CN115728793A - Precise single-point positioning gross error detection and processing method based on DIA theory - Google Patents

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

A Method of Gross Error Detection and Processing for Precise Single Point Positioning Based on DIA Theory

technical field

The invention relates to the field of GNSS satellite navigation system data processing and quality control, in particular to a precision single-point positioning gross error detection and processing method based on DIA theory.

Background technique

With the development of the GNSS market, GNSS modules, chips, boards, etc. can be seen everywhere in various fields. The acquisition of GNSS data is more convenient. Similarly, the impact of various environments on observation data is unpredictable, and it is easy to produce observations with gross errors, so quality control methods are particularly important. This process is reflected in the data preprocessing stage, and gross error detection and processing are necessary steps in the data preprocessing stage. If the observation data does not go through the step of gross error detection and processing, the subsequent parameter estimation stage will be greatly affected or even impossible to estimate. Therefore, gross errors must be processed before using GNSS observations to solve the problem.

Commonly used gross error detection algorithms include pseudorange comparison method, parity vector method, least squares residual method, RAIM algorithm, gross error detection method based on MW combination, gross error detection method based on ionosphere-free combination, etc. Pseudo-range comparison method, odd-even vector method, and least-squares 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. Traditional RAIM algorithms also focus on single outliers caused by satellite service failures, because the probability of multiple satellite outliers is very small when using a single GPS system. The RAIM algorithm for multiple fault detection and identification based on gross error detection and elimination theory can handle two satellite faults, but cannot handle more than two faults. The gross error detection of the MW combination needs to be carried out one by one according to the observation arc, and the filtering and smoothing procedures inside the receiver may bring some systematic errors, so that the MW combination cannot completely detect the gross error; the gross error detection method based on the ionosphere-free combination Detection is performed by deionospheric combined subtraction of code and phase, but amplifies system noise.

Contents of the invention

The purpose of this section is to outline some aspects of embodiments of the invention and briefly describe some preferred embodiments. Some simplifications or omissions may be made in this section, as well as in the abstract and titles of this application, to avoid obscuring the purpose of this section, the abstract and titles, and such simplifications or omissions should not be used to limit the scope of the invention.

In view of the above problems, the present invention has been proposed.

Therefore, the technical problem that the present invention solves is: overcome the limitation of existing method, have higher accuracy, stability and detection precision

In order to solve the above-mentioned technical problems, the present invention provides the following technical solutions: a method for detecting and processing gross errors in precise single-point positioning based on DIA theory, including:

Obtain the GNSS observation data of the observation object, and construct a precise single point positioning Kalman filter equation according to the GNSS observation data;

Create null and alternative hypotheses;

Calculate the test statistic under the null hypothesis;

Carry out a chi-square test on the test statistic under the null hypothesis. If the test passes, the null hypothesis is considered to be true, and no subsequent steps are performed; otherwise, there is at least one alternative hypothesis to be true;

Calculate the test statistic under the alternative hypothesis;

According to the alternative hypothesis that the test statistic under the alternative hypothesis is established, adjust the original biased solution under the null hypothesis, and eliminate the abnormal observation value corresponding to the alternative hypothesis;

Re-execute the above steps for the set of observations excluding abnormal observations until the observations are normal.

As a preferred solution of the DIA theory-based precision single-point positioning gross error detection and processing method of the present invention, wherein: the Kalman filter equation includes obtaining the GNSS observation data of the observation object including:

Carry out data preprocessing to described GNSS observation data;

Construct phase and pseudorange observation equations;

Get the precise point positioning Kalman filter equation.

As a preferred solution of the DIA theory-based precision single-point positioning gross error detection and processing method of the present invention, wherein: the GNSS observation data for data preprocessing includes:

Pseudo-range single-point positioning of the observed object, satellite cut-off elevation angle setting, satellite clock correction, atmospheric delay correction, satellite orbit correction, hardware delay correction, earth rotation correction, tidal correction, and satellite and receiver antenna phase center correction.

As a preferred solution of the DIA theory-based precision single-point positioning gross error detection and processing method of the present invention, wherein: the establishment of the null hypothesis and the alternative hypothesis includes: establishing all GNSS observations without gross errors. Hypothesis; establish an alternative hypothesis that any GNSS observation contains gross errors.

As a preferred solution of the DIA theory-based precision single-point positioning gross error detection and processing method of the present invention, wherein: the calculation of test statistics under the null hypothesis includes:

Assume that all GNSS observations obey the null hypothesis;

Calculate the innovation vector and its variance according to the Kalman filter equation;

Constructs a test statistic from the innovation vector and its variance.

As a preferred solution of the DIA theory-based precision single-point positioning gross error detection and processing method of the present invention, wherein: the chi-square test includes:

Perform a chi-square test on the test statistic under the calculated null hypothesis;

If the test passes, the GNSS observations do not contain gross errors, the null hypothesis is established, and the detection and processing of gross errors is successful; if the test fails, the GNSS observations contain gross errors, the null hypothesis does not hold, and the next step is performed.

As a preferred solution of the DIA theory-based precision single-point positioning gross error detection and processing method described in the present invention, wherein: the calculation of the test statistics under the alternative hypothesis includes:

Establish the error equation of the innovation vector according to different alternative assumptions;

Calculate the least squares estimate of the gross error and its variance according to the error equation;

Constructs a test statistic from gross error estimates and their variances.

As a preferred solution of the DIA theory-based precision single-point positioning gross error detection and processing method described in the present invention, wherein: the alternative assumptions include:

It is considered that the alternative hypothesis corresponding to the test statistic with the largest absolute value among the test statistics under the alternative hypothesis is established;

Adjust the original biased solution under the null hypothesis;

Eliminate abnormal GNSS observations corresponding to alternative hypotheses.

As a preferred solution of the DIA theory-based precision single-point positioning gross error detection and processing method of the present invention, wherein: the adjustment method of the original partial solution of the Kalman filter under the null hypothesis is expressed as:

为零假设下参数后验估值，

为零假设下参数后验估值的方差，K_k为卡尔曼滤波增益。in,

is the posterior estimate of the parameter under the null hypothesis,

is the variance of the parameter posterior estimate under the null hypothesis, and K _k is the Kalman filter gain.

As a preferred solution of the DIA theory-based precision single-point positioning gross error detection and processing method of the present invention, wherein: the chi-square test is expressed as:

则检验不通过。Among them, n represents the number of observations in the current epoch, 0 represents the non-centralization parameter, and α represents the significance level. If

then the test fails.

Beneficial effects of the present invention: the existing gross error detection methods generally focus on a single satellite navigation system, and generally can only detect a single gross error in one observation epoch. Gross errors may exist in any one or more GNSS observations, and DIA theory can establish multiple alternative constructions to ensure that all observations are covered, and eliminate abnormal observations one by one through recursive thinking until the GNSS observations of the current epoch It does not contain gross errors, and can effectively deal with the situation of many gross errors. The DIA theory relies on the statistical characteristics of the observations themselves to detect, and can detect and repair any gross error with a small number of cycles, and is not limited by the minimum detectable cycle of conventional combined observations. When dealing with abnormal observations, conventional gross error detection and processing methods generally use the method of marking gross errors, removing gross errors, and re-adjusting the observed values to obtain correct positioning results. DIA theory does not need to remove observed values and re-adjust Adjustment can repair the influence of gross errors on positioning results.

Description of drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the accompanying drawings that need to be used in the description of the embodiments. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For Those of ordinary skill in the art can also obtain other drawings based on these drawings without any creative effort. in:

Fig. 1 is an overall flowchart of a method for detecting and processing gross errors of precise single point positioning based on DIA theory provided by an embodiment of the present invention;

FIG. 2 is a comparison diagram of experimental results of a precision single point positioning gross error detection and processing method based on the DIA theory provided by the second embodiment of the present invention.

Detailed ways

In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation modes of the present invention will be described in detail below in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, not all of them. Example. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in the art without creative efforts shall fall within the protection scope of the present invention.

In the following description, a lot of specific details are set forth in order to fully understand the present invention, but the present invention can also be implemented in other ways different from those described here, and those skilled in the art can do it without departing from the meaning of the present invention. By analogy, the present invention is therefore not limited to the specific examples disclosed below.

Second, "one embodiment" or "an embodiment" referred to herein refers to a specific feature, structure or characteristic that may be included in at least one implementation of the present invention. "In one embodiment" appearing in different places in this specification does not all refer to the same embodiment, nor is it a separate or selective embodiment that is mutually exclusive with other embodiments.

The present invention is described in detail in conjunction with schematic diagrams. When describing the embodiments of the present invention in detail, for the convenience of explanation, the cross-sectional view showing the device structure will not be partially enlarged according to the general scale, and the schematic diagram is only an example, which should not limit the present invention. scope of protection. In addition, the three-dimensional space dimensions of length, width and depth should be included in actual production.

At the same time, in the description of the present invention, it should be noted that the orientation or positional relationship indicated by "upper, lower, inner and outer" in the terms is based on the orientation or positional relationship shown in the accompanying drawings, and is only for the convenience of describing the present invention. The invention and the simplified description do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation, and thus should not be construed as limiting the present invention. In addition, the terms "first, second or third" are used for descriptive purposes only, and should not be construed as indicating or implying relative importance.

Unless otherwise specified and limited in the present invention, the term "installation, connection, connection" should be understood in a broad sense, for example: it can be a fixed connection, a detachable connection or an integrated connection; it can also be a mechanical connection, an electrical connection or a direct connection. A connection can also be an indirect connection through an intermediary, or it can be an internal communication between two elements. Those of ordinary skill in the art can understand the specific meanings of the above terms in the present invention in specific situations.

Example 1

Referring to Fig. 1, an embodiment of the present invention provides a method for detecting and processing gross errors in precise single-point positioning based on DIA theory, including:

With reference to Fig. 1, obtain the GNSS observation data of observation object, construct precise single-point positioning Kalman filter equation according to described GNSS observation data;

Further, obtaining the GNSS observation data of the observation object;

Carry out data preprocessing to described GNSS observation data;

Construct phase and pseudorange observation equations;

Get the precise point positioning Kalman filter equation.

It should be noted that data preprocessing includes but is not limited to pseudo-range point positioning, satellite cut-off elevation angle setting, satellite clock correction, atmospheric delay correction, satellite orbit correction, hardware delay correction, earth rotation correction, tide correction and satellite and Receiver antenna phase center correction.

Create null and alternative hypotheses;

The corresponding measurement equation under the null hypothesis is:

y _k =A _k x _k +n _k

Among them, k represents the current epoch, y _k represents the pseudorange or phase observation value, A _k represents the coefficient matrix after linearization, x _k represents the parameter to be estimated, and _nk represents the noise of the observation value.

The corresponding measurement equation under the alternative hypothesis is:

y _k ＝A _k x _k +C _k b _k +n _k

Among them, C _k is the unit column vector with 1 at the i-th position (i=0, 1, 2..., n, n is the number of redundant observations), b _k is the least squares of gross errors under the alternative hypothesis Multiply the valuation.

Calculate the test statistic under the null hypothesis;

Further, assume that all GNSS observations obey the null hypothesis;

Calculate the innovation vector and its variance according to the Kalman filter equation;

The state equation in the Kalman filter is:

为状态转移矩阵，x_k-1代表上一历元的参数估值，d_k代表状态方程的噪声。in,

is the state transition matrix, x _k-1 represents the parameter estimation of the previous epoch, and d _k represents the noise of the state equation.

The innovation vector is obtained by subtracting the state prediction value in the Kalman filter time update from the GNSS observation value, and the variance of the innovation vector is obtained by an error propagation law.

The calculation formula of the innovation vector and its variance under the null hypothesis is:

代表卡尔曼滤波时间更新中的状态预测值，

代表新息向量的方差，

代表参数先验估计误差方差，R_k代表量测方程的噪声方差。Among them, v _k represents the innovation vector,

represents the state prediction value in the Kalman filter time update,

represents the variance of the innovation vector,

Represents the parameter prior estimation error variance, and R _k represents the noise variance of the measurement equation.

被认为是不含噪声的“纯净值”，

的计算式为：at this time

is considered a "pure value" without noise,

The calculation formula is:

代表先验状态估计，

的计算式为：in,

represents the prior state estimate,

The calculation formula is:

为上一历元的参数后验状态估计。in,

is the parameter posterior state estimate for the previous epoch.

Construct test statistics from the innovation vector and its variance;

The formula for calculating the test statistic is:

代表整体的检验统计量。in,

Represents the overall test statistic.

Carry out a chi-square test on the test statistic. If the test is passed, the null hypothesis is considered to be true, and the next step is not performed; otherwise, at least one alternative hypothesis is true, and the next step is entered;

The formula for calculating the chi-square test on the test statistic is:

则检验不通过。Among them, n represents the number of observations in the current epoch, 0 represents the non-centralization parameter, and α represents the significance level. If

then the test fails.

Calculate the test statistic under the alternative hypothesis;

Furthermore, the error equation of the innovation vector is established according to different alternative assumptions;

The error equation of the innovation vector under the alternative hypothesis is:

Rewrite it as follows:

代表零假设下的新息向量。Among them, _H0 represents the null hypothesis,

represents the innovation vector under the null hypothesis.

Calculate the least squares estimate of the gross error and its variance according to the error equation;

The least squares estimate of the gross error and its variance are:

Construct test statistics from gross error estimates and their variances;

The formula for calculating the test statistic is:

Select the established alternative hypothesis according to the test statistic, adjust the original biased solution under the null hypothesis, and eliminate the abnormal observation value corresponding to the alternative hypothesis;

It is considered that the alternative hypothesis corresponding to the test statistic with the largest absolute value in the test statistic is established, and according to the alternative hypothesis, the Kalman filter solution under the alternative hypothesis is calculated:

为零假设下参数后验估值，

为零假设下参数后验估值的方差，K_k为卡尔曼滤波增益。in,

is the posterior estimate of the parameter under the null hypothesis,

is the variance of the parameter posterior estimate under the null hypothesis, and K _k is the Kalman filter gain.

According to the above formula, the biased solution under the null hypothesis can be corrected, and the observations corresponding to the alternative hypothesis can be eliminated after the correction.

Re-execute the above steps for the set of observations excluding abnormal observations until the observations are normal.

Example 2

In order to verify and explain the technical effect adopted in this method, this embodiment chooses the traditional technical scheme and adopts this method to conduct a comparative test, and compares the test results by means of scientific demonstration to verify the real effect of this method.

Traditional technical solution: traditional RAIM algorithm. The RAIM algorithm detects and eliminates faulty satellites based on redundant observations from user receivers to ensure navigation and positioning accuracy. The RAIM algorithm focuses on single outliers caused by satellite service failures because the probability of multiple satellite outliers is very small when using a single GPS system.

The method adopted by our invention is: obtain the GNSS observation data of the observation object, construct the precise single-point positioning Kalman filter equation according to the GNSS observation data; establish the null hypothesis and alternative hypothesis; calculate the test statistics under the null hypothesis; Chi-square test is performed on the test statistic under the hypothesis. If the test passes, the null hypothesis is considered to be established, and no subsequent steps are performed; otherwise, there is at least one alternative hypothesis established; the test statistic under the alternative hypothesis is calculated; the test statistic under the alternative hypothesis is calculated Select the established alternative hypothesis, adjust the original biased solution under the null hypothesis, and eliminate the abnormal observations corresponding to the alternative hypothesis; repeat the above steps for the observation set that eliminates the abnormal observations until the observations are normal.

The present invention uses the GNSS static observation data collected next to the third floor of the Siping Road Campus of Tongji University, and uses a China Paint i70 brand GNSS receiver. The static point collection time is 45 minutes, and the RTKLIB software is used for differential processing to solve the static state. The point reference coordinates are (XYZ direction): (-2850276.9895, 4651712.2680, 3293208.4976) (unit: m).

In order to verify that this method overcomes the limitations of existing methods compared with traditional technical solutions, and has higher accuracy, stability and detection accuracy, the RAIM algorithm in traditional technical solutions and this method will be used as GNSS positioning in this embodiment. Gross error detection and processing methods in . The positioning mode adopts pseudorange single point positioning (SPP) and dynamic precise point positioning (KINEPPP).

Result as shown in Figure 2, Fig. 2 compares the east (E) direction residual of this method with the traditional method, the north (N) direction residual, the sky (U) direction residual data contrast, can see the method of the present invention intuitively Compared with traditional methods, it has better accuracy, stability and detection precision.

It should be noted that the above embodiments are only used to illustrate the technical solution of the present invention without limitation, although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solution of the present invention can be carried out Modifications or equivalent replacements without departing from the spirit and scope of the technical solution of the present invention shall 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, characterized in that, comprising: Obtain the GNSS observation data of the observation object, and construct a precise single point positioning Kalman filter equation according to the GNSS observation data; Create null and alternative hypotheses; Calculate the test statistic under the null hypothesis; Carry out a chi-square test on the test statistic under the null hypothesis. If the test passes, the null hypothesis is considered to be true, and no subsequent steps are performed; otherwise, there is at least one alternative hypothesis to be true; Calculate the test statistic under the alternative hypothesis; According to the alternative hypothesis that the test statistic under the alternative hypothesis is established, adjust the original biased solution under the null hypothesis, and eliminate the abnormal observation value corresponding to the alternative hypothesis; Re-execute the above steps for the set of observations excluding abnormal observations until the observations are normal. 2. the precise single point positioning gross error detection and processing method based on DIA theory as claimed in claim 1, is characterized in that, described acquisition observation object GNSS observation data comprises: Carry out data preprocessing to described GNSS observation data; Construct phase and pseudorange observation equations; Get the precise point positioning Kalman filter equation. 3. the precise single point positioning gross error detection and processing method based on DIA theory as claimed in claim 2, is characterized in that, described GNSS observation data carries out data preprocessing and comprises: Pseudo-range single-point positioning of the observed object, satellite cut-off elevation angle setting, satellite clock correction, atmospheric delay correction, satellite orbit correction, hardware delay correction, earth rotation correction, tidal correction, and satellite and receiver antenna phase center correction. 4. the precise single point positioning gross error detection and processing method based on DIA theory as claimed in claim 1, is characterized in that, described establishment null hypothesis and alternate hypothesis comprise: establish all GNSS observations and do not contain the zero of gross error Hypothesis; establish an alternative hypothesis that any GNSS observation contains gross errors. 5. the precise single point positioning gross error detection and processing method based on DIA theory as claimed in claim 1, is characterized in that, the test statistic under the described calculation null hypothesis comprises: Assume that all GNSS observations obey the null hypothesis; Calculate the innovation vector and its variance according to the Kalman filter equation; Constructs a test statistic from the innovation vector and its variance. 6. the precise single point positioning gross error detection and processing method based on DIA theory as claimed in claim 1, is characterized in that, described chi-square test comprises: Perform a chi-square test on the test statistic under the calculated null hypothesis; If the test passes, the GNSS observations do not contain gross errors, the null hypothesis is established, and the gross error detection and processing is successful; If the test fails, the GNSS observations contain gross errors, the null hypothesis is not established, and proceed to the next step. 7. The precision single point positioning gross error detection and processing method based on DIA theory as claimed in claim 1, is characterized in that, the test statistic under the described calculation alternative hypothesis comprises: Establish the error equation of the innovation vector according to different alternative assumptions; Calculate the least squares estimate of the gross error and its variance according to the error equation; Constructs a test statistic from gross error estimates and their variances. 8. the precise single point positioning gross error detection and processing method based on DIA theory as claimed in claim 1, is characterized in that: It is considered that the alternative hypothesis corresponding to the test statistic with the largest absolute value among the test statistics under the alternative hypothesis is established; Adjust the original biased solution under the null hypothesis; Eliminate abnormal GNSS observations corresponding to alternative hypotheses. 9. the precise single point positioning gross error detection and processing method based on DIA theory as claimed in claim 1, is characterized in that, under the described null hypothesis, the adjustment mode that Kalman filter originally has partial solution is expressed as:

in,

is the posterior estimate of the parameter under the null hypothesis,

is the variance of the parameter posterior estimate under the null hypothesis, and K _k is the Kalman filter gain. 10. the precise single point positioning gross error detection and processing method based on DIA theory as claimed in claim 1, is characterized in that, described chi-square test is expressed as:

Among them, n represents the number of observations in the current epoch, 0 represents the non-centralization parameter, and α represents the significance level. If

then the test fails.

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