CN109143286B - Satellite navigation positioning method considering non-modeling errors - Google Patents
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Abstract
The invention relates to a satellite navigation positioning method taking account of non-modeling errors, which takes account of some non-modeling errors which are ignored in the traditional method and cannot be corrected through a model and absorbed by parameters, so that the positioning precision and reliability are improved compared with the traditional method; according to the invention, because the non-modeling errors have space-time correlation, an observation equation with obvious non-modeling errors is optimized by adopting a multi-epoch partial parameterization method, so that the accuracy of a model is improved; according to the invention, the significance of the non-modeling error is checked by utilizing the observation value residual error, and the problem of rank deficiency of the residual error is improved due to the fact that the redundant observation number is increased in the application environment of the multi-frequency multi-mode GNSS, so that the method is particularly suitable for processing multi-frequency multi-mode GNSS observation data. In summary, the precise satellite navigation positioning method taking the non-modeling errors into consideration has the advantages of high precision, strong reliability, wide application range and the like.
Description
Technical Field
The invention relates to a processing method for considering non-modeling errors in applications such as satellite navigation positioning, in particular to a precise satellite navigation positioning method considering non-modeling errors.
Background
The measured values of the global satellite navigation system (GNSS) include various types of errors, i.e., coarse errors, random noise, and systematic errors. Systematic errors that cannot be corrected by the model and absorbed by the parameters without taking into account occasional errors and gross errors are called non-modeled errors. Non-modeling errors affect the nature of the observations and thus related studies have been conducted on such errors as colored noise, multipath effects, atmospheric bias, etc. that are significantly affected for different application modes and observation environments.
Most of the current research is directed mainly to the modelable part of these errors, and little is done on the unmodeled part. The processing schemes of the modelable part are mainly divided into two types, namely random model compensation and function model correction.
By adopting a random model compensation method, a reasonable colored noise random model is determined, and a sequential adjustment method or a Kalman filtering method is adopted for solving, so that the effect of compensating non-modeling errors is achieved. Therefore, systematic studies on system quality control are lacking in error refinement from the viewpoint of stochastic model compensation, and most of the research results are to treat it as colored noise.
In the aspect of function model correction, troposphere and ionosphere errors are key factors restricting the application of high-precision GNSS, and a function model compensation mode is generally adopted to absorb system errors, reduce parameter estimation deviation and improve parameter estimation precision. The troposphere delay usually adopts zenith delay and mapping function parameterization, but because of the space dissimilarity of the troposphere delay and the limited precision of a projection function, the troposphere non-modeling error exists remarkably, and the quick fixation and high-precision positioning of the ambiguity are seriously affected. Ionospheric first order delays can be eliminated by parameterization or inter-frequency combining, but non-modeled higher order term errors can reach several millimeters or even centimeters, and vary very irregularly in low latitude areas, which is also a major factor affecting high precision GNSS applications. The multipath effect is closely related to the observation environment, and particularly, the special constellation distribution characteristics of the Beidou satellite system in China lead to the failure to establish a reasonable and universal multipath model. Most of the existing multipath research results are based on the periodicity of satellite orbits, and static CORS data is processed by sun-and-sun filtering, so that multipath research related to dynamic positioning is rarely performed. In summary, the current error refinement from the function model perspective is essentially limited to the error processing of the modelable parts of specific forms such as multipath, troposphere and ionosphere, and the comprehensive amount of the errors is not systematically researched and controlled.
Therefore, the invention provides a satellite navigation positioning method taking non-modeling errors into consideration, which improves the precision and reliability of GNSS application.
Disclosure of Invention
The invention aims to provide a satellite navigation positioning method taking non-modeling errors into consideration, which has high precision and high reliability.
In order to achieve the above object, the present invention provides a satellite navigation positioning method considering non-modeling errors, comprising the steps of:
l1: acquiring a residual sequence of an N-th single epoch dynamic solution and an observed value of a global satellite navigation system, wherein N=1;
l2: performing stability test on the observation value residual error sequence to obtain all observation values with non-modeling errors, selecting a target observation value from the observation values, and executing a step L3 on the target observation value;
l3: obtaining error equations of the (i-1), the (i-2), the … and the (i-n) th epoch, establishing a multi-epoch error equation, wherein n is more than or equal to 5 and less than i, n and i are positive integers, and executing the step L4;
l4: obtaining an error equation of the ith epoch, obtaining a (n+1) th single epoch dynamic solution, and executing step L5;
l5: judging whether the N value is 1, if so, taking the N value as N+1, executing the steps L2-L4, and if not, executing the step L6;
l6: judging whether the precision of the (n+1) th single epoch dynamic solution is lower than that of the N th single epoch dynamic solution, if so, executing the step L7, and if not, taking the N value as n+1, and executing the steps L2-L5, wherein N is a positive integer;
l7: and carrying out satellite navigation positioning according to the N-th single epoch dynamic solution.
Optionally, the step L1 includes:
obtaining an observation value of the global satellite navigation system;
preprocessing the observed value;
establishing a phase and pseudo-range double-difference observation equation, and obtaining an N-th single epoch dynamic solution;
and obtaining an observation value residual sequence according to the Nth single epoch dynamic solution, wherein N=1.
Optionally, the step of preprocessing the observed value includes satellite cut-off altitude setting, phase observed value cycle slip detection and repair, coarse difference detection and processing, pseudo-range single-point positioning, troposphere delay correction model and integer ambiguity fixing of the phase observed value.
Optionally, the step L2 includes:
when the observation value residual sequence is stable, satellite navigation positioning is carried out according to the N single epoch dynamic solution;
and when the observation value residual error sequence is not stable, acquiring all observation values with non-modeling errors.
Optionally, the method for performing stationarity check on the observation residual sequence includes ADF check or KPSS check.
Optionally, the method for obtaining all the observations with non-modeling errors includes: and selecting a target observation value according to the time correlation of the residual sequence of the observation value, wherein the time correlation coefficient of the target observation value is larger than the time correlation coefficient of all the observation values with non-modeling errors except the target observation value.
Optionally, the step L4 includes:
calculating the correction of the non-modeling error according to a least square criterion;
and (3) establishing an error equation of the ith epoch, and obtaining the (n+1) th single epoch dynamic solution.
Optionally, in the step L6, the method for determining whether the accuracy of the (n+1) -th single epoch dynamic solution is lower than the accuracy of the nth single epoch dynamic solution includes:
obtaining an N th covariance matrix of the N th single epoch dynamic solution, wherein N is more than or equal to 2;
obtaining an (n+1) -th covariance matrix of the (n+1) -th single epoch dynamic solution;
when the (n+1) th covariance matrix is larger than the nth covariance matrix, the accuracy of the (n+1) th single epoch dynamic solution is lower than that of the nth single epoch dynamic solution; when the (n+1) th covariance matrix is smaller than the nth covariance matrix, the accuracy of the (n+1) th single epoch dynamic solution is higher than that of the nth single epoch dynamic solution.
In summary, the satellite navigation positioning method taking into account the non-modeling errors in the present invention takes into account some non-modeling errors which cannot be corrected by a model and absorbed by parameters, which are ignored in the conventional method, so that the positioning accuracy and reliability are improved.
Further, the existing methods are mainly directed to the modelable part and do not control the errors of the non-modelled part, and the error refining methods are essentially limited to the specific forms of errors of multipath, troposphere, ionosphere and the like, and the comprehensive amount of the errors is not systematically researched and controlled. The invention considers that the non-modeling errors have space-time correlation, so that an observation equation with obvious non-modeling errors is optimized by adopting a multi-epoch partial parameterization method, thereby improving the accuracy of the model.
Furthermore, the existing methods have pertinence and do not have universality. The application mode and the observation environment of the multi-frequency multi-mode GNSS have diversity, and the invention is simultaneously applicable to application scenes such as an observation model taking into consideration or neglecting troposphere, ionosphere and multipath, a static and dynamic application mode, a single-system and multi-system combined mode and the like, and has strong practicability.
Further, because there is a systematic deviation between different systems, the existing method tends to cause a larger positioning error. According to the invention, the significance of the non-modeling error is checked by utilizing the observation value residual error, and the problem of rank deficiency of the residual error is improved due to the fact that the redundant observation number is increased in the application environment of the multi-frequency multi-mode GNSS, so that the method is particularly suitable for processing multi-frequency multi-mode GNSS observation data, and the problem of system deviation is solved.
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FIG. 1 is a flow chart of a satellite navigation positioning method taking non-modeling errors into account in a preferred embodiment of the invention;
FIG. 2 is a flowchart of a satellite navigation positioning method taking into account non-modeling errors in accordance with another preferred embodiment of the present invention.
Detailed Description
Specific embodiments of the present invention will be described in more detail below with reference to the drawings. Advantages and features of the invention will become more apparent from the following description and claims. It should be noted that the drawings are in a very simplified form and are all to a non-precise scale, merely for convenience and clarity in aiding in the description of embodiments of the invention.
The satellite navigation positioning method taking the non-modeling errors into consideration, provided by the invention, allows the non-modeling errors to be taken into consideration, so that the positioning is more precise. Specifically, as shown in fig. 1, in a preferred embodiment of the present invention, the method includes:
step S1: acquiring a residual sequence of an N-th single epoch dynamic solution and an observed value of a global satellite navigation system, wherein N=1;
step S2: performing stability test on the observation value residual error sequence to obtain all observation values with non-modeling errors, selecting a target observation value from the observation values, and executing a step S3 on the target parameter value;
step S3: obtaining error equations of the (i-1), the (i-2), the … and the (i-n) th epoch, establishing a multi-epoch error equation, wherein n is more than or equal to 5 and less than i, n and i are positive integers, and executing the step S4;
step S4: acquiring an error equation of the ith epoch, acquiring a (n+1) th single epoch dynamic solution, and executing step S5;
step S5: and carrying out satellite navigation positioning according to the (N+1) th single epoch dynamic solution, namely the 2 nd single epoch dynamic solution.
Specifically, step S1 includes:
obtaining an observation value of the global satellite navigation system;
preprocessing the observed value;
establishing a phase and pseudo-range double-difference observation equation, and obtaining a 1 st single epoch dynamic solution;
and obtaining an observation value residual sequence according to the 1 st single epoch dynamic solution.
Preferably, in the step of preprocessing the observed value, the step of preprocessing the observed value includes satellite cut-off altitude angle setting, phase observed value cycle slip detection and repair, coarse difference detection and processing, pseudo-range single-point positioning, troposphere delay correction model and integer ambiguity fixing of the phase observed value, which is not limited in the invention.
Preferably, the phase and pseudo-range double difference observation equation is expressed as:
wherein the subscripts "1" and "2" denote the meanings associated with L, respectively 1 And L 2 Carrier phase dependent; phi and P represent double-difference phase and pseudo-range observations, respectively; ρ * Is the true value of the distance from the double-difference satellite to the earth; i 1 Represents L 1 Frequency double difference ionospheric delay; f (f) 1 And f 2 Represents L 1 And L 2 Frequency on; lambda (lambda) 1 And lambda (lambda) 2 Represents L 1 And L 2 Is a wavelength of (2); n (N) 1 And N 2 Represents L 1 And L 2 Whole-cycle ambiguity over; epsilon is the noise term.
The formula (1) is linearized and transformed as follows:
y＝Ax+e (2)，
where y is the observation vector, A is the design matrix, x is the parameter vector sought, and e is the error vector.
Combining the observed value covariance matrix Q to obtain a 1 st single epoch dynamic solution as follows:
the corresponding covariance matrix is:
specifically, the observation residuals are calculated as follows:
a residual sequence Y for each set of observations is obtained.
Specifically, in step S2, the residual sequence Y is subjected to a stationarity test, so as to determine whether the non-modeling error in the observed value is significant.
In a preferred embodiment of the present invention, the method of stationarity test comprises at least one of an ADF test or a KPSS test, and the stationarity of the residual sequence Y is preferably tested using the ADF test.
Specifically, the detected sequence Y is assumed to be an AR model, as follows:
Y t ＝c+δt+φY t-1 +α 1 ΔY t-1 +…+α p ΔY t-p +E t (6)，
wherein the subscript t represents time; c, delta, phi and alpha are model parameters; p is the time interval; e is white noise; delta represents a time difference operator. After phi is obtained, ADF test statistics are calculated by using the parameters to be tested, and the method comprises the following steps:
where SE () represents Standard error (Standard error). Let the original assumption H 0 ：φ<1, alternative hypothesis H 1 : phi=1, and then determines from the statistics which hypothesis holds, i.e. whether the observation residual is stationary.
Judging whether the non-modeling error in the observed value is obvious or not according to the test result: if the observation value residual error is stable, the non-modeling error is not obvious; otherwise, the non-modeling errors are significant.
Specifically, when the test results are all stable, the non-modeling errors of each group of observed values are considered to be insignificant, and satellite navigation positioning is performed according to the 1 st single epoch dynamic solution (3) without considering the non-modeling errors; if the inspection result is partially stable or totally unstable, the non-modeling error of the unstable observed value is obvious, and all the observed values with the non-modeling error are obtained.
Preferably, the method for acquiring all observations with non-modeling errors in a preferred embodiment of the present invention includes: the coefficient size of the time correlation function is used to determine the observed value which needs to be parameterized, namely the target observed value. Physical correlation is caused by non-modeling errors, and the effect of temporal correlation is most pronounced in physical correlation. Therefore, when the observed value is more severely affected by the non-modeling error, the time correlation of the residual is also stronger, i.e. the severity of the non-modeling error can be judged by the time correlation function. Specifically, the residual sequence with the strongest temporal correlation is selected.
The calculation formula of the time correlation coefficient is as follows:
wherein the method comprises the steps of
In addition, k represents a time interval; n represents the total epoch number;
is the mean value of v.
Specifically, step S3 in this embodiment includes: constructing a multi-epoch error equation containing non-modeling error parameters; calculating the correction of the non-modeling error according to a least square criterion; and establishing an error equation of the ith epoch, and obtaining a second single epoch dynamic solution. The number of the epochs is greater than or equal to 5, and preferably, in this embodiment, a multi-epoch error equation of 5 epochs is established, which is not limited in any way. Specifically, assuming that the non-modeling error correction of the ith epoch needs to be calculated, the error equations of the ith-5 to ith-1 epoch are combined:
wherein y is an observation value vector, A is a design matrix, B is a coefficient matrix of the non-modeling error, x is a parameter vector, ω is a non-modeling error correction, and e is an error vector.
Observed value covariance matrix Q combining the 5 epochs * The least square criterion is adopted, and the corresponding solution containing the non-modeling error correction is as follows:
the corresponding covariance matrix is:
wherein, the liquid crystal display device comprises a liquid crystal display device,
Y＝[y i-5 y i-4 y i-3 y i-2 y i-1 ] T (13)，
X＝[x i-5 x i-4 x i-3 x i-2 x i-1 ω i ] T (15)，
specifically, the error equation for the ith epoch is expressed as follows:
covariance matrix Q combined with observed value i The 2 nd single epoch dynamic solution is obtained as:
the corresponding covariance matrix is
Specifically, satellite navigation positioning is performed according to equation (17), i.e., the 2 nd single epoch dynamic solution.
The specific problems to be noted in the practice of the method of a preferred embodiment of the present invention are as follows:
the reference station needs to be arranged, the reference station is arranged at the central part of the coverage area of the measuring area as far as possible, the surrounding field of view is required to be wide, the cut-off height angle is more than 10 degrees, and the cut-off height angle comprises 12 degrees, 15 degrees, 20 degrees, 25 degrees, 30 degrees, 50 degrees or 65 degrees; no signal reflectors (large-area water areas, large buildings and the like) are arranged around the system to reduce multipath interference and avoid the interference of traffic major roads and pedestrians as much as possible; the reference station should be set at the relatively high point as much as possible to facilitate broadcasting the differential correction signal; the reference station is far away from the large electromagnetic emission sources such as a microwave tower, a communication tower and the like by 200 meters, and optionally, the distance between the reference station and the large electromagnetic emission sources such as the microwave tower, the communication tower and the like comprises 210 meters, 240 meters, 252 meters, 300 meters or 400 meters; the reference station is located 50 meters away from the high voltage transmission line and the communication line, and optionally, the distance between the reference station and the high voltage transmission line and the communication line includes 55 meters, 60 meters, 70 meters or 100 meters, which is not limited in the present invention.
Referring to fig. 2, in a further preferred embodiment of the present invention, the method comprises:
step Sa: acquiring a residual sequence of an N-th single epoch dynamic solution and an observed value of a global satellite navigation system, wherein N=1;
step Sb: performing stability test on the observation value residual error sequence to obtain all observation values with non-modeling errors, selecting a target observation value from the observation values, and executing step Sc on the target observation value;
step Sc: obtaining error equations of the (i-1), the (i-2), the … and the (i-n) th epoch, establishing a multi-epoch error equation, wherein n is more than or equal to 5 and less than i, n and i are positive integers, and executing the step Sd;
step Sd: acquiring an error equation of an ith epoch, acquiring a (n+1) th single epoch dynamic solution, and executing step Se;
step Se: judging whether the N value is 1, if so, taking the N value as N+1, executing the step Sb-Sd, and if not, executing the step Sf;
step Sf: judging whether the precision of the (n+1) th single epoch dynamic solution is lower than that of the N th single epoch dynamic solution, if so, executing the step Sg, and if not, taking the N value as n+1, and executing the step Sb-Se, wherein N is a positive integer;
step Sg: and carrying out satellite navigation positioning according to the N-th single epoch dynamic solution.
Unlike the preferred embodiment of the present invention, step Sa is the same as step S1, step Sb is the same as step S2, step Sc is the same as step S3, and step Sd is the same as step S4, in which step Se, sf and Sg are used to select the N-th single epoch dynamic solution with higher precision, and satellite navigation positioning is performed according to the N-th single epoch dynamic solution, where N is a positive integer greater than 2.
Specifically, after the step of obtaining the 2 nd single epoch dynamic solution, performing stationarity test on the observation value residual sequence Y again to obtain all observation values with non-modeling errors, selecting the observation values needing parametrization from the observation values, and then establishing a multi-epoch error equation to obtain the 3 rd single epoch dynamic solution; the most needed parameterized observations are target observations, and the time correlation coefficient of the target observations is greater than the time correlation coefficient of all observations with non-modeling errors except the target observations.
Comparing the precision of the 3 rd single epoch dynamic solution with the precision of the 2 nd single epoch dynamic solution, and performing satellite navigation positioning according to the 2 nd single epoch dynamic solution when the precision of the 3 rd single epoch dynamic solution is lower than the precision of the 2 nd single epoch dynamic solution;
otherwise, repeatedly carrying out stability test on the observation value residual sequence Y, obtaining all observation values with non-modeling errors, selecting the observation value which needs parameterization, namely a target observation value, and then establishing a multi-epoch error equation, sequentially obtaining the (N+1) -th single epoch dynamic solution until the precision of the (N+1) -th single epoch dynamic solution is lower than or equal to that of the (N) -th single epoch dynamic solution, and carrying out satellite navigation positioning according to the (N) -th single epoch dynamic solution.
Specifically, an nth covariance matrix of an nth single epoch dynamic solution can be obtained; and acquiring an (N+1) -th covariance matrix of an (N+1) -th single epoch dynamic solution, wherein when the (N+1) -th covariance matrix is larger than the N-th covariance matrix, the precision of the (N+1) -th single epoch dynamic solution is lower than that of the N-th single epoch dynamic solution, and at the moment, satellite navigation positioning is performed according to the N-th single epoch dynamic solution.
Otherwise, repeating the observation value residual sequence Y to perform stability test, obtaining all observation values with non-modeling errors, selecting the observation value and the target observation value which are most needed to be parameterized, and then establishing a multi-epoch error equation until the accuracy of the obtained single epoch dynamic solution is not improved compared with the accuracy of the previous single epoch dynamic solution, and selecting a single epoch dynamic solution with highest accuracy to perform satellite navigation positioning.
In summary, the satellite navigation positioning method taking into account the non-modeling errors in the present invention takes into account some non-modeling errors which cannot be corrected by a model and absorbed by parameters, which are ignored in the conventional method, so that the positioning accuracy and reliability are improved.
Further, the existing methods are mainly directed to the modelable part and do not control the errors of the non-modelled part, and the error refining methods are essentially limited to the specific forms of errors of multipath, troposphere, ionosphere and the like, and the comprehensive amount of the errors is not systematically researched and controlled. The invention considers that the non-modeling errors have space-time correlation, so that an observation equation with obvious non-modeling errors is optimized by adopting a multi-epoch partial parameterization method, thereby improving the accuracy of the model.
Furthermore, the existing methods have pertinence and do not have universality. The application mode and the observation environment of the multi-frequency multi-mode GNSS have diversity, and the invention is simultaneously applicable to application scenes such as an observation model taking into consideration or neglecting troposphere, ionosphere and multipath, a static and dynamic application mode, a single-system and multi-system combined mode and the like, and has strong practicability.
Further, because there is a systematic deviation between different systems, the existing method tends to cause a larger positioning error. According to the invention, the significance of the non-modeling error is checked by utilizing the observation value residual error, and the problem of rank deficiency of the residual error is improved due to the fact that the redundant observation number is increased in the application environment of the multi-frequency multi-mode GNSS, so that the method is particularly suitable for processing multi-frequency multi-mode GNSS observation data, and the problem of system deviation is solved.
The foregoing is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Any person skilled in the art will make any equivalent substitution or modification to the technical solution and technical content disclosed in the invention without departing from the scope of the technical solution of the invention, and the technical solution of the invention is not departing from the scope of the invention.
Claims (6)
1. A satellite navigation positioning method considering non-modeling errors is characterized by comprising the following steps:
l1: obtaining an observation value of a global satellite navigation system; preprocessing the observed value; establishing a phase and pseudo-range double-difference observation equation, and obtaining an N-th single epoch dynamic solution; obtaining an observation value residual sequence according to the N-th single epoch dynamic solution, wherein N=1;
l2: performing stability test on the observation value residual error sequence to obtain all observation values with non-modeling errors, selecting a target observation value from the observation values, and executing a step L3 on the target observation value;
l3: obtaining error equations of the (i-1), the (i-2), the … and the (i-n) th epoch, establishing a multi-epoch error equation containing non-modeling error parameters, wherein n is more than or equal to 5 and less than i, n and i are positive integers, and executing the step L4;
l4: calculating the correction of the non-modeling error according to a least square criterion; establishing an error equation of the ith epoch, obtaining a (n+1) th single epoch dynamic solution, and executing a step L5;
l5: judging whether the N value is 1, if so, taking the N value as (N+1), executing the steps L2-L4, and if not, executing the step L6;
l6: judging whether the precision of the (n+1) th single epoch dynamic solution is lower than that of the N th single epoch dynamic solution, if so, executing the step L7, and if not, taking the N value as n+1, and executing the steps L2-L5, wherein N is a positive integer;
l7: and carrying out satellite navigation positioning according to the N-th single epoch dynamic solution.
2. The method of claim 1, wherein the step of preprocessing the observations comprises satellite cutoff altitude setting, phase observations cycle slip detection and repair, coarse detection and processing, pseudorange single point positioning, tropospheric delay correction model, and integer ambiguity fixing of phase observations.
3. The satellite navigation positioning method according to claim 1, wherein said step L2 comprises:
when the observation value residual sequence is stable, satellite navigation positioning is carried out according to the N single epoch dynamic solution;
and when the observation value residual error sequence is not stable, acquiring all observation values with non-modeling errors.
4. A satellite navigation positioning method taking account of non-modeling errors according to claim 3, wherein the method of stationarity checking the sequence of observations residuals comprises ADF checking or KPSS checking.
5. A satellite navigation positioning method according to claim 3 wherein said method of selecting target observations includes: and selecting a target observation value according to the time correlation of the residual sequence of the observation value, wherein the time correlation coefficient of the target observation value is larger than the time correlation coefficient of all the observation values with non-modeling errors except the target observation value.
6. The satellite navigation positioning method according to claim 1, wherein the step L6 of determining whether the accuracy of the (n+1) -th single epoch dynamic solution is lower than the accuracy of the nth single epoch dynamic solution comprises:
obtaining an N th covariance matrix of the N th single epoch dynamic solution, wherein N is more than or equal to 2;
obtaining an (n+1) -th covariance matrix of the (n+1) -th single epoch dynamic solution;
when the (n+1) th covariance matrix is larger than the nth covariance matrix, the accuracy of the (n+1) th single epoch dynamic solution is lower than that of the nth single epoch dynamic solution; when the (n+1) th covariance matrix is smaller than the nth covariance matrix, the accuracy of the (n+1) th single epoch dynamic solution is higher than that of the nth single epoch dynamic solution.
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