CN109884679B - Cross-frequency point mixed double-difference RTK resolving method of single-mode GNSS system - Google Patents
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Abstract
The invention belongs to the field of satellite precision navigation and positioning, and particularly relates to a cross-frequency point mixed double-difference RTK resolving method of a single-mode GNSS system, which comprises the following steps: acquiring original pseudo-range and carrier phase observed quantity output by a base station and a mobile station receiver; performing inter-station single difference on the obtained original observed quantity to obtain pseudo range and carrier phase single difference observed quantity; carrying out linear combination on the carrier phase single-difference observed quantities by utilizing a multi-frequency combination technology to obtain combined observed quantities with consistent frequencies; constructing an RB-IFB parameter estimation model by using the combined observed quantities with consistent frequencies to obtain an RB-IFB estimation sequence; performing stability analysis on the RB-IFB estimation sequence, and if a stability condition is met, taking the RB-IFB mean value as a correction value to increase the redundancy of the model; according to the method, the stability characteristic of inter-frequency deviation of a receiver end is fully excavated, the influence of the wavelength difference between the cross-frequency points is eliminated by using a multi-frequency combination technology, the correction value of the RB-IFB is accurately solved and is used as the observed quantity redundancy information, and higher model redundancy is obtained.
Description
Technical Field
The invention belongs to the field of satellite precision navigation and positioning, and particularly relates to a cross-frequency point mixed double-difference RTK resolving method of a single-mode GNSS system.
Background
Integer ambiguity resolution is one of the key technologies for obtaining high-precision and high-reliability positioning by a real-time dynamic method based on carrier phase difference. The least squares ambiguity decorrelation method becomes a widely used integer ambiguity resolution method that requires sufficient available observations to resolve the ambiguity correctly. Under the severe shielding environment, the available observed quantity is relatively less, and how to increase the number of the available observed quantity becomes one of effective ways for increasing the resolving success rate of the ambiguity.
According to actual measurement verification, the receiver end inter-frequency deviation has long-term stability, and the prior correction value can be determined through early-stage parameter estimation, so that the redundancy of the model is increased, and a chance is provided for realizing a cross-frequency point mixed double-difference model. However, the prior art still fails to solve the influence of the frequency difference between the cross-frequency points, so that the Receiver-frequency and inter-frequency bias (RB-IFB) is difficult to estimate accurately, and the integer ambiguity resolution success rate of the cross-frequency point mixed double difference model is further influenced.
In order to solve the limitation problem that the cross-frequency point mixed double-difference model is difficult to realize due to large frequency difference in the single-mode GNSS system, the multi-frequency combination technology is one of feasible solutions. Original frequency points of the GNSS system are converted into combined frequency points with consistent or similar frequency points through a multi-frequency combination technology, and frequency difference among the frequency points is greatly reduced, so that related deviation terms of the frequency difference are effectively eliminated, and a cross-frequency point mixed double-difference model in the single-mode GNSS system becomes possible. Therefore, the invention provides a cross-frequency point mixed double-difference RTK positioning method of a single-mode GNSS system, which is used for searching an optimal multi-frequency combination technology to enable a new combination frequency point to have a very small frequency difference, completely eliminating the influence of the frequency difference on the resolution of the integer ambiguity, further increasing the observation redundancy of a model by correcting an RB-IFB value and obtaining the success rate of the resolution of the integer ambiguity higher than the standard double-difference.
Disclosure of Invention
According to the cross-frequency point mixed double-difference RTK resolving model of the single-mode GNSS system, the stability characteristic of the inter-frequency deviation at the receiver end is fully excavated, so that the model redundancy rate higher than that of a traditional RTK resolving model can be obtained, and the ambiguity resolving efficiency and the positioning accuracy are further improved. The method adopts a multi-frequency combination technology to eliminate the influence of the wavelength difference among the cross-frequency points, obtains the RB-IFB estimated value in real time through a parameter estimation method, increases the redundancy of the model by taking the RB-IFB as a correction after a stable condition is met, and plays a role in improving the ambiguity resolution and positioning accuracy of the model. The method specifically comprises the following steps:
a single-mode GNSS system cross-frequency point mixed double-difference RTK resolving method comprises the following steps:
(1) acquiring original pseudo range and carrier phase observed quantity output by a base station and a mobile station receiver;
(2) performing inter-station single difference on the original observed quantity obtained in the step (1) to obtain pseudo-range and carrier phase single difference observed quantity;
(3) linearly combining the carrier phase single-difference observed quantities in the step (2) by utilizing a multi-frequency combination technology to obtain combined observed quantities with consistent frequencies;
(4) constructing an RB-IFB model by using the combined observed quantity with consistent frequency acquired in the step (3) to obtain an RB-IFB estimation sequence;
(5) performing stability analysis on the RB-IFB estimation sequence, and if a stability condition is met, taking the RB-IFB mean value as a correction value to increase the redundancy of the model;
(6) establishing a cross-frequency point mixed double-difference model, and resolving the integer ambiguity to obtain an integer ambiguity resolution success rate superior to that of the traditional double-difference model;
(7) and monitoring the starting state of the receiver, and returning to the step (4) and the step (5) once the receiver is restarted, and estimating the correction value of the RB-IFB.
The acquiring of the original pseudo-range and carrier phase observed quantity output by the base station and mobile station receiver comprises:
the pseudo-range and carrier phase observation equation is as follows:
wherein the content of the first and second substances,
and with
Respectively representing residual errors of the pseudo-range and the observed value minus the calculated value of the carrier phase; r denotes different receivers; s represents different satellite numbers; j corresponds to different frequency points B of the satellitej(j＝1,2,3)；xrRepresenting the user position and tropospheric non-diffuse term increment;
represents a correspondence xrA linearized geometric design matrix of (a); t is trAnd tsRespectively representing the clock difference between the receiver and the satellite;
corresponding frequency point B1The first-order ionospheric delay error of (a),
representing ionospheric scaling factors; d is a radical ofr,jAnd with
Respectively representing pseudo range deviations of a receiver and a satellite terminal related to the frequency points; lambdajRepresents a carrier phase wavelength;
expressing the integer ambiguity; delta. for the preparation of a coatingr,jAnd
respectively representing the carrier phase deviation of a receiver related to a frequency point and a satellite terminal, including the hardware deviation of the carrier phase, the initial phase and the like;
and
respectively representing pseudorange and carrier phase observation noise.
Performing inter-station single difference on the original observed quantity obtained in the step (1) to obtain pseudo-range and carrier phase single difference observed quantity, wherein the method comprises the following steps:
the equation for single-difference observation between stations is as follows:
wherein, the first layer is formed by the first layer and the second layerbr＝(*)r-(*)b，(*)bRepresenting a reference receiver, ()rRepresenting the user receiver.
The linearly combining the carrier phase single-difference observed quantities in the step (2) by using a multi-frequency combination technology to obtain combined observed quantities with consistent frequencies comprises the following steps:
the three-frequency combination model based on the interstation single-difference observation equation is as follows:
wherein i, j, k are integers representing observation quantity combination coefficients;
ionospheric amplification factor beta(i,j,k)And a combined wavelength lambda(i,j,k)Combined ambiguity N(i,j,k)Combination, combination RB-IFB delta(i,j,k)And a noise amplification factor gamma(i,j,k)Expressed as:
where c represents the speed of light.
The method for constructing the RB-IFB parameter estimation model by using the combined observed quantities with consistent frequencies obtained in the step (3) to obtain the RB-IFB estimation sequence comprises the following steps:
the cross-frequency point mixed double difference model with the full overlap characteristic is represented as follows:
wherein:
obtaining d of pseudo range RB-IFB by using cross-frequency point mixed double difference modelbr,1jInvolving the carrier phase RB-IFB
Wherein the modified values of the pseudo-range RB-IFB are directly solved, and the RB-IFB of the carrier phase is required to be in
Extracting.
The stability analysis of the RB-IFB estimation sequence is carried out, if the stability condition is met, the RB-IFB mean value is used as a correction value to increase the redundancy of the model, and the method comprises the following steps:
continuously taking 300 epochs from the initial estimation sequence of the solved pseudo range and the carrier phase RB-IFB, averagely dividing the epochs into 5 parts, and solving the mean value mu of the pseudo rangepiCarrier phase mean μφiStandard deviation sigma from carrier phaseφiIf max (| μ) is satisfiedpi-μpj|)<0.15m，max(|μφi-μφj|)<0.05cycles，max(|σpi|)<0.15m，max(|σφi|)<0.01cycles, which means that RB-IFB has already become stable, can be used as a correction value to increase the model redundancy.
The establishing of the cross-frequency point mixed double-difference model and the resolving of the integer ambiguity to obtain the integer ambiguity resolving success rate superior to the traditional double-difference model comprises the following steps:
the mixed double difference model based on RB-IFB correction is as follows:
wherein:
the invention has the beneficial effects that:
according to the method, the stability characteristic of inter-frequency deviation of the receiver end is fully excavated, the influence of the wavelength difference between the cross-frequency points is eliminated by utilizing a multi-frequency combination technology, the correction value of the RB-IFB is accurately solved to be used as the observation quantity redundancy information, and the model redundancy rate higher than that of a traditional RTK resolving model is obtained. Therefore, it is anticipated that this new method will have better performance for ambiguity resolution.
Drawings
Fig. 1 is a flowchart of a cross-frequency point hybrid double-difference RTK solution model of a single-mode GNSS system.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The following is the multi-frequency signal of the beidou system: b1＝1561.098MHZ，B2＝1207.14MHZ，B3The technical solution of the present invention is further described in detail with reference to fig. 1 as an example of 1268.52 MHZ.
Example (b):
step 1, obtaining original pseudo range and carrier phase observed quantity output by a base station and a mobile station receiver;
the observation equation of the pseudo range and the carrier phase of the Beidou tri-band can be expressed as follows:
wherein
And
respectively representing residual errors of the pseudo-range and the observed value minus the calculated value of the carrier phase; r denotes different receivers; s represents a different satellite number; j corresponds to different frequency points B of big dipperj(j＝1,2,3)；xrRepresenting the position of a user, the increment of non-dispersive items such as troposphere and the like;
represents a correspondence xrA linearized geometric design matrix of (a); t is trAnd tsRespectively representing the clock difference between the receiver and the satellite;
corresponding frequency point B1The first-order ionospheric delay error of (a),
representing ionospheric scaling factors; d is a radical ofr,jAnd with
Respectively representing pseudo range deviation of a receiver and a satellite related to the frequency point; lambda [ alpha ]jRepresents a carrier phase wavelength;
expressing the integer ambiguity; delta. for the preparation of a coatingr,jAnd
respectively representing the carrier phase deviation of a receiver related to a frequency point and a satellite terminal, including the hardware deviation of the carrier phase, the initial phase and the like;
and with
Respectively representing pseudorange and carrier phase observation noise.
Step 2, performing inter-station single difference on the original observed quantity obtained in the step 1 to obtain pseudo-range and carrier phase single difference observed quantity;
only the case of a short baseline is considered here, and the influence of atmospheric delay errors is ignored, so that the inter-station single-difference observation equation can be expressed as,
wherein ()br＝(*)r-(*)bThere is a reference receiver denoted "b" and a user receiver denoted "r".
Step 3, carrying out linear combination on the carrier phase single-difference observed quantities in the step 2 by utilizing a multi-frequency combination technology to obtain combined observed quantities with consistent or similar frequencies;
firstly, a three-frequency combination model based on the carrier phase single difference observed quantity of the above formula is given,
for clarity of presentation, the above equation ignores the receiver's relative identity to the satellite; wherein i, j, k are integers representing observation combination coefficients. Corresponding ionospheric amplification factor beta(i,j,k)And a combined wavelength lambda(i,j,k)And combined ambiguity N(i,j,k)Combination, combination RB-IFB delta(i,j,k)And a noise amplification factor gamma(i,j,k)Can be expressed as a number of times as,
where c represents the speed of light.
According to the description of the formula, searching a multi-frequency combination strategy with consistent or similar frequency in an integer range of (i, j, k) epsilon (-10,10) to replace the original frequency point. It should be noted that, when searching for an optimal multi-frequency combination strategy, in addition to satisfying the constraint condition of consistent or close frequency, the following constraint conditions should be followed: 1) the determinant formed by the combination coefficients of the constructed new combined frequency points is equal to +/-1, and the independence of the three new combined frequency points is ensured; 2) the ionosphere and noise amplification coefficients are suppressed as much as possible, and the observation quantity error of amplification is avoided, so that the estimation precision of the model is influenced. Based on the above constraints and search ranges, 4 sets of optimal multi-frequency combination strategies are determined and are summarized in table 1. Wherein, Bc1～Bc3Respectively representing new multi-frequency combination observed quantities; Δ λ represents the frequency difference across the frequency points;
TABLE 1 statistics for multi-frequency combination strategies
As can be seen from Table 1, all frequency difference coefficients are less than 0.025, and have less influence on integer ambiguity resolution, and can be ignored by the model. This indicates that if a new combined signal is used to construct a cross-frequency point mixed double-difference model, the disadvantage that the ambiguity of the original frequency point cannot be resolved correctly due to the large frequency difference coefficient can be fundamentally solved.
Step 4, constructing an RB-IFB parameter estimation model by using the multi-frequency combination observed quantity with consistent or similar frequencies obtained in the step 3, and obtaining an RB-IFB estimation sequence;
the cross-bin mixed double difference model with the full overlap property is expressed as,
wherein the content of the first and second substances,
we can obtain d of pseudo range RB-IFB by using the above formulabr,1jWith inclusion of carrier phase RB-IFB
The estimated sequence of (2). Wherein the correction value of the pseudo range RB-IFB can be directly solved, while the RB-IFB of the carrier phase needs to be solved
Extracting. Due to the adoption of the novel multi-frequency combinationObserved quantity, the frequency difference of which is very small, so that with lambdaj-λ1The related items may be ignored.
Step 5, performing stability analysis on the RB-IFB estimation sequence, and if a stability condition is met, taking the RB-IFB mean value as a correction value to increase the redundancy of the model;
continuously taking 300 epochs from the initial estimation sequence of the solved pseudo range and the carrier phase RB-IFB, averagely dividing the epochs into 5 parts, and solving the mean value mu of the pseudo rangepi(i＝1,2,3,4,5),μφiStandard deviation sigma from carrier phasepi,σφi. If max (| μ) is satisfiedpi-μpj|)<0.15m，max(|μφi-μφj|)<0.05cycles，max(|σpi|)<0.15m，max(|σφi|)<0.01cycles can be regarded that RB-IFB tends to be stable, and the RB-IFB can be used as a correction value to increase model redundancy.
And 6, after obtaining the RB-IFB correction value, shielding the steps 4 and 5, establishing a cross-frequency point mixed double-difference model, and resolving the integer ambiguity, so that the integer ambiguity resolution success rate superior to that of the traditional double-difference model can be obtained.
The mixed double difference model based on RB-IFB correction is expressed as,
wherein
Therefore, on the basis of the hybrid double-difference model, the state quantity related to RB-IFB is eliminated, and the model redundancy of the above formula is increased by 2 redundancies compared with that of a traditional double-difference model. If the number of the visible observations in the open environment is large, the performance difference of the two models in the integer ambiguity resolution cannot be caused by the increase of 2 redundancies. However, in the case of less occluded environment visible observation, the improvement of the integer ambiguity resolution performance due to 2 redundancies will be enormous.
And 7, monitoring the starting state of the receiver, once the receiver is restarted, the original RB-IFB correction value is invalid, resetting the stable state of the step 5, and re-executing the step 4 and the step 5 to estimate the RB-IFB correction value.
There are, of course, many other embodiments of the invention and the modifications and variations that will be apparent to those skilled in the art without departing from the spirit and scope of the invention.
According to the cross-frequency point mixed double-difference RTK resolving model of the single-mode GNSS system, stability of Receiver-end inter-frequency bias (RB-IFB) is fully excavated, model redundancy higher than that of a traditional RTK resolving model can be obtained, and ambiguity resolving efficiency and positioning accuracy are further improved. The method adopts a multi-frequency combination technology to eliminate the influence of the wavelength difference among the cross-frequency points, obtains the RB-IFB estimated value in real time through a parameter estimation method, increases the redundancy of the model by taking the RB-IFB as a correction after a stable condition is met, and plays a role in improving the ambiguity resolution and positioning accuracy of the model. The method specifically comprises the following steps:
step 1, obtaining original pseudo-range and carrier phase observed quantity output by a base station and a mobile station receiver;
step 2, performing inter-station single difference on the original observed quantity obtained in the step 1 to obtain pseudo-range and carrier phase single difference observed quantity;
step 3, carrying out linear combination on the carrier phase single-difference observed quantities in the step 2 by utilizing a multi-frequency combination technology to obtain combined observed quantities with consistent or similar frequencies;
step 4, constructing an RB-IFB parameter estimation model by using the multi-frequency combination observed quantity with consistent or similar frequencies obtained in the step 3, and obtaining an RB-IFB estimation sequence;
step 5, performing stability analysis on the RB-IFB estimation sequence, and if a stability condition is met, taking the RB-IFB mean value as a correction value to increase the redundancy of the model;
and 6, after obtaining the RB-IFB correction value, shielding the step 4 and the step 5, establishing a cross-frequency point mixed double-difference model, and resolving the integer ambiguity to obtain the integer ambiguity resolution success rate superior to the traditional double-difference model.
And 7, monitoring the starting state of the receiver, and once the receiver is restarted, the original RB-IFB correction value is invalid, resetting the stable state of the step 5, and re-executing the step 4 and the step 5 to estimate the RB-IFB correction value.
Compared with the traditional method, the invention discloses a construction method of a cross-frequency point mixed double-difference RTK (real-time kinematic) solution model of a single-mode GNSS (global navigation satellite system). The method utilizes a multi-frequency combination technology to eliminate the influence of cross-frequency point wavelength difference by fully excavating the stability characteristic of a Receiver end inter-frequency bias (RB-IFB), accurately solves the corrected value of the RB-IFB as observed quantity redundant information, and obtains the model redundancy higher than that of the traditional RTK solution model. Therefore, it is anticipated that this new method will have better performance for ambiguity resolution.
Claims (6)
1. A single-mode GNSS cross-frequency point mixed double-difference RTK resolving method is characterized by comprising the following steps:
(1) acquiring original pseudo-range and carrier phase observed quantity output by a base station and a mobile station receiver;
(2) performing inter-station single difference on the original observed quantity obtained in the step (1) to obtain pseudo-range and carrier phase single difference observed quantity;
(3) linearly combining the carrier phase single-difference observed quantities in the step (2) by utilizing a multi-frequency combination technology to obtain combined observed quantities with consistent frequencies;
(4) constructing an inter-Receiver-inter-frequency deviation (RB-IFB) model by using the combined observed quantity with consistent frequency obtained in the step (3) to obtain an RB-IFB estimation sequence, wherein the model is expressed as a RB-IFB estimation sequence
Wherein:
in the formula, p and phi respectively represent the residual error of the observed value minus the calculated value of the pseudo-range phase; (*)br＝(*)r-(*)b，(*)bRepresenting a reference receiver, ()rRepresenting a user receiver; (*)1s＝(*)s-(*)1，(*)sIndicating different satellite numbers ()1Represents a reference satellite; x represents the user position and troposphere non-dispersive item increment; u represents a linearized geometric design matrix corresponding to x; λ represents a carrier phase wavelength; n represents the integer ambiguity; j corresponds to different frequency points B of the satellitej(j ═ 1,2, 3); d is the deviation related to the pseudo range; delta is the phase dependent deviation; e and e represent the pseudorange and carrier phase observation noise, respectively. Obtaining d of pseudo range RB-IFB by using cross-frequency point mixed double difference modelbr,1jWith inclusion of carrier phase RB-IFB
Wherein the modified values of the pseudo-range RB-IFB are directly solved, and the RB-IFB of the carrier phase is required to be in
Extracting;
(5) performing stability analysis on the RB-IFB estimation sequence, and if a stability condition is met, taking the RB-IFB mean value as a correction value to increase the redundancy of the model;
(6) establishing a cross-frequency point mixed double-difference model, and resolving the integer ambiguity to obtain an integer ambiguity resolution success rate superior to that of the traditional double-difference model;
(7) and monitoring the starting state of the receiver, and returning to the step (4) and the step (5) once the receiver is restarted, and estimating the correction value of the RB-IFB.
2. The method of claim 1, wherein the obtaining of the raw pseudorange and carrier phase observations output by the base station and the rover receiver comprises:
the pseudo-range and carrier phase observation equation is as follows:
wherein the content of the first and second substances,
and
respectively representing residual errors of the pseudo-range and the observed value minus the calculated value of the carrier phase; r denotes different receivers; s represents a different satellite number; j corresponds to different frequency points B of the satellitej(j＝1,2,3)；xrRepresenting the user position and tropospheric non-diffuse term increment;
represents a correspondence xrIs a linear tableWhat design matrix; t is trAnd tsRespectively representing the clock difference between the receiver and the satellite;
corresponding frequency point B1The first-order ionospheric delay error of (a),
representing ionospheric scaling factors; dr,jAnd
respectively representing pseudo range deviations of a receiver and a satellite terminal related to the frequency points; lambda [ alpha ]jRepresents the carrier phase wavelength;
expressing the integer ambiguity; deltar,jAnd with
Respectively representing carrier phase deviations of a receiver and a satellite terminal related to a frequency point, including carrier phase hardware deviation, initial phase and the like;
and with
Respectively representing pseudorange and carrier phase observation noise.
3. The method for single-mode GNSS system cross-frequency point hybrid double-difference RTK solution according to claim 2, wherein the obtaining the pseudo-range and carrier phase single-difference observation by performing inter-station single-difference on the original observation obtained in step (1) comprises:
the equation for single-difference observation between stations is as follows:
wherein, (+)br＝(*)r-(*)b，(*)bRepresenting a reference receiver, ()rRepresenting the user receiver.
4. The method according to claim 3, wherein the linear combination of the carrier phase single-difference observations in the step (2) is performed by using a multi-frequency combination technique to obtain the combined observations with consistent frequencies, and the method comprises:
the three-frequency combination model based on the interstation single-difference observation equation is as follows:
wherein i, j, k are integers representing observation quantity combination coefficients;
ionospheric amplification factor beta(i,j,k)Combined wavelength lambda(i,j,k)Combined ambiguity N(i,j,k)Combination, combination RB-IFB delta(i,j,k)And a noise amplification factor gamma(i,j,k)Expressed as:
where c represents the speed of light.
5. The cross-frequency point hybrid double-difference RTK solution method of claim 4, wherein the performing stability analysis on the RB-IFB estimation sequence, and if a stability condition is satisfied, using the RB-IFB mean as a correction value to increase model redundancy comprises:
continuously taking 300 epochs from the initial estimation sequence of the solved pseudo range and the carrier phase RB-IFB, averagely dividing the epochs into 5 parts, and solving the mean value mu of the pseudo rangepiCarrier phase mean μφiStandard deviation sigma from carrier phaseφiIf max (| μ) is satisfiedpi-μpj|)<0.15m，max(|μφi-μφj|)<0.05cycles，max(|σpi|)<0.15m，max(|σφi|)<0.01cycles, which means that RB-IFB has already become stable, and can be used as a correction value to increase the redundancy of the model.
6. The single-mode GNSS system cross-frequency point mixed double difference RTK resolving method of claim 5, wherein the establishing of the cross-frequency point mixed double difference model is used for resolving the integer ambiguity to obtain the integer ambiguity resolving success rate superior to that of the traditional double difference model, and comprises:
the mixed double difference model based on RB-IFB correction is as follows:
wherein:
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