CN110646823A - GPS \ BDS tightly-combined precise single-point positioning method based on Helmet post-verification-authority method - Google Patents

GPS \ BDS tightly-combined precise single-point positioning method based on Helmet post-verification-authority method Download PDF

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CN110646823A
CN110646823A CN201910968030.4A CN201910968030A CN110646823A CN 110646823 A CN110646823 A CN 110646823A CN 201910968030 A CN201910968030 A CN 201910968030A CN 110646823 A CN110646823 A CN 110646823A
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杨乾炜
茅旭初
吴博钊
苏红
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Shanghai Jiaotong University
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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
    • G01S19/38—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
    • 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
    • G01S19/421—Determining position by combining or switching between position solutions or signals derived from different satellite radio beacon positioning systems; by combining or switching between position solutions or signals derived from different modes of operation in a single system
    • G01S19/425—Determining position by combining or switching between position solutions or signals derived from different satellite radio beacon positioning systems; by combining or switching between position solutions or signals derived from different modes of operation in a single system by combining or switching between signals derived from different satellite radio beacon positioning systems

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Abstract

The invention discloses a GPS \ BDS dual-system tightly-combined precise single-point positioning method based on a Helmet post-verification right method, which relates to the field of GNSS high-precision real-time precise positioning, and comprises the following steps: step 1, establishing a PPP function model by using a combination of pseudo-range observed values and carrier phase observed values; step 2, establishing a random model by using a Helmet-based posterior verification method; step 3, unifying the space-time reference of the double systems; step 4, processing errors; and 5, positioning and solving by using an iterative least square method. The method effectively solves the difficult problem of PPP ambiguity fixation caused by large orbit error of the Beidou satellite and frequent orbit maneuver of the GEO satellite, enables the multiple systems to realize ambiguity fixation resolving of deep fusion, successfully solves the problem of overlarge variance of parameter estimation values during fusion positioning of the multiple systems, and improves the PPP ambiguity fixation rate to a limited extent on the premise of ensuring the fixation accuracy rate.

Description

GPS \ BDS tightly-combined precise single-point positioning method based on Helmet post-verification-authority method
Technical Field
The invention relates to the field of GNSS high-precision real-time precision positioning, in particular to a GPS \ BDS dual-system tightly-combined precision single-point positioning method based on a Helmet post-verification-authorization method.
Background
With the modernization of the American GPS and Russian GLONASS systems and the construction of the European Galileo system, the global satellite navigation system has entered the multi-GNSS era. The multi-system fusion calculation can obviously increase the number of available satellites and observation signals, improve the geometrical structure of a constellation, reduce the precision attenuation factor, provide more redundant information, enhance the reliability of a positioning system and the like. The multi-system data fusion processing is a development trend in the field of international GNSS research and application and is a current research hotspot.
At present, in the field of GNSS high-precision real-time precision positioning, two positioning modes, namely network RTK and precision single point positioning (PPP), mainly exist. Network RTK technology is mature, but requires dense reference stations with a distance of no more than 80 km, and it is difficult to realize coverage of real-time positioning service in a wide area. The PPP technology can realize real-time decimeter and even centimeter-level positioning only by wide-area sparsely-distributed reference stations, and can effectively make up for the deficiencies of network RTK. Meanwhile, the PPP technology can flexibly fuse the enhanced information of each regional reference station to perform precise positioning on the basis of a set of global orbital clock error products, and can fully utilize the existing reference station network.
However, the conventional PPP technology is based on ambiguity floating solution, the positioning convergence time is long, and the positioning accuracy and reliability are inferior to that of network RTK, which greatly limits the development and application of PPP, especially in the field of implementing high-accuracy positioning. Therefore, scholars in recent years have proposed a PPP ambiguity fixing technology, but the current research is limited to a single GPS system, and the PPP ambiguity fixing still has the problems of long fixing time and low fixing reliability. Further research on the theory and method of multi-system PPP ambiguity fixing needs to be deeply carried out, a multi-system PPP ambiguity fixing resolving model is established, and the PPP ambiguity is quickly fixed. The method plays an important role in popularizing the PPP technology in the fields of mapping, remote sensing, geographic information and the like.
With the construction and development of multiple systems, the combination of multiple systems is an important research direction for improving the PPP ambiguity fixing performance. Galileo is still under construction, few satellites are available, and the research of the published literature is basically focused on the combination of GPS + GLONASS and GPS + BDS. Qu and other 24 multi-mode tracking stations based on a terrestrial network perform PPP ambiguity fixing of a BDS system, and the result shows that the PPP ambiguity fixing time of a single GPS system can be shortened and the positioning accuracy can be improved after the BDS is added. But they fix only MEO and IGSO satellite ambiguities, fail to achieve GEO satellite FCB estimation and ambiguity fixing, however the narrow lane ambiguity fixing time is longer due to the larger satellite orbit error. In order to eliminate the large influence of Beidou orbit errors, Liu and the like use a small-range observation network to realize FCB estimation and PPP ambiguity fixation of Beidou MEO, IGSO and GEO satellites. The results show that the fixation rate of GPS alone is only 17.6% in 10 minutes, and the fixation rate is improved to 57.7% after BDS is added. Liu provides a narrow-lane FCB method for simultaneously estimating tangential and normal orbital errors of a satellite, high-precision FCB estimation and PPP ambiguity fixation of three types of Beidou satellites in the Chinese range are achieved, and results equivalent to those of experiments adopting a small network are obtained.
Disclosure of Invention
The invention aims to research the theory and the method for PPP ambiguity fixing by utilizing multimode GNSS data (BDS/GPS/GLONASS), research a pseudo-range error modeling method of a specific system and realize widelane ambiguity fixing. The method is mainly used for solving the problem that the larger satellite orbit error of the Beidou system has fixed ambiguity of the PPP widelane. A multi-system tightly-combined PPP ambiguity fixing method and a stable and reliable PPP ambiguity fixing and checking method are researched, the problems that the PPP ambiguity fixing time is long and the fixing reliability is not high on the basis of a single GPS system at present are solved, and a new thought is provided for the PPP engineering application.
In order to achieve the above object, the present invention provides a GPS \ BDS tight combination precise single-point positioning method based on a Helmet post-verification right method, which comprises the following steps:
step 1, establishing a PPP function model by using a combination of pseudo-range observed values and carrier phase observed values;
step 2, establishing a random model by using a Helmet-based posterior verification method;
step 3, unifying the space-time reference of the double systems;
step 4, processing errors;
and 5, positioning and solving by using an iterative least square method.
Further, the calculation formula of the pseudo-range observation and the carrier-phase observation in step 1 is as follows:
Figure BDA0002231147830000022
wherein P is the pseudo-range observed quantity of different frequency signals, phi is the carrier phase observed value of different frequency signals, f is the frequency of the carrier phase, rho is the true distance from the satellite to the receiver, and deltatrIs the clock difference, δ t, of the receiver rsIs the clock error of the satellite s, c is the speed of light in vacuum, T is the tropospheric delay, δ m is the multipath delay, dr(t)、
Figure BDA0002231147830000023
Time delays, P, of receiver and satellite, respectivelyIF、
Figure BDA0002231147830000024
Ionospheric-free combined observations, λ, of pseudorange and carrier phase, respectivelyIFTo combine the wavelengths of the observed values, bIFFor the ambiguity of the ionospheric-free combined observation, ε PIF，εφIFThe observed noise and the unmodeled error for the two combined observations, respectively.
Further, the ambiguity of the ionospheric-free combined observation in step 1 is:
Figure BDA0002231147830000025
further, the function model in step 1 is:
L＝BX+Δ (4)。
in the formula, L is an observed value, B is a state function, X is a solution value, and Δ is an error value.
Further, the method for determining posterior weights based on Helmet in step 2 is to determine initial weights for various observation values, perform pre-adjustment, estimate the pre-adjustment variance and covariance of the various observation values by using the information obtained after the pre-adjustment, and determine weights in sequence.
Further, the stochastic model in step 2 is:
Figure BDA0002231147830000031
wherein the content of the first and second substances,is an optimal estimate of X, X0In an initial approximation of X,
Figure BDA0002231147830000033
least squares correction number of X, approximate correction value
Figure BDA0002231147830000034
Is shown asE (L), E (delta) are the expected values of the observed value and the error value, respectively, D (L), D (delta) are the variance of the observed value and the error value, respectively,
Figure BDA0002231147830000036
is the unit weight variance, and the error equation is obtained as follows:
wherein l is an observed value
The derivation is performed on equation (6), and the obtained normal equation and its solution are:
wherein：N＝BTPB，W＝BTPL；
Wherein, N is a normal equation state transition matrix, W is a value obtained after derivation of an observed value, and P is a weight matrix of the observed value.
Set up in L and contain two kinds of observation values L independent of each other1，L2，…，LMTheir weight arrays are respectively P1，P2，…，PM；
Wherein: pij0(i ≠ j), and the error equations are respectively as follows:
Figure BDA0002231147830000039
wherein P isijIs a unit variable in the observation value weight array and has the following relation:
the first adjustment, the weight P of m types of observed values1，P2，…，PmImproper; the unit weight variance corresponding to the m-type observed values is respectivelyThen the formula of Helmet variance component estimation of the m-class observed values is:
Figure BDA00022311478300000312
wherein the content of the first and second substances,
Figure BDA0002231147830000041
Figure BDA0002231147830000042
the only solution to the formula for the Helmet variance component estimate is:
Figure BDA0002231147830000043
further, the iterative calculation step of the Helmet variance component estimation is as follows:
(1) classifying the observed values according to different sources, and performing pre-test weight estimation, namely determining the initial value P of the weight of each type of observed values1，P2，…，Pm；
(2) Performing the first adjustment to obtain Vi TPiVi；
(3) The first power difference estimation is carried out according to the formula (10) to obtain the first estimation value of unit weight variance of various observation values
Figure BDA0002231147830000044
Then, the weighting is performed according to the following formula (13):
Figure BDA0002231147830000045
wherein c is any constant.
(4) Repeating (1) and (3), namely: adjusting-estimating variance component-weighting and then adjusting untilUntil now.
Further, in the processing error of the step 4, the PPP calculation parameters of the dual system include a position parameter, a clock error parameter, an inter-system bias parameter, a zenith troposphere estimation parameter, and an ambiguity parameter.
Further, in the location solution in the step 5, the actual position (x) of the receivers，ys，zs) Expressed as approximate positionAnd the offset (Δ x) of the true positionr，Δyr，Δzr)。
Further, the combined observation equation set and the solution found are expressed in matrix form as:
Δρ＝HΔx (15)
Δx＝(HTH)-1HTΔρ (16)
the iterative least square method resolving process comprises the following steps: calculating a deviation value delta x of an estimated value and an actual value through a formula (16), correcting the estimated value obtained in the previous stage by using the deviation value, inputting the corrected estimated value again, and repeating the steps until the deviation value is smaller than an acceptable range, so that the iteration can be finished; the estimated value at this time is the final result of the iterative least square method.
Compared with the prior art, the invention has the following improvements and beneficial effects:
1. the invention provides a set of integer satellite clock error estimation method considering satellite orbit errors, which effectively solves the problem of PPP ambiguity fixation caused by large orbit errors of Beidou satellites and frequent orbital maneuver of GEO satellites;
2. the invention provides a PPP ambiguity fixing method of a multi-GNSS tight combination, which enables multi-systems with different frequencies and different wavelengths to realize ambiguity fixing resolution of deep fusion;
3. the invention uses Helmet post-verification-right method to establish a random model of PPP combined observed values, successfully solving the problem of overlarge variance of parameter estimation values when multi-system fusion positioning is carried out;
4. the invention provides a method for testing the threshold value of multi-system PPP ambiguity fixation based on the measured data, and the PPP ambiguity fixation rate is improved in a limited way on the premise of ensuring the fixation accuracy.
The conception, the specific structure and the technical effects of the present invention will be further described with reference to the accompanying drawings to fully understand the objects, the features and the effects of the present invention.
Drawings
FIG. 1 is a diagram of PPP positioning;
FIG. 2 is a PPP resolution flow chart;
FIG. 3 is the convergence times of 6 different PPP models in the E, N and U directions;
FIG. 4 shows the PPP positioning results of BDS, GPS, BDS/GPS under ambiguity fixed solution;
FIG. 5 is the RMS of the ambiguity-fixed solution PPP location results for BDS, GPS, BDS/GPS.
Detailed Description
The technical contents of the preferred embodiments of the present invention will be more clearly and easily understood by referring to the drawings attached to the specification. The present invention may be embodied in many different forms of embodiments and the scope of the invention is not limited to the embodiments set forth herein.
The purpose of the invention can be realized by the following technical scheme:
the first step is as follows: and comprehensively analyzing the possible deviation and source of the pseudo-range observed value and the carrier phase observed value in the positioning and the influence of the deviation and the source on the positioning result precision. And fixing the single-epoch ambiguity of the GPS double-difference observed value.
The second step is that: and establishing a PPP data processing model based on a GPS single system according to different combination modes of the observed values. And comparing the positioning accuracy and the reliability of different models. Various errors in the PPP resolving process are researched, a mathematical model of PPP resolving is optimized, and the precision and the stability of the solution are improved.
The third step: the method solves the problem that the big orbit error of the Beidou satellite (especially the GEO satellite) has influence on the PPP narrow lane ambiguity fixation, researches an integer satellite clock error estimation method for simultaneously estimating the orbit error correction number, and explores whether the PPP ambiguity fixation performance of the multimode GNSS system with good orbit precision can be further improved by the method.
The fourth step: and B1/B2 of BDS and L1/L2 of GPS are utilized to form a multimode GNSS combined observation value. For example, the combination of the Beidou signal and the GPS signal can form a wide lane observation value, which is more favorable for resolving the ambiguity. The multi-frequency signals are used to form various combinations without the influence of an ionized layer at the first order. Characteristics and properties of the method, including ionospheric refraction, multipath, measurement noise and the like, are researched and analyzed to explore an optimal combination observation value suitable for network ambiguity single epoch solution, PPP ambiguity solution and PPP parameter estimation of the long-distance reference station.
The fifth step: and interpolating various precise orbit and clock error information provided by IGS to obtain satellite orbit and clock error data meeting PPP requirements. The time domain stability of the receiver ISB is researched by utilizing an integer satellite clock difference product with unified multi-system time reference, and a corresponding modeling method is explored, so that only one receiver clock difference parameter is estimated in PPP positioning, only one reference satellite is needed when ambiguity is fixed, and multi-system tightly-combined PPP ambiguity fixing is realized.
As shown in fig. 1, a PPP positioning diagram is shown.
The invention provides a GPS \ BDS tightly-combined precise single-point positioning method based on a Helmet post-verification right method, which can realize the fusion PPP positioning of a GPS \ BDS dual system.
The implementation of the method comprises the following steps:
step 1, establishing a PPP function model by using a combination of pseudo-range observed values and carrier phase observed values;
step 2, establishing a random model by using a Helmet-based posterior verification method;
step 3, unifying the space-time reference of the double systems;
step 4, processing errors;
and 5, positioning and solving by using an iterative least square method.
Step 1 is to build a function model. In precise point positioning, an ionosphere-free combination (IF) of dual-frequency pseudoranges and carrier-phase observations is typically used as a functional model of PPP, and the expression is:
Figure BDA0002231147830000061
Figure BDA0002231147830000062
wherein P is pseudo-range observed quantity of different frequency signals, and phi is differentA carrier phase observation of the frequency signal, f is the frequency of the carrier phase, ρ is the true distance from the satellite to the receiver, trTime at which a signal is received by a receiver r, tsTime of signal transmission from satellite s, c is speed of light in vacuum, T is tropospheric delay, δ m is multipath delay, PIF、
Figure BDA0002231147830000063
Ionosphere-free combined observations of pseudorange and carrier phase, respectively, bIFAmbiguity, ε P, for ionospheric-free combined observationsIF，εφIFThe observed noise and the unmodeled error for the two combined observations, respectively.
The ambiguity of the ionosphere-free combined observed value in the step 1 is as follows:
the ionospheric-free model is the earliest and most extensive mathematical model applied, and can eliminate the influence of first-order ionospheric delay and internal frequency offset.
And step 2, establishing a random model. When the dual-system fusion positioning of the GPS and the BDS is carried out, if the weight ratio between different constellations and different observation values is unreasonable, the variance of the unit weight after the test is biased, and the variance minimization of the parameter estimation is influenced. For the problem of determining the weight ratio value between various types of observed quantities in the combined adjustment, the method is improved from a first weight verification method to a second weight verification method.
The present invention uses the Helmet method to determine the different types of variance-covariance components.
The basic idea of the posterior estimation of the stochastic model is as follows: the method comprises the steps of firstly, setting initial weights for various observed values, carrying out pre-adjustment, utilizing information obtained after pre-adjustment, mainly correcting numbers of various observed values, estimating the pre-test variance and covariance of various observed values according to a certain principle, and sequentially setting weights. The basic formula is as follows:
the function model is:
L＝BX+Δ (4)。
the stochastic model is:
wherein the content of the first and second substances,
Figure BDA0002231147830000072
is an optimal estimate of X, X0In an initial approximation of X,
Figure BDA0002231147830000073
is a least-squares correction of X,
Figure BDA0002231147830000074
is shown as
Figure BDA0002231147830000075
Further, the error equation is obtained as follows:
Figure BDA0002231147830000076
the normal equation and its solution are:
Figure BDA0002231147830000077
wherein: n ═ BTPB，W＝BTPL；
Set up in L and contain two kinds of observation values L independent of each other1，L2，…，LMTheir weight arrays are respectively P1，P2，…，PM；
Wherein: pij0(i ≠ j), and the error equations are respectively as follows:
Figure BDA0002231147830000078
and has the following relationship:
Figure BDA0002231147830000079
considering the first adjustment, the weight P of m types of observed values1，P2，…，PmImproper; the unit weight variance corresponding to the m-type observed values is respectively
Figure BDA00022311478300000710
Then the formula of Helmet variance component estimation of the m-class observed values is:
Figure BDA0002231147830000081
wherein the content of the first and second substances,
Figure BDA0002231147830000082
Figure BDA0002231147830000083
the only solution to the formula for Helmet variance component estimation is:
the iterative calculation steps of Helmet variance component estimation are as follows:
(1) classifying the observed values according to different sources, and performing pre-test weight estimation, namely determining the initial value P of the weight of each type of observed values1，P2，…，Pm；
(2) Performing the first adjustment to obtain Vi TPiVi；
(3) The first power difference estimation is performed according to the equation (10) to obtain the first estimation of unit weight variance of each type of observation value
Figure BDA0002231147830000085
Then, the weighting is performed according to the following formula (13):
Figure BDA0002231147830000086
(4) repeating (1) and (3), namely: adjusting-estimating variance component-weighting and then adjusting untilUntil now.
In step 3: in the unified dual-system space-time reference, the parameters of the WGS-84 and the CGS2000 coordinate systems are almost consistent, so that in practical application, the two coordinate systems do not need to be converted, and can be regarded as belonging to the same WGS-84 coordinate system. For the uniformity of time, it can be seen from table 1 that the start time of the beidou time and the GPS time are different, and there is a difference of 1356 weeks. And there is a 14 second system difference between the two systems in addition to the cycle difference due to the presence of UTC leap seconds.
In the error processing in step 4, the PPP calculation parameters of the dual systems include a position parameter, a clock error parameter, an intersystem deviation parameter, a zenith troposphere estimation parameter, and an ambiguity parameter. Cycle slip detection is an important link in data preprocessing, and the cycle slip detection is carried out by comprehensively using a polynomial fitting method and a phase pseudo-range combination method in the embodiment.
Table 1: data processing strategy and model for PPP
In the positioning solution in step 5, the essence of the iterative least squares method is to perform curve fitting on the nonlinear function, thereby obtaining an approximate function. The fitting criterion is to ensure the minimum sum of squares of residual errors (difference between observed values and fitted values), and the method for obtaining the approximate function by the method is the least square approximation of curve fitting, which is also called as the best square approximation.
In the positioning solution, the actual position (x) of the receivers，ys，zs) Expressed as approximate position
Figure BDA0002231147830000092
And the offset (Δ x) of the true positionr，Δyr，Δzr)。
The combined observation equation set and the solution found are expressed in matrix form as:
Figure BDA0002231147830000093
Δρ＝HΔx (15)
Δx＝(HTH)-1HTΔρ (16)
the iterative least square method solution process is as follows: calculating a deviation value delta x of the estimated value and the actual value through a formula (16), correcting the estimated value obtained in the previous stage by using the deviation value, inputting the corrected estimated value again, and repeating the steps until the deviation value is smaller than an acceptable range, so that the iteration can be finished; the estimated value at this time is the final result of the iterative least square method.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.

Claims (10)

1. A GPS \ BDS tightly-combined precise single-point positioning method based on a Helmet post-verification-authority method is characterized by comprising the following steps:
step 1, establishing a PPP function model by using a combination of pseudo-range observed values and carrier phase observed values;
step 2, establishing a random model by using a Helmet-based posterior verification method;
step 3, unifying the space-time reference of the double systems;
step 4, processing errors;
and 5, positioning and solving by using an iterative least square method.
2. The method for tightly-combined precise point positioning by GPS \ BDS based on hellmet post-verification weight method according to claim 1, wherein the calculation formula of the pseudo-range observed quantity and the carrier phase observed value in step 1 is:
Figure FDA0002231147820000011
Figure FDA0002231147820000012
wherein P is the pseudo-range observed quantity of different frequency signals, phi is the carrier phase observed value of different frequency signals, f is the frequency of the carrier phase, rho is the true distance from the satellite to the receiver, and deltatrIs the clock difference, δ t, of the receiver rsIs the clock error of the satellite s, c is the speed of light in vacuum, T is the tropospheric delay, δ m is the multipath delay, dr(t)、
Figure FDA0002231147820000013
Time delays, P, of receiver and satellite, respectivelyIF、
Figure FDA0002231147820000014
Ionospheric-free combined observations, λ, of pseudorange and carrier phase, respectivelyIFTo combine the wavelengths of the observed values, bIFFor the ambiguity of the ionospheric-free combined observation, ε PIF，εφIFThe observed noise and the unmodeled error for the two combined observations, respectively.
3. The method of claim 2, wherein the ambiguity of the ionosphere-free combined observation value in step 1 is as follows:
Figure FDA0002231147820000015
4. the method of claim 1, wherein the function model in step 1 is:
L＝BX+Δ (4)。
in the formula, L is an observed value, B is a state function, X is a solution value, and Δ is an error value.
5. The Helmet post-verification-right-method-based GPS \ BDS tightly-combined precise single-point positioning method as claimed in claim 4, wherein the Helmet-based post-verification-right method in the step 2 is to initially determine the initial right of each type of observation value, perform pre-adjustment, estimate the pre-verification variance and covariance of each type of observation value by using the information obtained after the pre-adjustment, and sequentially determine the right.
6. The Helmet post-qualification-based GPS \ BDS tightly-combined precise point positioning method as claimed in claim 5, wherein said random model in step 2 is:
Figure FDA0002231147820000021
wherein the content of the first and second substances,
Figure FDA0002231147820000022
is an optimal estimate of X, X0In an initial approximation of X,
Figure FDA0002231147820000023
least squares correction number of X, approximate correction value
Figure FDA0002231147820000024
Is shown as
Figure FDA0002231147820000025
E (L), E (delta) are expected values of observed value and error value, respectively, and D (L), D (delta) are observed value and error value, respectivelyThe variance of the difference value is determined,
Figure FDA0002231147820000026
is the unit weight variance, and the error equation is obtained as follows:
Figure FDA0002231147820000027
wherein l is an observed value
The derivation is performed on equation (6), and the obtained normal equation and its solution are:
Figure FDA0002231147820000028
wherein: n ═ BTPB，W＝BTPL；
Wherein, N is a normal equation state transition matrix, W is a value obtained after derivation of an observed value, and P is a weight matrix of the observed value.
Set up in L and contain two kinds of observation values L independent of each other1,L2,…,LMTheir weight arrays are respectively P1,P2,…,PM；
Wherein: pij0(i ≠ j), and the error equations are respectively as follows:
Figure FDA0002231147820000029
wherein P isijIs a unit variable in the observation value weight array and has the following relation:
Figure FDA00022311478200000210
the first adjustment, the weight P of m types of observed values1,P2,…,PmImproper; the unit weight variance corresponding to the m-type observed values is respectively
Figure FDA00022311478200000211
Obtaining m-class observed valuesThe formula for Helmet variance component estimate of (1) is:
Figure FDA00022311478200000212
wherein the content of the first and second substances,
Figure FDA0002231147820000031
Figure FDA0002231147820000032
the only solution to the formula for the Helmet variance component estimate is:
7. the Helmet post-verification-weight method-based GPS \ BDS tightly-combined precise point positioning method as claimed in claim 6, wherein said Helmet variance component estimation iterative computation steps are as follows:
(1) classifying the observed values according to different sources, and performing pre-test weight estimation, namely determining the initial value P of the weight of each type of observed values1,P2,…,Pm；
(2) The first adjustment is performed to obtain
Figure FDA0002231147820000034
(3) The first power difference estimation is carried out according to the formula (10) to obtain the first estimation value of unit weight variance of various observation values
Figure FDA0002231147820000035
Then, the weighting is performed according to the following formula (13):
Figure FDA0002231147820000036
wherein c is any constant.
(4) Repeating (1) and (3), namely: adjusting-estimating variance component-weighting and then adjusting until
Figure FDA0002231147820000037
Until now.
8. The Helmet post-verification-weight-method-based GPS \ BDS tightly-combined precise single-point positioning method as recited in claim 1, wherein in the processing error of the step 4, the PPP calculation parameters of the dual systems comprise a position parameter, a clock error parameter, an inter-system deviation parameter, a zenith troposphere estimation parameter and an ambiguity parameter.
9. The method of claim 2, wherein in the step 5, the actual position (x) of the receiver is solved for the positioning solutions,ys,zs) Expressed as approximate position
Figure FDA0002231147820000038
And the offset (Δ x) of the true positionr,Δyr,Δzr)。
10. The Helmet post-verification-right-based GPS \ BDS tightly-combined precise single-point positioning method as claimed in claim 9, wherein the combination observation equation set and the solution obtained are expressed in matrix form as:
Figure FDA0002231147820000041
Δρ＝HΔx (15)
Δx＝(HTH)-1HTΔρ (16)
the iterative least square method resolving process comprises the following steps: calculating a deviation value delta x of an estimated value and an actual value through a formula (16), correcting the estimated value obtained in the previous stage by using the deviation value, inputting the corrected estimated value again, and repeating the steps until the deviation value is smaller than an acceptable range, so that the iteration can be finished; the estimated value at this time is the final result of the iterative least square method.
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