period, the satellite receiving signal data can be effectively extracted and processed by using a proper algorithm for further research, the analysis process can be optimized, the differential error item appearing in the multipath problem can be solved, the determined optimization parameters are substituted by combining the initial modeling objective equation, and the measured value is regularly updated to achieve the effects of reducing the multipath error and improving the positioning accuracy.
In another embodiment, one implementation manner of the step S101 includes:
step S1011: determining a multipath error corresponding to the satellite signal received in the previous period based on a preset measurement model of the satellite;
step S1012: and based on the multipath error, sparsely correcting the satellite signal received in the previous period.
In particular, to ensure that the base station is not affected by multipath effects and that the rover has significant multipath effects, it is desirable to turn off the anti-multipath function of the rover when the base station function is turned on. The received signal data set is processed with processing software developed based on GNSS data processing software RTKLIB to mitigate multipath errors.
In another embodiment, one implementation manner of the step S102 includes:
step S1021: constructing a Gaussian elimination equation solver by means of a special tri-diagonal matrix algorithm;
step S1022: and performing iterative recursion of a forward recursion and a least square method, and extending the baseline vector equation to a preset matrix transformation space for analysis.
Specifically, a gaussian elimination equation solver is constructed by means of a special tri-diagonal matrix algorithm, iterative recursion of a forward recursion and a least square method is executed, and a J-base line vector equation is extended to a preset matrix transformation space for analysis.
Wherein the predetermined matrix transformation space includes: a coefficient matrix space; moreover, the coefficient matrix space includes:
Figure RE-GDA0002472599050000061
in another embodiment, one implementation manner of the step S103 includes:
step S1031: substituting the integer ambiguity and the baseline vector into a double-difference equation one by one, and performing model expansion on each coefficient of the candidate set, wherein the model expansion comprises the following steps:
step S1031: based on a Thomas algorithm and a Cholesky rank-one updating algorithm, respectively serving as the core of first-order and second-order differential iteration, executing a model extension process on each coefficient of a candidate set;
wherein, the Cholesky rank-one updating algorithm is formula decomposed:
Figure RE-GDA0002472599050000071
after the factorization decomposition process, a normalized residual error formula is defined:
Figure RE-GDA0002472599050000072
and performing model extension on each coefficient of the candidate set based on the normalized residual error formula.
In another embodiment, one implementation manner of the step S104 includes:
step S1041: optimizing original measurement data by using a bootstrap estimation method;
step S1042: determining the error information amount by a preset method:
Figure RE-GDA0002472599050000073
Figure RE-GDA0002472599050000074
these error statistics represent the overall modeling error with different modeling strategies (first or second derivative regularization) and super coefficients, the resulting regularization coefficients are represented as:
Figure RE-GDA0002472599050000075
Figure RE-GDA0002472599050000076
wherein, an implementation manner of the step S1041 includes:
step S10411: obtaining a corresponding multipath error based on a preset satellite measurement model;
step S10412: based on the multipath error, performing minimization operation through a joint formula, and extracting multipath signals to optimize original measurement data;
wherein the preset satellite measurement model comprises:
Figure RE-GDA0002472599050000077
wherein the subscript k represents the time period,
Figure RE-GDA0002472599050000078
representing a carrier phase measurement residual for use as an observation; m iskIndicating multipath errorsThe difference, considered as the reconstructed signal; etakIs equivalent noise representing all other unmodeled errors;
the joint formula includes:
Figure RE-GDA0002472599050000079
Figure RE-GDA0002472599050000081
process for thinning out corrected signal
(1) Firstly, a measurement model of any satellite is determined:
Figure RE-GDA0002472599050000082
wherein the subscript k represents the time period,
Figure RE-GDA0002472599050000083
representing a carrier phase measurement residual for use as an observation; m iskRepresenting multipath errors, considered as a reconstructed signal; etakIs equivalent noise representing all other unmodeled errors. Wherein, the following joint formula is used for carrying out minimization operation, and multipath signals are extracted to obtain a multipath model:
Figure RE-GDA0002472599050000084
Figure RE-GDA0002472599050000085
the process of sparsely correcting signals is mainly involved, and specifically, two modes are possible for the obtained multipath model. The first is a post-processing mode, which uses the model to correct the measurements that build the model. The second mode is a prediction mode, which is to use the model to correct measurements taken in the future. The latter can be used when a system mode of multipath error is repeated. From the viewpoint of denoising, an alternative method is proposed in advance for constructing a GNSS multipath error model based on Tikhonov regularization. In this way the norm of the first or second derivative of the variables for modeling with size 2 is constrained. Therefore, small or smooth models or models with small derivatives of the corresponding order are preferred.
The technology adopts an iterative weighted least square algorithm to iterate, and then solves the problem of regularization of the first-order derivative effectively by means of matrixing and a numerical equation machine.
Wherein the iterative least squares algorithm adapts the above equation set as follows:
Figure RE-GDA0002472599050000086
Figure RE-GDA0002472599050000087
the regularization coefficients are then modified using the Bootstrap technique:
modeling errors inevitably occur in empirical models. The modeling error was evaluated by using a bootstrap method. First, the regularization coefficient corresponding to the smallest modeling error is selected. Then, a candidate set of regularization coefficients is determined. Such as the coefficients lambda and mu in the above operation.
Furthermore, in another embodiment, an electronic device is also presented, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, the processor implementing the method for multipath error correction based on sparsity-facilitated regularization as described above when executing the program.
The term and the implementation principle related to an electronic device in this embodiment may specifically refer to a method for correcting a multipath error based on sparsity-promoted regularization in the embodiment of the present invention, and are not described herein again.
Furthermore, in another embodiment, a non-transitory computer-readable storage medium is also presented, which stores computer instructions for causing the computer to perform the above-described sparsity-based regularization-facilitated multipath error correction method.
The terms and implementation principles related to a non-transitory computer-readable storage medium in this embodiment may specifically refer to a multipath error correction method based on sparsity-promoting regularization in the embodiment of the present invention, and are not described herein again.
Spatially relative terms, such as "above … …," "above … …," "above … …," "above," and the like, may be used herein for ease of description to describe one device or feature's spatial relationship to another device or feature as illustrated in the figures. It will be understood that the spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if a device in the figures is turned over, devices described as "above" or "on" other devices or configurations would then be oriented "below" or "under" the other devices or configurations. Thus, the exemplary term "above … …" can include both an orientation of "above … …" and "below … …". The device may be otherwise variously oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly.
It should be noted that the terms "first", "second", and the like are used to define the components, and are only used for convenience of distinguishing the corresponding components, and the terms have no special meanings unless otherwise stated, and therefore, the scope of the present invention should not be construed as being limited.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (10)

1. A method for multipath error correction based on sparsity-facilitated regularization, the method comprising:
initializing satellite data received in the previous period;
determining a baseline vector based on the initialized satellite data;
substituting the integer ambiguity and the baseline vector into a double-difference equation one by one, and performing model expansion on each coefficient of the candidate set;
optimizing the satellite data received in the previous period based on the expanded coefficient model, determining error statistical data, and determining a regularization coefficient based on the error information amount, wherein the error statistical data is characterized by a model expansion strategy corresponding to the coefficient and an overall modeling error of a super coefficient.
2. The method of claim 1, wherein initializing satellite data received from a previous cycle comprises:
determining a multipath error corresponding to the satellite signal received in the previous period based on a preset measurement model of the satellite;
and based on the multipath error, sparsely correcting the satellite signal received in the previous period.
3. The method of claim 1, wherein determining a baseline vector based on the initialized satellite data comprises:
constructing a Gaussian elimination equation solver by means of a special tri-diagonal matrix algorithm;
and performing iterative recursion of a forward recursion and a least square method, and extending the baseline vector equation to a preset matrix transformation space for analysis.
4. The method of claim 3, wherein the pre-set matrix transformation space comprises: a coefficient matrix space;
moreover, the coefficient matrix space includes:
Figure FDA0002427439940000011
5. the method of claim 1, wherein substituting integer ambiguities and the baseline vector into a double difference equation one by one, performing model extension on each coefficient of a candidate set, comprising:
based on a Thomas algorithm and a Cholesky rank-one updating algorithm, respectively serving as the core of first-order and second-order differential iteration, executing a model extension process on each coefficient of a candidate set;
wherein, the Cholesky rank-one updating algorithm is formula decomposed:
Figure FDA0002427439940000021
after the factorization decomposition process, a normalized residual error formula is defined:
Figure FDA0002427439940000026
and performing model extension on each coefficient of the candidate set based on the normalized residual error formula.
6. The method of claim 1, wherein optimizing the satellite data received from the previous cycle based on the extended coefficient model, determining error statistics, and determining regularization coefficients based on the error information amount comprises:
optimizing original measurement data by using a bootstrap estimation method;
determining the error information amount by a preset method:
Figure FDA0002427439940000022
Figure FDA0002427439940000023
these error statistics represent the overall modeling error with different modeling strategies (first or second derivative regularization) and super coefficients, the resulting regularization coefficients are represented as:
Figure FDA0002427439940000024
Figure FDA0002427439940000025
7. the method of claim 6, wherein the optimization of raw measurement data using bootstrap estimation comprises:
obtaining a corresponding multipath error based on a preset satellite measurement model;
based on the multipath error, performing minimization operation through a joint formula, and extracting multipath signals to optimize original measurement data;
wherein the preset satellite measurement model comprises:
Figure FDA0002427439940000033
wherein the subscript k represents the time period,
Figure FDA0002427439940000034
representing a carrier phase measurement residual for use as an observation; m iskRepresenting multipath errors, considered as a reconstructed signal;ηkis equivalent noise representing all other unmodeled errors;
the joint formula includes:
Figure FDA0002427439940000031
Figure FDA0002427439940000032
8. a sparsity-based regularization-facilitated multipath error correction system, comprising:
the initialization module is used for initializing satellite data received in the previous period;
the baseline vector module is used for determining a baseline vector based on the initialized satellite data;
the model expansion module is used for substituting the integer ambiguity and the baseline vector into a double difference equation one by one and executing model expansion on each coefficient of the candidate set;
and the regularization module is used for optimizing the satellite data received in the previous period based on the expanded coefficient model, determining error statistical data and determining a regularization coefficient based on the error information quantity, wherein the error statistical data are represented by a model expansion strategy corresponding to the coefficient and an overall modeling error of a super-coefficient.
9. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor implements the method according to any of claims 1 to 7 when executing the program.
10. A non-transitory computer-readable storage medium storing computer instructions for causing a computer to perform the method of any one of claims 1 to 7.
CN202010225275.0A 2020-03-26 2020-03-26 Multi-path error correction method, system and equipment based on sparsity-promoted regularization Pending CN113449263A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010225275.0A CN113449263A (en) 2020-03-26 2020-03-26 Multi-path error correction method, system and equipment based on sparsity-promoted regularization

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010225275.0A CN113449263A (en) 2020-03-26 2020-03-26 Multi-path error correction method, system and equipment based on sparsity-promoted regularization

Publications (1)

Publication Number Publication Date
CN113449263A true CN113449263A (en) 2021-09-28

Family

ID=77807314

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010225275.0A Pending CN113449263A (en) 2020-03-26 2020-03-26 Multi-path error correction method, system and equipment based on sparsity-promoted regularization

Country Status (1)

Country Link
CN (1) CN113449263A (en)

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109061687A (en) * 2018-07-31 2018-12-21 太原理工大学 It is a kind of based on adaptive threshold and double with reference to the multipaths restraint method for translating strategy
CN109471083A (en) * 2018-11-09 2019-03-15 西安电子科技大学 Airborne external illuminators-based radar clutter suppression method based on space-time cascade
CN110058273A (en) * 2019-04-23 2019-07-26 杭州电子科技大学 A kind of poor observation GPS carrier multi-path correction method of list
CN110068848A (en) * 2019-03-08 2019-07-30 江苏北斗星通汽车电子有限公司 A kind of high-performance RTK processing technique method
CN110332987A (en) * 2019-08-22 2019-10-15 广东电网有限责任公司 A kind of imaging method of vocal print image formation method and microphone array signals

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109061687A (en) * 2018-07-31 2018-12-21 太原理工大学 It is a kind of based on adaptive threshold and double with reference to the multipaths restraint method for translating strategy
CN109471083A (en) * 2018-11-09 2019-03-15 西安电子科技大学 Airborne external illuminators-based radar clutter suppression method based on space-time cascade
CN110068848A (en) * 2019-03-08 2019-07-30 江苏北斗星通汽车电子有限公司 A kind of high-performance RTK processing technique method
CN110058273A (en) * 2019-04-23 2019-07-26 杭州电子科技大学 A kind of poor observation GPS carrier multi-path correction method of list
CN110332987A (en) * 2019-08-22 2019-10-15 广东电网有限责任公司 A kind of imaging method of vocal print image formation method and microphone array signals

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
CHAO CHEN等: "GNSS Multipath Error Modeling and Mitigation by Using Sparsity-Promoting Regularization", 《IEEE ACCESS》 *

Similar Documents

Publication Publication Date Title
CN109477900B (en) Estimation of inter-frequency bias for ambiguity resolution in a global navigation satellite system receiver
Dai et al. Multipath mitigation via component analysis methods for GPS dynamic deformation monitoring
CN103941220B (en) The outer target Wave arrival direction estimating method of a kind of grid based on sparse reconstruct
Souza et al. Wavelet shrinkage: high frequency multipath reduction from GPS relative positioning
CN107766291B (en) Method and computer equipment for obtaining residual time delay in very long baseline interferometry
CN110933630A (en) Indoor three-dimensional positioning method and device based on ultra-wideband communication
CN101506682A (en) Method for using three GPS frequencies to resolve whole-cycle carrier-phase ambiguities
CN110161547B (en) Medium-long baseline ambiguity resolution method of adaptive ionosphere estimation model
CN109145251B (en) Atmospheric parameter solving method of improved synchronous disturbance random approximation algorithm
Mosavi et al. Multipath error mitigation based on wavelet transform in L1 GPS receivers for kinematic applications
CN109725290B (en) Error extraction method and device, electronic equipment and readable storage medium
CN110907975A (en) Ambiguity fixing method based on sequential least squares
US20110181462A1 (en) System and Method for Positioning with GNSS Using Multiple Integer Candidates
CN108427131B (en) Integer ambiguity fast search algorithm under base line length constraint
CN111273328B (en) Ambiguity fixing method and device and positioning system
CN113051739A (en) Robustness self-adaptive processing method based on sparse constraint
CN113449263A (en) Multi-path error correction method, system and equipment based on sparsity-promoted regularization
CN109917330B (en) Arrival angle estimation method based on sparse orthogonal matching pursuit theory in the presence of phase errors
CN112087235A (en) Sparsity self-adaptive DOA estimation method and system based on pseudo-inverse perception dictionary
Greiff et al. Optimal measurement projections with adaptive mixture Kalman filtering for GNSS positioning
CN113740802B (en) Signal source positioning method and system for performing matrix completion by using adaptive noise estimation
CN114966687A (en) Sparse ISAR imaging method and system based on low rank and non-local self-similarity
CN109459768A (en) A kind of quick satellite selection method based on Big Dipper satellite signal intensity weight optimization model
Wang et al. Accurate and computationally efficient interpolation-based method for two-dimensional harmonic retrieval
CN110045634B (en) Non-error modeling method for GNSS reference station

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
WD01 Invention patent application deemed withdrawn after publication
WD01 Invention patent application deemed withdrawn after publication

Application publication date: 20210928