KR102592494B1 - Correct Fix Probability Improvement Method of Carrier-Phase Based CNSS-INS Loosely Coupled Kalman Filter System - Google Patents

Abstract

The present invention relates to a method of improving the Correct Fix probability value in a carrier-based GNSS/INS weakly coupled Kalman filter system. More specifically, in the process of calculating the unknown integer solution of carrier measurements in a GNSS receiver, prediction through INS This is to improve the unknown integer estimation performance by using the navigation solution. In other words, the purpose is to benefit in terms of navigation integrity by improving the Correct Fix probability value, which is the probability that the final unknown solution is correct, by utilizing the relative vector predicted through INS, which is additional prior information.

Description

Correct Fix Probability Improvement Method of Carrier-Phase Based CNSS-INS Loosely Coupled Kalman Filter System}

The present invention relates to a method of improving the Correct Fix probability value in a carrier-based GNSS/INS weakly coupled Kalman filter system. More specifically, in the process of calculating the unknown integer solution of carrier measurements in a GNSS receiver, prediction through INS This is to improve the unknown integer estimation performance by using the navigation solution. In other words, the purpose is to benefit in terms of navigation integrity by improving the Correct Fix probability value, which is the probability that the final unknown solution is correct, by utilizing the relative vector predicted through INS, which is additional prior information.

Recently, enormous investments are being made in the field of utilizing unmanned aerial vehicles for the purpose of maximizing human convenience and economic efficiency, such as drone logistics systems and delivery of emergency relief supplies to remote areas by small startup companies. However, because unmanned aerial vehicles are operated at relatively low altitudes and target environments and missions where various risk factors may occur, navigation stability must be guaranteed at a very high level. In particular, in order for multiple unmanned aerial vehicles to be operated simultaneously, centimeter (cm) level navigation accuracy may be required to prevent collisions between each aircraft, and accordingly, a highly accurate carrier-based navigation system is required.

In a carrier-based navigation system, the integrity threat probability depends on P(CF), which represents the probability that an unknown integer is determined to be a true value. JPALS, which is applied to the precision landing of fighter aircraft on aircraft carriers, collects carrier measurements for a long time to meet integrity requirements and performs a pre-filtering process to ensure the 1-P(CF) value is 10 ^-8 or less. At this time, if the condition is met, the 1-P(CF) value can be conservatively assumed to be 10 ^-8 during the integrity threat probability calculation process and the case where an unknown number is incorrectly determined during the calculation process can be ignored. In the case of unmanned aerial vehicles, there are limitations in performing pre-filtering due to the diversity of missions and limited environmental conditions. If this process is not performed, a problem arises in which the P(CF) requirement cannot be satisfied even if all dual frequency measurements of the dual satellite constellation are used.

KR 10-0980762 B1

The present invention was created to solve this problem. In the process of calculating the unknown integer solution of the carrier measurement value in the GNSS receiver, the navigation solution predicted through INS is used to improve the unknown integer estimation performance. The purpose is to provide a method for improving the Correct Fix probability value of the GNSS/INS weakly coupled Kalman filter system.

In order to achieve this purpose, the method of improving the Correct Fix probability value in the carrier wave-based GNSS/INS weakly coupled Kalman filter system for ensuring navigation integrity according to the present invention is (a) from the IMU sensor to the GNSS/INS weakly coupled Kalman filter. A step in which dual IMU measurements are input; (b) predicting a state vector from the dual IMU measurement values input in step (a); (c) calculating a Correct Fix probability value using the relative vector information included in the state vector predicted in step (b) together with the measured value from the GNSS receiver and inputting it as a measured value to the GNSS/INS weakly coupled Kalman filter; and (d) updating the state vector from the measurement value input in step (c).

Calculating the Correct Fix probability value in step (c) includes (c1) calculating an unknown real number solution using the relative vector information; (c2) converting the covariance matrix of the unknown real solution calculated in step (c1) into a decorrelation state; and (c3) calculating the Correct Fix probability value from the covariance matrix transformed in step (c2).

The unknown real number solution of step c1 is,

It is calculated by .

Step c2 uses Z-transform,

It is.

In step c3,

It is calculated by .

Another aspect of the present invention is a program for improving the Correct Fix probability value in a carrier-based GNSS/INS weakly coupled Kalman filter system for ensuring navigation integrity, which is stored in a non-transitory storage medium and is operated by a processor, (a) IMU sensor Inputting dual IMU measurements from GNSS/INS weakly coupled Kalman filter; (b) predicting a state vector from the dual IMU measurement values input in step (a); (c) calculating a Correct Fix probability value using the relative vector information included in the state vector predicted in step (b) together with the measured value from the GNSS receiver and inputting it as a measured value to the GNSS/INS weakly coupled Kalman filter; and (d) updating the state vector from the measurement value input in step (c).

Calculating the Correct Fix probability value in step (c) includes (c1) calculating an unknown real number solution using the relative vector information; (c2) converting the covariance matrix of the unknown real solution calculated in step (c1) into a decorrelation state; and (c3) calculating the Correct Fix probability value from the covariance matrix transformed in step (c2).

The unknown real number solution of step c1 is,

It is calculated by .

Step c2 uses Z-transform,

It is.

In step c3,

It is calculated by .

Another aspect of the present invention is a system for improving the Correct Fix probability value using a carrier-based GNSS/INS weakly coupled Kalman filter by improving the Correct Fix probability value, comprising: at least one processor; and at least one memory storing computer-executable instructions, wherein the computer-executable instructions stored in the at least one memory are configured to: (a) transmit, by the at least one processor, GNSS/INS approx. Inputting dual IMU measurements to a combined Kalman filter; (b) predicting a state vector from the dual IMU measurement values input in step (a); (c) calculating a Correct Fix probability value using the relative vector information included in the state vector predicted in step (b) together with the measured value from the GNSS receiver and inputting it as a measured value to the GNSS/INS weakly coupled Kalman filter; and (d) updating the state vector from the measurement value input in step (c).

According to the present invention, it is possible to benefit from an integrity guarantee perspective by providing a method for improving the Correct Fix probability value of a carrier-based GNSS/INS weakly coupled Kalman filter system to improve unknown number estimation performance by utilizing the navigation solution predicted through INS. There is an effect.

Figure 1 is a diagram schematically showing the concept and configuration of a carrier-based GNSS/INS weakly coupled Kalman filter system according to the present invention.
Figure 2 is a flowchart showing a method for improving the Correct Fix probability value of the carrier-based GNSS/INS weakly coupled Kalman filter system according to the present invention.
Figure 3 is a flowchart showing the process of calculating the Correct Fix probability value in the method of Figure 2.
Figure 4 is a graph showing simulation results through improving the Correct Fix probability value of the carrier-based GNSS/INS weakly coupled Kalman filter system according to the present invention.

Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the attached drawings. Prior to this, the terms or words used in this specification and claims should not be construed as limited to their usual or dictionary meanings, and the inventor should appropriately use the concept of terms to explain his or her invention in the best way. It must be interpreted as meaning and concept consistent with the technical idea of the present invention based on the principle of definability. Accordingly, the embodiments described in this specification and the configurations shown in the drawings are only one of the most preferred embodiments of the present invention and do not represent the entire technical idea of the present invention, so at the time of filing this application, various alternatives are available to replace them. It should be understood that equivalents and variations may exist.

Figure 1 is a diagram schematically showing a carrier-based GNSS/INS weakly coupled Kalman filter system according to the present invention.

Referring to FIG. 1, the carrier-based GNSS/INS weakly coupled Kalman filter system 10 of the present invention includes an IMU sensor 100, a CNSS receiver 200, and an IMU filter 310 that filters multiple IMU measurements input from the IMU sensor. ) and the GNSS filter 320, which filters the GNSS measurements input from the GNSS receiver 200, is composed of a carrier wave-based weakly coupled GNSS/INS weakly coupled Kalman filter 300.

In general, the Kalman filter predicts the navigation solution using an IMU (Inertial Measurement Unit) sensor and updates the navigation solution through measurements from a GNSS (Global Navigation Satellite System) sensor. The prediction and update process is performed through the following [Equation 1].

[Equation 1]

Navigation prediction:

Navigation updates:

here, is the predicted state vector or navigation solution (state), is the updated state vector, is the state transition matrix, is the process noise vector, is Kalmangain, is a GNSS pseudorange-based measurement, means the observation matrix.

However, in the case of the carrier-based GNSS/INS loosely coupled Kalman filter, the state vector includes the relative vector, relative velocity, and bias value of the inertial sensor. Therefore, the relative position navigation solution calculated from the GNSS receiver is used as a filter input value in the navigation solution update stage.

And, unlike existing pseudorange measurements, carrier measurements must additionally estimate an unknown number (Integer Ambiguity). In general, carrier-based navigation systems utilize double differential carriers and pseudorange measurements to calculate navigation solutions for unknown numbers and relative vectors with ground stations through the linear equation shown in [Equation 2] below.

[Equation 2]

Measurement equation for carrier-based navigation system:

Here, y is a GNSS measurement vector containing double-difference pseudorange and carrier measurements. And a and b respectively mean an unknown number and the relative vector between the two antennas, is the measurement error vector. From [Equation 2] above, the least squares method-based relative vector and unknown real number solution are calculated through the following [Equation 3].

[Equation 3]

Relative vector and unknown real number solution:

Here, the unknown real number solution is used as an input to the LAMBDA (Least-squares AMBuity Decorrelation Adjustment) technique and is finally determined as an integer. At this time, P(CF), the probability that the unknown number is correctly determined, is calculated within the LAMBDA technique based on the covariance matrix of the unknown real solution.

Therefore, the present invention improves the Correct Fix probability value by using relative vector prior information in the availability of the carrier-based GNSS/INS weakly coupled Kalman filter system (10).

Figure 2 is a flowchart showing a method for improving the Correct Fix probability value of the carrier-based GNSS/INS weakly coupled Kalman filter system according to the present invention.

Referring to Figure 2, first, dual IMU measurement values are input from the IMU sensor to the GNSS/INS weakly coupled Kalman filter (S100). Here, since the GNSS/INS weakly coupled Kalman filter system is a relative navigation system, the input values to the GNSS/INS weakly coupled Kalman filter are the input values from the ground station and the dual IMU sensors of the unmanned vehicle, respectively.

Afterwards, from the dual IMU measurement values input by the GNSS/INS weakly coupled Kalman filter, the GNSS/INS weakly coupled Kalman filter updates the system and predicts the navigation solution state vector using Equation 3 below (S200) .

[Equation 3]

Navigation prediction:

Estimating the covariance matrix of the navigation solution:

here, means the covariance matrix of the predicted state vector, is the covariance matrix of the state vector updated in the previous step, is the processor noise vector, It means the covariance matrix of .

And in step S200, the relative vector information included in the predicted state vector is calculated along with the value measured from the GNSS receiver, and a Correct Fix probability value is calculated and input as a measured value to the GNSS/INS weakly coupled Kalman filter (S300). Hereinafter, the method of deriving and performing the formula will be described in detail with reference to FIG. 3. And the state vector is updated from the measured value input in step S300 (S400).

Figure 3 is a flowchart showing the process of calculating the Correct Fix probability value in Figure 2.

Referring to FIG. 3, an unknown real number solution is calculated using relative vector information (S310).

Previously, the real solution of an unknown number was calculated by applying the least squares method using the linear equation below [Equation 4].

[Equation 4]

Measurements linear:

In the above linear equation refers to the measurement vector and includes double-difference pseudorange and carrier measurements. refers to the observation matrix, which includes the LOS (Line Of Sight) direction unit vector of each satellite. The matrix is differentiated with respect to the reference satellite. A diagonal matrix where the frequencies of the matrix and GNSS measurements are the diagonal values. It includes. Estimated state vector is the relative vector and undetermined number It includes. means the noise of the measurement vector, and the covariance matrix of the corresponding noise is defined as [Equation 5] below, and is the state vector calculated through the least squares method. The covariance matrix of is calculated as follows.

[Equation 5]

Covariance matrix:

where the calculated covariance matrix is the covariance matrix of the unknown real solution It includes, and the corresponding matrix is derived as [Equation 6] below.

[Equation 6]

Covariance matrix:

However, in the present invention, when additional relative vector prior information is used, the linear equation is transformed as shown in [Equation 7] below.

[Equation 7]

Measurements linear:

Covariance matrix:

In the above equation means the covariance matrix of the relative vector prior information. In the same way, the covariance matrix of the unknown real solution is is derived as follows [Equation 8].

[Equation 8]

Covariance matrix:

At this time, each covariance matrix and is a positive definite matrix, and the difference between the two matrices is satisfies the properties of a positive semidefinite matrix.

Therefore, because the diagonal component of the semidefinite matrix is always a non-negative real number, when additional relative vectors are used, the diagonal component of the covariance matrix of the undefined real number changes in the direction of decreasing.

Next, the covariance matrix of the unknown real solution calculated in step S310 is converted to a decorrelation state using Z-transformation (S320).

The covariance matrix of the real solution of unknown numbers previously calculated based on the least squares method has a correlation coefficient between each unknown number. The maximum value of P(CF), the Correct Fix probability value, is calculated when the covariance matrix is in a decorrelation state where all correlation coefficients are 0. Therefore, Z-transformation is applied to convert the covariance matrix of the unknown real solution into a decorrelation state, and is mathematically expressed as [Equation 9] below.

[Equation 9]

Z transformation:

Here, the Z-transform used is The matrix is calculated numerically from the covariance matrix before transformation. The matrix is then an unknown number Since it also applies to the process of converting to a domain, there is a constraint that the component values of all matrices must be integers and the absolute value of the determinant must be 1. and , by applying the same process to each of the two covariance matrices, , A matrix is calculated, , Each is converted to . The diagonal component of is If the transformation matrix tkeyed to the Z-transform is different than the diagonal component of The diagonal component of is always The property of being smaller than the diagonal component of is not satisfied and an exception may occur. Therefore, in order to eliminate exceptional cases in the present invention, also Calculated from Using a matrix, it was converted as shown in [Equation 10] below.

[Equation 10]

As a result, and The difference between the two matrices is Likewise, it satisfies the properties of a positive semidefinite matrix. Therefore, even after Z-transformation, the method of the present invention is applied without exception. The diagonal components of the matrix are It appears lower than the diagonal component of .

Afterwards, the Correct Fix probability value is calculated from the covariance matrix transformed in step S320 (S330). Here, it is impossible to estimate an accurate P(CF) value in the LAMBDA technique, which determines unknown numbers through the ILS (Integer Least Squares) technique. However, it has been proven that the P(CF) value when applying the LAMBDA technique is always greater than the P(CF) value when applying the IB (Integer Booststrapping) technique. Therefore, in general, the P(CF) value calculated when applying the IB technique is conservatively applied as the P(CF) value when applying the LAMBDA technique. When applying the IB technique, P(CF) can be calculated from the following [Equation 11] by applying Cholesky Decomposition to the covariance matrix of the Z-transformed unknown real number solution.

[Equation 11]

Szolesky decomposition:

P(CF) calculation formula:

Earlier in step S320 It was mentioned that is a semidefinite matrix. thereafter All diagonal elements of the matrix are It is a smaller value than the corresponding diagonal component of the execution, and is summarized in the following [Equation 12].

[Equation 12]

The P(CF) value is Since the smaller the value of the diagonal component of the matrix, the larger it becomes, when the present invention is applied, the value of P(CF) is always improved compared to the existing one. Also, by the same logic, as the noise of the additional relative vector prior information becomes smaller, P(CF) is improved more.

Figure 4 is a graph showing simulation results through improving the Correct Fix probability value of the carrier-based GNSS/INS weakly coupled Kalman filter system according to the present invention.

Referring to Figure 4, it shows the aspect of P(CF) according to the noise level of the additional relative vector in a situation where a carrier-based GNSS/INS weakly coupled Kalman filter is used. It can be seen that P(CF) increases when the present invention is applied to all 86,400 time points, and the lower the noise level, the greater the improvement, confirming that the features of the present invention are effective.

As described above, although the present invention has been described with limited examples and drawings, the present invention is not limited thereto, and the technical idea of the present invention and the following will be understood by those skilled in the art to which the present invention pertains. Of course, various modifications and variations are possible within the scope of equivalence of the patent claims to be described.

10: Carrier-based GNSS/INS weakly coupled Kalman filter system
100: IMU sensor
200: GNSS receiver
300: GNSS/INS weakly coupled Kalman filter
310: IMU filter
320: GNSS filter

Claims (11)

As a method of improving the Correct Fix probability value in a carrier-based GNSS/INS weakly coupled Kalman filter system to ensure navigation integrity,
(a) inputting dual IMU measurement values from the IMU sensor to the GNSS/INS weakly coupled Kalman filter;
(b) predicting a state vector from the dual IMU measurement values input in step (a);
(c) calculating a Correct Fix probability value using the relative vector information included in the state vector predicted in step (b) together with the measured value from the GNSS receiver and inputting it as a measured value to the GNSS/INS weakly coupled Kalman filter; and
(d) updating the state vector from the measurement value input in step (c).
Method for improving Correct Fix probability value of carrier-based GNSS/INS weakly coupled Kalman filter system including. In claim 1,
The calculation of the Correct Fix probability value in step (c) is,
(c1) calculating an unknown real number solution using the relative vector information;
(c2) converting the covariance matrix of the unknown real solution calculated in step (c1) into a decorrelation state; and
(c3) Calculating the Correct Fix probability value from the covariance matrix converted in step (c2)
A method for improving the Correct Fix probability value of a carrier-based GNSS/INS weakly coupled Kalman filter system, comprising: In claim 2,
The unknown real number solution of step c1 is,

What is calculated by
Method for improving the Correct Fix probability value of the carrier-based GNSS/INS weakly coupled Kalman filter system characterized by . In claim 2,
Step c2 uses Z-transform,
thing
Method for improving the Correct Fix probability value of the carrier-based GNSS/INS weakly coupled Kalman filter system characterized by .
In claim 2,
In step c3,

What is calculated by
Method for improving the Correct Fix probability value of the carrier-based GNSS/INS weakly coupled Kalman filter system characterized by . A program to improve the Correct Fix probability value in the carrier-based GNSS/INS weakly coupled Kalman filter system to ensure navigation integrity,
stored on a non-transitory storage medium, by the processor,
(a) inputting dual IMU measurement values from the IMU sensor to the GNSS/INS weakly coupled Kalman filter;
(b) predicting a state vector from the dual IMU measurement values input in step (a);
(c) calculating a Correct Fix probability value using the relative vector information included in the state vector predicted in step (b) together with the measured value from the GNSS receiver and inputting it as a measured value to the GNSS/INS weakly coupled Kalman filter; and
(d) updating the state vector from the measurement value input in step (c).
A computer program for improving the Correct Fix probability value in a carrier-based GNSS/INS weakly coupled Kalman filter system including. In claim 6,
The calculation of the Correct Fix probability value in step (c) is,
(c1) calculating an unknown real number solution using the relative vector information;
(c2) converting the covariance matrix of the unknown real solution calculated in step (c1) into a decorrelation state; and
(c3) Calculating the Correct Fix probability value from the covariance matrix converted in step (c2)
A computer program for improving the Correct Fix probability value of a carrier-based GNSS/INS weakly coupled Kalman filter system comprising a. In claim 6,
The unknown real number solution of step c1 is,

What is calculated by
A computer program to improve the Correct Fix probability value of a carrier-based GNSS/INS weakly coupled Kalman filter system characterized by . In claim 6,
Step c2 uses Z-transform,
thing
A computer program to improve the Correct Fix probability value of a carrier-based GNSS/INS weakly coupled Kalman filter system characterized by . In claim 6,
In step c3,

What is calculated by
A computer program to improve the Correct Fix probability value of a carrier-based GNSS/INS weakly coupled Kalman filter system characterized by . A system for improving the Correct Fix probability value using a carrier-based GNSS/INS weakly coupled Kalman filter,
at least one processor; and
At least one memory storing computer-executable instructions,
The computer-executable instructions stored in the at least one memory are executed by the at least one processor,
(a) inputting dual IMU measurement values from the IMU sensor to the GNSS/INS weakly coupled Kalman filter;
(b) predicting a state vector from the dual IMU measurement values input in step (a);
(c) calculating a Correct Fix probability value using the relative vector information included in the state vector predicted in step (b) together with the measured value from the GNSS receiver and inputting it as a measured value to the GNSS/INS weakly coupled Kalman filter; and
(d) updating the state vector from the measurement value input in step (c).
A carrier-based GNSS/INS weakly coupled Kalman filter system to improve the Correct Fix probability value.