An error analysis method to suppress the influence of track timestamp

Abstract

The present invention discloses a method for track accuracy analysis based on the least squares curve fitting technology using orthogonal functions to suppress the influence of radar track timestamp errors, and belongs to the field of radar technology. The method utilizes the positioning information obtained by the GNSS module carried on the aircraft, and performs data quality control, coordinate conversion, curve fitting, extreme value solution to obtain extreme points and other data algorithm processing on the GNSS data and the track data measured by the radar. The time difference is solved by the obtained extreme points, and the time difference is introduced to obtain a stable accuracy value. The present invention can greatly suppress the accuracy fluctuations caused by the timestamp error, and the obtained accuracy is more stable. In addition, the radar accuracy can be evaluated without stopping the machine.

Description

Technical Field

[0001] The present invention belongs to the field of radar technology, and in particular relates to an error analysis method. Background Art

[0002] The significant role played by radar during World War II led to significant developments in radar technology. While the basic principle of radar is relatively simple, its implementation in various scenarios is challenging. It operates by radiating electromagnetic energy and detecting the echo reflected by the target. Information about the target is obtained by analyzing the characteristics of the echo signal and the signals from the positioning system. Faced with increasing user requirements for operational effectiveness and the increasing number of major combat operations, users are placing increasing emphasis on radar accuracy. The mature development of differential GNSS technology, particularly my country's BeiDou global positioning technology, has enabled GNSS systems to provide ultra-high-precision positioning and timing services. Most aircraft now carry GNSS positioning modules. Currently, operational verification of accuracy metrics relies primarily on collecting the target's global positioning information as the true value. The target information collected by radar is then compared with this true value to assess measurement accuracy. However, these two pieces of information are collected from two independent systems. Even with separate timing systems, differences in information processing methods, sampling rates, and hardware are unavoidable. This time difference inevitably leads to computational errors when matching the two pieces of information, and in severe cases, can even lead to the failure of accuracy algorithms. The present invention proposes a method for suppressing the influence of time difference on precision analysis based on extreme value seeking, which simplifies the difficulty of precision analysis and improves the accuracy of precision calculation. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for suppressing the influence of radar track timestamp error on track accuracy analysis based on the curve fitting technology of least squares method using orthogonal function. This method effectively suppresses the uncertainty of the accuracy analysis result caused by the randomness of the timestamp difference between the true track data and the measured data, thereby making the accuracy analysis result more stable and scientific.

[0004] The technical problem to be solved by the present invention is to overcome the influence of the inevitable time difference between the time stamps of the true value data and the time stamps of the measured data on the accuracy analysis, and provide a track accuracy analysis method based on the least squares curve fitting technology using orthogonal functions. This method can calculate stable and effective radar accuracy in a simple and fast manner. The technical solution of the present invention is:

[0005] This method does not involve any hardware equipment and only requires the track data recorded by the radar of the measured object and the geodetic coordinate data recorded by the aircraft equipped with GNSS. The technical solution of the present invention can be divided into numerical quality control, coordinate transformation, curve fitting, solving the maximum value and time difference, and accuracy solution.

[0006] An error analysis method to suppress the influence of track timestamps, the steps are as follows:

[0007] Step 1: Obtain GNSS data of the object under test and corresponding radar measurement track data.

[0008] Step 2: Convert the GNSS data into coordinates. The conversion process goes through three stages: from the earth coordinate system to the earth rectangular coordinate system, from the earth rectangular coordinate system to the station center rectangular coordinate system, and from the station center rectangular coordinate system to the station center polar coordinate system. The specific formula is as follows:

[0009] From geodetic coordinates (latitude B, longitude L and altitude H) to geodetic rectangular coordinates (X, Y, Z), then to the station center rectangular coordinates (x, y, z), and finally to the station center polar coordinates (R, A, E). The geodetic rectangular coordinates of the station center are ( ), the target's geodetic rectangular coordinates are ( The formula involved is as follows.

[0010] Formula (1)

[0011] in, is the radius of curvature of the zonal curve; , a is the major semi-axis of the ellipsoid, b is the minor semi-axis of the ellipsoid,

[0012] Formula (2)

[0013] Formula (3).

[0014] Step 3: Extract any pair of data elements from time distance and time elevation, and use median filtering to preprocess the collected GNSS data and track data respectively.

[0015] Step 4: Use the least squares curve fitting algorithm based on orthogonal function to fit the two types of data. The specific algorithm is as follows:

[0016] According to the given point set ,in is an integer greater than 0, construct the following orthogonal polynomial ,in is an integer greater than 0. The polynomial is expressed as follows using a recursive formula:

[0017] Formula (4)

[0018] In the formula

[0019] Formula (5)

[0020] It can be seen from the above The highest term coefficient is 1 The constructed polynomial can be proved by induction. About the trace For a given set of data , according to formula 4 and formula 5, we can gradually solve , and calculate the corresponding coefficients according to Formula 6

[0021] Formula (6)

[0022] and gradually By gradually accumulating, we finally get the required fitting curve equation (Formula 7)

[0023] Formula (7)

[0024] According to the demand curve fitting of this application, select the third-order fitting.

[0025] Step 5: Solve the extreme value of the curve obtained in the previous step. The steps for solving the extreme value are as follows:

[0026] (1) Find all stable points and points where the derivative does not exist on the curve function, and calculate the function values ​​corresponding to these points;

[0027] (2) Calculate the function values ​​corresponding to the two ends of the range,

[0028] (3) Finally, find the maximum or minimum value of these function values.

[0029] Step 6: Subtract the time corresponding to the obtained extreme feature point to obtain the timestamp error of the two data.

[0030] Step 7: Use the time difference calibrated data to calculate the accuracy.

[0031] The beneficial effects of the present invention are:

[0032] Compared with the prior art, the present invention has the following beneficial effects:

[0033] The present invention utilizes positioning information acquired by a GNSS module carried on an aircraft to more simply and accurately evaluate the accuracy of the equipment. It can also evaluate the accuracy of the equipment without shutting down the equipment, effectively reducing losses caused by downtime. It overcomes the impact of the inevitable time difference between the timestamps of the true value data and the timestamps of the measurement data on the accuracy analysis, and provides a method for suppressing the impact of radar track timestamp errors on track accuracy analysis based on a curve fitting technique using the least squares method using an orthogonal function. This method effectively suppresses the uncertainty of the accuracy analysis results caused by the randomness of the timestamp difference between the true value track data and the measurement data, thereby making the accuracy analysis results more stable and scientific. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 Method flow chart;

[0035] Figure 2 Track distance-time diagram with time difference (vertical axis is distance, horizontal axis is time);

[0036] Figure 3 Track distance-time diagram after suppressing time difference (vertical axis is distance, horizontal axis is time);

[0037] Figure 4 Track distance difference diagram with time difference (vertical axis is distance, horizontal axis is time);

[0038] Figure 5 Track distance difference diagram after suppressing time difference (vertical axis is distance, horizontal axis is time). DETAILED DESCRIPTION

[0039] The technical solutions provided by the present invention will be described in detail below with reference to specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention.

[0040] Attachment Figure 1 A flowchart of the method is provided. Based on this method, a set of application examples for radar track accuracy analysis was developed. This example was developed using the C++ language and the Qt integrated development environment. It has cross-platform capabilities and can run on operating systems such as Windows and Linux. The system was developed by adding this method to the conventional accuracy processing method to preprocess the data to be processed, and then passing it into the accuracy processing method to obtain stable analysis results. The specific steps of this method are as follows:

[0041] Step 1: Develop a data parsing program module to parse the imported data and obtain the GNSS data of the measured object and the corresponding radar measurement track data.

[0042] Step 2: Use the coordinate conversion formula to convert the GNSS data into the station center polar coordinate data.

[0043] Coordinate conversion goes through the following three stages: geodetic coordinate system to geodetic rectangular coordinate system, geodetic rectangular coordinate system to station center rectangular coordinate system, and station center rectangular coordinate system to station center polar coordinate system. The specific formula is as follows:

[0044] From geodetic coordinates (latitude B, longitude L and altitude H) to geodetic rectangular coordinates (X, Y, Z), then to the station center rectangular coordinates (x, y, z), and finally to the station center polar coordinates (R, A, E). The geodetic rectangular coordinates of the station center are ( ), the target's geodetic rectangular coordinates are ( The formula involved is as follows.

[0045] Formula (1)

[0046] in, is the radius of curvature of the zonal curve; , a is the major semi-axis of the ellipsoid, b is the minor semi-axis of the ellipsoid,

[0047] Formula (2)

[0048] Formula (3).

[0049] Step 3: Extract data from the parsed data based on the data pairs (distance time, elevation time, etc.) selected through the interface interaction; use median filtering on the extracted data (the window size can be selected, generally a 7-point window is selected) to eliminate the influence of singular values ​​on subsequent curve fitting.

[0050] Step 4: Use the least squares curve fitting algorithm based on orthogonal function to perform curve fitting on the two types of data respectively.

[0051] The specific algorithm is as follows:

[0052] According to the given point set ,in is an integer greater than 0, construct the following orthogonal polynomial ,in is an integer greater than 0. The polynomial is expressed as follows using a recursive formula:

[0053] Formula (4)

[0054] In the formula

[0055] Formula (5)

[0056] It can be seen from the above The highest term coefficient is 1 The constructed polynomial can be proved by induction. About the trace For a given set of data , according to formula 4 and formula 5, we can gradually solve , and calculate the corresponding coefficients according to Formula 6

[0057] Formula (6)

[0058] and gradually By gradually accumulating, we finally get the required fitting curve equation (Formula 7)

[0059] Formula (7)

[0060] According to the demand curve fitting of this application, select the third-order fitting.

[0061] Step 5: Solve for the extreme value. Solve for the extreme value of the curve obtained in the previous step, select the characteristic inflection point value, and solve the time difference.

[0062] The steps for finding the extreme value are as follows:

[0063] (1) Find all stable points and points where the derivative does not exist on the curve function, and calculate the function values ​​corresponding to these points;

[0064] (2) Calculate the function values ​​corresponding to the two ends of the range,

[0065] (3) Finally, find the maximum or minimum value of these function values.

[0066] Step 6: Correct the time of the selected data based on the time difference.

[0067] The time difference between the two data points is obtained by taking the time difference corresponding to the extreme feature points.

[0068] Step 7: Use the time difference calibrated data to calculate the accuracy.

[0069] The processed data is passed to the accuracy solution module to obtain the accuracy results and the corresponding analysis curves (see the attached Figure 2 To the attached Figure 5 ).

[0070] Attachment Figure 2 and attached Figure 3 The lowest point of the curve in is the desired characteristic point of the present invention.

[0071] The above description is only the best specific implementation method of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or replacements that can be easily thought of by any technician familiar with this technical field within the technical scope disclosed by the present invention should be covered by the scope of protection of the present invention.

[0072] The contents not described in detail in the specification of the present invention belong to the common knowledge of professionals in this field.

Claims

1. An error analysis method for suppressing the influence of track timestamps, characterized in that: The steps of this method are as follows: Step 1: Obtain GNSS data of the object under test and corresponding radar measurement track data; Step 2: Use the coordinate conversion formula to convert the GNSS data into the station center polar coordinate data; Step 3: Extract data from the parsed data based on the data pairs selected through the interface interaction; use median filtering on the extracted data to eliminate the influence of singular values ​​on subsequent curve fitting; Step 4: Use curve fitting algorithm to fit the two types of data respectively; Step 5: Solve for the extreme value. Solve for the extreme value of the curve obtained in the previous step, select the characteristic inflection point value, and solve the time difference. Step 6: Correct the time of the selected data based on the time difference; The time difference between the two data points is calculated based on the time difference between the extreme feature points. Step 7: Use the time difference calibrated data to calculate the accuracy; The processed data is passed into the accuracy solution module to obtain the accuracy results and corresponding analysis curves.

2. The method according to claim 1, characterized in that In step 2, the coordinate transformation goes through the following three stages: geodetic coordinate system to geodetic rectangular coordinate system, geodetic rectangular coordinate system to station-center rectangular coordinate system, and station-center rectangular coordinate system to station-center polar coordinate system. The specific formula is as follows: From geodetic coordinates to geodetic rectangular coordinates (X, Y, Z), then to the station center rectangular coordinates (x, y, z), and finally to the station center polar coordinates (R, A, E); the geodetic rectangular coordinates of the station center are ( ), the target's geodetic rectangular coordinates are ( ); the formula involved is as follows: Formula (1) in, is the radius of curvature of the zonal curve; , a is the major semi-axis of the ellipsoid, b is the minor semi-axis of the ellipsoid, in geodetic coordinates, latitude B, longitude L and altitude H; Formula (2) Formula (3).

3. The method according to claim 1, characterized in that The data pairs in step 3 include range time and elevation time.

4. The method according to claim 1, wherein The median filter processing window size in step 3 can be selected, and a 7-point window is selected.

5. The method according to claim 1, wherein In step 4, the curve fitting algorithm is a least squares curve fitting algorithm based on an orthogonal function.

6. The method according to claim 1, wherein In step 4, the curve fitting algorithm is as follows: According to the given point set , ,in is an integer greater than 0, construct the following orthogonal polynomial ,in is an integer greater than 0; the polynomial is expressed by the recursive formula as follows: Formula (4) In the formula Formula (5) It can be seen from the above The highest term coefficient is 1 The constructed polynomial can be proved by induction. For a point set , , orthogonal polynomials; for a given set of data , , according to formula (4) and formula (5), we can gradually solve , and calculate the corresponding coefficients according to formula (6) （6） and gradually By gradually accumulating, we finally get the required fitting curve equation (Formula 7) Official (7).

7. The method according to claim 1, characterized in that The steps for solving the extreme value in step 5 are as follows: (1) Find all stable points and points where the derivative does not exist on the curve function, and calculate the function values ​​corresponding to these points; (2) Calculate the function values ​​corresponding to the two ends of the range, (3) Finally, find the maximum or minimum value of these function values.

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