CN109143286A - A kind of satellite navigation locating method for taking non-model errors into account - Google Patents
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Abstract
The present invention relates to a kind of satellite navigation locating method for taking non-model errors into account, some non-model errors that can not be absorbed by model correction and parameter neglected in conventional method are accounted for, therefore positioning accuracy and reliability increase compared with conventional method；The present invention is in view of these non-model errors with temporal correlation using the method for more epoch partial parameterizations due to the significant observational equation of non-model errors being optimized, to improve the accuracy of model；The present invention examines the conspicuousness of non-model errors using observation residual error, since in multi-frequency multi-mode GNSS application environment, redundant observation number increases, will improve the rank defect problem of residual error, therefore is especially suitable for processing multi-frequency multi-mode GNSS and observes data.In conclusion the precise satellite navigation locating method for taking non-model errors into account has many advantages, such as that precision is high, highly reliable, applied widely.
Description
Technical Field
The invention relates to a processing method for considering non-modeling errors in applications such as satellite navigation positioning and the like, in particular to a precision satellite navigation positioning method considering non-modeling errors.
Background
The measured values of a Global Navigation Satellite System (GNSS) contain various types of errors, i.e., gross errors, random noise, and systematic errors. Without considering accidental errors and gross errors, systematic errors that cannot be corrected by the model and absorbed by the parameters are referred to as unmodeled errors. Unmodeled errors affect the properties of observed values, and therefore, for different application modes and observation environments, relevant research is carried out on errors with significant influence, such as colored noise, multipath effects, atmospheric deviation and the like.
Most of the current research is mainly directed to the modelable part of these errors, and few studies are made on the unmodeled part. And the processing schemes of the modelable part are mainly divided into two types, namely random model compensation and function model correction.
The random model compensation method is adopted, and usually a reasonable colored noise random model is determined, and a sequential adjustment or Kalman filtering method is adopted for solving, so that the effect of compensating the non-modeling error is achieved. Therefore, error refinement from the perspective of stochastic model compensation lacks systematic research into system quality control, and most of the research results deal with it as colored noise.
In the aspect of function model correction, troposphere and ionosphere errors are key factors for restricting the application of the high-precision GNSS, and a function model compensation mode is usually adopted to absorb system errors, reduce parameter estimation deviation and improve parameter estimation precision. Troposphere delay usually adopts a zenith delay and mapping function parameterization mode, but because the space diversity of troposphere delay and the projection function precision are limited, the troposphere non-modeling error obviously exists, and the fast fixing and high-precision positioning of ambiguity are seriously influenced. Ionospheric first-order delays can be eliminated through parameterization or inter-frequency combination, but non-modeled high-order term errors can reach several millimeters to several centimeters, and the variation is extremely irregular in low-latitude areas, and is also a main factor influencing the application of high-precision GNSS. The multipath effect is closely related to the observation environment, and particularly, a reasonable and universal multipath model cannot be established due to the special constellation distribution characteristics of the Beidou satellite system in China. Most of the existing multipath research results are based on the satellite orbit, the star daily filtering is adopted to process static CORS data, and multipath research related to dynamic positioning is rare. In short, currently, the error refinement from the perspective of the functional model is essentially limited to the error processing of the modelable parts in 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 considering the unmodeled error, which considers the unmodeled error and improves the accuracy and reliability of the GNSS application.
Disclosure of Invention
The invention aims to provide a satellite navigation positioning method taking account of non-modeling errors, which takes account of the non-modeling errors and has high precision and high reliability.
In order to achieve the above object, the present invention provides a satellite navigation positioning method considering unmodeled errors, comprising the steps of:
l1: acquiring a residual sequence of an N-th single-epoch dynamic solution and an observed value of the global satellite navigation system, wherein N is 1;
l2: performing stationarity test on the observation residual sequence to obtain all observations with non-modeled errors, selecting a target observation from the observations, and executing a step L3 on the target observation;
l3: acquiring error equations of (i-1), (i-2), (…) and (i-n) th epochs, 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 a step L4;
l4: acquiring an error equation of the ith epoch, acquiring a dynamic solution of the (N +1) th single epoch, and executing the 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 type of single-epoch dynamic solution is lower than that of the N type of single-epoch dynamic solution, if so, executing a step L7, if not, taking the value of N as N +1, and executing steps L2-L5, wherein N is a positive integer;
l7: and performing satellite navigation positioning according to the Nth single epoch dynamic solution.
Optionally, the step L1 includes:
acquiring an observed value of the global satellite navigation system;
preprocessing the observed value;
establishing a phase and pseudo-range double-difference observation equation, and obtaining an Nth single epoch dynamic solution;
and obtaining an observation value residual error sequence according to the Nth single epoch dynamic solution, wherein N is 1.
Optionally, the step of preprocessing the observation value includes setting a satellite cut-off altitude angle, detecting and repairing cycle slip of the phase observation value, detecting and processing gross error, pseudo-range single-point positioning, troposphere delay correction model, and fixing integer ambiguity of the phase observation value.
Optionally, the step L2 includes:
when the observed value residual sequence is stable, satellite navigation positioning is carried out according to the N single epoch dynamic solution;
and when the observation residual error sequence is not stable, acquiring all the observations 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 observed values with unmodeled errors includes: and selecting a target observation value according to the time correlation of the residual sequence of the observation values, wherein the time correlation coefficient of the target observation value is greater than the time correlation coefficients of all the observation values except the target observation value with the unmodeled errors.
Optionally, the step L4 includes:
calculating the correction number of the unmodeled error according to a least square criterion;
and 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 precision of the (N +1) th single epoch dynamic solution is lower than that of the nth single epoch dynamic solution includes:
acquiring an Nth covariance matrix of the Nth single epoch dynamic solution, wherein N is more than or equal to 2;
acquiring 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 precision 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 precision 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 considering the non-modeling error in the present invention considers some non-modeling errors that cannot be corrected by the model and absorbed by the parameters, which are ignored in the conventional method, so that the positioning accuracy and reliability are improved.
Furthermore, the existing methods mainly deal with the error in the modelable part, but do not control the error in the unmodeled part, and these error refinement methods are essentially limited to the errors in the specific forms of multipath, troposphere, ionosphere, and the like, and do not systematically study and control the comprehensive amount of these errors. The invention considers that the non-modeling errors have space-time correlation, so that the 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, the invention is simultaneously suitable for application scenes comprising observation models considering or neglecting troposphere, ionosphere and multipath, static and dynamic application modes, single-system and multi-system combined modes and the like, and has strong practicability.
Furthermore, because of systematic deviation between different systems, the existing method is prone to cause large positioning error. The invention utilizes the observed value residual error to check the significance of the unmodeled error, and the problem of rank deficiency of the residual error is improved because the number of redundant observations is increased in the multi-frequency multi-mode GNSS application environment, so that the method is particularly suitable for processing multi-frequency multi-mode GNSS observation data, and the problem of system deviation is solved.
Drawings
FIG. 1 is a flow chart of a method for providing unmodeled error-tolerant satellite-based navigation positioning in a preferred embodiment of the invention;
FIG. 2 is a flow chart of a method for positioning a satellite based navigation system with consideration of unmodeled errors according to another preferred embodiment of the present invention.
Detailed Description
The following describes in more detail embodiments of the present invention with reference to the schematic drawings. Advantages and features of the present invention will become apparent from the following description and claims. It is to be noted that the drawings are in a very simplified form and are not to precise scale, which is merely for the purpose of facilitating and distinctly claiming the embodiments of the present invention.
The satellite navigation positioning method considering the unmodeled error provided by the invention considers the unmodeled error, 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 the global satellite navigation system, wherein N is 1;
step S2: performing stationarity test on the observation residual sequence to obtain all observation values with non-modeling errors, selecting a target observation value from the observation values, and executing the step S3 on the target parameter value;
step S3: acquiring error equations of (i-1), (i-2), (…) and (i-n) th epochs, 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 a step S4;
step S4: acquiring an error equation of the ith epoch, acquiring a dynamic solution of the (N +1) th single epoch, and executing the step S5;
step S5: and performing 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:
acquiring an observed 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 observation, the step of preprocessing the observation includes satellite cut-off height angle setting, phase observation cycle slip detection and restoration, gross error detection and processing, pseudo-range single-point positioning, troposphere delay correction model, and integer ambiguity fixing of the phase observation, which is not limited in this respect.
Preferably, the phase and pseudorange double difference observation equation is expressed as:
wherein the subscripts "1" and "2" are each independently designated as L1And L2Carrier phase dependent; phi and P respectively represent double-difference phase and pseudo-range observed values; rho*Is the true value of the distance from the double-difference satellite to the earth; i is1Represents L1Double differential ionospheric delay in frequency; f. of1And f2Represents L1And L2A frequency of (d); lambda [ alpha ]1And λ2Represents L1And L2The wavelength of (a); n is a radical of1And N2Represents L1And L2Integer ambiguity above; ε is the noise term.
Equation (1) is linearized and transformed as follows:
y＝Ax+e (2)，
wherein y is an observed value vector, A is a design matrix, x is a parameter vector to be solved, and e is an error vector.
Combining the observation value covariance matrix Q to obtain the 1 st single epoch dynamic solution as:
the corresponding covariance matrix is:
specifically, the observed value residual is calculated as follows:
and obtaining a residual error sequence Y of each group of observed values.
Specifically, in step S2, a stationarity check is performed on the residual sequence Y, so as to determine whether an unmodeled error in the observed value is significant.
In the present invention, the method for stationarity testing includes at least one of ADF testing or KPSS testing, and preferably, in a preferred embodiment of the present invention, the ADF testing is used to test stationarity of the residual sequence Y.
Specifically, assume that the detected sequence Y is an AR model, as follows:
Yt＝c+δt+φYt-1+α1ΔYt-1+…+αpΔYt-p+Et(6)，
the subscript t represents time, c, delta, phi and α are model parameters, p is a time interval, E is white noise, and delta represents a time difference operator, after phi is obtained, the ADF test statistic is calculated by using the parameters to be tested, and the method comprises the following steps:
wherein SE () represents Standard error (Standard error). Hypothesis H0：φ<1, alternative hypothesis H1: and phi is 1, and then the statistic is used to judge which hypothesis is satisfied, namely whether the observed value residual is stable.
And judging whether the unmodeled error in the observed value is significant according to the test result: if the observed value residual error is stable, the non-modeling error is not significant; otherwise, the unmodeled error is significant.
Specifically, when the test results are all stable, and the unmodeled error of each group of observed values is considered to be insignificant, the unmodeled error is not considered, and satellite navigation positioning is performed according to the 1 st single epoch dynamic solution (3); if the test result is partially stable or not stable, the unmodeled error of the unstable observed value is obvious, and all the observed values with the unmodeled error are obtained.
Preferably, in a preferred embodiment of the present invention, the method for obtaining all observed values with unmodeled errors includes: and determining the observation value needing parameterization, namely the target observation value by utilizing the coefficient size of the time correlation function. The physical correlation is caused by unmodeled errors, and the influence of the time correlation is most significant in the physical correlation. Therefore, when the observed value is more serious than the unmodeled error, the residual error has stronger time correlation, i.e., the severity of the unmodeled 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
Further, 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 number of the unmodeled 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 epochs can be selected to be greater than or equal to 5, and preferably, a multi-epoch error equation of 5 epochs is established in the embodiment, which is not limited in any way by the present invention. Specifically, if the unmodeled error correction number of the ith epoch needs to be calculated, the error equations of the ith-5 th epoch to the ith-1 st epoch are established:
wherein y is an observed value vector, A is a design matrix, B is a coefficient matrix of the unmodeled error, x is a solved parameter vector, omega is an unmodeled error correction number, and e is an error vector.
Observed value covariance matrix Q combining the 5 epochs*And adopting a least square criterion, wherein the corresponding solution containing the non-modeling error correction number is as follows:
the corresponding covariance matrix is:
wherein,
Y＝[yi-5yi-4yi-3yi-2yi-1]T(13)，
X＝[xi-5xi-4xi-3xi-2xi-1ωi]T(15)，
specifically, the error equation for the ith epoch is expressed as follows:
covariance matrix Q combined with observed valuesiObtaining a 2 nd single epoch dynamic solution as:
corresponding covariance matrix of
Specifically, the satellite navigation positioning is performed according to equation (17), i.e., the 2 nd single epoch dynamic solution.
The method in a preferred embodiment of the present invention should be noted in practice with the following specific problems:
a reference station is required to be arranged, the reference station is required to be arranged at the central part of the coverage area of the measuring area as much as possible, the peripheral part is required to have a wide visual field, the cut-off height angle is required to exceed 10 degrees, and optionally, the cut-off height angle comprises 12 degrees, 15 degrees, 20 degrees, 25 degrees, 30 degrees, 50 degrees or 65 degrees; no signal reflector (large water area, large building, etc.) is arranged around the road to reduce multi-path interference and avoid the interference of traffic main road and passing pedestrian as much as possible; the reference station should be located at the relative elevation as much as possible to facilitate the propagation of the differential correction signal; the reference station is far away from the large electromagnetic emission sources such as the microwave tower and the communication tower by 200 meters, and optionally, the distances from the reference station to the large electromagnetic emission sources such as the microwave tower and the communication tower include 210 meters, 240 meters, 252 meters, 300 meters or 400 meters; the reference station is far away from the high-voltage transmission line and the communication line by 50 meters, and optionally, the distance from the reference station to 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 the global satellite navigation system, wherein N is 1;
and Sb: performing stationarity test on the observation value residual sequence to obtain all observation values with non-modeling errors, selecting a target observation value from the observation values, and executing the step Sc on the target observation value;
step Sc: acquiring error equations of (i-1), (i-2), (…) and (i-n) th epochs, 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 step Sd;
step Sd: obtaining an error equation of the ith epoch, obtaining a dynamic solution of the (N +1) th single epoch, and executing a step Se;
step Se: judging whether the N value is 1, if the judgment result is yes, taking the N value as N +1, executing the step Sb-Sd, and if the judgment result is no, executing the step Sf;
step Sf: judging whether the precision of the (N +1) th type of single-epoch dynamic solution is lower than that of the N type of single-epoch dynamic solution, if so, executing step Sg, if not, taking the value of N as N +1, and executing step Sb-Se, wherein N is a positive integer;
step Sg: and performing satellite navigation positioning according to the Nth single epoch dynamic solution.
Different from the preferred embodiment of the present invention, the steps Sa and S1, Sb and S2, Sc and S3, and Sd and S4 are used to select the nth single epoch dynamic solution with higher precision, and perform satellite navigation and positioning according to the nth single epoch dynamic solution, where N includes a positive integer greater than 2.
Specifically, after the step of obtaining the 2 nd single epoch dynamic solution, stability inspection is performed on the observation value residual sequence Y again to obtain all observation values with non-modeling errors, the observation value which needs parameterization most is selected from the observation values, then a multi-epoch error equation is established, and the 3 rd single epoch dynamic solution is obtained; and the observation value needing parameterization most is a target observation value, and the time correlation coefficient of the target observation value is larger than the time correlation coefficients of all the observation values with the unmodeled errors except the target observation value.
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 that of the 2 nd single-epoch dynamic solution;
otherwise, repeating the step of performing stationarity check on the observation residual sequence Y, obtaining all observations with non-modeling errors, selecting the observation which needs parameterization most, namely a target observation, 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 performing satellite navigation positioning according to the (N) th single-epoch dynamic solution.
Specifically, an nth covariance matrix of an nth single epoch dynamic solution may be obtained; and acquiring an (N +1) th covariance matrix of the (N +1) th single-epoch dynamic solution, wherein when the (N +1) th covariance matrix is larger than the Nth covariance matrix, the precision of the (N +1) th single-epoch dynamic solution is lower than that of the Nth single-epoch dynamic solution, and at the moment, satellite navigation positioning is performed according to the Nth single-epoch dynamic solution.
Otherwise, repeating the observation value residual error sequence Y to carry out stability test, obtaining all observation values with non-modeling errors, selecting the observation value which needs parameterization most and a target observation value, and then establishing a multi-epoch error equation until the precision of the obtained single-epoch dynamic solution is not improved compared with that of the previous single-epoch dynamic solution, selecting a certain single-epoch dynamic solution with the highest precision, and carrying out satellite navigation positioning.
In summary, the satellite navigation positioning method considering the non-modeling error in the present invention considers some non-modeling errors that cannot be corrected by the model and absorbed by the parameters, which are ignored in the conventional method, so that the positioning accuracy and reliability are improved.
Furthermore, the existing methods mainly deal with the error in the modelable part, but do not control the error in the unmodeled part, and these error refinement methods are essentially limited to the errors in the specific forms of multipath, troposphere, ionosphere, and the like, and do not systematically study and control the comprehensive amount of these errors. The invention considers that the non-modeling errors have space-time correlation, so that the 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, the invention is simultaneously suitable for application scenes comprising observation models considering or neglecting troposphere, ionosphere and multipath, static and dynamic application modes, single-system and multi-system combined modes and the like, and has strong practicability.
Furthermore, because of systematic deviation between different systems, the existing method is prone to cause large positioning error. The invention utilizes the observed value residual error to check the significance of the unmodeled error, and the problem of rank deficiency of the residual error is improved because the number of redundant observations is increased in the multi-frequency multi-mode GNSS application environment, 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 above description is only a preferred embodiment of the present invention, and does not limit the present invention in any way. It will be understood by those skilled in the art that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (8)
1. A satellite navigation positioning method considering unmodeled errors is characterized by comprising the following steps:
l1: acquiring a residual sequence of an N-th single-epoch dynamic solution and an observed value of the global satellite navigation system, wherein N is 1;
l2: performing stationarity test on the observation residual sequence to obtain all observations with non-modeled errors, selecting a target observation from the observations, and executing a step L3 on the target observation;
l3: acquiring error equations of (i-1), (i-2), (…) and (i-n) th epochs, 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 a step L4;
l4: acquiring an error equation of the ith epoch, acquiring a dynamic solution of the (N +1) th single epoch, and executing the 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 type of single-epoch dynamic solution is lower than that of the N type of single-epoch dynamic solution, if so, executing a step L7, if not, taking the value of N as N +1, and executing steps L2-L5, wherein N is a positive integer;
l7: and performing satellite navigation positioning according to the Nth single epoch dynamic solution.
2. The method for unmodeled error tolerant satellite navigation and positioning of claim 1, wherein said step L1 comprises:
acquiring an observed value of the global satellite navigation system;
preprocessing the observed value;
establishing a phase and pseudo-range double-difference observation equation, and obtaining an Nth single epoch dynamic solution;
and obtaining an observation value residual error sequence according to the Nth single epoch dynamic solution, wherein N is 1.
3. The unmodeled error-tolerant satellite navigation positioning method of claim 2, wherein the step of preprocessing the observations comprises satellite cutoff altitude setting, phase observation cycle slip detection and remediation, gross error detection and processing, pseudorange single-point positioning, tropospheric delay correction model, and integer ambiguity fixing of phase observations.
4. The method for unmodeled error tolerant satellite navigation and positioning of claim 1, wherein said step L2 comprises:
when the observed value residual sequence is stable, satellite navigation positioning is carried out according to the N single epoch dynamic solution;
and when the observation residual error sequence is not stable, acquiring all the observations with non-modeling errors.
5. The method for unmodeled error-tolerant satellite navigation positioning according to claim 4, wherein the method for stationarity checking the observation residual sequence comprises an ADF check or a KPSS check.
6. The method for unmodeled error tolerant satellite navigation positioning according to claim 4, wherein the method for selecting a target observation comprises: and selecting a target observation value according to the time correlation of the residual sequence of the observation values, wherein the time correlation coefficient of the target observation value is greater than the time correlation coefficients of all the observation values except the target observation value with the unmodeled errors.
7. The method for unmodeled error tolerant satellite navigation and positioning of claim 1, wherein said step L4 comprises:
calculating the correction number of the unmodeled error according to a least square criterion;
and establishing an error equation of the ith epoch, and obtaining the (N +1) th single epoch dynamic solution.
8. The method for satellite navigation positioning based on the unmodeled error as claimed in 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:
acquiring an Nth covariance matrix of the Nth single epoch dynamic solution, wherein N is more than or equal to 2;
acquiring 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 precision 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 precision of the (N +1) th single-epoch dynamic solution is higher than that of the nth single-epoch dynamic solution.
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