CN111123315A - Optimization method and device of non-differential non-combination PPP model and positioning system - Google Patents

Optimization method and device of non-differential non-combination PPP model and positioning system Download PDF

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CN111123315A
CN111123315A CN201811303802.4A CN201811303802A CN111123315A CN 111123315 A CN111123315 A CN 111123315A CN 201811303802 A CN201811303802 A CN 201811303802A CN 111123315 A CN111123315 A CN 111123315A
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ionospheric delay
model
ppp
delay parameter
observation
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周锋
汪登辉
冯绍军
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Qianxun Spatial Intelligence Inc
Qianxun Position Network Co Ltd
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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
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Abstract

The invention is suitable for the technical field of positioning, and provides an optimization method, an optimization device and a positioning system of a non-differential non-combination PPP model, wherein the optimization method comprises the following steps: acquiring GNSS data, wherein the GNSS data comprises observation data; constructing a non-differential non-combination PPP observation equation based on the observation data; constructing a random model of an ionospheric delay parameter; and optimizing the stochastic model of the ionospheric delay parameter based on the non-difference non-combination PPP observation equation to constrain the ionospheric delay parameter and obtain an optimized result. In the invention, the stochastic model of the ionospheric delay parameter is optimized by the observation equation, and the ionospheric delay parameter is constrained, so that the positioning performance and the positioning accuracy can be improved.

Description

Optimization method and device of non-differential non-combination PPP model and positioning system
Technical Field
The invention belongs to the technical field of internet, and particularly relates to an optimization method and device of a non-differential non-combination PPP model and a positioning system.
Background
The Precise Point Positioning (PPP) technology is a method for implementing Precise absolute Positioning of a single station by using a Precise product provided by a Global Navigation Satellite System (GNSS) service organization (International GNSS), comprehensively considering the Precise correction of each error model, and using a pseudo range and a carrier phase observed value.
The PPP is realized by two steps: the server side estimates to obtain precise satellite orbit and clock error information through a global tracking network; a satellite orbit and clock error are fixed by a user end, and on the basis of strictly considering various error accurate corrections, a reasonable parameter estimation strategy (such as least square or Kalman filtering) is adopted, parameters such as user coordinates, receiver clock error, troposphere delay, ionosphere delay, carrier phase ambiguity and the like are simultaneously solved, and the positioning accuracy from centimeter to decimeter can be obtained in a global range.
The PPP technology comprises an ionosphere-free combined PPP model and a non-differential non-combined PPP model, and due to the superiority of the non-differential non-combined PPP model in processing multi-frequency data and the fact that high-precision ionosphere delay information can be provided, more and more PPP theoretical researches and applications begin to turn to the non-differential non-combined PPP model.
The existing modeling of non-differential non-combination PPP on ionospheric delay parameters is mostly based on a random walk model, and because ionospheric delay variation has obvious seasonal and regional characteristics, the variation of the ionospheric delay cannot be reasonably constrained, and the positioning accuracy is influenced.
Disclosure of Invention
The embodiment of the invention provides an optimization method, an optimization device and a positioning system of a non-differential non-combination PPP model, and aims to solve the problem that the positioning precision in the later period is influenced by a random walk model in the prior art.
A method for optimizing a non-differential non-combination PPP model comprises the following steps:
acquiring GNSS data, wherein the GNSS data comprises observation data;
constructing a non-differential non-combination PPP observation equation based on the observation data;
constructing a random model of an ionospheric delay parameter;
and optimizing the stochastic model of the ionospheric delay parameter based on the non-difference non-combination PPP observation equation to constrain the ionospheric delay parameter and obtain an optimized result.
Preferably, after constructing the non-differential non-combined PPP observation equation based on the observation data and before constructing the stochastic model of the ionospheric delay parameter, the method further includes:
and preprocessing the non-difference non-combination PPP observation equation to obtain a processed non-difference non-combination PPP observation equation.
Preferably, the stochastic model of the ionospheric delay parameter includes a stochastic walk model, and the stochastic walk model specifically includes:
Figure BDA0001851431310000021
Figure BDA0001851431310000022
wherein the content of the first and second substances,
Figure BDA0001851431310000023
an initial value of an ionospheric delay parameter representing a kth epoch;
Figure BDA0001851431310000024
is an estimated value of ionospheric delay of the k-1 epoch;
Figure BDA0001851431310000025
is random disturbance;
Figure BDA0001851431310000026
which represents the variance of the random process,
Figure BDA0001851431310000027
Figure BDA0001851431310000028
is the spectral density of the random walk process.
Preferably, optimizing the stochastic model of the ionospheric delay parameter based on the non-differential non-combined PPP observation equation to constrain the ionospheric delay parameter, and obtaining an optimization result includes:
defining a variable model;
correcting the non-difference non-combination PPP observation equation based on the variable model to obtain a correction equation;
obtaining an ionospheric delay parameter vector to be estimated based on the correction equation;
and optimizing the stochastic model of the ionospheric delay parameters based on the ionospheric delay parameter vector to be estimated so as to constrain the ionospheric delay parameters and obtain an optimization result.
Preferably, the ionospheric delay parameter vector to be estimated specifically is:
Figure BDA0001851431310000031
in the formula, s is a PPP parameter estimation vector; x is a three-dimensional coordinate increment; ZWDr is the receiver zenith troposphere wet delay;
Figure BDA0001851431310000032
and
Figure BDA0001851431310000033
the receiver clock error, ionospheric delay, and carrier phase ambiguity parameters are re-parameterized.
Preferably, optimizing the stochastic model of the ionospheric delay parameter based on the non-differential non-combined PPP observation equation further includes, after obtaining an optimization result:
and carrying out residual error statistics on the optimization result to obtain a statistical result.
Preferably, the performing residual statistics on the optimization result further includes, after obtaining the statistical result:
judging whether gross errors occur or not based on the statistical result;
and when the judgment result is negative, outputting the optimization result.
Preferably, after determining whether the difference is a gross difference based on the statistical result, the method further includes:
if yes, the gross error removal processing is performed.
The invention also provides an optimization device of the non-differential non-combination PPP model, which comprises:
an acquisition unit configured to acquire GNSS data, the GNSS data including observation data;
the first construction unit is used for constructing a non-differential non-combination PPP observation equation based on the observation data;
the second construction unit is used for constructing a random model of the ionospheric delay parameter;
and the optimization unit is used for optimizing the random model of the ionospheric delay parameter based on the non-differential non-combination PPP observation equation so as to constrain the ionospheric delay parameter and obtain an optimization result.
The present invention also provides a positioning system comprising an optimization apparatus of a non-differential non-combination PPP model, said optimization apparatus comprising:
an acquisition unit configured to acquire GNSS data, the GNSS data including observation data;
the first construction unit is used for constructing a non-differential non-combination PPP observation equation based on the observation data;
the second construction unit is used for constructing a random model of the ionospheric delay parameter;
and the optimization unit is used for optimizing the random model of the ionospheric delay parameter based on the non-differential non-combination PPP observation equation so as to constrain the ionospheric delay parameter and obtain an optimization result.
The invention also provides a memory storing a computer program executed by a processor to perform the steps of:
acquiring GNSS data, wherein the GNSS data comprises observation data;
constructing a non-differential non-combination PPP observation equation based on the observation data;
constructing a random model of an ionospheric delay parameter;
and optimizing the stochastic model of the ionospheric delay parameter based on the non-difference non-combination PPP observation equation to constrain the ionospheric delay parameter and obtain an optimized result.
The invention also provides a positioning terminal, which comprises a memory, a processor and a computer program stored in the memory and capable of running on the processor, wherein the processor executes the computer program to realize the following steps:
acquiring GNSS data, wherein the GNSS data comprises observation data;
constructing a non-differential non-combination PPP observation equation based on the observation data;
constructing a random model of an ionospheric delay parameter;
and optimizing the stochastic model of the ionospheric delay parameter based on the non-difference non-combination PPP observation equation to constrain the ionospheric delay parameter and obtain an optimized result.
In the embodiment of the invention, the stochastic model of the ionospheric delay parameter is optimized through the observation equation, and the ionospheric delay parameter is restrained, so that the positioning performance and the positioning accuracy can be improved.
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FIG. 1 is a flowchart of a method for optimizing a non-differential non-combination PPP model according to a first embodiment of the present invention;
fig. 2 is a detailed flowchart of step S4 of a method for optimizing a non-differential non-combination PPP model according to a first embodiment of the present invention;
FIG. 3 is a flowchart of a preferred embodiment of a method for optimizing a non-differential non-combination PPP model according to a first embodiment of the present invention;
fig. 4 is a structural diagram of an optimization apparatus of a non-differential non-combination PPP model according to a second embodiment of the present invention;
fig. 5 is a structural diagram of a positioning terminal according to a third embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
In the embodiment of the invention, a method for optimizing a non-differential non-combination PPP model comprises the following steps: acquiring GNSS data, wherein the GNSS data comprises observation data; constructing a non-differential non-combination PPP observation equation based on the observation data; constructing a random model of an ionospheric delay parameter; and optimizing the stochastic model of the ionospheric delay parameter based on the non-difference non-combination PPP observation equation to constrain the ionospheric delay parameter and obtain an optimized result.
In order to explain the technical means of the present invention, the following description will be given by way of specific examples.
The first embodiment is as follows:
fig. 1 is a flowchart illustrating a method for optimizing a non-differential non-combination PPP model according to a first embodiment of the present invention, where the method includes:
step S1, GNSS data are obtained;
specifically, first, GNSS data is prepared, which may include: observation data of a monitoring station, a precise track, clock error, code deviation products, antenna phase center correction files and the like.
Step S2, constructing a non-differential non-combination PPP observation equation based on the observation data;
specifically, a non-differential non-combination PPP observation equation is constructed according to the GNSS observation data, the observation equation includes a non-differential pseudo-range observation equation and a carrier observation equation, and the observation equation is as follows:
Figure BDA0001851431310000061
Figure BDA0001851431310000062
wherein s, r, j respectively denote a satellite, a receiver and a frequency number (j ═ 1, 2);
Figure BDA0001851431310000063
and
Figure BDA0001851431310000064
subtracting the calculated values (OMC) from the observed values;
Figure BDA0001851431310000065
direction cosine representing the line connecting the satellite and the receiver; x is the three-dimensional position increment; dtrAnd dtsRespectively representing receiver and satellite clock offsets; ZWDrFor wet stretching of the zenith direction of the receiverThe latest time of the day is,
Figure BDA0001851431310000066
expressed as a corresponding wet projection function;
Figure BDA0001851431310000067
representing an ionospheric slant delay at a first frequency; q represents a satellite system, such as G represents GPS, C represents BDS, R represents GLONASS, E represents Galileo;
Figure BDA0001851431310000068
the amplification factors for ionospheric delays of different frequencies are dependent on the satellite system, and not on the satellite number,
Figure BDA0001851431310000069
wherein
Figure BDA00018514313100000610
Is the GNSS carrier frequency;
Figure BDA00018514313100000611
is the carrier wavelength;
Figure BDA00018514313100000612
is the carrier phase integer ambiguity; dr，jAnd
Figure BDA00018514313100000613
respectively representing the hardware delay of the pseudo range of the receiver and the hardware delay of the satellite, and the corresponding hardware delay of the carrier of the receiver and the satellite is br，jAnd
Figure BDA00018514313100000614
Figure BDA00018514313100000615
and
Figure BDA00018514313100000616
is a combination of observed noise and multipath error.
Step S3, constructing a random model of the ionospheric delay parameter;
specifically, a stochastic model of ionospheric delay parameters is constructed, and the stochastic model may include a white noise model and a stochastic walk model, where the white noise model specifically is:
Figure BDA00018514313100000617
in the formula (I), the compound is shown in the specification,
Figure BDA00018514313100000618
is the initial value of the ionospheric delay parameter of the kth epoch,
Figure BDA00018514313100000619
calculating an ionospheric delay value for the dual-frequency pseudo-range observed value;
Figure BDA00018514313100000620
representing the initial variance of ionospheric delay.
Further, the random walk model is specifically:
Figure BDA00018514313100000621
Figure BDA0001851431310000071
in the formula (I), the compound is shown in the specification,
Figure BDA0001851431310000072
resolving the estimated ionospheric delay value for the k-1 epoch PPP;
Figure BDA0001851431310000073
is random disturbance;
Figure BDA0001851431310000074
is the random walk process variance;
Figure BDA0001851431310000075
is the spectral density of the random walk process.
Step S4, optimizing the stochastic model of the ionospheric delay parameter based on the non-differential non-combination PPP observation equation to constrain the ionospheric delay parameter and obtain an optimization result;
specifically, a stochastic model of the ionospheric delay parameters is optimized according to the aforementioned observation equation to constrain the ionospheric delay parameters to obtain optimized ionospheric delay parameters.
In this embodiment, the stochastic model of the ionospheric delay parameter is optimized by the observation equation, and the ionospheric delay parameter is constrained, so that the positioning performance and the positioning accuracy can be improved.
In a preferable embodiment of this embodiment, after the step S2 and before the step S3, the method further includes:
step S5, preprocessing the PPP observation equation to obtain a processed non-differential non-combination PPP observation equation;
specifically, the PPP observation equation is preprocessed, which may include: 1) and repairing the clock jump. The clock jump of the millisecond-level receiver is mainly repaired, and the consistency of a carrier phase observation value and a pseudo-range observation value is ensured; 2) and detecting cycle slip. Performing cycle slip detection by jointly using Melbourne-Wubbena (MW) combination and ionospheric residual error combination observed quantity; 3) and (6) correcting the model. According to the IERS 2010 specification, errors such as antenna phase center correction, relativistic effect, Sagnac effect (Sagnac effect), inclined troposphere stem delay, tidal load deformation (including solid tide, extreme tide and ocean tide) and phase winding of a satellite and a receiver are mainly corrected; 4) and (3) coarse difference detection, which is mainly used for detecting and identifying coarse differences of pseudo-range observation values, wherein only larger coarse differences are detected and removed in the PPP processing process, and small coarse differences are eliminated by adopting an anti-difference estimation method in the subsequent parameter estimation.
In a preferred embodiment of this embodiment, as shown in fig. 2, a specific flowchart of step S4 of the method for optimizing a non-differential non-combination PPP model according to the first embodiment of the present invention is provided, where the step S4 specifically includes:
step S41, defining a variable model;
specifically, a variable model is first defined, which specifically is:
Figure BDA0001851431310000081
in the formula (I), the compound is shown in the specification,
Figure BDA0001851431310000082
and
Figure BDA0001851431310000083
indicating the signal frequency (where m, n is 1, 2; m ≠ n); αmnAnd βmnIs an amplification factor related to the signal frequency;
Figure BDA0001851431310000084
and
Figure BDA0001851431310000085
is the satellite and receiver side differential code bias.
Step S42, correcting the non-difference non-combination PPP observation equation based on the variable model to obtain a correction equation;
specifically, the non-difference non-combination PPP observation equation is corrected based on the variable model, and the correction equation is obtained as follows:
Figure BDA0001851431310000086
Figure BDA0001851431310000087
wherein the content of the first and second substances,
Figure BDA0001851431310000088
in the formula (I), the compound is shown in the specification,
Figure BDA0001851431310000089
and
Figure BDA00018514313100000810
the receiver clock error, ionospheric delay, and carrier phase ambiguity parameters are re-parameterized.
Step S43, acquiring ionospheric delay parameter vectors to be estimated based on the correction equation;
specifically, an ionospheric delay parameter vector to be estimated is obtained based on a correction equation, where the parameter vector is:
Figure BDA0001851431310000091
in the formula, S is a PPP parameter estimation vector; x is a three-dimensional coordinate increment; ZWDr is the receiver zenith troposphere wet delay;
Figure BDA0001851431310000092
and
Figure BDA0001851431310000093
the receiver clock error, ionospheric delay, and carrier phase ambiguity parameters are re-parameterized.
Step S44, optimizing a random model of the ionospheric delay parameter based on the ionospheric delay parameter vector to be estimated so as to constrain the ionospheric delay parameter and obtain an optimization result;
specifically, a stochastic model for constraining ionospheric delay parameters is optimized based on an ionospheric delay parameter vector to be estimated to constrain the ionospheric delay parameters to obtain a corresponding optimization result, where the optimization result specifically is:
Figure BDA0001851431310000094
Figure BDA0001851431310000095
wherein the content of the first and second substances,
Figure BDA0001851431310000096
an initial value of an ionospheric delay parameter representing a kth epoch;
Figure BDA0001851431310000097
representing the ionospheric delay value estimated by the k-1 epoch PPP solution;
Figure BDA0001851431310000098
is the random walk process variance;
Figure BDA0001851431310000099
spectral density for a random walk process;
Figure BDA00018514313100000910
under the condition that the satellite s does not generate cycle slip, the ionospheric delay variation of the kth epoch and the k-1 th epoch can be accurately determined through a dual-frequency carrier phase observed value, and the accurate result is obtained as follows:
Figure BDA00018514313100000911
in the formula (f)1And f2Representing first and second carrier frequencies;
Figure BDA00018514313100000912
and
Figure BDA00018514313100000913
a carrier phase observation representing the first and second frequencies.
In a preferred embodiment of this embodiment (see fig. 3), the step S4 may further include:
and step S6, carrying out residual error statistics on the optimization result to obtain a statistical result.
Specifically, the optimized result is subjected to residual error statistics, and a quadratic form of the residual error is tested by using a chi-square test method in probability statistics, for example, the accurate result is subjected to residual error statistics to obtain a statistical result.
In a further preferable solution of this embodiment, after step S6, the method may further include:
step S7, judging whether gross error occurs based on the statistical result;
specifically, whether a residual error occurs is judged according to the statistical result, if so, the step is switched to the step S8, otherwise, the step is switched to the step S9;
step S8, removing gross errors;
specifically, the gross error is first removed, and then the process goes to step S4;
step S9, outputting an optimization result;
specifically, when there is no gross error, the optimization result is output, and the optimization result may include: the coordinates of the observation station, the receiver clock error, the tropospheric delay, the ambiguity and the ionospheric delay are correlated.
In this embodiment, the stochastic model of the ionospheric delay parameter is optimized by the observation equation, and the ionospheric delay parameter is constrained, so that the positioning performance and the positioning accuracy can be improved.
Secondly, the ionospheric delay of the current epoch is constructed by integrating the ionospheric delay of the previous epoch and the variation data among the ionospheric delay epochs, the time variation characteristic of the ionospheric delay is represented by a smaller spectral density value so as to stabilize the random variation characteristic of the ionospheric delay parameter and improve the positioning accuracy.
Example two:
as shown in fig. 4, a block diagram of an optimizing apparatus of a non-differential non-combination PPP model according to a second embodiment of the present invention is provided, where the optimizing apparatus includes: an obtaining unit 1, a first building unit 2 connected with the obtaining unit 1, a second building unit 3 connected with the first building unit 2, and an optimizing unit 4 connected with the second building unit 3, wherein:
an acquisition unit 1, configured to acquire GNSS data;
specifically, first, GNSS data is prepared, which may include: observation data of a monitoring station, a precise track, clock error, code deviation products, antenna phase center correction files and the like.
The first construction unit 2 is used for constructing a non-differential non-combination PPP observation equation based on observation data;
specifically, a non-differential non-combination PPP observation equation is constructed according to the GNSS observation data, the observation equation includes a non-differential pseudo-range observation equation and a carrier observation equation, and the observation equation is as follows:
Figure BDA0001851431310000111
Figure BDA0001851431310000112
in the formula, s, r, j respectively represent a satellite, a receiver and a frequency number (j is 1, 2);
Figure BDA0001851431310000113
and
Figure BDA0001851431310000114
subtracting the calculated values (OMC) from the observed values;
Figure BDA0001851431310000115
direction cosine representing the line connecting the satellite and the receiver; x is the three-dimensional position increment; dtrAnd dtsRespectively representing receiver and satellite clock offsets; ZWDrFor the wet delay in the zenith direction of the receiver,
Figure BDA0001851431310000116
expressed as a corresponding wet projection function;representing an ionospheric slant delay at a first frequency; q represents a satellite system, such as G represents GPS, C represents BDS, R represents GLONASS, E represents Galileo;
Figure BDA0001851431310000118
the amplification factors for ionospheric delays of different frequencies are dependent on the satellite system, and not on the satellite number,
Figure BDA0001851431310000119
wherein
Figure BDA00018514313100001110
Is the GNSS carrier frequency;
Figure BDA00018514313100001111
is the carrier wavelength;
Figure BDA00018514313100001112
is the carrier phase integer ambiguity; dr，jAnd
Figure BDA00018514313100001113
respectively representing the hardware delay of the pseudo range of the receiver and the hardware delay of the satellite, and the corresponding hardware delay of the carrier of the receiver and the satellite is br，jAnd
Figure BDA00018514313100001114
Figure BDA00018514313100001115
and
Figure BDA00018514313100001116
is a combination of observed noise and multipath error.
The second construction unit 3 is used for constructing a random model of the ionospheric delay parameter;
specifically, a stochastic model of ionospheric delay parameters is constructed, and the stochastic model may include a white noise model and a stochastic walk model, where the white noise model specifically is:
Figure BDA00018514313100001117
wherein the content of the first and second substances,
Figure BDA00018514313100001118
is the initial value of the ionospheric delay parameter of the kth epoch,
Figure BDA00018514313100001119
calculating an ionospheric delay value for the dual-frequency pseudo-range observed value;
Figure BDA00018514313100001120
representing the initial variance of ionospheric delay.
Further, the random walk model is specifically:
Figure BDA00018514313100001121
Figure BDA0001851431310000121
in the formula (I), the compound is shown in the specification,
Figure BDA0001851431310000122
resolving the estimated ionospheric delay value for the k-1 epoch PPP;
Figure BDA0001851431310000123
is random disturbance;
Figure BDA0001851431310000124
is the random walk process variance;
Figure BDA0001851431310000125
is the spectral density of the random walk process.
The optimization unit 4 is used for optimizing the random model of the ionospheric delay parameter based on the non-differential non-combination PPP observation equation so as to constrain the ionospheric delay parameter and obtain an optimization result;
specifically, a stochastic model of the ionospheric delay parameters is optimized according to the aforementioned observation equation to constrain the ionospheric delay parameters to obtain optimized ionospheric delay parameters.
In this embodiment, the stochastic model of the ionospheric delay parameter is optimized by the observation equation, and the ionospheric delay parameter is constrained, so that the positioning performance and the positioning accuracy can be improved.
In a preferable aspect of this embodiment, the optimizing device further includes: a preprocessing unit 5 connected to both the first building unit 2 and the second building unit 3, wherein:
the preprocessing unit 5 is used for preprocessing the PPP observation equation to obtain a processed non-differential non-combination PPP observation equation;
specifically, the PPP observation equation is preprocessed, which may include: 1) and repairing the clock jump. The clock jump of the millisecond-level receiver is mainly repaired, and the consistency of a carrier phase observation value and a pseudo-range observation value is ensured; 2) and detecting cycle slip. Performing cycle slip detection by jointly using Melbourne-Wubbena (MW) combination and ionospheric residual error combination observed quantity; 3) and (6) correcting the model. According to the IERS 2010 specification, errors such as antenna phase center correction, relativistic effect, Sagnac effect (Sagnac effect), inclined troposphere stem delay, tidal load deformation (including solid tide, extreme tide and ocean tide) and phase winding of a satellite and a receiver are mainly corrected; 4) and (3) coarse difference detection, which is mainly used for detecting and identifying coarse differences of pseudo-range observation values, wherein only larger coarse differences are detected and removed in the PPP processing process, and small coarse differences are eliminated by adopting an anti-difference estimation method in the subsequent parameter estimation.
In a preferred embodiment of this embodiment, the optimizing unit 4 specifically includes: the system comprises a definition subunit, a modification subunit connected with the definition subunit, a vector acquisition subunit connected with the modification subunit, and an optimization subunit connected with the vector acquisition subunit, wherein:
a definition subunit, configured to define a variable model;
specifically, a variable model is first defined, which specifically is:
Figure BDA0001851431310000131
in the formula (I), the compound is shown in the specification,
Figure BDA0001851431310000132
and
Figure BDA0001851431310000133
indicating the signal frequency (where m, n is 1, 2; m ≠ n); αmnAnd βmnIs an amplification factor related to the signal frequency;
Figure BDA0001851431310000134
and
Figure BDA0001851431310000135
is the satellite and receiver side differential code bias.
The correcting subunit is used for correcting the non-difference non-combination PPP observation equation based on the variable model to obtain a correction equation;
specifically, the non-difference non-combination PPP observation equation is corrected based on the variable model, and the correction equation is obtained as follows:
Figure BDA0001851431310000136
Figure BDA0001851431310000137
wherein the content of the first and second substances,
Figure BDA0001851431310000138
in the formula (I), the compound is shown in the specification,
Figure BDA0001851431310000139
and
Figure BDA00018514313100001310
the receiver clock error, ionospheric delay, and carrier phase ambiguity parameters are re-parameterized.
The vector acquisition subunit is used for acquiring an ionospheric delay parameter vector to be estimated based on the correction equation;
specifically, an ionospheric delay parameter vector to be estimated is obtained based on a correction equation, where the parameter vector is:
Figure BDA0001851431310000141
in the formula, S is a PPP parameter estimation vector; x is a three-dimensional coordinate increment; ZWDrFor the receiver zenith troposphereA wet delay;
Figure BDA0001851431310000142
and
Figure BDA0001851431310000143
the receiver clock error, ionospheric delay, and carrier phase ambiguity parameters are re-parameterized.
The optimization subunit is used for optimizing a random model of the ionospheric delay parameter based on the ionospheric delay parameter vector to be estimated so as to constrain the ionospheric delay parameter and obtain an optimization result;
specifically, a stochastic model for constraining ionospheric delay parameters is optimized based on an ionospheric delay parameter vector to be estimated to constrain the ionospheric delay parameters to obtain a corresponding optimization result, where the optimization result specifically is:
Figure BDA0001851431310000144
Figure BDA0001851431310000145
in the formula (I), the compound is shown in the specification,
Figure BDA0001851431310000146
an initial value of an ionospheric delay parameter representing a kth epoch;
Figure BDA0001851431310000147
representing the ionospheric delay value estimated by the k-1 epoch PPP solution;
Figure BDA0001851431310000148
is the random walk process variance;
Figure BDA0001851431310000149
spectral density for a random walk process;
Figure BDA00018514313100001410
ionospheric delay variation for k and k-1 epochsAnd (3) quantifying, wherein under the condition that the satellite s does not generate cycle slip, the quantification can be accurately determined through a dual-frequency carrier phase observed value, and the accurate result is obtained as follows:
Figure BDA00018514313100001411
in the formula (f)1And f2Representing first and second carrier frequencies;
Figure BDA00018514313100001412
and
Figure BDA00018514313100001413
a carrier phase observation representing the first and second frequencies.
In a preferable aspect of this embodiment, the apparatus may further include: the statistical unit is connected with optimizing unit 4, the judgement unit is connected with statistical unit, the processing unit and the output unit are connected with the judgement unit, wherein:
and the statistical unit is used for carrying out residual statistics on the optimization result to obtain a statistical result.
Specifically, the optimized result is subjected to residual error statistics, and a quadratic form of the residual error is tested by using a chi-square test method in probability statistics, for example, the accurate result is subjected to residual error statistics to obtain a statistical result.
A judging unit for judging whether gross error occurs based on the statistical result;
specifically, whether residual errors occur or not is judged according to the statistical result, if yes, the residual errors are fed back to the processing unit, and if not, the residual errors are fed back to the output unit;
a processing unit for removing gross errors;
specifically, the gross error is first removed and then fed back to the optimization unit 4.
An output unit for outputting the optimization result;
specifically, when there is no gross error, the optimization result is output, and the optimization result may include: the coordinates of the observation station, the receiver clock error, the tropospheric delay, the ambiguity and the ionospheric delay are correlated.
In this embodiment, the stochastic model of the ionospheric delay parameter is optimized by the observation equation, and the ionospheric delay parameter is constrained, so that the positioning performance and the positioning accuracy can be improved.
Secondly, the ionospheric delay of the current epoch is constructed by integrating the ionospheric delay of the previous epoch and the variation data among the ionospheric delay epochs, the time variation characteristic of the ionospheric delay is represented by a smaller spectral density value so as to stabilize the random variation characteristic of the ionospheric delay parameter and improve the positioning accuracy.
The present invention further provides a positioning system, which includes an optimization apparatus of a non-differential non-combined PPP model, and the specific structure, operation principle and corresponding technical effect of the optimization apparatus of the non-differential non-combined PPP model described in the second embodiment are substantially the same, and are not described herein again.
Example three:
fig. 5 is a block diagram illustrating a positioning terminal according to a third embodiment of the present invention, where the positioning terminal includes: a memory (memory)51, a processor (processor)52, a communication Interface (communication Interface)53 and a bus 54, wherein the processor 52, the memory 51 and the communication Interface 53 complete mutual communication through the bus 54.
A memory 51 for storing various data;
specifically, the memory 51 is used for storing various data, such as data in communication, received data, and the like, and is not limited herein, and the memory further includes a plurality of computer programs.
A communication interface 53 for information transmission between communication devices of the positioning terminal;
the processor 52 is used to call various computer programs in the memory 51 to execute an optimization method of the non-differential non-combination PPP model provided in the first embodiment, for example:
acquiring GNSS data, wherein the GNSS data comprises observation data;
constructing a non-differential non-combination PPP observation equation based on the observation data;
constructing a random model of an ionospheric delay parameter;
optimizing the stochastic model of the ionospheric delay parameter based on the non-differential non-combinatorial PPP observation equation to constrain the ionospheric delay parameter to an optimized result.
In this embodiment, the stochastic model of the ionospheric delay parameter is optimized by the observation equation, and the ionospheric delay parameter is constrained, so that the positioning performance and the positioning accuracy can be improved.
The invention also provides a memory, which stores a plurality of computer programs, and the computer programs are called by the processor to execute the optimization method of the non-differential non-combination PPP model described in the first embodiment.
In the invention, the stochastic model of the ionospheric delay parameter is optimized by the observation equation, and the ionospheric delay parameter is constrained, so that the positioning performance and the positioning accuracy can be improved.
Secondly, the ionospheric delay of the current epoch is constructed by integrating the ionospheric delay of the previous epoch and the variation data among the ionospheric delay epochs, the time variation characteristic of the ionospheric delay is represented by a smaller spectral density value so as to stabilize the random variation characteristic of the ionospheric delay parameter and improve the positioning accuracy.
Those of ordinary skill in the art will appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware or combinations of computer software and electronic hardware. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the implementation.
Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention. The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present invention, and all the changes or substitutions should be covered within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (12)

1. A method for optimizing a non-differential non-combination PPP model is characterized by comprising the following steps:
acquiring GNSS data, wherein the GNSS data comprises observation data;
constructing a non-differential non-combination PPP observation equation based on the observation data;
constructing a random model of an ionospheric delay parameter;
and optimizing the stochastic model of the ionospheric delay parameter based on the non-difference non-combination PPP observation equation to constrain the ionospheric delay parameter and obtain an optimized result.
2. The optimization method of claim 1, wherein after constructing the non-differential non-combined PPP observation equation based on the observation data and before constructing the stochastic model of the ionospheric delay parameter further comprises:
and preprocessing the non-difference non-combination PPP observation equation to obtain a processed non-difference non-combination PPP observation equation.
3. The optimization method according to claim 2, wherein the stochastic model of ionospheric delay parameters comprises a stochastic walk model, and the stochastic walk model is specifically:
Figure FDA0001851431300000011
Figure FDA0001851431300000012
wherein the content of the first and second substances,
Figure FDA0001851431300000013
an initial value of an ionospheric delay parameter representing a kth epoch;
Figure FDA0001851431300000014
is an estimated value of ionospheric delay of the k-1 epoch;
Figure FDA0001851431300000015
is random disturbance;
Figure FDA0001851431300000016
which represents the variance of the random process,
Figure FDA0001851431300000017
Figure FDA0001851431300000018
is the spectral density of the random walk process.
4. The optimization method of claim 3, wherein optimizing the stochastic model of ionospheric delay parameters based on the non-differential non-combined PPP observation equations to obtain an optimized result comprises:
defining a variable model;
correcting the non-difference non-combination PPP observation equation based on the variable model to obtain a correction equation;
obtaining an ionospheric delay parameter vector to be estimated based on the correction equation;
and optimizing the stochastic model of the ionospheric delay parameters based on the ionospheric delay parameter vector to be estimated so as to constrain the ionospheric delay parameters and obtain an optimization result.
5. The optimization method according to claim 4, wherein the ionospheric delay parameter vector to be estimated is specifically:
Figure FDA0001851431300000021
in the formula, s is a PPP parameter estimation vector; x is a three-dimensional coordinate increment; ZWDrIs the receiver zenith tropospheric wet delay;
Figure FDA0001851431300000022
and
Figure FDA0001851431300000023
the receiver clock error, ionospheric delay, and carrier phase ambiguity parameters are re-parameterized.
6. The optimization method of claim 1, wherein optimizing the stochastic model of the ionospheric delay parameters based on the non-differential non-combinatorial PPP observation equations to constrain the ionospheric delay parameters, and obtaining the optimization result further comprises:
and carrying out residual error statistics on the optimization result to obtain a statistical result.
7. The optimization method according to claim 5, wherein the performing residual statistics on the optimization result further comprises, after obtaining the statistical result:
judging whether gross errors occur or not based on the statistical result;
and when the judgment result is negative, outputting the optimization result.
8. The optimization method of claim 1, further comprising, after determining whether the gross error is based on the statistical result:
if yes, the gross error removal processing is performed.
9. An apparatus for optimizing a non-differential non-combination PPP model, comprising:
an acquisition unit configured to acquire GNSS data, the GNSS data including observation data;
the first construction unit is used for constructing a non-differential non-combination PPP observation equation based on the observation data;
the second construction unit is used for constructing a random model of the ionospheric delay parameter;
and the optimization unit is used for optimizing the random model of the ionospheric delay parameter based on the non-differential non-combination PPP observation equation so as to constrain the ionospheric delay parameter and obtain an optimization result.
10. A positioning system comprising means for optimizing the non-differential non-combinatorial PPP model as defined in claim 9.
11. A memory storing a computer program, the computer program being executable by a processor to perform the steps of:
acquiring GNSS data, wherein the GNSS data comprises observation data;
constructing a non-differential non-combination PPP observation equation based on the observation data;
constructing a random model of an ionospheric delay parameter;
and optimizing the stochastic model of the ionospheric delay parameter based on the non-difference non-combination PPP observation equation to constrain the ionospheric delay parameter and obtain an optimized result.
12. A positioning terminal comprising a memory, a processor and a computer program stored in said memory and executable on said processor, characterized in that said processor, when executing said computer program, implements the steps of the method for optimizing a non-differential non-combined PPP model as defined in any one of claims 1 to 8.
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