CN115728793A - Precise single-point positioning gross error detection and processing method based on DIA theory - Google Patents
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Abstract
The invention relates to a precise single-point positioning gross error detecting and processing method based on DIA theory, comprising the following steps: the method comprises the steps of obtaining GNSS observation data of an observation object, and constructing a precise single-point positioning Kalman filtering equation according to the GNSS observation data; establishing a zero hypothesis and an alternative hypothesis; calculating test statistic under the null hypothesis; performing chi-square test on the test statistic in the test statistic under the zero hypothesis, and if the test is passed, considering that the zero hypothesis is true, and not executing the subsequent steps; otherwise, at least one alternative hypothesis is established; calculating test statistic under alternative assumption; selecting a valid alternative hypothesis according to the test statistic under the alternative hypothesis, adjusting an original biased solution under a zero hypothesis, and removing an abnormal observation value corresponding to the alternative hypothesis; and re-executing the steps on the observation value set with the abnormal observation values removed until the observation values are normal. The invention effectively improves the continuity and the availability of the GNSS service in the navigation positioning application.
Description
Technical Field
The invention relates to the field of data processing and quality control of a GNSS satellite navigation system, in particular to a precise single-point positioning gross error detection and processing method based on DIA theory.
Background
With the development of the GNSS market, GNSS modules, chips, boards, and the like are available everywhere in various fields. The acquisition of GNSS data is more convenient. Similarly, the influence of various environments on the observed data is unpredictable, and an observed value containing gross errors is easily generated, so that the quality control means is particularly important. This process is embodied in the data preprocessing stage, and the gross error detection and processing are necessary steps in the data preprocessing stage. If the observed data is not subjected to the step of detecting and processing the gross errors, the subsequent parameter estimation stage is greatly affected or even cannot be estimated, so the gross errors must be processed before the GNSS observed values are used for solving.
Common gross error detection algorithms include pseudo-range comparison, parity vector, least square residual, RAIM, gross error detection based on MW combination, gross error detection based on ionosphere-free combination, etc. The three methods of a pseudo-range comparison method, a parity vector method and a least square residual method are all designed under a single satellite navigation system, and generally only a single gross error can be detected in one observation epoch. Conventional RAIM algorithms also focus on a single gross error due to satellite service failure because there is a small probability that multiple satellite gross errors will occur when using a GPS single system. The RAIM algorithm for multi-fault detection and identification based on gross error detection and elimination theory can process an algorithm for processing two satellite faults, and can not process more than two faults. The gross error detection of the MW combination needs to be carried out one by one according to an observation arc segment, and a filtering and smoothing program in a receiver may bring some system errors, so that the MW combination cannot completely detect the gross error; gross error detection methods based on ionosphere-free combinations detect by subtracting ionosphere-free combinations of code and phase, but amplify system noise.
Disclosure of Invention
This section is for the purpose of summarizing some aspects of embodiments of the invention and to briefly introduce some preferred embodiments. In this section, as well as in the abstract and the title of the invention of this application, simplifications or omissions may be made to avoid obscuring the purpose of the section, the abstract and the title, and such simplifications or omissions are not intended to limit the scope of the invention.
The present invention has been made in view of the above-mentioned problems.
Therefore, the technical problem solved by the invention is as follows: overcomes the limitation of the prior method, and has higher accuracy, stability and detection precision
In order to solve the technical problems, the invention provides the following technical scheme: a precision single point positioning gross error detection and processing method based on DIA theory comprises the following steps:
the method comprises the steps of obtaining GNSS observation data of an observation object, and constructing a precise single-point positioning Kalman filtering equation according to the GNSS observation data;
establishing a zero hypothesis and an alternative hypothesis;
calculating test statistic under the null hypothesis;
performing chi-square test on test statistic under the zero hypothesis, and if the test is passed, considering that the zero hypothesis is established, and not executing subsequent steps; otherwise, at least one alternative hypothesis is established;
calculating test statistic under alternative assumption;
selecting a valid alternative hypothesis according to the test statistics under the alternative hypothesis, adjusting an original biased solution under the zero hypothesis, and removing an abnormal observation value corresponding to the alternative hypothesis;
and re-executing the steps on the observation value set with the abnormal observation values removed until the observation values are normal.
As a preferred embodiment of the precise single-point positioning gross error detection and processing method based on DIA theory according to the present invention, wherein: the kalman filtering equation includes acquiring GNSS observation data of the observation object including:
performing data preprocessing on the GNSS observation data;
constructing a phase and pseudo-range observation equation;
and acquiring a precise single-point positioning Kalman filtering equation.
As a preferred solution of the precision single-point positioning gross error detection and processing method based on DIA theory according to the present invention, wherein: the data preprocessing of the GNSS observation data comprises the following steps:
pseudo-range single-point positioning of an observation object, satellite cut-off altitude setting, satellite clock correction, atmospheric delay correction, satellite orbit correction, hardware delay correction, earth rotation correction, tide correction, and antenna phase center correction of a satellite and a receiver.
As a preferred solution of the precision single-point positioning gross error detection and processing method based on DIA theory according to the present invention, wherein: the establishing of the null hypothesis and the alternative hypothesis comprises the following steps: establishing a zero hypothesis that all GNSS observations do not contain gross errors; an alternative hypothesis is created that any GNSS observation contains gross errors.
As a preferred solution of the precision single-point positioning gross error detection and processing method based on DIA theory according to the present invention, wherein: the calculating test statistics under the null hypothesis includes:
assuming all GNSS observations obey a null hypothesis;
calculating an innovation vector and a variance thereof according to a Kalman filtering equation;
test statistics are constructed from the innovation vectors and their variances.
As a preferred embodiment of the precise single-point positioning gross error detection and processing method based on DIA theory according to the present invention, wherein: the chi-square test comprises the following steps:
performing chi-square test on test statistic under the condition of zero hypothesis calculation;
if the GNSS observation value passes the verification, the GNSS observation value does not contain gross error, the zero hypothesis is established, and the gross error detection and processing are successful; if the check is not passed, the GNSS observation value contains rough error, the zero hypothesis is not established, and the next step is continuously executed.
As a preferred solution of the precision single-point positioning gross error detection and processing method based on DIA theory according to the present invention, wherein: the computing candidate assumes that the test statistics include:
establishing an error equation of an innovation vector according to different alternative assumptions;
calculating a least square estimation value of the gross error and a variance thereof according to an error equation;
test statistics are constructed from the gross error estimates and their variances.
As a preferred embodiment of the precise single-point positioning gross error detection and processing method based on DIA theory according to the present invention, wherein: the alternative assumptions include:
considering that the alternative hypothesis corresponding to the test statistic with the maximum absolute value in the test statistics under the alternative hypothesis is established;
adjusting the original biased solution under the null hypothesis;
and eliminating abnormal GNSS observation values corresponding to the alternative hypotheses.
As a preferred embodiment of the precise single-point positioning gross error detection and processing method based on DIA theory according to the present invention, wherein: the original biased adjustment mode of the kalman filter under the null hypothesis is represented as follows:
wherein,
the posterior estimates of the parameters under the assumption of zero,
variance of a posterior estimate of a parameter under the assumption of zero, K k Is the kalman filter gain.
As a preferred embodiment of the precise single-point positioning gross error detection and processing method based on DIA theory according to the present invention, wherein: the chi-square test is expressed as:
wherein n represents the number of observed values of the current epoch, 0 represents a non-centralization parameter, and alpha represents a significance level if
The check does not pass.
The invention has the beneficial effects that: the existing gross error detection method generally focuses on a single satellite navigation system, and generally only a single gross error can be detected in one observation epoch. While gross errors may exist in any one or more GNSS observation values, the DIA theory can establish a plurality of alternative constructions to ensure that all observation values are covered, and abnormal observation values are eliminated one by one through a similar recursion idea until the GNSS observation value of the current epoch does not contain the gross errors, so that the condition of multiple gross errors is effectively dealt with. DIA theory relies on the statistical properties of the observations themselves to detect and recover any gross small cycle count, not limited by the minimum detectable cycle count of conventional combination observations. When the abnormal observed value is processed, the conventional gross error detection and processing method generally adopts a method of marking the gross error, removing the gross error and re-balancing the observed value to obtain a correct positioning result, and the DIA theory can repair the influence of the gross error on the positioning result without removing the observed value and re-balancing.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without inventive exercise. Wherein:
FIG. 1 is an overall flowchart of a method for detecting and processing precision single point positioning gross error based on DIA theory according to an embodiment of the present invention;
fig. 2 is a graph comparing experimental results of a precise single point positioning gross error detection and processing method based on DIA theory according to a second embodiment of the present invention.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, specific embodiments accompanied with figures are described in detail below, and it is apparent that the described embodiments are a part of the embodiments of the present invention, not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making creative efforts based on the embodiments of the present invention, shall fall within the protection scope of the present invention.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways than those specifically described and will be readily apparent to those of ordinary skill in the art without departing from the spirit of the present invention, and therefore the present invention is not limited to the specific embodiments disclosed below.
Furthermore, reference herein to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one implementation of the invention. The appearances of the phrase "in one embodiment" in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments.
The present invention will be described in detail with reference to the drawings, wherein the cross-sectional views illustrating the structure of the device are not enlarged partially in general scale for convenience of illustration, and the drawings are only exemplary and should not be construed as limiting the scope of the present invention. In addition, the three-dimensional dimensions of length, width and depth should be included in the actual fabrication.
Also in the description of the present invention, it should be noted that the terms "upper, lower, inner and outer" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, which are only for convenience of description and simplification of description, but do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus, should not be construed as limiting the present invention. Furthermore, the terms first, second, or third are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
The terms "mounted, connected and connected" in the present invention are to be understood broadly, unless otherwise explicitly specified or limited, for example: can be fixedly connected, detachably connected or integrally connected; they may be mechanically, electrically, or directly connected, or indirectly connected through intervening media, or may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
Example 1
Referring to fig. 1, for an embodiment of the present invention, a method for detecting and processing a precision single point positioning gross error based on DIA theory is provided, which includes:
referring to fig. 1, GNSS observation data of an observation object is acquired, and a precise single-point positioning kalman filter equation is constructed according to the GNSS observation data;
further, acquiring GNSS observation data of the observation object;
performing data preprocessing on the GNSS observation data;
constructing a phase and pseudo-range observation equation;
and acquiring a precise single-point positioning Kalman filtering equation.
It should be noted that the data preprocessing includes, but is not limited to, pseudorange single point positioning, satellite cutoff altitude setting, satellite clock correction, atmospheric delay correction, satellite orbit correction, hardware delay correction, earth rotation correction, tide correction, and antenna phase center correction for satellites and receivers.
Establishing a zero hypothesis and an alternative hypothesis;
the corresponding measurement equation under the null hypothesis is:
y k ＝A k x k +n k
wherein k represents the current epoch, y k Representing pseudorange or phase observations, A k Representing the linearized coefficient matrix, x k Representing the parameter to be estimated, n k Representing the observation noise.
The alternative assumption is that the corresponding measurement equation is:
y k ＝A k x k +C k b k +n k
wherein, C k Is a unit column vector of 1 at the ith position (i =0,1,2 \8230; n, n is the number of redundant observations), b k A least squares estimate of the gross error under the alternative assumption.
Calculating test statistic under the null hypothesis;
further, all GNSS observations are assumed to obey a null hypothesis;
calculating an innovation vector and a variance thereof according to a Kalman filtering equation;
the state equation in kalman filtering is:
wherein,
is a state transition matrix, x k-1 Estimate of the parameters representing the last epoch, d k Representing the noise of the equation of state.
And subtracting a state prediction value in Kalman filtering time updating from the GNSS observation value to obtain the innovation vector, and obtaining the variance of the innovation vector through an error propagation law.
The formula for the innovation vector and its variance under the assumption of zero is:
wherein v is k Representing the information vector of the message,
representing the state predictors in the kalman filter time update,
representing the variance of the innovation vector and,
representing the parameter firstError variance, R, is estimated by experiment k Representing the noise variance of the metrology equation.
At this time
Considered as a "pure value" free of noise,
the calculation formula of (A) is as follows:
wherein,
on behalf of the a-priori state estimates,
the calculation formula of (c) is:
wherein,
the state estimate is a posteriori of the parameters for the last epoch.
Constructing test statistics according to the innovation vector and the variance thereof;
the test statistic is calculated as:
wherein,
representing the overall test statistic.
Performing chi-square test on the test statistic, and if the test is passed, considering that a zero hypothesis is established, and not executing subsequent steps; otherwise, at least one alternative hypothesis is established, and the next step is carried out;
the calculation formula for chi-square test on test statistics is:
wherein n represents the number of observed values of the current epoch, 0 represents a non-centralised parameter, and α represents the level of significance if
The test does not pass.
Calculating test statistic under the alternative assumption;
furthermore, an error equation of the innovation vector is established according to different alternative assumptions;
the error equation of the innovation vector under the alternative assumption is:
it is rewritten as follows:
wherein H 0 The assumption of zero is represented by the fact that,
representing the innovation vector under the null hypothesis.
Calculating a least square estimation value of the gross error and a variance thereof according to an error equation;
the least squares estimate of the gross error and its variance are:
constructing test statistic according to the gross error estimated value and the variance thereof;
the test statistic was calculated as:
selecting a satisfied alternative hypothesis according to the test statistic, adjusting an original biased solution under a zero hypothesis, and removing an abnormal observation value corresponding to the alternative hypothesis;
and considering that the candidate hypothesis corresponding to the test statistic with the maximum absolute value in the test statistics is established, and calculating a Kalman filtering solution under the candidate hypothesis according to the candidate hypothesis:
wherein,
the posterior estimates of the parameters under the null hypothesis,
variance of a posterior estimate of a parameter under the assumption of zero, K k Is the kalman filter gain.
And correcting the biased solution under the zero hypothesis according to the formula, and removing the observation value corresponding to the alternative hypothesis after the correction is finished.
And re-executing the steps on the observation value set with the abnormal observation values removed until the observation values are normal.
Example 2
In order to verify and explain the technical effects adopted in the method, the embodiment selects the traditional technical scheme and adopts the method to carry out comparison test, and compares the test results by means of scientific demonstration to verify the real effects of the method.
The traditional technical scheme is as follows: the conventional RAIM algorithm. And the RAIM algorithm detects the failed satellite according to the redundant observed value of the user receiver and eliminates the failed satellite, thereby ensuring the navigation positioning precision. The RAIM algorithm focuses on a single gross error due to satellite service failure because there is a small probability that multiple satellite gross errors will occur when using a GPS single system.
The method adopted by the invention of our part is as follows: the method comprises the steps of obtaining GNSS observation data of an observation object, and constructing a precise single-point positioning Kalman filtering equation according to the GNSS observation data; establishing a zero hypothesis and an alternative hypothesis; calculating test statistic under the null hypothesis; performing chi-square test on test statistic under the zero hypothesis, and if the test is passed, considering that the zero hypothesis is established, and not executing subsequent steps; otherwise, at least one alternative hypothesis is established; calculating test statistic under the alternative assumption; selecting a valid alternative hypothesis according to the test statistic under the alternative hypothesis, adjusting an original biased solution under a zero hypothesis, and removing an abnormal observation value corresponding to the alternative hypothesis; and re-executing the steps on the observation value set with the abnormal observation values removed until the observation values are normal.
The invention uses GNSS static observation data acquired by a third floor of four-level road school of college university, uses a GNSS receiver with a middle drawing i70 plate, the acquisition time of a static point is 45 minutes, and an RTKLIB software is adopted to carry out differential processing and calculation to obtain a reference coordinate of the static point (XYZ direction): (-2850276.9895, 4651712.2680, 3293208.4976) (unit: m).
In order to verify that the method overcomes the limitations of the existing method compared with the traditional technical scheme, and has higher accuracy, stability and detection precision, the RAIM algorithm and the method in the traditional technical scheme are adopted in the embodiment as the gross error detection and processing method in GNSS positioning for comparison. The positioning mode adopts pseudo range point positioning (SPP) and dynamic precision point positioning (KINEPPP).
The result is shown in fig. 2, and fig. 2 compares the east (E) direction residual error, the north (N) direction residual error, and the sky (U) direction residual error data of the method with those of the conventional method, so that it can be seen intuitively that the method of the present invention has better accuracy, stability, and detection accuracy compared with the conventional method.
It should be noted that the above-mentioned embodiments are only for illustrating the technical solutions of the present invention and not for limiting, and although the present invention is described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, which should be covered by the claims of the present invention.
Claims (10)
1. A precision single-point positioning gross error detection and processing method based on DIA theory is characterized by comprising the following steps:
the method comprises the steps of obtaining GNSS observation data of an observation object, and constructing a precise single-point positioning Kalman filtering equation according to the GNSS observation data;
establishing a zero hypothesis and an alternative hypothesis;
calculating test statistic under the null hypothesis;
performing chi-square test on test statistic under the zero hypothesis, and if the test is passed, considering that the zero hypothesis is true, and not executing subsequent steps; otherwise, at least one alternative hypothesis is established;
calculating test statistic under alternative assumption;
selecting a valid alternative hypothesis according to the test statistics under the alternative hypothesis, adjusting an original biased solution under the zero hypothesis, and removing an abnormal observation value corresponding to the alternative hypothesis;
and re-executing the steps on the observation value set with the abnormal observation values removed until the observation values are normal.
2. The DIA theory based precise single point positioning gross error detection and processing method of claim 1, wherein the acquiring observation object GNSS observation data comprises:
performing data preprocessing on the GNSS observation data;
constructing a phase and pseudo-range observation equation;
and acquiring a precise single-point positioning Kalman filtering equation.
3. The method for DIA-theory based precise single point positioning gross error detection and processing as claimed in claim 2, wherein the GNSS observation data pre-processing comprises:
pseudo-range single-point positioning of an observation object, satellite cut-off altitude setting, satellite clock correction, atmospheric delay correction, satellite orbit correction, hardware delay correction, earth rotation correction, tide correction, and antenna phase center correction of a satellite and a receiver.
4. The method for precision single point positioning gross error detection and processing over DIA theory according to claim 1, wherein the establishing the null hypothesis and the alternative hypotheses comprises: establishing a zero hypothesis that all GNSS observations do not contain gross errors; an alternative hypothesis is created that any GNSS observation contains gross errors.
5. The method for DIA theory based fine single point positioning gross error detection and processing as claimed in claim 1, wherein said calculating the test statistic under null hypothesis comprises:
assuming that all GNSS observations obey a null hypothesis;
calculating an innovation vector and a variance thereof according to a Kalman filtering equation;
test statistics are constructed from the innovation vectors and their variances.
6. The DIA theory-based precise single point positioning gross error detection and processing method as in claim 1, wherein the chi-square test comprises:
performing chi-square test on test statistic under the condition of zero hypothesis calculation;
if the GNSS observation value passes the checking, the GNSS observation value does not contain gross errors, the zero hypothesis is established, and the gross error detection and processing are successful;
if the check is not passed, the GNSS observation value contains gross error, the zero hypothesis is not established, and the next step is continuously executed.
7. The method for precision single-point positioning gross error detection and processing over DIA theory according to claim 1, wherein the calculating test statistics under alternative assumptions comprises:
establishing an error equation of an innovation vector according to different alternative assumptions;
calculating a least square estimation value of the gross error and a variance thereof according to an error equation;
test statistics are constructed from the gross error estimates and their variances.
8. The method for precision single point positioning gross error detection and processing over DIA theory as defined in claim 1, wherein:
considering that the alternative hypothesis corresponding to the test statistic with the maximum absolute value in the test statistics under the alternative hypothesis is established;
adjusting the original biased solution under the null hypothesis;
and eliminating abnormal GNSS observation values corresponding to the alternative hypotheses.
9. The method for precision single-point positioning gross error detection and processing over DIA theory according to claim 1, wherein the original biased tuning mode of kalman filtering under the null hypothesis is expressed as:
wherein,
the posterior estimates of the parameters under the assumption of zero,
variance of the posterior estimates of the parameters under the null hypothesis, K k Is the kalman filter gain.
10. The DIA theory-based precise single point positioning gross error detection and processing method as claimed in claim 1, wherein the chi-squared test is expressed as:
wherein n represents the number of observed values of the current epoch, 0 represents a non-centralization parameter, and alpha represents a significance level if
The test does not pass.
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