CN114859389A - GNSS multi-system robust adaptive fusion RTK resolving method - Google Patents

GNSS multi-system robust adaptive fusion RTK resolving method Download PDF

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CN114859389A
CN114859389A CN202210405810.XA CN202210405810A CN114859389A CN 114859389 A CN114859389 A CN 114859389A CN 202210405810 A CN202210405810 A CN 202210405810A CN 114859389 A CN114859389 A CN 114859389A
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rtk
observation
formula
equation
bds
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冯彪
王超
帅路
张平
吴小波
马磊
刘解华
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Huali Zhixin Chengdu Integrated Circuit 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
    • G01S19/13—Receivers
    • G01S19/33—Multimode operation in different systems which transmit time stamped messages, e.g. GPS/GLONASS
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/13—Receivers
    • G01S19/35—Constructional details or hardware or software details of the signal processing chain
    • G01S19/37—Hardware or software details of the signal processing chain
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/40—Correcting position, velocity or attitude
    • G01S19/41—Differential correction, e.g. DGPS [differential GPS]

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Abstract

The invention discloses a GNSS multi-system robust adaptive fusion RTK resolving method, which comprises the following steps: step 1: establishing a conventional RTK double-difference observation equation according to BDS/GPS/GLONASS/GLILEO multi-system observation data of the base station and the rover station; step 2: conventional Kalman filtering solution; and step 3: robust Kalman adaptive filtering estimation; and 4, step 4: the estimation of Helmert variance component is fused in the BDS/GPS/GLONASS/GLILEO multi-system; and 5: BDS/GPS/GLONASS/GLILEO multisystem RTK ambiguity fix. The method can effectively reduce the influence of the inaccuracy of the GNSS positioning prior random model and the observation containing abnormity and the abnormity of the dynamic model on the positioning of the multi-system fusion RTK, and improve the positioning precision of the GNSS (BDS/GPS/GLONASS/GLILEO) multi-system fusion RTK, so that the RTK positioning result is more stable and reliable in a complex environment.

Description

GNSS multi-system robust adaptive fusion RTK resolving method
Technical Field
The invention belongs to the field of GNSS satellite navigation positioning, and particularly relates to a GNSS multi-system robust self-adaptive fusion RTK resolving method.
Background
With the continuous development of global satellite navigation systems and the combination of different satellite constellations, the number of visible satellites provided is gradually increased, and the space geometric distribution of the satellites is more perfect. The GNSS (BDS/GPS/GLONASS/GLILEO) multi-system fusion provides more reliable guarantee for high-precision positioning due to the introduction of more visible satellites. However, due to the difference of the constellation and satellite orbit distribution of each satellite navigation system, the navigation positioning performance and the accuracy of the observed value of each system are different, and the GNSS multi-system fusion positioning only determines that the weight ratio of the observed value of each system is inaccurate and reliable according to the prior accuracy. Meanwhile, in the regions such as cities, canyons and the like, due to the fact that the observation environment is complex, multipath or non-line-of-sight signals are formed by satellite signals due to reflection or scattering of buildings, the probability that an observation value contains gross errors or is abnormal is increased, and a carrier motion model is difficult to model accurately under a dynamic condition, so that large deviation and even divergence are prone to occur in conventional Kalman filtering positioning calculation.
Therefore, for GNSS multi-system fusion positioning, especially for application in complex environments, how to determine the weight of each observation value among navigation systems and each satellite without relying on prior theory or empirical value is important for improving the precision and the availability of GNSS multi-system fusion RTK positioning by self-adaptively adjusting the weight of each observation value among navigation systems and satellites.
Disclosure of Invention
The invention aims to provide a GNSS multi-system robust adaptive fusion RTK resolving method which is used for effectively reducing the influence of inaccuracy of a GNSS positioning prior random model, observation containing abnormality and dynamics model abnormality on positioning of a multi-system fusion RTK and improving the positioning precision of the GNSS (BDS/GPS/GLONASS/GLILEO) multi-system fusion RTK so that an RTK positioning result is more stable and reliable in a complex environment.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a GNSS multi-system robust adaptive fusion RTK resolving method comprises the following steps:
step 1: establishing a conventional RTK double-difference observation equation according to BDS/GPS/GLONASS/GLILEO multi-system observation data of the base station and the rover station;
step 2: conventional Kalman filtering solution;
and step 3: robust Kalman adaptive filtering estimation;
and 4, step 4: the estimation of Helmert variance component is fused in the BDS/GPS/GLONASS/GLILEO multi-system;
and 5: BDS/GPS/GLONASS/GLILEO multisystem RTK ambiguity fix.
Further, as a preferred technical scheme, the specific process of the step 1 is as follows:
step 1-1: establishing a basic observation equation based on the non-difference original pseudo range and the carrier phase observation value, which comprises the following specific steps:
Figure BDA0003601817370000021
Figure BDA0003601817370000022
in the formula, subscripts i and r are frequency and station survey of observed quantity respectively, and superscript j is a satellite;
Figure BDA0003601817370000023
respectively, a pseudo range and a carrier phase original observed value, taking meters as a unit,
Figure BDA0003601817370000024
as phase observations (weeks);
Figure BDA0003601817370000025
geometric distance from satellite to station at the moment of signal transmission, c speed of light in vacuum, dt r And dt j Respectively receiver clock error and satellite clock error, T j In order to delay the tropospheric delay,
Figure BDA0003601817370000026
is the ionospheric delay at the frequency i,
Figure BDA0003601817370000027
and
Figure BDA0003601817370000028
receiver-side and satellite-side pseudorange hardware delay biases,
Figure BDA0003601817370000029
and
Figure BDA00036018173700000210
phase hardware delay biases including carrier phase hardware delay bias and initial phase bias, λ, at the receiver end and at the satellite end, respectively i And
Figure BDA00036018173700000211
carrier phase wavelength at frequency i and integer ambiguity,
Figure BDA00036018173700000212
and
Figure BDA00036018173700000213
the measurement noise is respectively the pseudo range and the carrier phase observation value;
step 1-2: according to the RTK double-difference model, the satellite clock difference and the receiver clock difference in the step 1-1 can be eliminated, the influences of satellite orbit errors, troposphere delay errors, ionosphere delay errors, multipath effects and the like are weakened, and a carrier phase double-difference observation equation is established, which specifically comprises the following steps:
Figure BDA00036018173700000214
in the formula, superscripts j and k represent satellite numbers; the r, b subscripts denote rover and reference stations;
Figure BDA00036018173700000215
a double-difference phase observed value of an epoch t;
Figure BDA00036018173700000216
the distance from the satellite s to the survey station r;
Figure BDA00036018173700000217
is double-difference ambiguity; since the reference coordinates are known, the above equation can be converted into:
Figure BDA00036018173700000218
step 1-3: the prior coordinate of the rover station adopts single-point positioning estimation to approximate an estimated value X r ＝(x r ,y r ,z r ) T Let its correction number be δ X r ＝(δx r ,δy r ,δz r ) T And linearizing the equation finally converted in the step 1-2 to obtain a carrier phase double-difference error equation:
Figure BDA0003601817370000031
in the formula (I), the compound is shown in the specification,
Figure BDA0003601817370000032
Figure BDA0003601817370000033
similarly, a pseudorange double difference error equation may be obtained:
Figure BDA0003601817370000034
wherein the content of the first and second substances,
Figure BDA0003601817370000035
double differenced pseudorange observations.
Further, as a preferred technical scheme, the specific process of the step 2 is as follows:
step 2-1: establishing a Kalman filtering state equation and an observation equation:
X k ＝Φ k,k-1 X k-1 +W k-1
L k ＝A k X k +V k
wherein k represents an observation epoch time, X k Representing the state vector at time k, phi k,k-1 A transition matrix, W, representing the state of the system from time k-1 to time k k-1 Is a dynamic noise vector, L k For the observation vector at time k, A k For observing the coefficient matrix of the equation, V k To observe the noise vector;
step 2-2: the observed values are regarded as mutually independent, and the dynamic noise and the observed noise are white noise with zero mean and mutually irrelevant, namely the following conditions are met:
Figure BDA0003601817370000036
in the formula, omega k Is an array of variances of process noise, Q k A variance matrix for the observed noise;
step 2-3: the state equation and the observation equation are respectively rewritten as an error equation:
Figure BDA0003601817370000041
in the formula (I), the compound is shown in the specification,
Figure BDA0003601817370000042
and V k Respectively predicting values for state parameters
Figure BDA0003601817370000043
And the observed value L k Residual vector of (2), and state parameter prediction value
Figure BDA0003601817370000044
Comprises the following steps:
Figure BDA0003601817370000045
Figure BDA0003601817370000046
the covariance matrix of (a) can be obtained:
Figure BDA0003601817370000047
constructing an objective function according to a least square criterion:
Figure BDA0003601817370000048
in the formula, P k And
Figure BDA0003601817370000049
respectively are observed values L k And status parameter prediction value
Figure BDA00036018173700000410
Is expressed as
Figure BDA00036018173700000411
Figure BDA00036018173700000412
Solving by pair formula
Figure BDA00036018173700000413
Partial derivatives and let their partial derivatives equal 0, with:
Figure BDA00036018173700000414
further, the following can be obtained:
Figure BDA00036018173700000415
step 2-4: substituting an error equation corresponding to the observation equation into the formula (1) to obtain:
Figure BDA00036018173700000416
further, as a preferred technical solution, a general process of further deriving Kalman filter calculation by matrix identity transformation and matrix inversion formula is as follows:
step 2-4-1: calculating a Kalman filtering gain matrix K according to the prediction precision of the current epoch by the previous epoch k ，
Figure BDA00036018173700000417
Step 2-4-2: updating the current epoch observed value, namely performing weighted correction by using the weight of the current epoch measured value,
Figure BDA00036018173700000418
Figure BDA00036018173700000419
step 2-4-3: and updating the time, namely predicting the observation value of the next epoch.
Further, as a preferred technical solution, the specific process of step 3 is:
step 3-1: the robust adaptive Kalman filter solution is:
Figure BDA0003601817370000051
in the formula (I), the compound is shown in the specification,
Figure BDA0003601817370000052
is L k Is an adaptive estimate of the observation vector weight matrix, alpha k Alpha is 0-alpha for the adaptive factor k ≤1；
Step 3-2: equivalent weight factors and adaptive weight factors are determined.
Further, as a preferred technical solution, the specific calculation process of the equivalent weight factor is as follows:
step 3-2-1: in BDS/GPS/GLONASS/GALILEO fusion positioning, the observed values among systems are independent, and the corresponding equivalence weights are as follows:
Figure BDA0003601817370000053
in the formula, P i Is the original weight matrix, w i Is an adaptive weight factor;
step 3-2-2: determining the weight factor by adopting an IGGIII equivalent weight factor-based function or a two-factor equivalent weight factor-based function, wherein the function expression based on the IGGIII equivalent weight factor is as follows:
Figure BDA0003601817370000054
in the formula (I), the compound is shown in the specification,
Figure BDA0003601817370000055
to normalize the residual, k 1 、k 2 Is a constant, typically take k 1 ＝1.5～2.0，k 2 ＝3.0～8.0；
The function expression based on the two-factor equivalent weight factor is as follows:
Figure BDA0003601817370000056
Figure BDA0003601817370000057
wherein c is a constant, c is 2.5-3.0, and i and j represent row and column numbers of the matrix;
step 3-2-3: calculating a normalized residual
Figure BDA0003601817370000058
Figure BDA0003601817370000059
Step 3-2-4: normalized residual error for different types of observations
Figure BDA00036018173700000510
Comprises the following steps:
Figure BDA00036018173700000511
in the formula (I), the compound is shown in the specification,
Figure BDA0003601817370000061
σ MAD ＝1.483·med|v i -med|v i ||。
further, as a preferred technical solution, the specific calculation process of the adaptive weight factor is as follows:
calculating adaptive weight factor a by using two-segment function k Namely:
Figure BDA0003601817370000062
wherein c is a constant, c is 1.0 to 2.5,
Figure BDA0003601817370000063
Figure BDA0003601817370000064
in the formula (I), the compound is shown in the specification,
Figure BDA0003601817370000065
in order to normalize the prediction residual error,
Figure BDA0003601817370000066
the residual is predicted for the state parameters,
Figure BDA0003601817370000067
the trace of the residual covariance matrix is predicted for the state parameters.
Further, as a preferred technical solution, the specific process of step 4 is as follows:
step 4-1: during the first filtering, the BDS, GPS, GLONASS and GLILEO observed values are firstly verified according to the altitude angle of the satellite to obtain the weight P C :P G :P R :P E ；
Step 4-2: performing filtering calculation to obtain V i T P i V i (i＝C,G,R,E)；
Step 4-3: and (3) carrying out variance component estimation:
Figure BDA0003601817370000068
in the formula (I), the compound is shown in the specification,
Figure BDA0003601817370000069
N＝A T PA＝A C T P C A C +A G T P G A G +A R T P R A R +A E T P E A E ＝N C +N G +N R +N E
wherein n is C 、n G 、n R And n E The numbers of BDS, GPS, GLONASS and GALILEO observed values respectively;
step 4-4: re-weighting:
Figure BDA00036018173700000610
wherein c is any constant, optionally
Figure BDA0003601817370000071
A certain value of;
and 4-5: repeating the step 4-2 to the step 4-4 until
Figure BDA0003601817370000072
The difference is less than 0.01.
Further, as a preferred technical solution, when iteration fails to converge or convergence distortion occurs in step 4, the satellites are rescreened or the weights of some satellites are appropriately reduced, and then solution is performed.
Further, as a preferred technical solution, in the step 5, the BDS/GPS/GLONASS/glieo multi-system RTK ambiguity fix is performed by using a least square ambiguity downcorrelation adjustment method in combination with a partial ambiguity fix strategy.
Compared with the prior art, the invention has the following beneficial effects:
aiming at GNSS multi-system fusion RTK, firstly, the weight of each satellite observation value is adjusted by adopting robust Kalman adaptive filtering to inhibit the influence of observation abnormity and dynamic model errors on RTK estimation parameters, secondly, the weight of the observation value among each satellite navigation system (BDS/GPS/GLONASS/GLILEO) is adaptively adjusted by adopting variance component estimation, and the weight ratio among observation values with different types or unequal precision is adaptively adjusted by iterative calculation to ensure that the weight distribution is more reasonable, so that the GNSS multi-system fusion RTK positioning is more accurate and reliable in a complex environment.
Drawings
FIG. 1 is a schematic view of the process structure of the present invention.
Detailed Description
The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
Examples
As shown in fig. 1, the method for solving the GNSS multi-system robust adaptive fusion RTK according to this embodiment includes the following steps:
step 1: establishing a conventional RTK double-difference observation equation according to BDS/GPS/GLONASS/GLILEO multi-system observation data of the base station and the rover station;
step 2: conventional Kalman filtering solution;
and step 3: robust Kalman adaptive filtering estimation;
and 4, step 4: the estimation of Helmert variance component is fused in the BDS/GPS/GLONASS/GLILEO multi-system;
and 5: BDS/GPS/GLONASS/GLILEO multisystem RTK ambiguity fix.
In this embodiment, the specific process of step 1 is as follows:
step 1-1: establishing a basic observation equation based on the non-difference original pseudo range and the carrier phase observation value, which comprises the following specific steps:
Figure BDA0003601817370000081
Figure BDA0003601817370000082
in the formula, subscripts i and r are frequency and station survey of observed quantity respectively, and superscript j is a satellite;
Figure BDA0003601817370000083
respectively, a pseudo range and a carrier phase original observed value, taking meters as a unit,
Figure BDA0003601817370000084
as phase observations (weeks);
Figure BDA0003601817370000085
geometric distance from satellite to station at the moment of signal transmission, c speed of light in vacuum, dt r And dt j Respectively receiver clock error and satellite clock error, T j In order to delay the tropospheric delay,
Figure BDA0003601817370000086
is the ionospheric delay at the frequency i,
Figure BDA0003601817370000087
and
Figure BDA0003601817370000088
receiver-side and satellite-side pseudorange hardware delay biases,
Figure BDA0003601817370000089
and
Figure BDA00036018173700000810
phase hardware delay biases including carrier phase hardware delay bias and initial phase bias, λ, at the receiver end and at the satellite end, respectively i And
Figure BDA00036018173700000811
carrier phase wavelength at frequency i and integer ambiguity,
Figure BDA00036018173700000812
and
Figure BDA00036018173700000813
the measurement noise is respectively the pseudo range and the carrier phase observation value;
step 1-2: according to the RTK double-difference model, the satellite clock difference and the receiver clock difference in the step 1-1 can be eliminated, the influences of satellite orbit errors, troposphere delay errors, ionosphere delay errors, multipath effects and the like are weakened, and a carrier phase double-difference observation equation is established, which specifically comprises the following steps:
Figure BDA00036018173700000814
in the formula, superscripts j and k represent satellite numbers; the r, b subscripts denote rover and reference stations;
Figure BDA00036018173700000815
a double-difference phase observed value of an epoch t;
Figure BDA00036018173700000816
the distance from the satellite s to the survey station r;
Figure BDA00036018173700000817
is double-difference ambiguity; since the reference coordinates are known, the above equation can be converted into:
Figure BDA00036018173700000818
step 1-3: the prior coordinate of the rover station adopts single-point positioning estimation to approximate an estimated value X r ＝(x r ,y r ,z r ) T Let its correction number be δ X r ＝(δx r ,δy r ,δz r ) T And linearizing the equation finally converted in the step 1-2 to obtain a carrier phase double-difference error equation:
Figure BDA0003601817370000091
in the formula (I), the compound is shown in the specification,
Figure BDA0003601817370000092
Figure BDA0003601817370000093
similarly, a pseudorange double difference error equation may be obtained:
Figure BDA0003601817370000094
wherein the content of the first and second substances,
Figure BDA0003601817370000095
double differenced pseudorange observations.
In this embodiment, the specific process of conventional Kalman filter solution is as follows:
the Kalman filtering is based on a set of observation sequences L k (k 1, 2.., n) and the kinetic model information of the system to solve the state vector estimate. In the precision positioning, a state vector consists of parameters to be estimated, a dynamic model is established according to the correlation of the before and after epochs of the parameters to be estimated, and a filtering state equation and an observation equation are as follows:
X k ＝Φ k,k-1 X k-1 +W k-1
L k ＝A k X k +V k
wherein k represents an observation epoch time, X k Representing the state vector at time k, phi k,k-1 A transition matrix, W, representing the state of the system from time k-1 to time k k-1 Is a dynamic noise vector, L k For the observation vector at time k, A k For observing the coefficient matrix of the equation, V k To observe the noise vector;
generally, the observed values are regarded as mutually independent, and the dynamic noise and the observed noise are white noises which are zero-mean and mutually uncorrelated, that is, the following conditions are satisfied:
Figure BDA0003601817370000096
in the formula, omega k Is an array of variances of process noise, Q k A variance matrix for the observed noise;
in order to solve the least square solution of the state parameters, Kalman filtering is used for solving according to the free extreme value principle, and a state equation and an observation equation are respectively rewritten into error equations:
Figure BDA0003601817370000101
in the formula (I), the compound is shown in the specification,
Figure BDA0003601817370000102
and V k Respectively predicting values for state parameters
Figure BDA0003601817370000103
And the observed value L k Residual vector of (2), and state parameter prediction value
Figure BDA0003601817370000104
Comprises the following steps:
Figure BDA0003601817370000105
Figure BDA0003601817370000106
the covariance matrix of (a) can be obtained:
Figure BDA0003601817370000107
constructing an objective function according to a least square criterion:
Figure BDA0003601817370000108
in the formula, P k And
Figure BDA0003601817370000109
respectively is an observed value L k And status parameter prediction value
Figure BDA00036018173700001010
Is expressed as
Figure BDA00036018173700001011
Figure BDA00036018173700001012
Solving by pair formula
Figure BDA00036018173700001013
Partial derivatives and let their partial derivatives equal 0, with:
Figure BDA00036018173700001014
further, the method can be obtained as follows:
Figure BDA00036018173700001015
step 2-4: substituting the error equation into the above formula to obtain:
Figure BDA00036018173700001016
the general process of further deducing Kalman filtering calculation by a matrix identity transformation and matrix inversion formula is as follows:
step 2-4-1: calculating a Kalman filtering gain matrix K according to the prediction precision of the current epoch by the previous epoch k ，
Figure BDA00036018173700001017
Step 2-4-2: updating the current epoch observed value, namely performing weighted correction by using the weight of the current epoch measured value,
Figure BDA00036018173700001018
Figure BDA00036018173700001019
step 2-4-3: and updating the time, namely predicting the observed value of the next epoch.
In this embodiment, the specific process of robust Kalman adaptive filtering estimation is as follows:
in order to control the influence of the dynamic model abnormity and the observation abnormity, the robust estimation principle is adopted, the influence of the observation value abnormity is reduced or eliminated by selecting proper equivalent weight instead of an observation noise covariance matrix, and the influence of the dynamic model abnormity on the filtering solution is controlled by adjusting the proportion of the covariance matrix of the predicted value and the observation noise covariance matrix by using the adaptive factor. The robust adaptive Kalman filter solution is:
Figure BDA0003601817370000111
in the formula (I), the compound is shown in the specification,
Figure BDA0003601817370000112
is L k Is an adaptive estimate of the observation vector weight matrix, alpha k Alpha is 0-alpha for the adaptive factor k ≤1；
Then, determining an equivalent weight factor and an adaptive weight factor, wherein the specific calculation process of the equivalent weight factor is as follows:
in BDS/GPS/GLONASS/GALILEO fusion positioning, the observed values among systems are independent, and the corresponding equivalence weights are as follows:
Figure BDA0003601817370000113
in the formula, P i Is the original weight matrix, w i Is an adaptive weight factor;
determining the weight factor by adopting an IGGIII equivalent weight factor-based function or a two-factor equivalent weight factor-based function, wherein the function expression based on the IGGIII equivalent weight factor is as follows:
Figure BDA0003601817370000114
in the formula (I), the compound is shown in the specification,
Figure BDA0003601817370000115
to normalize the residual, k 1 、k 2 Is a constant, typically take k 1 ＝1.5～2.0，k 2 ＝3.0～8.0；
The function expression based on the two-factor equivalent weight factor is as follows:
Figure BDA0003601817370000116
Figure BDA0003601817370000117
wherein c is a constant, c is 2.5-3.0, and i and j represent row and column numbers of the matrix;
calculating a normalized residual
Figure BDA0003601817370000118
Figure BDA0003601817370000119
For GNSS multi-system fusion positioning, due to the difference of the precision of observed values of different systems, the residual vector of the observed values may have system errors, and the variance factor sigma v And the consistency is that the residual error information of the gross error and the correct observation values of different types cannot be accurately distinguished during the weight reduction processing of the adaptive factors. Normalized residual error for different types of observations
Figure BDA0003601817370000121
Comprises the following steps:
Figure BDA0003601817370000122
in the formula (I), the compound is shown in the specification,
Figure BDA0003601817370000123
σ MAD ＝1.483·med|v i -med|v i ||。
the specific calculation process of the adaptive weight factor is as follows:
the dynamic model prediction innovation is that the state innovation of the current moment and a covariance matrix weighted gain matrix are updated by using the state estimation value of the previous moment and the observation value of the current moment, and the self-adaptive factor obtained based on the statistic of the innovation residual error structure can better reflect the disturbance condition of the dynamic system. Meanwhile, in order to fully utilize the kinetic model information, avoid a k In case of 0, the adaptive weight factor function is a two-stage function, that is:
Figure BDA0003601817370000124
wherein c is a constant, c is 1.0 to 2.5,
Figure BDA0003601817370000125
Figure BDA0003601817370000126
in the formula (I), the compound is shown in the specification,
Figure BDA0003601817370000127
in order to normalize the prediction residual error,
Figure BDA0003601817370000128
the residual is predicted for the state parameters,
Figure BDA0003601817370000129
the trace of the residual covariance matrix is predicted for the state parameters.
In this embodiment, the Helmert variance component estimation adaptively adjusts the weight ratio between different types or unequal precision observation values through iterative computation, so that the weight distribution is more reasonable. The specific idea is that the initial weight of each kind of observation value is determined according to the experience value, the adjustment is carried out, the difference before the test of each kind of observation value is estimated according to the posterior residual error of the posterior observation value of the adjustment, the weight between each kind of observation value is obtained, and the adjustment is carried out again until the given test condition is satisfied. Performing Helmert variance component estimation according to the established BDS/GPS/GLONASS/GLILEO multi-system double-difference error equation and the prior weight ratio of each system observation value, wherein the specific calculation process comprises the following steps:
step 4-1: during the first filtering, the BDS, GPS, GLONASS and GLILEO observed values are firstly verified according to the altitude angle of the satellite to obtain the weight P C :P G :P R :P E ；
Step 4-2: performing filtering calculation to obtain V i T P i V i (i＝C,G,R,E)；
Step 4-3: and (3) carrying out variance component estimation:
Figure BDA0003601817370000131
in the formula (I), the compound is shown in the specification,
Figure BDA0003601817370000132
N＝A T PA＝A C T P C A C +A G T P G A G +A R T P R A R +A E T P E A E ＝N C +N G +N R +N E
wherein n is C 、n G 、n R And n E The numbers of BDS, GPS, GLONASS and GALILEO observed values respectively;
step 4-4: re-weighting:
Figure BDA0003601817370000133
wherein c is any constant, optionally
Figure BDA0003601817370000134
A certain value of;
and 4-5: repeating the step 4-2 to the step 4-4 until
Figure BDA0003601817370000135
The difference is less than 0.01.
When iteration is not converged or convergence distortion occurs in the step 4, the analysis reason is that the number of various observation values is unbalanced, and if the number of one kind of observation values is too small, the weight ratio determined by Helmert variance component estimation is easy to distort; secondly, in the observation data preprocessing process, if the difference of the residuals of various observation values is too large, the iteration process may have unconvergence or too many iteration times, and the S matrix is a singular matrix and cannot be positioned and solved. Therefore, in the resolving process, attention needs to be paid to various satellite numbers in the epoch to determine whether Helmert variance component estimation is adopted or not; when the iterative process diverges, the residual errors of all the satellites need to be analyzed, the satellites are screened again or the weights of some satellites are reduced properly, and then calculation is carried out.
In this embodiment, the BDS/GPS/GLONASS/glieo multi-system RTK Ambiguity fixing is preferably performed by using an lamb-square Ambiguity correction (Least-squares Ambiguity correction) method in combination with a partial Ambiguity fixing strategy. The method of lamb-square Ambiguity resolution Adjustment belongs to the prior art, and the fixing in combination with the partial Ambiguity fixing strategy is easy to be realized by those skilled in the art, and the present embodiment merely gives such a preferable mode.
Although the invention has been described in detail above with reference to a general description and specific examples, it will be apparent to one skilled in the art that modifications or improvements may be made thereto based on the invention. Accordingly, such modifications and improvements are intended to be within the scope of the invention as claimed.

Claims (10)

1. A GNSS multi-system robust adaptive fusion RTK resolving method is characterized by comprising the following steps:
step 1: establishing a conventional RTK double-difference observation equation according to BDS/GPS/GLONASS/GLILEO multi-system observation data of the base station and the rover station;
and 2, step: conventional Kalman filtering solution;
and 3, step 3: robust Kalman adaptive filtering estimation;
and 4, step 4: the estimation of Helmert variance component is fused in the BDS/GPS/GLONASS/GLILEO multi-system;
and 5: BDS/GPS/GLONASS/GLILEO multisystem RTK ambiguity fix.
2. The GNSS multi-system robust adaptive fusion RTK solution method according to claim 1, characterized in that the specific process of step 1 is as follows:
step 1-1: establishing a basic observation equation based on the non-difference original pseudo-range and the carrier phase observation value, which comprises the following steps:
Figure FDA0003601817360000011
Figure FDA0003601817360000012
in the formula, subscripts i and r are frequency and station survey of observed quantity respectively, and superscript j is a satellite;
Figure FDA0003601817360000013
respectively, a pseudo range and a carrier phase original observed value, taking meters as a unit,
Figure FDA0003601817360000014
as phase observations (weeks);
Figure FDA0003601817360000015
geometric distance from satellite to station at the moment of signal transmission, c speed of light in vacuum, dt r And dt j Respectively receiver clock error and satellite clock error, T j In order to delay the tropospheric delay,
Figure FDA0003601817360000016
is the ionospheric delay at the frequency i,
Figure FDA0003601817360000017
and
Figure FDA0003601817360000018
receiver-side and satellite-side pseudorange hardware delay biases,
Figure FDA0003601817360000019
and
Figure FDA00036018173600000110
phase hardware delay biases including carrier phase hardware delay bias and initial phase bias, λ, at the receiver end and at the satellite end, respectively i And
Figure FDA00036018173600000111
carrier phase wavelength at frequency i and integer ambiguity,
Figure FDA00036018173600000112
and
Figure FDA00036018173600000113
the measurement noise is respectively the pseudo range and the carrier phase observation value;
step 1-2: according to the RTK double-difference model, the satellite clock difference and the receiver clock difference in the step 1-1 can be eliminated, the influences of satellite orbit errors, troposphere delay errors, ionosphere delay errors, multipath effects and the like are weakened, and a carrier phase double-difference observation equation is established, which specifically comprises the following steps:
Figure FDA0003601817360000021
in the formula, superscripts j and k represent satellite numbers; the r, b subscripts denote rover and reference stations;
Figure FDA0003601817360000022
the observation value of the double-difference phase of the epoch t is obtained;
Figure FDA0003601817360000023
the distance from the satellite s to the survey station r;
Figure FDA0003601817360000024
is double-difference ambiguity; since the reference coordinates are known, the above equation can be converted into:
Figure FDA0003601817360000025
step 1-3: the prior coordinate of the rover station adopts single-point positioning estimation to approximate an estimated value X r ＝(x r ,y r ,z r ) T Let its correction number be δ X r ＝(δx r ,δy r ,δz r ) T And linearizing the equation finally converted in the step 1-2 to obtain a carrier phase double-difference error equation:
Figure FDA0003601817360000026
in the formula (I), the compound is shown in the specification,
Figure FDA0003601817360000027
Figure FDA0003601817360000028
similarly, a pseudorange double difference error equation may be obtained:
Figure FDA0003601817360000029
wherein the content of the first and second substances,
Figure FDA00036018173600000210
double differenced pseudorange observations.
3. The GNSS multi-system robust adaptive fusion RTK solution method according to claim 2, characterized in that the specific process of step 2 is as follows:
step 2-1: establishing a Kalman filtering state equation and an observation equation:
X k ＝Φ k,k-1 X k-1 +W k-1
L k ＝A k X k +V k
wherein k represents an observation epoch time, X k Representing the state vector at time k, phi k,k-1 A transition matrix, W, representing the state of the system from time k-1 to time k k-1 Is a dynamic noise vector, L k For the observation vector at time k, A k For observing the coefficient matrix of the equation, V k To observe the noise vector;
step 2-2: the observed values are regarded as mutually independent, and the dynamic noise and the observed noise are white noises which are zero-mean and mutually uncorrelated, namely the following conditions are met:
Figure FDA0003601817360000031
in the formula, omega k Is an array of variances of process noise, Q k A variance matrix for the observed noise;
step 2-3: and respectively rewriting the state equation and the observation equation into error equations:
Figure FDA0003601817360000032
in the formula (I), the compound is shown in the specification,
Figure FDA0003601817360000033
and V k Respectively predicting values for state parameters
Figure FDA0003601817360000034
And the observed value L k Residual vector of (2), and state parameter prediction value
Figure FDA0003601817360000035
Comprises the following steps:
Figure FDA0003601817360000036
Figure FDA0003601817360000037
the covariance matrix of (a) can be obtained:
Figure FDA0003601817360000038
constructing an objective function according to a least square criterion:
Figure FDA0003601817360000039
in the formula, P k And
Figure FDA00036018173600000310
respectively are observed values L k And state parameter preReporting value
Figure FDA00036018173600000311
Is expressed as
Figure FDA00036018173600000312
Figure FDA00036018173600000313
Solving by pair formula
Figure FDA00036018173600000314
Partial derivatives and let their partial derivatives equal 0, with:
Figure FDA00036018173600000315
further, the method can be obtained as follows:
Figure FDA00036018173600000316
step 2-4: substituting an error equation corresponding to the observation equation into the formula (1) to obtain:
Figure FDA0003601817360000041
4. the GNSS multi-system robust adaptive fusion RTK solution method according to claim 3, characterized in that the general process of further deriving Kalman filtering calculation from matrix identity transformation and matrix inversion formula is:
step 2-4-1: calculating a Kalman filtering gain matrix K according to the prediction precision of the current epoch by the previous epoch k ，
Figure FDA0003601817360000042
Step 2-4-2: updating the current epoch observed value, namely performing weighted correction by using the weight of the current epoch measured value,
Figure FDA0003601817360000043
Figure FDA0003601817360000044
step 2-4-3: and updating the time, namely predicting the observation value of the next epoch.
5. The GNSS multi-system robust adaptive fusion RTK solution method according to claim 3 or 4, characterized in that the specific process of the step 3 is as follows:
step 3-1: the robust adaptive Kalman filter solution is:
Figure FDA0003601817360000045
in the formula (I), the compound is shown in the specification,
Figure FDA0003601817360000046
is L k Is an adaptive estimate of the observation vector weight matrix, alpha k Alpha is 0-alpha for the adaptive factor k ≤1；
Step 3-2: equivalent weight factors and adaptive weight factors are determined.
6. The GNSS multi-system robust adaptive fusion RTK solution method according to claim 5, wherein the specific calculation process of the equivalent weight factors is as follows:
step 3-2-1: in BDS/GPS/GLONASS/GALILEO fusion positioning, the observed values among systems are independent, and the corresponding equivalence weights are as follows:
Figure FDA0003601817360000047
in the formula, P i Is the original weight matrix, w i Is an adaptive weight factor;
step 3-2-2: determining the weight factor by adopting an IGGIII equivalent weight factor-based function or a two-factor equivalent weight factor-based function, wherein the function expression based on the IGGIII equivalent weight factor is as follows:
Figure FDA0003601817360000051
in the formula (I), the compound is shown in the specification,
Figure FDA0003601817360000052
to normalize the residual, k 1 、k 2 Is a constant, typically take k 1 ＝1.5～2.0，k 2 ＝3.0～8.0；
The function expression based on the two-factor equivalent weight factor is as follows:
Figure FDA0003601817360000053
Figure FDA0003601817360000054
wherein c is a constant, c is 2.5-3.0, and i and j represent row and column numbers of the matrix;
step 3-2-3: calculating a normalized residual
Figure FDA0003601817360000055
Figure FDA0003601817360000056
σ v ＝1.483med|v i |
Step 3-2-4: normalized residual error for different types of observations
Figure FDA0003601817360000057
Comprises the following steps:
Figure FDA0003601817360000058
in the formula (I), the compound is shown in the specification,
Figure FDA0003601817360000059
σ MAD ＝1.483·med|v i -med|v i ||。
7. the GNSS multi-system robust adaptive fusion RTK solution method according to claim 5, wherein the specific calculation process of the adaptive weight factor is as follows:
calculating adaptive weight factor a by using two-segment function k Namely:
Figure FDA00036018173600000510
wherein c is a constant, c is 1.0 to 2.5,
Figure FDA00036018173600000511
Figure FDA00036018173600000512
in the formula (I), the compound is shown in the specification,
Figure FDA00036018173600000513
in order to normalize the prediction residual error,
Figure FDA00036018173600000514
the residual is predicted for the state parameters,
Figure FDA00036018173600000515
the trace of the residual covariance matrix is predicted for the state parameters.
8. The GNSS multi-system robust adaptive fusion RTK solution method according to claim 5, wherein the specific process of step 4 is as follows:
step 4-1: during the first filtering, the BDS, GPS, GLONASS and GLILEO observed values are firstly verified according to the altitude angle of the satellite to obtain the weight P C :P G :P R :P E ；
Step 4-2: performing filtering calculation to obtain V i T P i V i (i＝C,G,R,E)；
Step 4-3: and (3) carrying out variance component estimation:
Figure FDA0003601817360000061
in the formula (I), the compound is shown in the specification,
Figure FDA0003601817360000062
N＝A T PA＝A C T P C A C +A G T P G A G +A R T P R A R +A E T P E A E ＝N C +N G +N R +N E
wherein n is C 、n G 、n R And n E The numbers of BDS, GPS, GLONASS and GALILEO observed values respectively;
step 4-4: re-weighting:
Figure FDA0003601817360000063
wherein c is any constant, optionally
Figure FDA0003601817360000064
A certain value of;
and 4-5: repeating the step 4-2 to the step 4-4 until
Figure FDA0003601817360000065
The difference is less than 0.01.
9. The GNSS multi-system robust adaptive fusion RTK solution method of claim 8, wherein when iteration non-convergence or convergence distortion occurs in step 4, the satellites are rescreened or the weights of some satellites are reduced appropriately, and then the solution is performed.
10. The GNSS multi-system robust adaptive fusion RTK solution method of claim 1, wherein in the step 5, the BDS/GPS/GLONASS/GLILEO multi-system RTK ambiguity fix is fixed by using least square ambiguity downcorrelation adjustment and partial ambiguity fix strategy.
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