KR20030082147A - Method for Providing Error Correction and Navigation Solution in SA-removed GPS environment - Google Patents

Abstract

PURPOSE: A method for compensating an error and calculating a navigation solution at a global positioning system environment removing selective availability is provided to compensate the error by using a weighted least squares estimation(WLSQ) after the weight value is calculated by a predetermined method. CONSTITUTION: A method for compensating an error and calculating a navigation solution at a global positioning system environment removing selective availability includes a first step of calculating a weighting matrix WΨ by using an elevation for each of the satellites and a second step of calculating a final navigation solution by compensating the error. In the second step, the final navigation solution is obtained by using the weighted least squares estimation(WLSQ) based on the calculated weighting matrix.

Description

Method for calculating error compensation and navigation solution in GPS environment with intentional noise removal {Method for Providing Error Correction and Navigation Solution in SA-removed GPS environment}

The present invention provides a method for calculating an error compensation and GPS navigation solution in a GPS environment in which intentional noise (SA) has been removed, and more specifically, a weighted least square method and / or integrity test method using a weighted matrix that is a function of satellite elevation angles (maximum). Flow method) to provide a GPS navigation solution with precision close to DGPS.

Global Positioning System (GPS) is a radio navigation system that uses satellites to provide position, speed, and visual information anywhere in the world, and its use is expanding in land, sea, and air navigation as well as visual synchronization.

In general, the field where GPS is used is connected to each satellite by using one antenna to one receiver and using Coarse / Acquistion (P / A) or P (Precision) code received from four or more GPS satellites. After determining the distance between the receivers (Pseudorange), the pseudorange is used to determine the absolute position of the receiver on the earth.

On the other hand, the US Department of Defense inserts a long 'Selective Availability' (SA) that is almost impossible to decipher in GPS signals (C / A codes) that are open to the private sector to prevent the use of enemy nations. It has an error of 100m (2dRMS (Root Mean Square)).

Therefore, in the conventional GPS receiver, it is common to use the least-squares method to obtain a navigation solution (position, time, attitude, etc.), and the most accurate noise (SA) of the error components of the GPS is known and the exact characteristics can be known. The solution was obtained without separating it from other error components. Intentional noise was implemented by including the error in the satellite clock and the position of the satellite so that the position obtained could maintain 100 m (2dRMS) accuracy on the horizontal plane.

However, from May 2001, even more accurate navigation solution can be calculated by removing these deliberate noises, but it is known that the error in the horizontal plane is about 25 m due to the remaining error. The remaining errors except deliberate noise include ionospheric delay, tropospheric delay, multipath and receiver measurement noise.

The receiver measurement noise is white noise and generally assumes a 1% error of the code length, and appears to be about 3 m (1σ) when using a C / A (Coarse Acquisition) code. Narrow Correlator is known to reduce the chip spacing up to 30 cm for signal tracking (A. J van Dierendonck, "Theory and Performance of Narrow Correlator Spacing in a GPS Receiver", ION GPS-92 , pp. 115-124, 1992)

Multipath error is difficult to model because it is the result of the reflected wave generated by the surrounding environment to the signal reaching the receiver directly from the satellite. Generally, satellite signals with low elevation angles are known to cause more multipath errors. For fixed receivers, such as DGPS (Differential GPS) reference stations, the effects are periodic and can be compensated for, and techniques for estimating using multiple antennas are also used (ME Cannon and G. Lachapelle, "Analysis of a High-Performance C / A Code GPS Receiver in Kinematic Mode ", NAVIGATION: Journal of the Institute of Navigation , Vol. 39, No. 3, 1992).

However, in general navigation, such a technique is difficult to apply, and thus a technique for reducing the effects of multipath errors in the signal processing of the receiver is used (A. J van Dierendonck, "Theory and Performance of Narrow Correlator Spacing in a GPS Receiver"). , ION GPS-92 , pp. 115-124, 1992 and DJ R van Nee, Multipath and Multi-transmitter Interference in Spread-Spectrum Communication and Navigation Systems, Delft University, 1995). In addition, a method of reducing the effects of reflected waves by installing a choke ring around the antenna has been proposed (ME Cannon and G. Lachapelle, "Analysis of a High-Performance C / A Code GPS Receiver in Kinematic Mode"). , NAVIGATION: Journal of the Institute of Navigation , Vol. 39, No. 3, 1992).

The ionospheric delay error occurs in the course of the GPS signal passing through the ionospheric layer and acts as a delay for the code and a lead for the carrier and has the same magnitude. Low satellites are more affected than high-angle satellites, and the effect is large during the day when the ionosphere is active and the size is about 20 to 60 m. The ionospheric delay is inversely proportional to the square of the frequency, which can be effectively eliminated when using a dual frequency receiver. In case of using a single frequency receiver, the ionospheric model is used to estimate the delay and the Klobuchar model is used in GPS. However, this model is known to cover only 50-75% of the entire Earth (BH Hofmann-Wellenhof, H. Lichtenegger and J. Collins, Global Positioning System Theory and Practice, Springer-Verlag, Wien, 1993).

The tropospheric delay error is an error that occurs when a GPS signal passes through the troposphere and is affected by humidity, temperature, and altitude. Tropospheric delays, like ionospheric delays, are affected by satellite elevation and range from 2.1 to 24 m in size. GPS does not provide a separate model for tropospheric compensation, and some receivers use modified Hopfield models (BH Hofmann-Wellenhof, H. Lichtenegger and J. Collins, Global Positioning System Theory and Practice, Springer-Verlag, Wien, 1993).

After the deliberate noise is removed, the ionospheric delay and tropospheric delay errors act as the biggest error factors.The characteristics of these errors are different from those obtained by solutions that last several hours, unlike intentional noise with periods of several minutes. ), So you can use a navigation algorithm that includes it in additional unknowns. In other words, pseudorange can be expressed as a function of the shape and elevation of the ionospheric and troposphere where the receiver is located, so if more than 6 GPS satellites are visible, a total of six models can be added by adding models for ionospheric delay and convective delay. We can calculate the position, time, ionospheric coefficient and tropospheric coefficient at the same time by calculating the navigation equation with Integer Ambiguity (Park Soon, Lim Young Jae, Park Chan Sik, "Development of GPS Navigation Algorithm Considering Intentional Noise Reduction", Journal of Automatic Control Conference, Yongin, 2000).

However, this method has a significant effect on the accuracy of the ionosphere and tropospheric delay model used, and increases the calculation error due to an ill-conditioned matrix, especially when satellites with similar elevation angles exist. There is a difficulty.

First, the characteristics of the error present in the GPS navigation solution and the conventional error compensation method are described.

The pseudo range measurement between the GPS receiver and satellite i may be represented by Equation 1. here Is the pseudorange measurement, Is the distance between satellite and receiver, cB is the speed of light multiplied by the clock error of satellite and receiver, Is the distance calculated using the satellite and the nominal position A ₀ , Is the position of the satellite, (x, y, z) is the position of the reference point, Is the line of sight vector between the satellite and the receiver, Denotes a position error with respect to the reference point.

Pseudorange measurement error Represents the error plus satellite position error, ionospheric delay, tropospheric delay, multipath error, and receiver measurement noise.

In order to calculate the three-dimensional position and the receiver clock error, measurements from m (≥4) satellites must be obtained. In this case, it can be represented by using a vector and a matrix as shown in Equation 2. here, , , , The measurement error is Suppose we have a distribution of. When the positional error and the receiver clock error are obtained by applying the weighted least-squares method to Equation 2, Equation 3 is obtained, and the covariance thereof is as shown in Equation 4.

In case of intentional noise (SA), the mean value of the measurement error is 0 and covariance It was common to save the solution. That is, since the magnitude of the high noise is much larger than the other errors, only the characteristics of the high noise have to be considered. Therefore, if there is deliberate noise, there is no meaning of the weighted least-squares method, and only the effects of satellite placement can be analyzed using the geometric dilution of precision (GDOP) defined using the covariance of the estimate obtained from Equation 5. (See BW Parkinson and JJ Spilker, Jr., Global Positioning System: Theory and Applications Vol. I, II , AIAA, Washington, 1996).

This measurement error nu consists of the sum of ionospheric delay, tropospheric delay, multipath error and receiver measurement noise. Reducing the magnitude of these errors can improve the accuracy of the position and time obtained for the same size GDOP, so it is necessary to compensate the measurement error in an appropriate manner. Hereinafter, a conventional method of compensating for an error caused by each element will be described.

Compensation for ionospheric delay

GPS uses the Klobuchar model to compensate for ionospheric delay. In this model, we assume that the ionosphere is located at an average of 350 km above the ground, and the ionosphere activity is affected by the global magnetic latitude and local time, so we use this to calculate the vertical charge density ( Iv ). (See JA Klobuchar, "Ionospheric Time-Delay Algorithm for Single-Frequency GPS Users", IEEE Trans.on Aerospace and Electronics System , Vol. 23, No. 3, 1987). The coefficients necessary for the calculation of the vertical charge density are included in the navigation signal, and the obtained vertical charge density is multiplied by the obliquity factor (F (Ei)) according to the satellite's elevation (Ei) as shown in Equation 6 _Find the magnitude of the ionospheric delay (T _iono ) and compensate it from the pseudorange measurements.

Although the accuracy of the Klobuchar model depends on the accuracy of the vertical charge density and the slope, the GPS model can be used to construct the model for the entire Earth and change the model once every three days. Only up to 50-75% compensation is possible.

Compensation for Tropospheric Delays

GPS does not support a separate method to compensate for tropospheric delays. In some receivers, Hopfield, Modified Hopfield, and Sastaamoinen models are used, but the effects have not yet been confirmed (BH Hofmann-Wellenhof, H. Lichtenegger and J. Collins, Global Positioning System Theory and Practice, Springer-Verlag, Wien, 1993). In addition, since these models are too complicated to be used in general GPS receivers, a simple method of calculating the tropospheric error (T _Tropo ) and compensating them from pseudorange measurements is mainly used (BW Parkinson and JJ Spilker). , Jr, Global Positioning System: Theory and Applications Vol. I, II , AIAA, Washington, 1996).

Hereinafter, the characteristics of the error caused by each element will be examined, and the navigation solution calculation method considering the error will be described.

As described above, when intentional noise is present, since intentional noise is the largest component of the error, the compensating effect of the ionospheric delay and the troposphere delay is not large. However, by eliminating the intentional noise, the effect of such compensation is large, and the accuracy of the error before compensation and the error after compensation can be understood to improve accuracy.

To determine the nature of the error, the day-to-day measurements were collected in 1-minute increments from 7 pm on June 28, 2001, using a Novatel 12-channel 3010R receiver at a known location.

Figure 1 shows the number of visible satellites and GDOP during the experimental period of the present invention. As can be seen in Figure 1, at least 6 to 12 visible satellites are observed during the experimental period, GDOP can be seen to have a value of around 2.

FIG. 2 shows the total error value obtained by adding the difference between the pseudorange and the actual distance calculated by the GPS signal, that is, the receiver clock error and the measurement error. FIG. 2A shows the time-phase error and FIG. 2B shows the satellite elevation error. . As can be seen in FIG. 2A, the elevation angle changes as the satellite moves, and the magnitude of the error changes according to the elevation angle, and a large error value of 200 m or more may be seen in some sections. As can be seen in Figure 2b, it can be confirmed that such a large error is an error that occurs mainly in a satellite having a low elevation angle.

It can also be seen that an error around -100m occurs for all measurements at the same time. This is an effect of the receiver clock error and will not affect the accuracy of the location if it works the same size for all satellites. In addition, as can be seen in Figure 2b, it can be seen that the magnitude of the error is a function of the elevation angle of the satellite.

3 shows the vertical charge density of the distance unit obtained by using the coefficient value included in the GPS navigation signal, and it can be seen that the maximum charge is obtained at about 2 o'clock in the day and the charge density value decreases at night.

FIG. 4 illustrates error values after error compensation for ionospheric and tropospheric delays according to the above-described method. Similar to FIG. 2, FIG. 4A is time-phase error and FIG. 4B is elevation-angle error.

That is, the pseudo-range and actual distance after compensating the ionospheric delay using the charge density value calculated as shown in FIG. 3 and the above-mentioned compensation equation for the ionospheric delay (Equation 7), and the tropospheric delay using Equation 8 It shows a street car.

The effects of error compensation can be seen from FIGS. 2 and 4, and it can be seen that the error of the bias component is whitened by the error compensation. In addition, as can be seen in Figure 4b, the compensation value obtained from the model is larger than the actual error can be seen that the remaining error appears in the form of a parabola according to the elevation angle. This is because the model used is not accurate, and therefore, the compensation of up to 50-75% can be achieved even with the model described above.

In addition, in order to compensate for the error, the "Method of Least Squares" generally used in regression analysis can be used. Since the least square method is generally widely used, the detailed principle thereof is omitted.

5 shows the covariance of the error The error obtained using the general least squares method, which is used to exclude satellites with low elevation angles (Mask Angle, described below), is set to 0 degrees and does not compensate for ionospheric and tropospheric delays. . As can be seen in Figures 4 and 5, if the error included in the pseudo-range measurement value is large it can be confirmed that a large error occurs in the obtained position and time. FIG. 5A shows the positional error divided into east, west, and north and south, and FIG. 5B shows Epochs, that is, a change in error over time. In FIG. 5B, latitude, longitude, clock error cB, and altitude errors are shown in the clockwise direction from the upper left end.

Figure 6 shows the error of the position and time obtained from pseudorange measurements that compensated the ionosphere and tropospheric delay using equations (7) and (8). The drawing format is the same as in the case of FIG.

5 and 6, it can be seen that the accuracy of the receiver clock is greatly improved compared to the position by the ionosphere and tropospheric error compensation. This is because the average of the ionospheric and tropospheric delays of all satellites shown in the least-squares method are included in the receiver clock error, and the effects of the compensation of the error are shown directly.

On the other hand, it can be seen that error compensation does not help much on the horizontal plane. This is because abnormally large errors included in some satellites have not been compensated for properly, and it can be seen that a sudden change of position occurs when such satellites are added or deleted.

In order to improve the accuracy of the position and time from the above results, a technique for removing abnormally large errors is required.

In summary, the conventional ionospheric delay compensation model, tropospheric delay compensation model, weighted square method, etc. can be used to compensate for pseudorange or navigation solution (position, time) error in the current GPS where SA is removed. In addition, there is a limit to the degree of error compensation, and the effect on an abnormally large error cannot be eliminated.

Of course, if the abnormal error is concentrated in a low elevation angle, it can be easily removed by using a mask angle. The compensation method using the elimination angle effectively eliminates the influence of pseudorange measurement error by not using the satellite measurement value having an elevation angle smaller than the elimination angle which is usually set at a value between 5 and 15 degrees. However, if the number of visible satellites is not enough, such as downtown, the number of visible satellites may be less than four, so this method can be effectively applied only where visibility is good.

The following describes the error compensation experiment using the erase angle.

FIG. 7 shows the number of visible satellites (FIG. 7A) and the GDOP (FIG. 7B) when the deletion angle is 0, 5, 10, and 15 degrees. In FIG. 7, when the erase angle is 15 degrees, only 4 visible satellites may occur, and as the number of satellites decreases, the GDOP increases. This means that the error of the measured value can be reduced by removing all the measured values with a large measurement error by increasing the deletion angle. However, the GDOP is worsened and the position and visual error are increased. Therefore, the setting of the deletion angle should be selected in consideration of the application field and the surrounding environment.

Tables 1 and 2 summarize the results of the error compensation method using the angle of elimination. Table 1 shows the results of measurements without compensating the ionospheric and tropospheric errors, and Table 2 shows the results of compensations.

Error after application of the angle of removal (no compensation for ionospheric and tropospheric delays) Degree angle Plane Error (2dRMS) East-West Error North-south error Altitude error Receiver clock error Average 1σ Average 1σ Average 1σ Average 1σ 0 25.0 0.5 7.9 3.1 9.2 33.3 19.6 29.0 9.1 5 15.3 0.3 4.3 2.1 6.0 26.8 11.0 24.3 10.6 10 7.6 0.1 1.6 1.7 3.0 21.2 20.2 4.5 20.2 15 7.2 0.07 1.6 1.4 2.9 18.0 4.3 17.7 11.0

Error after elimination angle (Ion layer and tropospheric delay compensation) Degree angle Plane Error (2dRMS) East-West Error North-south error Altitude error Receiver clock error Average 1σ Average 1σ Average 1σ Average 1σ 0 21.6 0.7 6.7 2.6 8.0 7.5 15.7 0.8 4.6 5 13.8 0.4 3.6 2.1 5.5 5.1 8.7 -1.0 9.2 10 6.8 0.2 1.1 1.7 2.8 3.8 3.3 -2.0 10.2 15 6.7 0.1 1.3 1.4 2.7 3.5 3.9 -2.2 10.2

From the table, we can see that we can improve performance by about 20% in the horizontal plane by compensating ionosphere and tropospheric errors. In both the ionospheric and tropospheric errors, the accuracy is improved as the erase angle is increased.However, if the erase angle is more than 10 degrees, the GDOP increases as the error of the measured value decreases. It can be seen that. Therefore, it would be advantageous to determine the erase angle around 10 degrees and to use pseudorange measurements compensated using ionospheric and tropospheric delay error models.

However, when the angle of elimination is used in a situation where sufficient visibility satellites are not secured, such as downtown, the number of visible satellites is four or less, so that navigation solutions cannot be obtained. Therefore, there is a need for a method that can improve positioning accuracy without using an erasure angle.

As described above, in the GPS environment in which intentional noise has been removed, the error can be reduced to some extent using the conventional error compensation method as it is, but there is a limit to the degree and shows a larger error range than DGPS.

Accordingly, the present invention seeks to approximate the accuracy of DGPS by compensating for an error in pseudorange or navigation solution using weighted least square method and / or integrity test method using weights calculated using satellite elevation angle.

Therefore, an object of the present invention is to experimentally obtain the relationship between the elevation angle and the covariance of the error from the characteristics of the residual error before and after compensating the ionospheric delay and tropospheric delay error, and using this method to obtain the weight by a predetermined method and then weighted minimum The present invention provides a method for calculating an error compensation and a GPS navigation solution in GPS, which compensates for an error using a weighted least squares estimation (WLSQ).

Another object of the present invention, after compensating for the error by the weighted least square method described above, to create a condition that can be applied to the integrity verification technique (RAIM: Receiver Autonomous Integrity Monitoring), GPS to remove abnormally large errors therefrom It is to provide a method for calculating the error compensation and GPS navigation in.

1 shows the number of visible satellites and the GDOP during the experimental period in the present invention.

2 illustrates an error value obtained by adding a difference between a pseudorange calculated from a GPS signal and an actual distance, that is, a receiver clock error and a measurement error.

3 shows vertical charge densities in units of distance obtained using coefficient values included in GPS navigation signals.

4 shows error values after compensating for the ionospheric and tropospheric delays according to the conventional scheme.

5 shows the covariance of the error Shows an error obtained using a conventional general least square method.

FIG. 6 shows errors in position and time obtained from pseudorange measurements that compensate for ionospheric and tropospheric delays using equations (7) and (8).

FIG. 7 shows the number of visible satellites and the GDOP when the mask angle is 0, 5, 10, and 15 degrees.

FIG. 8 illustrates errors and clock errors for each coordinate axis with respect to a position obtained by applying the weighted least square method according to the first embodiment of the present invention.

9 illustrates residual values calculated by Equation 11 after performing the method according to the first embodiment of the present invention.

Fig. 10 is a flowchart showing the procedure of the GPS navigation solution determination method according to the second embodiment of the present invention.

11 shows positional errors obtained by applying the integrity verification technique according to the second embodiment of the present invention to actual measurements.

Figure 12 shows the residual after the performance of the second embodiment of the present invention.

Figure 13 shows the maximum runoff obtained after the implementation of the second embodiment of the present invention.

14 shows the number of visible satellites and the GDOP during the experiment of the second embodiment of the present invention.

FIG. 15 shows a comparison of the horizontal plane error between the case of applying the conventional least square method and the case of applying the second embodiment of the present invention.

Figure 16 shows the flow after applying the integrity verification technique according to the second embodiment of the present invention.

In order to achieve the object of the present invention as described above, the method according to the present invention is configured as follows.

In a GPS environment in which intentional noise is removed, a final navigation solution is obtained by compensating a navigation solution error of an object calculated based on GPS signals from four or more visible satellites (SV).

A first step of calculating a weighting matrix using elevation angles of satellites and a second step of calculating a final navigation solution by compensating for an error by applying a weighted least square method based on the calculated weighting matrix.

In the weighting matrix calculation in the first step, a constant weight is given to a measurement value of a satellite that is greater than or equal to a predetermined elevation angle, and a weighting factor that is smaller than the constant and a weight proportional to the elevation angle is used for a measurement value of the satellite that is less than or equal to the predetermined elevation angle, The predetermined elevation angle may be determined by analyzing measurement results of individual GPS receivers.

For example, the calculation of the weighted matrix may be determined by the following equations 9 and 10, n may be set to -3 to -1, and α may be set to 20 to 40 degrees.

Where Ei is the elevation angle of satellite i and W _Ψ is the weight matrix.

Of course, the method may further include compensating the ionospheric delay and tropospheric delay error by a predetermined model before the first step.

In another embodiment of the present invention, a new object after excluding a measurement of a satellite having an unusually large error by using weighted least squares method and Receiver Autonomus Integrity Monitoring (RAIM) or Maximum Residual Method Calculate the location and time.

Specifically, in a GPS environment in which noise is removed, a method for obtaining a navigation solution of an object calculated based on GPS signals from six or more visible satellites (SV),

When the residual is calculated by applying the weighting matrix and weighted least-squares method calculated using the elevation angles of each satellite, and there is an overflow value (maximum value) exceeding the normalized uncorrelated flow threshold for each satellite. It is characterized in that the measurement of the satellite is excluded from the calculation by navigation.

Looking at this step in detail as follows.

a first step of calculating a weighting matrix using elevation angles of respective satellites when there are m (≥6) visible satellites; Based on the calculated weighted matrix, the weighted least-squares method is applied to position, time, and flow rate ( Obtaining a second step; By multiplying the square root of the weighted matrix with the runoff obtained in the second step, Obtaining a third step; Normalized correlation correlation for each satellite ( ) And the maximum normalized correlation run of the satellite that maximizes the normalized correlation run ( Obtaining a fourth step; Maximum normalized correlation run above (5) removing the measurement value for the corresponding satellite when the value of h) exceeds a predetermined threshold; And a sixth step of repeating the first to fifth steps until there is no satellite whose maximum normalized correlation runoff value exceeds the threshold, or m is less than six, and determining the position and time at that time as the final navigation solution. Consists of steps.

Similar to the first embodiment, the weighting matrix calculation in the first step gives a constant weight to measurements of satellites that are above a predetermined elevation angle and is proportional to the elevation angle while being smaller than the constant to measurements of satellites that are below a predetermined elevation angle. Using a weighted model, the predetermined elevation can be determined by analyzing the measurement results of the individual GPS receivers.

For example, the weighting matrix is determined by Equations 9 and 10, and the flow rate in the second step ( ) Is calculated by Equation 11 below.

The normalized correlation run above ( ) And maximum normalized uncorrelated flow values ( ) May be calculated by Equation 12 and Equation 13 below.

Where S _w (j, j) means (j, j) th term of the matrix S _w and S _w is the matrix And G _w is to be.

The threshold is determined differently by the number of target satellites (m), and may be a value determined by Bonferroni inequalities or Jash inequalities.

In addition, as in the foregoing embodiment, the method may further include compensating the ionospheric delay and tropospheric delay error by a predetermined model before the first step.

Hereinafter, with reference to the accompanying drawings will be described in detail a first embodiment and a second embodiment of the present invention.

First, the first embodiment of the present invention will be described in detail.

As described above, in the case of using the erasing angle, the navigation solution cannot be obtained because the number of visible satellites is four or less, so that the weight is determined from the error characteristic and the weighted least square method is used.

Since the weight is not known to the exact covariance of the measurement, it was determined from the actual measurement of Figure 4b, which may vary depending on the receiver used and the surrounding environment. The weight determined in this way is closely related to the elevation angle of the satellite, and Equation 9, which shows the best performance through experiments among several models approximating FIG. 4, is used, and Equation 10 expresses the weighted matrix. to be.

[Equation 9]

[Equation 10]

Here, E i is the elevation angle of the satellite i, W ψ is a weight matrix, n can be set to -3 to -1, α can be set to 20 to 40 degrees. The values most consistent with the results in FIG. 4 are n = -3 and α = 30 degrees.

Of course, the weighting matrix does not necessarily need to be determined by this equation. Instead, other models can be used as long as a constant weight is given to measurements of satellites that are above a predetermined elevation angle and weights that are proportional to the elevation angle are smaller than the constant and are measured by satellites that are below a predetermined elevation angle. In addition, the predetermined elevation angle is preferably determined individually by analyzing the measurement results of the individual GPS receivers.

Table 4 shows the position and visual errors obtained by applying the weighted least square method according to the present invention without compensating ionospheric delay and tropospheric delay, and the results obtained by the present invention.

Error after application of weighted least-squares method according to the present invention Degree angle Plane Error (2dRMS) East-West Error North-south error Altitude error Receiver clock error Average 1σ Average 1σ Average 1σ Average 1σ 0 6.9 0.05 1.4 1.5 2.7 19.1 3.8 18.6 10.5 5 6.8 0.04 1.4 1.5 2.7 19.0 3.7 18.5 10.6 10 6.8 0.03 1.4 1.5 2.7 18.3 3.6 18.0 10.8 15 7.0 0.04 1.5 1.3 2.9 17.0 4.0 16.8 10.8

Error after application of weighted least-squares method according to the present invention (Ion layer and troposphere delay compensation) Degree angle Plane Error (2dRMS) East-West Error North-south error Altitude error Receiver clock error Average 1σ Average 1σ Average 1σ Average 1σ 0 6.38 0.1 1.1 1.5 2.6 3.7 3.2 -2.1 9.8 5 6.36 0.1 1.1 1.5 2.6 3.7 3.2 -2.1 9.9 10 6.37 0.1 1.1 1.5 2.6 3.6 3.3 -2.2 10.0 15 6.57 0.1 1.3 1.3 2.7 3.4 4.0 -2.4 10.2

In addition, FIG. 8 illustrates errors and clock errors for each coordinate axis of a position obtained by applying a weighted least square method according to the present invention to a measurement that compensates for an ion angle and an ionosphere and tropospheric delay.

In Tables 3, 4 and 8 it can be seen that the application of the weighted least squares method according to the present invention provides an improvement in performance. In particular, it can be seen that more than three times the performance improvement can be obtained when the erase angle is low. However, the performance improvement is not large for the deletion angle of 5 degrees or more. In particular, it can be seen in Table 3 that the result of the deletion angle of 15 degrees is worse than that of the 10 degrees. This is due to the increased number of visible satellites and the larger GDOP as the erase angle increases.

8 and 9 show the result of the error compensated in the manner according to the first embodiment of the present invention.

Specifically, FIG. 8 illustrates error and clock error for each coordinate axis for a position obtained by applying the weighted least-squares method according to the present invention to a measurement that compensates for 0 degree of erase angle, ionospheric layer, and tropospheric delay, and FIG. 9 described above. The residual calculated by Equation 11 is shown.

[Equation 11]

As can be seen in FIG. 9, the size of the flowing water is almost the same when the elevation angle is 30 degrees or more under the influence of the weighting matrix, and the size of the flowing water increases when the elevation angle is low. In particular, some satellites with a low elevation have an unusually large runoff and their influence cannot be avoided by using the weighted least-squares method. In the case of using the erasing angle, these effects can be avoided, but the problem of eliminating many measurements at the same time with a normal magnitude of error occurs. This problem can be solved by identifying satellites with abnormally large runoff and removing only this measurement, which can be solved by the method according to the second embodiment of the present invention.

From the above results, using the weighted least squares method according to the first embodiment of the present invention can obtain better performance than using the deletion angle. Particularly, when the number of visible satellites is insufficient (4-5), In case of using the solution, the solution cannot be obtained, but there is an advantage in that the solution can be obtained by applying the method according to the present invention.

In addition, by using the weighted least square method according to the present invention, even when a low elevation satellite is added or decreased, an advantage of reducing abrupt changes in position and time can be additionally obtained.

Hereinafter, a second embodiment of the present invention will be described in detail.

Using the weighted least-squares method as in the first embodiment, it was confirmed that accuracy within 7 m in the horizontal plane can be obtained. However, as can be seen in Figure 9, it can be seen that the measurement value giving an unusually large flow for the satellite with a low elevation angle is used to solve the solution. Abnormally large runoff occurs when the measurement includes an unusually large error, which is presumably due to multipath errors caused by the reflection of buildings.

In the case of a DGPS reference station that installs a receiver at a fixed location, the influence of the satellite can be reduced by simultaneously using the satellite elevation and azimuth angles. However, this method is difficult to apply in general navigation. Therefore, in the second embodiment of the present invention, the measurement value of the satellite having an abnormal error is navigated and removed from the calculation target by using the integrity verification technique.

Integrity testing techniques used in receivers are mostly methods for detecting and identifying errors when only one measurement contains bias error, and a snapshot method for checking integrity using redundant measurements is generally used. do. In the snapshot method, the current abnormality is determined only by the current measurement, and includes the method of using the sum of squares of the least squares flow, the method of using the parity space, and the maximum residual technique. . These methods are mathematically equivalent, and measurement noise Suppose we have a distribution of.

After the deliberate noise is removed, however, the distribution of measured noise This cannot be assumed, so a change is necessary.

In the second embodiment of the present invention, the maximum water flow technique is extended and applied in the form in consideration of the distribution of measured noise in a situation where intentional noise is removed.

Distribution of measured noise In the case of, the measurement equation of Equation 2 is modified as follows. In other words Is a positive definite symmetric matrix In this case, Equation 2 may be represented by Equation 14, and may be represented by a simple form of Equation 15 again.

here Distribution and the covariance matrix of the weighted If you satisfy the relationship Since the existing integrity verification technique can be applied. That is, since the integrity verification technique cannot be used as it is in the method represented by Equation 2, the integrity verification technique is used after converting Equation 2 into the form of Equation 15 using a weighted matrix.

The flow rate obtained by applying the least square method to Equation 15 may be expressed as Equation 16.

The runoff calculated by Equation 16 is independent for each satellite. That is, the flow of unrelated correlations of the flows for each satellite according to Equation 16 is transformed into 'correlation flows ( )'to be.

In equation (16) Is, Is an Idempotent matrix projecting from the measurement space into the flowing space as a parity vector. Free correlation at this time Is average 0, variance Has

The relationship between the flow rate obtained by the weighted least square method of Equation 11 and the correlation free correlation by Equation 16 may be expressed as in Equation 17 below. That is, the correlation-free flow is expressed by multiplying the square root of the weighted matrix by the general flow obtained from Equation (11).

Since these correlations are independent for each satellite (that is, they have the same weight), the maximum flow technique or the integrity test technique can be applied.

Probability of false detection in the aerospace sector in general The integrity test technique is designed to be 0.33 × 10 ^-6 or less, and the maximum flow technique is performed by the following process.

As a first step, we apply the weighted least-squares method for m≥6 visible satellites to determine position, time, ) And using this equation (17), Obtain) Next, the normalized correlation run, that is, Is obtained using Equation 12 described above. here _Represents the (j, j) th term of the matrix S _W.

[Equation 12]

In the second step, the calculated normalized correlation flow ( Maximum normalized correlation run ( ) And the satellite j having the value are obtained by using Equation 13 described above.

[Equation 13]

The maximum normalized correlation run value obtained ( ) When it exceeds a pre-determined threshold value is determined to contain an abnormal error in the satellite j calculate the new position and time and to remove an estimate of the satellite j. If the threshold is not exceeded, it is determined to be normal.

Fig. 10 is a flowchart showing the procedure of the GPS navigation solution determination method according to the second embodiment of the present invention.

First, using the 'weighted least square method (WLSQ)' according to the first embodiment of the present invention, the navigation solution (position, time) of the object and the flow by the equation (11) ) Is calculated (S110). Next, the number of visible satellites m used for navigation solution calculation is measured, and it is determined whether the number m of visible satellites is 6 or more (S111). If the number of visible satellites is less than six, the calculated navigation solution is determined as the final navigation solution without using the integrity verification technique according to the present invention (S116).

If the number of visible satellites is six or more, the flow rate for each satellite obtained in step S110 ( Unrelated correlation from ) Is calculated (S112: using Equation 17). ) And Equation 12 to normalize uncorrelated flows for all target ) (S113), and the maximum value (maximum normalized unrelated flow rate value: ) Is calculated (S114). Next, it is determined whether the maximum normalized correlation free flow value exceeds a predetermined threshold (S115).

Maximum normalized uncorrelated flow value ( ) Exceeds the threshold, the measured value of the satellite having the maximum normalized correlation flow value is removed from the calculation target and then goes back to step S110 (S117), if the maximum normalized correlation flow value is less than or equal to the threshold, the navigation at that time is performed. The solution is determined as the final navigation solution (S116). The threshold value mentioned above is mentioned later.

As a result, steps S110 to S115 are repeated until the number of target visible satellites used for the navigation solution calculation is less than six or the normalized correlation free flow value for all the satellites is less than or equal to the threshold, and when the above conditions are satisfied, The navigation solution is determined as the final navigation solution.

In determining the above-mentioned thresholds, Bonferroni or Jashi's inequality is generally used and error detection probability Thresholds according to the number of visible satellites for the case are shown in Table 5.

Thresholds calculated by Bonferroni and self-inequalities Visible satellites Degrees of freedom Bonferroni threshold Jashi threshold 5 One 5.1045 5.1045 6 2 5.4343 5.30773 7 3 5.4617 5.33576 8 4 5.4890 5.35994 9 5 5.5062 5.38118 10 6 5.5247 5.4001 11 7 5.5414 5.41718 12 8 5.5567 5.43272

The threshold determined by Jashi inequality is the variance of the error ( ) Can be applied if it is known exactly, and it is lower than the threshold obtained by Bonferroni method in the table.

FIG. 11 is a diagram showing positional errors obtained by applying the integrity verification technique according to the second embodiment of the present invention to actual measurements.

That is, the weighting matrix of Equation 10 is used, and the weighted least square method (WLSQ) according to the first embodiment of the present invention is applied. At this time, the angle of elimination was set at 0 degrees and the measured values compensated for ionospheric and tropospheric delays. In addition, the error variance ( ) Is assumed to be 8m.

Using the Bonferroni threshold and the Jashi threshold, the performance is almost the same, and the errors in the horizontal plane are 6.3422m and 6.3392m, respectively.

FIG. 12 shows the running water after the execution of the second embodiment of the present invention. As compared with FIG. 9 showing the running water according to the first embodiment, it can be seen that the running water having a size of 100 m or more is removed.

FIG. 13 shows the Jashi threshold and the maximum runoff calculated by Equation 17. FIG. FIG. 13A is a view before removing the abnormal satellite and FIG. 13B is a view after removing the abnormal satellite through the integrity verification technique according to the present invention. As shown, after performing the integrity test method according to the present invention, it can be seen that all the maximum flow values are below the threshold value. When using the Jashi threshold, a total of 33 abnormal measurements (abnormal satellites) were removed. Using the Bonferroni threshold, a total of 31 abnormal measurements were eliminated.

In order to explain the effect of the GPS navigation solution error compensation or navigation solution calculation method according to the present invention, the results compared with the existing error compensation degree is summarized in Table 6.

Experiments were conducted using a NovAtel 3010R receiver to collect 5000 measurements in 1 second increments from 7 pm on March 28, 2001. In addition, the deletion angle was set to 0 degrees, and the weighting matrix and the variance of the error were used as in the above equations. The Jashi threshold was used for the integrity test. (Although the Bonferroni threshold was used, the performance was almost the same and the error in the horizontal plane was 7.5104m.)

The ionospheric delay and tropospheric delay compensation are separately indicated, and after the error compensation in the conventional least square method (LSQ) and the first embodiment (weighted least square method: WLSQ) and the second embodiment (integrity verification method: RAIM) The position and clock error after error compensation are shown.

Position Error Comparison in Navigation Algorithms According to the Conventional and Present Invention division Way Plane Error (2dRMS) East-West North-south direction Altitude Receiver watch Average 1σ Average 1σ Average 1σ Average 1σ Conventional method Least-squares method (no error compensation) 40.51 6.0 7.2 10.2 14.8 50.0 25.0 50.0 10.0 Least-squares method (with error compensation) 33.84 3.9 6.5 9.6 11.7 6.4 23.4 -2.0 7.5 First embodiment Weighted Least Squares Method (No Error Compensation) 10.86 3.6 1.0 3.5 1.6 33.1 2.5 37.4 12.3 Weighted Least Squares Method (with Error Compensation) 7.61 2.3 1.0 2.6 1.2 2.2 2.0 -5.6 12.5 Second embodiment Weighted Least Squares Method + Integrity Test 7.49 2.3 1.0 2.6 1.2 2.1 1.8 -5.7 12.8

As shown in Table 6, the application of the present invention, based on the planar error (2dRMS), it can be seen that the error of 33 to 40m was reduced to 7.49 to 7.71m close to the precision of the DGPS. In other words, by compensating ionospheric and tropospheric delays and using the weighted least-squares method (WLSQ), errors in the horizontal plane can be reduced by about six times, and performance can be further improved by adding the integrity verification technique (RAIM).

14 shows the number of visible satellites and the GDOP during the experiment of the second embodiment of the present invention.

FIG. 15 compares a horizontal plane error when the least square method and the weighted least square method and the integrity verification method according to the present invention are used simultaneously without compensating for ionosphere and tropospheric errors, respectively, and are illustrated in FIGS. 15A and 15B, respectively. . As can be seen in Table 6, the horizontal plane error can be seen to decrease from several tens of meters to within 7 meters.

Figure 16 shows the flow after applying the integrity assay technique according to the present invention. As can be seen from the figure, the abnormally large measurement error is eliminated, and the remaining flow distribution follows the shape of the weighted matrix. In particular, some measurements can identify errors in the form of multipath. A total of 250 abnormal measurements were removed for the Jashi threshold and 232 measurements were removed for the Bonferroni threshold.

In summary, the present invention proposes a navigation algorithm that can analyze the characteristics of error factors and effectively compensate for them in a GPS environment in which intentional noise (SA) has been removed. The method according to the present invention is a form of a weighted least square method in which the elevation angle of the satellite is weighted using the ionotropic delay model and the tropospheric delay model as a function of the elevation angle of the satellite (first embodiment). By applying the maximum flow technique, which is a kind of integrity guarantee technique, to the characteristics of the error (second embodiment), it is possible to improve the accuracy of the GPS navigation solution by eliminating abnormal errors caused by the effects of multipath or low SNR.

Through experiments using the actual measurements, the performance can be improved even when the mask angle is used, but it is confirmed that there are limitations due to the decrease in the number of visible satellites and the increase of GDOP. By applying the weighted least-squares method using the weighting matrix obtained by characterizing the error, the position can be obtained with accuracy within 7m (2dRMS) similar to the performance of DGPS in the horizontal plane without using the erasure angle. In addition, it was confirmed that the performance was further improved by using the integrity test technique (maximum flow technique) according to the second embodiment to remove abnormal measurements caused by the influence of multipath.

In addition, the method of the present invention suppresses the rapid change in position caused by the increase and decrease of the satellites in addition to the improvement of the accuracy and the reliability, and secures more visible satellites than the case of unilaterally removing the satellites using the erase angle. Can provide a solution.

In addition, the method according to the present invention can be easily applied to existing receivers because only the software is processed without changing hardware such as GPS receivers. If the function is added, the performance of the GPS may be further improved.

Claims (12)

In a GPS environment in which intentional noise (SA) is removed, a final navigation solution is obtained by compensating a navigation solution error of an object calculated based on GPS signals from four or more visible satellites (SV). Weighting Matrix using satellite elevations Calculating a first step; And A second step of calculating a final navigation solution by compensating for an error using a weighted least square method based on the calculated weighted matrix; Error compensation and GPS navigation solution calculation method intentional noise removal GPS environment comprising a. The method of claim 1, The weighting matrix calculation in the first step is A constant weight is given to measurements of satellites that are above a predetermined elevation angle, and a model that gives weights proportional to the elevation angle that is smaller than the constant and is smaller than the constant is used for measurement of satellites that are below a predetermined elevation angle, and the predetermined elevation angle measures the measurement result of an individual GPS receiver. Method for calculating error compensation and GPS navigation in deliberate noise cancellation GPS environment, characterized in that determined by analyzing. The method of claim 2, Weighting matrix in the first step Is an equation here, Where Ei is the elevation angle of satellite i, And n is -3 to -1, and α is set to one value within a range of 20 to 40 degrees (Degree). The method according to any one of claims 1 to 3, Compensating the error of the ionospheric delay and tropospheric delay by the predetermined model before the first step, the error compensation and GPS navigation calculation method of the deliberate noise removal GPS environment. In a GPS environment in which intentional noise (SA) has been removed, a method for obtaining a precise GPS navigation solution by compensating a navigation solution error of an object calculated based on GPS signals from six or more visible satellites (SV), Using the weighting matrix and the weighted least-squares method calculated using the elevation angles of each satellite, the residuals are obtained, and there is an overflow value (maximum value) that exceeds the threshold among the normalized uncorrelated flows for each satellite. And a method for calculating an error compensation and a GPS navigation solution in a deliberate noise elimination GPS environment, wherein the measured satellite values are excluded from the navigation solution calculation. The method of claim 5, The method, a first step of calculating a weighting matrix by using elevation angles of respective satellites when a visible satellite of m (≥6) exists; Based on the calculated weighted matrix, the weighted least-squares method is applied to position, time, and flow rate ( Obtaining a second step; By multiplying the square root of the weighted matrix with the runoff obtained in the second step, Obtaining a third step; Normalized correlation correlation for each satellite ( ) And the maximum normalized correlation run of the satellite that maximizes the normalized correlation run ( A fourth step of obtaining; Maximum normalized correlation run above (5) removing the measurement value for the corresponding satellite when the value of h) exceeds a predetermined threshold; And A sixth step of repeating the first to fifth steps until no satellite has a maximum normalized correlation runoff value exceeding a threshold, or m is less than six, and determining the position and time at that time as the final navigation solution Error compensation and GPS navigation solution calculation method intentional noise removal GPS environment comprising a. The method of claim 6, The weighting matrix calculation in the first step is A constant weight is given to measurements of satellites that are above a predetermined elevation angle, and a model that gives weights proportional to the elevation angle that is smaller than the constant and is smaller than the constant is used for measurement of satellites that are below a predetermined elevation angle, and the predetermined elevation angle measures the measurement result of an individual GPS receiver. Method for calculating error compensation and GPS navigation in deliberate noise cancellation GPS environment, characterized in that determined by analyzing. The method of claim 7, wherein Weighting matrix in the first step Is the following equation here, Where Ei is the elevation angle of satellite i, And n is -3 to -1, and α is set to a value within a range of 20 to 40 degrees (Degree). The method of claim 8, Running water in the second step ( ) Is The error compensation and GPS navigation calculation method in the deliberate noise removal GPS environment characterized in that determined by. The method according to any one of claims 7 to 9, The normalized correlation run above ( ) And maximum normalized uncorrelated flow values ( ) Is Where S _w (j, j) means (j, j) th term of the matrix S _w and S _w is the matrix And G _w is , The error compensation and GPS navigation calculation method in the deliberate noise removal GPS environment characterized in that determined by. The method according to claim 6 or 7, The threshold is determined differently according to the number of target satellites (m) and is a value determined by Bonferroni inequalities or Jash inequalities. Solution calculation method. The method according to claim 6 or 7, Compensating the error compensation and GPS navigation solution intentionally noise-free GPS environment further comprising the step of compensating the ionospheric delay and tropospheric delay error by a predetermined model before the first step.