A method for analyzing and evaluating radar positioning errors

Abstract

A method for analyzing and evaluating radar positioning errors can be used to verify whether the radar's positioning error meets the requirements of ICAO standards through relevant analysis and evaluation results. The method includes the following steps: (1) calculating the positioning error of each track point; (2) estimating the statistical mean square error of the positioning error and its confidence interval; (3) fitting the empirical distribution of the positioning error sample; and (4) verifying the tail probability of the positioning error distribution.

Description

Technical Field

[0001] This invention relates to the technical field of civil aviation data processing, and in particular to a method for analyzing and evaluating radar positioning errors, which uses the time, longitude, and latitude information of the radar under test for target positioning to calculate and evaluate the positioning accuracy of the radar. Background Technology

[0002] The fundamental purpose of air traffic control is to ensure the safe, efficient, and planned flight of aircraft within airspace. Controllers need to monitor the flight dynamics of aircraft within the controlled airspace in real time. Radar surveillance is the primary method for implementing air traffic surveillance, and the accuracy of radar surveillance directly determines the safety of the system. Calculating radar system accuracy is extremely complex. To continuously evaluate the accuracy of the radar system, a sophisticated algorithm and system are needed to assess the accuracy from multiple perspectives and analyze the evaluation results to verify whether the radar system can meet the needs of air traffic control.

[0003] In November 2006, ICAO (International Civil Aviation Organization) established the Required Surveillance Performance (RSP) working group to study the RSP concept. RSP can help decision-makers verify whether newly built or upgraded surveillance systems can best meet the needs of practical applications. Radar surveillance accuracy is an important component of the RSP metric.

[0004] Under current operating conditions, several methods exist for evaluating the accuracy of radar systems, including calibration flights and simulation tests using radar simulators. However, each method has its drawbacks. Calibration flights require specialized calibration aircraft and utilize high-precision RTK technology to assess the accuracy of the radar surveillance system. This is expensive and complex, and can only be performed once when the radar is newly built, with subsequent assessments conducted annually. Using radar simulators requires purchasing expensive simulator equipment and employing specialized personnel for complex operations. Assessing the accuracy of the radar surveillance system using simulated data also suffers from high cost and complexity, limiting assessments to periodic evaluations. Neither of the existing methods is conducive to the continuous monitoring and evaluation of radar system accuracy. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, the technical problem to be solved by the present invention is to provide a method for analyzing and evaluating radar positioning errors. Through relevant analysis and evaluation results, it can be verified whether the positioning error of the radar meets the requirements of the ICAO standard.

[0006] The technical solution of this invention is: a method for analyzing and evaluating radar positioning errors, which includes the following steps: (1) Calculate the positioning error of each track point by track; (2) Estimate the statistical mean square error of the positioning error and its confidence interval; (3) Fit the empirical distribution to the positioning error samples; (4) Verify the tail probability of the positioning error distribution.

[0007] This invention estimates the positioning error of radar track points based on radar track information and analyzes the root mean square error and error distribution, thereby verifying the tail probability and finally completing the analysis and evaluation of radar error. Therefore, through the relevant analysis and evaluation results, it can be verified whether the positioning error of the radar meets the requirements of ICAO standards. Attached Figure Description

[0008] Figure 1 The diagram shown is a schematic diagram of step (1) of the present invention, which is the estimation of the track point positioning error.

[0009] Figure 2 The diagram shown is a schematic diagram of the statistical mean square error and its confidence interval for estimating the positioning error in step (2) of the present invention.

[0010] Figure 3 The diagram shown is a schematic diagram of fitting the empirical distribution of the positioning error sample in step (3) of the present invention.

[0011] Figure 4 The diagram shown is a schematic diagram of step (4) of the present invention to verify the tail probability of the positioning error distribution.

[0012] Figure 5 The flowchart shown is for step (1) of the present invention.

[0013] Figure 6 The flowchart shown is for step (2) of the present invention.

[0014] Figure 7 The flowchart shown is for step (3) of the present invention.

[0015] Figure 8 The flowchart shown is for step (3.3) of the present invention.

[0016] Figure 9 The flowchart shown is for step (3.5) of the present invention.

[0017] Figure 10 The flowchart shown is for step (4) of the present invention.

[0018] Figure 11 The flowchart shown is a process for steps (4.1) and (4.2) of the present invention.

[0019] Figure 12 The diagram shown is a flowchart of the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0021] To make the description of this disclosure more detailed and complete, illustrative descriptions of embodiments and specific examples of the present invention are provided below; however, these are not the only forms of implementing or utilizing the specific examples of the present invention. The embodiments cover features of multiple specific examples and methods and steps for constructing and operating these specific examples, and their order. However, other specific examples may also be used to achieve the same or equivalent functions and order of steps.

[0022] First, the symbols and meanings of the parameters used in the calculation are given below. Used for estimation The track point vector at the theoretical position of the point; The information used in the calculation for each message includes time, longitude, and latitude; and : Quadratic and cubic polynomials used for latitude estimation; and : Quadratic and cubic polynomial determination coefficients used for latitude estimation; : Polynomial for latitude estimation; : Latitude estimation results of the point; and : Quadratic and cubic polynomials used for longitude estimation; and : Quadratic and cubic polynomial determination coefficients used for longitude estimation; : Polynomial for latitude estimation; : Latitude estimation results of the point; : Point deviation value; : Track point error sequence of the target trajectory; Number of samples; Sample size; : The first step of the track point error sequence The sample sequence of the second sampling result. ; : No. The mean square error of the sample sequence of the sampling results; Mean squared error sequence The mean; : Standard deviation of the mean square error sequence; : The empirical distribution fitted by the distribution model; The number of parameters for fitting the target distribution; : The residual sequence that fits the target distribution. ; The discriminant value for fitting the target distribution; and Tail bias provides a lower and upper bound for the probability; and : and The corresponding lower and upper bound tail deviations.

[0023] like Figure 12 As shown, this method for analyzing and evaluating radar positioning errors includes the following steps: (1) Calculate the positioning error of each track point by track; (2) Estimate the statistical mean square error of the positioning error and its confidence interval; (3) Fit the empirical distribution to the positioning error samples; (4) Verify the tail probability of the positioning error distribution.

[0024] This invention estimates the positioning error of radar track points based on radar track information and analyzes the root mean square error and error distribution, thereby verifying the tail probability and finally completing the analysis and evaluation of radar error. Therefore, through the relevant analysis and evaluation results, it can be verified whether the positioning error of the radar meets the requirements of ICAO standards.

[0025] Preferably, such as Figure 5 As shown, step (1) includes the following sub-steps: (1.1) A track is uniquely identified by its track number, 24-bit address code, and secondary transponder code, and the number of track points is calculated as follows: ; (1.2) Using a traversal approach, from to Take respectively ; (1.3) Perform latitude estimation, in Winning and Fit quadratic and cubic polynomial models respectively. and ; (1.4) Obtain respectively and The determination coefficient is denoted as . and ; (1.5) and The smaller of the two values ​​corresponds to the polynomial result, which is taken as the latitude fitting result and is denoted as . ; (1.6) Utilization calculate The latitude estimate, i.e. ; (1.7) Perform longitude estimation, in Winning and Fit quadratic and cubic polynomial models respectively. and ; (1.8) Obtain respectively and The determination coefficient is denoted as . and ; (1.9) and The smaller of the two values ​​corresponds to the polynomial result, which is used as the longitude fitting result and is denoted as . ; (1.10) Utilization calculate The estimated longitude, i.e. ; (1.11) Calculate using the great circle route algorithm and The deviation value is denoted as ; (1.12) For to Repeat steps (1.3) to (1.11) to obtain the track point positioning error sequence for the track. ; (1.13) End.

[0026] Preferably, such as Figure 6 As shown, step (2) includes the following sub-steps: (2.1) Determine the number of samples Sample size ; (2.2) From the error sequence results of step (1) The sampling method without replacement is used in the middle. A number of deviation samples, denoted as... ,in Indicates the first Second sampling. ; (2.3) Calculate the mean square error of the current sample, denoted as . ,Right now ; (2.4) Repeat steps (2.2) and (2.3) to obtain the error sequence. Mean square error sequence ; (2.5) Calculate the mean square error sequence The mean and standard deviation of are denoted as . and ; (2.6) Calculate the mean square error sequence The confidence interval is ; (2.7) Kernel density estimation is performed on the sequence to obtain an array of kernel density estimates; (2.8) Histogram estimation is performed on the sequence to obtain an array of histogram estimates; (2.9) Determine the level of the mean square error of the deviation, such as If the value is less than the standard value for the corresponding level, it is considered to meet the requirements of the corresponding level. The standard deviation values ​​for different levels are shown in the table below: , (2.10) End.

[0027] Preferably, such as Figure 7 As shown, step (3) includes the following sub-steps: (3.1) Positioning error sequence of waypoints Perform kernel density estimation; (3.2) Divide the range into 4001 intervals with a range of ±2000, and calculate the positioning error sequence. The cumulative probability value in each interval; (3.3) Track point positioning error sequence Model fitting is performed for four empirical distributions, with the probability density functions of the empirical distributions as follows: normal distribution: ,in , The parameter is given by the parameter estimation method, which is maximum likelihood estimation, yielding estimated values ​​of the parameter. , Bi-exponential distribution: ,in , The parameter is given by the parameter estimation method, which is maximum likelihood estimation, yielding estimated values ​​of the parameter. , Mixed normal distribution: ,in , , The parameters are defined as follows: the parameter estimation method is least squares fitting. Mixed distribution of normal and biexponential distributions: ,in , , The parameters are defined as follows, and the parameter estimation method is least squares fitting. (3.4) Calculate the cumulative probability value of the fitting results for each distribution; (3.5) Calculate the fitting discriminant value for each distribution fitting result; (3.6) The model with the smallest fitting discriminant value is taken as the fitting result; (3.7) End.

[0028] Preferably, such as Figure 8 As shown, the least squares fitting described in step (3.3) includes the following sub-steps: (3.3.1) Set the target distribution parameters and The common lower and upper bounds are respectively and ; (3.3.2) Set the target distribution parameters The lower and upper bounds are respectively and ; (3.3.3) Calculate the least squares fitting values ​​based on the upper and lower bounds of the target parameters, so that the least squares values ​​reach the minimum values. and As a fitting result; (3.3.4) End.

[0029] Preferably, such as Figure 9As shown, the calculation of the fitting discriminant value described in step (3.5) includes the following sub-steps: (3.5.1) Take the number of parameters of the target distribution, denoted as . ; (3.5.2) Calculate the difference between the target distribution in steps (3.4) and (3.2) to obtain the fitted residual sequence, denoted as . ,in ; (3.5.3) Calculate the fitting discriminant value of the target distribution, denoted as . ,Right now ; (3.5.4) End.

[0030] Preferably, such as Figure 10 As shown, step (4) includes the following sub-steps: (4.1) The lower bound of the tail bias probability is determined by the probability value. To determine the performance level, such as Corresponding lower bound tail deviation value If the value is less than the standard value for the corresponding level, it is considered to meet the lower limit requirement of the corresponding level. (4.2) The upper bound of the tail bias probability is determined by the probability value. To determine the performance level, such as Corresponding upper bound tail deviation value If the value is less than the standard value for the corresponding level, it is considered to meet the upper limit requirement of the corresponding level. The upper and lower bound standard values ​​for different levels are shown in the table below: , (4.3) End.

[0031] Preferably, such as Figure 11 As shown, the calculation of the upper and lower bound tail deviation values ​​described in steps (4.1) and (4.2) includes the following sub-steps: (4.1.1) Take the corresponding upper and lower bound probability values ​​of the tail bias. ; (4.1.2) Calculate the two-sided cumulative probability values ​​respectively. , ; (4.1.3) Based on the empirical distribution fitting results of step (3), calculate and corresponding quantiles and ; (4.1.4) Take and The absolute value of the larger of the two values ​​is used as the upper bound tail deviation value. ,Right now ; (4.1.5) End.

[0032] After a radar is analyzed using the error analysis and evaluation methods described in steps (1) to (4), it can be considered to meet or not meet the requirements of a given level.

[0033] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for analyzing and evaluating radar positioning errors, characterized in that: It includes the following steps: (1) Calculate the positioning error of each track point by track; (2) Estimate the statistical mean square error of the positioning error and its confidence interval; (3) Fit the empirical distribution to the positioning error samples; (4) Verify the tail probability of the positioning error distribution; Step (1) includes the following sub-steps: (1.1) A track is uniquely identified by its track number, 24-bit address code, and secondary transponder code, and the number of track points is calculated as follows: ; (1.2) Using a traversal approach, from to Take respectively ; (1.3) Perform latitude estimation, in Winning and Fit quadratic and cubic polynomial models respectively. and ; (1.4) Obtain respectively and The determination coefficient is denoted as . and ; (1.5) and The smaller of the two values ​​corresponds to the polynomial result, which is taken as the latitude fitting result and is denoted as . ; (1.6) Utilization calculate The latitude estimate, i.e. ; (1.7) Perform longitude estimation, in Winning and Fit quadratic and cubic polynomial models respectively. and ; (1.8) Obtain respectively and The determination coefficient is denoted as . and ; (1.9) and The smaller of the two values ​​corresponds to the polynomial result, which is used as the longitude fitting result and is denoted as . ; (1.10) Utilization calculate The estimated longitude, i.e. ; (1.11) Calculate using the great circle route algorithm and The deviation value is denoted as ; (1.12) For to Repeat steps (1.3) to (1.11) to obtain the track point positioning error sequence for the track. ; (1.13) End; Step (2) includes the following sub-steps: (2.1) Determine the number of samples Sample size ; (2.2) From the error sequence results of step (1) The sampling method without replacement is used in the middle. A number of deviation samples, denoted as... ,in Indicates the first Second sampling. ; (2.3) Calculate the mean square error of the current sample, denoted as . ,Right now ; (2.4) Repeat steps (2.2) and (2.3) to obtain the error sequence. Mean square error sequence ; (2.5) Calculate the mean square error sequence The mean and standard deviation of are denoted as . and ; (2.6) Calculate the mean square error sequence The confidence interval is ; (2.7) Kernel density estimation is performed on the sequence to obtain an array of kernel density estimates; (2.8) Histogram estimation is performed on the sequence to obtain an array of histogram estimates; (2.9) Determine the level of the mean square error of the deviation, such as If the value is less than the standard value for the corresponding level, it is considered to meet the requirements of the corresponding level. (2.10) End; Step (3) includes the following sub-steps: (3.1) Positioning error sequence of waypoints Perform kernel density estimation; (3.2) Divide the range into 4001 intervals with a range of ±2000, and calculate the positioning error sequence. The cumulative probability value in each interval; (3.3) Track point positioning error sequence Model fitting is performed for four empirical distributions, with the probability density functions of the empirical distributions as follows: normal distribution: ,in , The parameter is given by the parameter estimation method, which is maximum likelihood estimation, yielding estimated values ​​of the parameter. , Bi-exponential distribution: ,in , The parameter is given by the parameter estimation method, which is maximum likelihood estimation, yielding estimated values ​​of the parameter. , Mixed normal distribution: ,in , , The parameters are defined as follows: the parameter estimation method is least squares fitting. Mixed distribution of normal and biexponential distributions: ,in , , The parameters are defined as follows, and the parameter estimation method is least squares fitting. (3.4) Calculate the cumulative probability value of the fitting results for each distribution; (3.5) Calculate the fitting discriminant value for each distribution fitting result; (3.6) The model with the smallest fitting discriminant value is taken as the fitting result; (3.7) End.

2. The method for analyzing and evaluating radar positioning errors according to claim 1, characterized in that: The least squares fitting described in step (3.3) includes the following sub-steps: (3.3.1) Set the target distribution parameters and The common lower and upper bounds are respectively and ; (3.3.2) Set the target distribution parameters The lower and upper bounds are respectively and ; (3.3.3) Calculate the least squares fitting values ​​based on the upper and lower bounds of the target parameters, so that the least squares values ​​reach the minimum values. and As a fitting result; (3.3.4) End.

3. The method for analyzing and evaluating radar positioning errors according to claim 2, characterized in that: The calculation of the fitting discriminant value described in step (3.5) includes the following sub-steps: (3.5.1) Take the number of parameters of the target distribution, denoted as . ; (3.5.2) Calculate the difference between the target distribution in steps (3.4) and (3.2) to obtain the fitted residual sequence, denoted as . ,in ; (3.5.3) Calculate the fitting discriminant value of the target distribution, denoted as . , ; (3.5.4) End.

4. The method for analyzing and evaluating radar positioning errors according to claim 3, characterized in that: Step (4) includes the following sub-steps: (4.1) The lower bound of the tail bias probability is determined by the probability value. To determine the performance level, such as Corresponding lower bound tail deviation value If the value is less than the standard value for the corresponding level, it is considered to meet the lower limit requirement of the corresponding level. (4.2) The upper bound of the tail bias probability is determined by the probability value. To determine the performance level, such as Corresponding upper bound tail deviation value If the value is less than the standard value for the corresponding level, it is considered to meet the upper limit requirement of the corresponding level. (4.3) End.

5. The method for analyzing and evaluating radar positioning errors according to claim 4, characterized in that: The calculation of the upper and lower bound tail deviation values ​​described in steps (4.1) and (4.2) includes the following sub-steps: (4.1.1) Take the corresponding upper and lower bound probability values ​​of the tail bias. ; (4.1.2) Calculate the two-sided cumulative probability values ​​respectively. , ; (4.1.3) Based on the empirical distribution fitting results of step (3), calculate and corresponding quantiles and ; (4.1.4) Take and The absolute value of the larger of the two values ​​is used as the upper bound tail deviation value. , ; (4.1.5) End.

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