CN117538914A - Inertial-assisted GNSS multiple gross error detection method in urban environment - Google Patents

Abstract

According to the GNSS multi-coarse-difference detection method under the inertial-aided urban environment, through introducing information of the inertial state model and the measurement model into autonomous integrity monitoring, test statistics are constructed, the situations that coarse differences are eliminated by mistake and the coarse differences are not eliminated completely are effectively solved, and compared analysis is carried out on the misjudgment rate and the omission rate of the traditional FDE method and the proposed improved method from the number and the size of the multi-coarse differences, and the result shows that the traditional FDE misdetection and omission rate are high when more than 2 coarse differences exist for a receiver, and the detection efficiency can be remarkably improved and the positioning accuracy can be improved through the inertial-aided detection method.

Description

Inertial-assisted GNSS multiple gross error detection method in urban environment

Technical field

The invention relates to the field of satellite navigation technology systems, specifically a GNSS multiple gross error detection method in an inertial-assisted urban environment.

Background technique

Nowadays, location services are widely used in autonomous driving, smart transportation, smart agriculture, etc., and the best infrastructure for precise positioning is the Global Navigation Satellite System (GNSS). Single-point positioning technology based on GNSS has multiple advantages such as low cost and simple data processing. It can provide meter-level positioning accuracy for the emerging multi-GNSS integration, opening up various new prospects. However, when GNSS wireless signals are used in harsh environments, such as urban canyons and areas with heavy vegetation coverage, multipath and non-line-of-sight signals will lead to increased satellite observation errors. With the development of multi-satellite navigation systems, it is easy to cause gross errors in multiple observations at the same time.

One type summarizes gross errors into functional models for theoretical processing of gross error detection and elimination. Receiver Autonomous Integrity Monitoring (RAIM) is considered an effective countermeasure against unintentional interference and intentional attacks. It is not only used for detection, but also provides accurate position, speed and time solutions after eliminating gross errors. Initially, RAIM was designed to detect and exclude single gross errors. For example, gross error detection and isolation (Fault Detection and Exclusion, FDE) methods include the least squares residual method and the odd-even vector method. Several RAIM-based strategies use different methods to detect and exclude multiple gross errors when considering multiple constellations. When dealing with multiple gross errors caused by intentional or unintentional actions, the RAIM FDE method usually eliminates multiple gross errors by iteratively searching for potential gross errors.

Another type of processing strategy is to summarize the gross errors into a random model and use an estimation method based on robust statistics to reduce the impact of inaccurate pseudorange measurements. In order to make up for the shortcomings caused by the limitations of GNSS signal availability, the theory and conclusions of combined positioning assisted by inertial sensors have been well proven.

Kalman filter is currently the most practical real-time optimal estimation method. However, when the model error has time-varying characteristics, it is difficult to obtain the required information. Inappropriate statistical information and outliers will reduce the performance, and sometimes may even cause filtering Divergence, especially when complex disturbances in the signal degradation environment cause abnormal observation values. In order to eliminate the influence of abnormal observation values, Kalman filter quality control methods are proposed, such as detection, identification and adaptive methods. When the measurement value contains multiple When there are outliers, the detection and identification process will be difficult to achieve. Therefore, in order to weaken the influence of outliers in the measured values, it is necessary to study the detection and elimination methods of multiple gross errors for inertial assistance satellites.

Contents of the invention

In order to solve the above technical problems, the present invention proposes an inertial-assisted GNSS multiple gross error detection method in an urban environment. By introducing information from the inertial state model and measurement model into autonomous integrity monitoring, global and local test statistics are constructed to detect coarse errors. Differences and effectively eliminate erroneous measurement values. When there are more than two gross errors in the receiver, the inertia-assisted detection method can significantly improve detection efficiency and positioning accuracy.

In order to achieve the above objects, the technical solutions adopted by the present invention are:

The inertial-assisted GNSS multi-gross error detection method in urban environment is characterized by: including the following steps:

Step 1. In the integrated navigation system of the inertial-assisted satellite, introduce the information of the state model and the measurement model into the autonomous integrity monitoring, and predict the state in the Kalman filter equation. Combined with the observation vector z _k ;

Step 2. The unknown parameters are estimated through least squares. The least squares form observation equation is:

In the formula, L _k is the observation vector, A _k is the design matrix, V _k is the residual vector, and

In the formula, H _k is the observation matrix, I is the identity matrix, v _zk is the observation value residual vector, v _xk is the residual vector of the predicted state, R _k is the observation value variance matrix, is the prediction variance matrix;

Step 3. Obtain the optimal estimate of the state parameters and its covariance matrix based on least squares:

The corresponding estimated residual and its covariance matrix are:

Step 4. Conduct a global test based on the estimated residuals and their covariance matrices to construct the variance factor statistic T _k :

When the statistic T _k obeys the χ ² distribution with m-4 degrees of freedom, there is no gross error. Once a gross error occurs, the statistic will obey the non-central χ ² distribution with m-4 degrees of freedom;

Step 5. In the case of significant level, when When , it is judged that there is a gross error; conversely, when the statistic is lower than the threshold, the observed value is considered credible;

Step 6. Use the data detection method to perform local testing, and identify gross errors through the size of the statistics. The test statistic for the i-th observation is:

In the formula, e _i =[0...1...0] ^T is a unitized vector whose i-th element is 1 and other elements are 0;

Step 7. When there is no gross error in the observation value, w _i ~N(0,1), the test statistic w _i ≤μ _1-α / ₂ , where μ _1-α / ₂ is the standard corresponding to the significance level Quantile values of normal distribution; otherwise, there are gross errors.

Further: assuming the significance level α=0.1%, the corresponding threshold is 3.291.

Compared with the prior art, the beneficial effects of the present invention are:

The present invention introduces the information of the inertial state model and the measurement model into the autonomous integrity monitoring, constructs the test statistics, effectively solves the problem of incorrectly eliminating gross errors and incompletely eliminating gross errors, and compares the number and size of multiple gross errors. The false detection rate and missed detection rate of the traditional FDE method and the proposed improved method were compared and analyzed. The results show that when there are more than 2 gross errors in the receiver, the traditional FDE has a high false detection and missed detection rate. The inertia-assisted detection method can significantly improve detection efficiency and positioning accuracy.

Description of drawings

Figure 1 Example diagram of abnormal observation values;

Figure 2 shows the GNSS gross error detection and identification function values;

Figure 3 shows the gross error detection and identification function values of inertial assistance;

Figure 4 shows the number of gross errors identified by GNSS;

Figure 5 shows the position of gross error in GNSS detection;

Figure 6 shows the number of gross errors identified by inertial assistance;

Figure 7 shows the location of gross errors identified by inertial assistance;

Figure 8 is the GNSS positioning error;

Figure 9 shows the positioning error of inertial assistance;

Figure 10 shows the number of GNSS gross error identifications.

Detailed ways

The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments:

The present invention proposes an inertia-assisted GNSS multiple gross error detection method in an urban environment, which includes the following steps:

Step 1. In the integrated navigation system of the inertial-assisted satellite, introduce the information of the state model and the measurement model into the autonomous integrity monitoring, and predict the state in the Kalman filter equation. Combined with the observation vector z _k ;

Step 2. The unknown parameters are estimated through least squares. The least squares form observation equation is:

In the formula, L _k is the observation vector, A _k is the design matrix, V _k is the residual vector, and

In the formula, H _k is the observation matrix, I is the identity matrix, v _zk is the observation value residual vector, v _xk is the residual vector of the predicted state, R _k is the observation value variance matrix, is the prediction variance matrix;

Step 3. Obtain the optimal estimate of the state parameters and its covariance matrix based on least squares:

The corresponding estimated residual and its covariance matrix are:

Step 4. Conduct a global test based on the estimated residuals and their covariance matrices to construct the variance factor statistic T _k :

When the statistic T _k obeys the χ ² distribution with m-4 degrees of freedom, there is no gross error. Once a gross error occurs, the statistic will obey the non-central χ ² distribution with m-4 degrees of freedom;

Step 5. In the case of significant level, when When , it is judged that there is a gross error; conversely, when the statistic is lower than the threshold, the observed value is considered credible;

Step 6. Use the data detection method to perform local testing, and identify gross errors through the size of the statistics. The test statistic for the i-th observation is:

In the formula, e _i =[0...1...0] ^T is a unitized vector whose i-th element is 1 and other elements are 0;

Step 7. When there is no gross error in the observation value, w _i ~N(0,1), the test statistic w _i ≤μ _1-α/2 , where μ _1-α/2 is the standard corresponding to the significance level Quantile values of normal distribution; otherwise, there are gross errors.

In this invention, if the significance level α=0.1%, the corresponding threshold is 3.291.

Experiments and analysis:

A tight combinatorial mathematical simulation platform for inertial assistance satellites was built in the experiment to verify the proposed FDE method. The gyro constant zero bias and white noise are 5°/h and The accelerometer constant zero bias and white noise are 500μg and/> respectively. The pseudorange accuracy of GNSS measurement is 1m; the simulation time length is 4476s. Simulates a typical urban environment with surrounding obstructions. Satellites below an altitude angle of 40° are invisible. 15 to 19 satellites can be observed. The PDOP value varies between 2 and 5, and the spatial geometry is average.

When the gross error detection function alarms, the GNSS gross error value is eliminated. There may be a single gross error or multiple gross errors. There are a series of alternative hypotheses for excluding gross errors. Each satellite is associated with a subset of all observations for the current epoch. This subset labels the satellite as gross/healthy based on the associated hypothesis test. Figure 1 provides Examples of various situations.

Table 1 shows four possible solutions for satellite gross error detection and elimination.

Single epoch gross error:

In order to verify the effect of gross error detection, a 10m step gross error was added to the 2nd, 5th and 7th observation values from 1st to 4476s respectively. Among them, the four corresponding solution results for the four epochs of 100s, 2028s, 2983s and 3038s respectively appeared. Taking scheme ① as an example, Table 2 shows the gross error test statistics and elimination conditions. Table 3 shows the positioning results of four schemes corresponding to four epochs. It can be seen from the table that scheme ① has the best result after excluding gross errors. Schemes ②, ③ and 4, after excluding gross errors, all make the positioning accuracy not as high as that of retaining gross errors. It shows that Both misjudgments and missed detections have an impact on positioning performance.

The gross errors added to the three observations in plan ① can be accurately identified, and the 7th, 5th and 2nd observations are identified in sequence. The corresponding test statistics are 9.187, 8.528 and 6.261 respectively, exceeding the threshold value of 3.291. In this epoch, all gross error satellites are eliminated, while all healthy satellites are retained. As shown in Table 3, scheme 1 significantly improves the impact of multiple gross errors on positioning accuracy when correctly eliminated.

Table 2 shows the GNSS test statistics for 100 epochs (unit: m).

Plan ② detected gross errors in five observations: 7, 1, 13, 2 and 5 respectively. In this epoch, two healthy observation values 1 and 13 were eliminated, and three gross error observation values 7, 5 and 2 were also eliminated. As can be seen from Table 3, although this epoch can completely and correctly eliminate all gross error satellites, it also removes two healthy satellites, resulting in a decrease in positioning performance. Plan ③ detected gross errors in the two observations 2 and 3 respectively. In this epoch, 1 healthy observation and 1 gross error satellite were eliminated, while 2 gross error observations failed to be detected. As can be seen from Table 3, this epoch not only retains gross satellites, but also eliminates healthy satellite observations, causing a serious decline in positioning accuracy. Plan ④ detected gross errors in the two observation quantities 2 and 5 respectively. In this epoch, two gross error satellites were eliminated, and one gross error satellite failed to be detected.

It can be seen from Table 3 that the accuracy after removing the gross errors of this epoch is worse than the result of retaining the gross errors.

Table 3 shows the GNSS positioning error (unit: m).

Under the condition of inertial assistance, the number and position of gross errors can be completely and correctly detected in the four epochs of schemes ① to ④. Taking the scenario ① as an example, Table 4 shows the local test statistics corresponding to the epoch, and it is completely correct to detect the presence of gross errors in the observation values 2, 5 and 7. Table 5 shows the positioning error of inertial assistance. Compared with Table 3, since gross errors can be accurately identified and eliminated in the inertial assistance environment, the positioning accuracy can be significantly better than the results of GNSS elimination and gross error retention.

Table 4 shows the test statistics of inertial assistance for 100 epochs (unit: m).

Table 5 shows the positioning error of inertial assistance (unit: m).

Continuous epoch gross error:

Figures 2 and 3 respectively show the global inspection volume and local inspection volume of each epoch under GNSS and inertial assistance after adding three 10m gross errors to each epoch. It can be seen from the two figures that the global inspection volume of all epochs exceeds the threshold, and the existence of gross errors can be detected. However, the inertia-assisted gross error identification function value is more stable than the GNSS gross error identification function value, and it is easier to accurately identify gross errors. .

Figure 4 shows the number of gross errors recognized by GNSS. It can be seen from the figure that most epochs can identify 3 gross errors. Some epochs missed the detection of gross errors and only identified 1 to 2 gross errors; some epochs misjudged gross errors. , 4 to 5 gross errors were identified.

Figure 5 shows the position of the gross error in each epoch. The actual gross error is added to the three observation values 2, 5 and 7. It can be clearly seen from the figure that the healthy observation values of multiple epochs are considered to be gross errors and are misjudged. The situation is obvious.

Figures 6 and 7 show the number and location of gross errors identified under inertial assistance respectively. Figure 6 shows that more than 3 gross errors can be identified in all epochs, and only 3 epochs have misjudgments, and there are no missed detections. As can be seen from Figure 7, the 10th, 15th and 11th health observation values were identified as gross errors at 286s, 2359s and 4136s respectively.

Figures 8 and 9 show the positioning results of GNSS and inertia-assisted gross error elimination and gross error retention respectively. Table 6 shows the positioning result statistics. As can be seen from Figure 8, since solutions ②-④ cannot completely eliminate gross errors, the positioning results of the traditional GNSSFDE method are not optimal. In the stages of 500s to 1500s and 2500s to 3500s, the accuracy after removing gross errors is significantly lower than the result of retaining gross errors; in other time stages, gross errors can be correctly identified, and the positioning performance is better than the result of retaining gross errors. When inertial assistance is used, only 3 observations in all epochs have misjudgments, and there are no missed detections. Figure 9 shows that the positioning accuracy is stable after gross errors are eliminated. Compared with the GNSS gross error elimination and gross error retention conditions, the positioning accuracy under inertial assistance is improved by 87.36% and 86.47% respectively.

Table 6 shows the positioning error (unit: m).

Gross differences of different quantities and sizes:

When there are different amounts of gross errors in the observed values, the two methods of traditional GNSS gross error detection and inertia-assisted gross error detection are compared and analyzed. Each epoch is added with 1, 2, 3 and 4 gross errors of 10m respectively. Table 7 shows the statistical results of misjudgment rate and missed detection rate in the four cases. When 1 and 2 gross errors are added, the GNSS false detection and missed detection rates are very low, and the gross error detection and elimination effects are good. When 3 and 4 gross errors are added, the misjudgment rates of GNSS detection are 8.445 and 9.869 respectively, and the missed detection rates are 5.950 and 8.568 respectively. The low positioning performance can be reflected from the 500s to 1500s and 2500s to 3500s stages in Figure 8 . Inertial assistance can significantly improve the detection performance of more than two gross errors. The missed detection rate and false detection rate are both 0, which significantly improves the identification efficiency of gross error detection.

Table 7 is a table of false detection and missed detection rates with a 10-meter gross error.

Figure 10 shows the number of identified gross errors when adding 10m, 15m and 20m. As the gross error becomes larger, when the gross error is 20m, the traditional FDE method can identify up to 8 gross errors and eliminate 5 more observations. This is due to the correlation between the observation values. When the gross error increases, it affects the remaining observations. value, which increases the probability of misjudgment, resulting in reduced positioning performance.

Table 8 shows the false detection and missed detection rates.

Table 8 shows the statistical results of false detection and missed detection rates of gross errors of different sizes. There are 4476 epochs in total. 3 gross errors are added to each epoch, and a total of 13428 gross errors are added. It can be seen from the table that as the error increases, the misjudgment rate of the traditional FDE method gradually increases, and the missed detection rate decreases. When inertial assistance is used, the probability of misdetection and missed detection for gross errors of different sizes is the same, indicating that as the gross error increases, inertial navigation assistance can effectively identify gross errors of different sizes and significantly improve the probability of misjudgment and missed detection.

Therefore, based on the above experiments and analysis: the inertial-assisted GNSS multiple gross error detection method in the urban environment proposed by the present invention can effectively solve the impact of multiple gross errors on positioning accuracy.

Through the above calculation and analysis, the following conclusions are drawn:

1) When there are multiple gross errors in the observation value, the traditional FDE method is prone to incorrectly eliminating gross errors or incompletely eliminating gross errors, resulting in reduced positioning performance;

2) When there are more than two gross errors in the observation value, the misjudgment rate and missed detection rate of the traditional FDE method increase with the number of gross errors, and when the gross errors increase, the misjudgment rate also increases; when using inertial assistance It can significantly improve the efficiency of multiple gross error detection, significantly reduce the probability of false detection and missed detection, and improve the performance of integrated navigation and positioning.

The present invention introduces the information of the inertial state model and the measurement model into the autonomous integrity monitoring, constructs a test statistic, effectively solves the problem of incorrectly eliminating gross errors and incompletely eliminating gross errors, and starts from the number and size of multiple gross errors. A comparative analysis of the false detection rate and missed detection rate of the traditional FDE method and the proposed improved method was conducted. The results show that when the receiver has more than two gross errors, the traditional FDE has a high false detection and missed detection rate. The detection efficiency and positioning accuracy can be significantly improved through the inertia-assisted detection method.

The above are only preferred embodiments of the present invention and are not intended to limit the present invention in any other way. Any modifications or equivalent changes based on the technical essence of the present invention still fall within the scope of protection claimed by the present invention. .

Claims (2)

1. The inertial-assisted GNSS multi-gross error detection method in urban environment is characterized by: including the following steps: Step 1. In the integrated navigation system of the inertial-assisted satellite, introduce the information of the state model and the measurement model into the autonomous integrity monitoring, and predict the state in the Kalman filter equation. Combined with the observation vector z _k ; Step 2. The unknown parameters are estimated through least squares. The least squares form observation equation is: In the formula, L _k is the observation vector, A _k is the design matrix, V _k is the residual vector, and In the formula, H _k is the observation matrix, I is the identity matrix, v _zk is the observation value residual vector, v _xk is the residual vector of the predicted state, R _k is the observation value variance matrix, is the prediction variance matrix; Step 3. Obtain the optimal estimate of the state parameters and its covariance matrix based on least squares: The corresponding estimated residual and its covariance matrix are: Step 4. Conduct a global test based on the estimated residuals and their covariance matrices to construct the variance factor statistic T _k : When the statistic T _k obeys the χ ² distribution with m-4 degrees of freedom, there is no gross error. Once a gross error occurs, the statistic will obey the non-central χ ² distribution with m-4 degrees of freedom; Step 5. In the case of significant level, when When , it is judged that there is a gross error; conversely, when the statistic is lower than the threshold, the observed value is considered credible; Step 6. Use the data detection method to perform local testing, and identify gross errors through the size of the statistics. The test statistic for the i-th observation is: In the formula, e _i =[0...1...0] ^T is a unitized vector whose i-th element is 1 and other elements are 0; Step 7. When there is no gross error in the observation value, The test statistic w _i ≤μ _1-α/2 , where μ _1-α/2 is the quantile value of the standard normal distribution corresponding to the significance level; otherwise, there is a gross error. 2. The GNSS multiple gross error detection method in an inertial-assisted urban environment according to claim 1, characterized in that assuming the significance level α=0.1%, the corresponding threshold is 3.291.