CN110058205B - Warning radar system error correction method based on iterative closest point algorithm - Google Patents

Warning radar system error correction method based on iterative closest point algorithm Download PDF

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CN110058205B
CN110058205B CN201910439582.6A CN201910439582A CN110058205B CN 110058205 B CN110058205 B CN 110058205B CN 201910439582 A CN201910439582 A CN 201910439582A CN 110058205 B CN110058205 B CN 110058205B
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CN110058205A (en
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李鹏飞
范恩
王敬华
魏冬峰
杨军佳
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People's Liberation Army Army Artillery Air Defense Academy Zhengzhou Campus
University of Shaoxing
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/40—Means for monitoring or calibrating
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/17—Function evaluation by approximation methods, e.g. inter- or extrapolation, smoothing, least mean square method

Abstract

The invention belongs to the technical field of radar system error correction, and particularly relates to an iterative nearest point algorithm-based warning radar system error correction method. According to the method, radar measurement data and ADS-B data are analyzed under a polar coordinate system, a linear equation coefficient is obtained by directly utilizing a linear fitting algorithm according to the ADS-B data, a cosecant curve is obtained, a curve corresponding to a radar measurement track is subjected to high-order polynomial fitting under the polar coordinate system according to the radar measurement track, and then the ICP algorithm is utilized to calculate the deviation between the fitting curve corresponding to the radar measurement and the fitting curve corresponding to the ADS-B data, so that the distance and azimuth system errors in radar measurement are obtained. The method uses related ideas of computer graphics for reference, effectively eliminates the influence of abnormal measurement on error correction through curve fitting, realizes system error correction by calculating the difference between a target curve and a reference curve, and skillfully avoids the problem of time registration.

Description

Warning radar system error correction method based on iterative closest point algorithm
Technical Field
The invention belongs to the technical field of radar system error correction, and particularly relates to a warning radar system error correction method based on an iterative closest point algorithm.
Background
In a radar networking system, a plurality of radars send detection data to a fusion center for data fusion, and the prerequisite condition of successful data fusion of a plurality of sensors is to transform measured data of each sensor into a common reference coordinate system after system errors are eliminated. If the system error is not compensated, the system error can increase the track tracking error, for multiple sensors, the system error causes that the same target has larger deviation between tracks of different radars, which brings ambiguity and difficulty to track association and fusion to reduce the performance of the fused system track and lose the advantages of the radars. Therefore, correcting for system errors is a key issue that must be addressed by multi-radar networking intelligence processing systems.
Currently, many studies have been made in the field of radar bias correction. Document 1 (RAFATIA, MOSHIIRR B, SALAHSHOOR K et al. Asynchronous radar sensor bias estimation in multiple-multiple target system [ C ]/IEEE International Conference on multiple sensor Fusion and Integration for Integration systems. Heidelberg: IEEE, 2006; document 2 (BESADA PORTAS JA, GARC A HERRERO J, de MIGUEL VELA G. New proproach to online optimization of Radar [ J ]. IET Procedingradar, sonar and Navigation,2004,151 (1): 31-40) introduces a new method for optimizing Radar bias in real time, which estimates errors of other radars to be corrected by using data of the radars with better accuracy and corrects the radars; because the broadcast automatic correlation monitoring (ADS-B) technology adopted by the civil aviation system uses GNSS for positioning, compared with the measurement precision of warning radar, the positioning precision of the GNSS for the target is very high, and therefore, the ADS-B data is used for correcting the system error of the radar in real time to become a new research direction; document 3 (He You, zhu Hongwei, tang Xiaoming. Joint system error estimation for Radar and automatic dependent measuring branched [ J ]. IET Radar Sonar Navigation,2013,4 (7): 361-370) and document 4 (Zhang, tang Ming, jinlin. ADS-B are used for researching the method for high-precision Radar calibration [ J ]. Aviation report ], 2015,35 (1): 1-10) propose a method for correcting errors by combining ADS-B and Radar, wherein the method is high in correction precision, but is complex in algorithm, difficult in engineering application and poor in real-time.
At present, a system error correction method mainly researches differences between a trace point with system errors and a reference trace, and in the method, accurate time alignment of different information sources must be strictly ensured firstly when error correction is performed, and due to differences of data updating periods of the information sources, the trace point needs to be predicted by using a state model prediction algorithm so as to ensure that the trace points of the different information sources can be compared and subjected to error calculation at the same moment, and finally, all calculated trace point errors are statistically averaged according to a statistical method to obtain final system errors such as an inclined distance, an azimuth angle and a height. Such methods have the following problems that are difficult to effectively solve when error correction is performed:
(1) When the error correction is carried out by using the civil aviation ADS-B data, the biggest problem is that the time of transmitting data information by ADS-B transmitting equipment cannot be obtained, so that the time alignment between radar measurement data and the ADS-B data cannot be carried out, and the accuracy cannot be ensured by the following error calibration.
(2) In order to ensure the time alignment of the traces, interpolation is also needed to correct the data of each sensor to the same time, and since the interpolation is an approximation for data processing, the value obtained by interpolation will bring larger error, which also reduces the accuracy of error calibration.
(3) Due to the fact that the radar measurement data have mutation conditions, the existence of the abnormal point influences the final error statistical result to a great extent.
Aiming at the problems of the calibration method of the radar orientation, a radar orientation calibration error calibration method based on multi-straight-line fusion is proposed in document 5 (Lepengfei, haoyu and the like, research on radar error calibration algorithms based on multi-straight-line fusion [ J ]. Radar science and technology, 2017,15 (6): 682-686). The method does not consider the time alignment problem any more when error correction is carried out, the influence of random errors on the error correction can be effectively reduced through a straight line fitting method, and the method has a good correction effect on system errors existing in north calibration.
Disclosure of Invention
Technical problem to be solved
The invention provides an iterative closest point algorithm-based warning radar system error correction method, which aims to solve the technical problem of how to correct radar distance system errors.
(II) technical scheme
In order to solve the technical problem, the invention provides an iterative closest point algorithm-based warning radar system error correction method, which comprises the following steps:
s1, obtaining ADS-B track and radar track data of the same target, and respectively obtaining cosecant curves of the ADS-B track and the radar track;
s2, determining a polar coordinate when the derivative is 0 by solving the derivative of the cosecant curve; then, sampling at equal intervals by taking the sampling point as a first point, and then taking N points to respectively obtain N +1 sampling points of an ADS-B track cosecant curve and a radar track cosecant curve;
and S3, taking a data set formed by ADS-B track cosecant curve sampling points as a reference point set, taking a data set formed by radar track cosecant curve sampling points as a target point set, and calculating the offset between the target point set and the reference point set by adopting an iterative closest point algorithm to obtain the radar system error needing to be corrected.
Further, in step S1, for the acquired ADS-B track, firstly, a straight line fitting algorithm is used to perform straight line fitting on the ADS-B track to obtain a linear equation coefficient, and then a cosecant curve of the ADS-B track is obtained through conversion between a rectangular coordinate system and a polar coordinate system.
Further, in step S1, curve fitting is performed on a curve corresponding to the acquired radar track in the polar coordinate system, so as to obtain a cosecant curve of the radar track.
Further, in step S3, the method specifically includes the following steps:
(1) Setting a threshold value tau >0 as a condition for iteration termination;
(2) Assume that in the k-th iteration, for each data point in the target point set P
Figure BDA0002071633600000041
Searching for corresponding from reference point set Q
Figure BDA0002071633600000042
So that
Figure BDA0002071633600000043
(3) Computing translation matrices
Figure BDA0002071633600000044
So that
Figure BDA0002071633600000045
(4) Computing
Figure BDA0002071633600000046
(5) The estimation error between the two iterations is calculated:
Figure BDA0002071633600000047
if d is k -d k+1 If the value is less than tau, stopping iteration, otherwise, returning to the step (2) to continue iteration;
(6) The iteration is finished, and the total offset of the target curve is calculated
Figure BDA0002071633600000048
Wherein
Figure BDA0002071633600000049
Delta theta in the formula sum And Δ r sum Namely the radar azimuth system deviation and the distance system deviation to be solved.
(III) advantageous effects
The invention provides an iterative closest point algorithm-based alert radar system error correction method, which analyzes radar measurement data and ADS-B data under a polar coordinate system aiming at distance and azimuth measurement system errors existing in an alert radar, obtains a linear equation coefficient by directly utilizing a linear fitting algorithm aiming at the high-precision ADS-B data so as to obtain a cosecant curve, and performs high-order polynomial fitting on a curve corresponding to a radar measurement track under the polar coordinate system for the radar measurement track, and calculates the deviation between the fitting curve corresponding to the radar measurement and the fitting curve corresponding to the ADS-B data by utilizing an ICP algorithm, thereby obtaining the distance and azimuth system errors in radar measurement.
The method uses related thinking of computer graphics for reference, effectively eliminates the influence of abnormal measurement on error correction through curve fitting, realizes system error correction by calculating the difference between a target curve and a reference curve, ingeniously avoids the problem of time registration, and is simple in design, convenient to operate, high in implementation, very obvious in correction effect on radar calibration errors and suitable for the field of engineering application through quantitative analysis of simulation experiments and measured data.
Drawings
FIG. 1 is a track chart of a rectangular coordinate system when a target makes uniform linear motion in a simulation experiment according to an embodiment of the present invention;
FIG. 2 is a comparison (a) of a measured track of a radar with a target real track and a corresponding cosecant curve in a simulation experiment according to an embodiment of the present invention;
FIG. 3 is a comparison graph before and after fitting a corresponding curve of a measured track in a simulation experiment according to an embodiment of the present invention;
FIG. 4 is a comparison between ADS-B and radar track calibration before and after actual measurement data analysis according to the embodiment of the present invention: comparing the flight path before calibration (a); comparing the flight path after calibration;
FIG. 5 is a comparison between ADS-B and radar track corresponding curve fitting in measured data analysis according to the embodiment of the present invention: a corresponding cosecant curve (a); and (b) fitting the cosecant curve.
Detailed Description
In order to make the objects, contents and advantages of the present invention clearer, the following detailed description of the embodiments of the present invention will be made in conjunction with the accompanying drawings and examples.
An Iterative Closest Point (ICP) algorithm is mainly used for three-dimensional model registration, and the registration idea of the algorithm is simple, convenient and efficient, and has good precision and robustness. The basic objective of the algorithm is to find the euclidean transformation matrix between the target point cloud and the reference point cloud so that the two sets of point clouds satisfy the optimal match under some metric criteria. For each data point in the target point set, searching the closest point in the reference point set as a matching point pair in each iteration process, estimating a transformation parameter through the obtained matching point pair, acting the transformation matrix on a target function, and iteratively performing the operation and updating the relative position between the point clouds until the difference value of the target function of two iterations is smaller than a set threshold value.
The embodiment provides an iterative closest point algorithm-based warning radar system error correction method, which specifically comprises the following steps:
s1, selecting ADS-B flight paths and straight line parts of radar flight path data of the same target by taking civil aviation flights as targets, and respectively converting the ADS-B flight paths and the straight line parts into a polar coordinate system.
And S2, respectively obtaining the cosecant curves of the ADS-B flight path and the radar flight path through a fitting algorithm. Because the position precision in the ADS-B data is very high, and civil aviation flights usually fly straight at a constant speed, a straight line fitting algorithm in the document [5] can be firstly utilized to perform straight line fitting on a flight path flying straight, a straight line equation coefficient is obtained, and then the cosecant curve of the ADS-B flight path is obtained through conversion between a rectangular coordinate system and a polar coordinate system.
For target track data acquired by a radar, because of a large random measurement error, if the target track data acquired by the radar is directly subjected to straight line fitting, a large error is caused, and therefore, high-order polynomial fitting needs to be performed on a curve corresponding to the target track data acquired by the radar in a polar coordinate system, so that a cosecant curve of the radar track is obtained.
S3, determining a polar coordinate when the derivative is 0 by solving the derivative of the cosecant curve; and then sampling at equal intervals by taking the sampling point as a first point, and then taking 9 points so as to respectively obtain 10 sampling points of the ADS-B track cosecant curve and the radar track cosecant curve.
Wherein, the extreme point of the cosecant curve corresponding to ADS-B data is assumed to be
Figure BDA0002071633600000061
The aftercut curve extreme point corresponding to the radar track is
Figure BDA0002071633600000062
In order to calculate the offset between two curves by using an ICP (inductively coupled plasma) algorithm, firstly, taking an extreme point as a center on a curve corresponding to ADS-B (automatic dependent surveillance broadcast system) -data, sampling 9 azimuth angle values on an azimuth angle coordinate axis at equal intervals, and obtaining corresponding 9 distance values on the curve to obtain a reference point set
Figure BDA0002071633600000063
Wherein i =1,10;
obtaining a target point set according to the same method
Figure BDA0002071633600000064
Wherein j =1,10.
Thus, 20 groups of data points obtained on the two curves are sampling points on the curves.
And S4, taking a data set formed by ADS-B track cosecant curve sampling points as a reference point set, taking a data set formed by radar track cosecant curve sampling points as a target point set, and then calculating the offset by adopting an ICP (inductively coupled plasma) algorithm, wherein the calculated offset is the system error of the radar.
And calculating the offset between the target point set and the reference point set when the two curves are optimally matched by utilizing an ICP (inductively coupled plasma) algorithm. Since only curve translation exists and no curve rotation exists, the iterative algorithm in the embodiment is as follows:
(1) Setting a threshold value tau >0 as a condition for iteration termination;
(2) Assume that in the kth iteration, for each data point in the target set of points P
Figure BDA0002071633600000071
Searching for corresponding from reference point set Q
Figure BDA0002071633600000072
So that
Figure BDA0002071633600000073
(3) Computing translation matrices
Figure BDA0002071633600000074
So that
Figure BDA0002071633600000075
(4) Calculating out
Figure BDA0002071633600000076
(5) The estimation error between the two iterations is calculated:
Figure BDA0002071633600000077
if d is k -d k+1 If the value is less than tau, stopping iteration, otherwise, returning to the step (2) to continue iteration;
(6) The iteration is finished, and the total offset of the target curve is calculated
Figure BDA0002071633600000078
Wherein
Figure BDA0002071633600000079
Delta theta in the formula sum And Δ r sum Namely, the radar azimuth system deviation and the range system deviation to be solved by the embodiment.
The method for correcting the error of the warning radar system is analyzed and verified by a simulation experiment and an actual measurement method respectively.
1. Analysis of simulation experiment
Assuming that the motion equation of the target is y-2.7x-52110=0, the start position of the target is (3000m, 44010m), and the motion speed of the target is (200 m/s, -540 m/s), the motion trajectory is as shown in fig. 1. ADS-B data and radar data are generated in a simulation mode on the basis of original flight paths, and because ADS-B is high in precision, random errors of ADS-B in an x axis and a y axis are assumed to be sigma x ＝10m,σ y ＝10m。
Assuming that radar measurement values have both random errors and system errors, if the range random error of the radar is sigma r =100m, angle measurement random error σ θ ＝0.01rad。
Ranging and goniometric system errors of radar are
Δ r ＝300m,Δ θ ＝0.14rad
The measured trajectory of the radar is compared with the actual trajectory of the target as shown in fig. 2 (a), and the corresponding curve is compared as shown in fig. 2 (b).
Firstly, linear fitting is carried out on the ADS-B track to obtain the coefficient of the linear, and then the extreme value of the cosecant curve in the interval is solved
Figure BDA0002071633600000081
The fitted curve obtained by fitting the "-" curve in fig. 2 (b) with a higher order polynomial is shown in fig. 3.
According to the curve shown in fig. 3, an extreme value is found on the curve by utilizing a method based on golden section search and parabolic interpolation (fminbnd function in matlab)
Figure BDA0002071633600000082
To be provided with
Figure BDA0002071633600000083
And
Figure BDA0002071633600000084
taking the central point as the center, sampling the two curves at equal intervals respectively, obtaining 10 data point sets by each curve, and calculating the system error of the azimuth angle and the distance into
Δ′ r ＝314m,Δ′ θ ＝0.138rad
The result is basically consistent with the radar ranging and angle measuring system errors set in a simulation experiment, and the effectiveness of the method in correcting the system errors is shown.
2. Analysis of measured data
In order to verify the performance of the method, the measured data is used for error correction of the radar system. In fig. 4 (a), "+ -" is ADS-B track data, and "-" is original track of radar, and it can be seen from comparison that there is obvious system error in radar, and the two track data are displayed on azimuth distance plane as shown in fig. 5 (a), and the curve is fitted to obtain the cosecant curve as shown in fig. 5 (B), and then the distance and azimuth system error is calculated by using the calibration method of the present invention, and the error is compensated to radar measurement, and the corrected track is shown in fig. 4 (B), in which "-" is ADS-B track data, and "-" is corrected radar track, and as can be seen from the comparison of fig. 4 (a) and (B), the radar track calibrated by the method of the present invention is highly coincident with ADS-B track, thus fully showing the effectiveness of the method.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.

Claims (3)

1. An iterative closest point algorithm-based alert radar system error correction method is characterized by comprising the following steps:
s1, obtaining ADS-B track and radar track data of the same target, and respectively obtaining cosecant curves of the ADS-B track and the radar track;
s2, determining a polar coordinate when the derivative is 0 by solving the derivative of the cosecant curve; then, sampling at equal intervals by taking the sampling point as a first point, and then taking N points to respectively obtain N +1 sampling points of an ADS-B track cosecant curve and a radar track cosecant curve;
s3, taking a data set formed by sampling points of the ADS-B track cosecant curve as a reference point set, taking a data set formed by sampling points of the radar track cosecant curve as a target point set, and calculating the offset between the target point set and the reference point set by adopting an iterative closest point algorithm to obtain a radar system error needing to be corrected; the method specifically comprises the following steps:
(1) Setting a threshold value tau >0 as a condition for iteration termination;
(2) Assume that in the k-th iteration, for each data point in the target point set P
Figure FDA0004062465330000011
Searching for corresponding from reference point set Q
Figure FDA0004062465330000012
So that
Figure FDA0004062465330000013
(3) Computing translation matrices
Figure FDA0004062465330000014
So that
Figure FDA0004062465330000015
(4) Calculating out
Figure FDA0004062465330000016
(5) The estimation error between the two iterations is calculated:
Figure FDA0004062465330000017
if d is k -d k+1 If the value is less than tau, stopping iteration, otherwise, returning to the step (2) to continue iteration;
(6) The iteration is finished, and the total offset of the target curve is calculated
Figure FDA0004062465330000018
Wherein
Figure FDA0004062465330000019
Delta theta in the formula sum And Δ r sum Namely the radar azimuth angle system deviation and the distance system deviation to be solved.
2. The radar system error correction method according to claim 1, wherein in step S1, for the acquired ADS-B track, a line fitting algorithm is first used to perform a line fitting on the ADS-B track to obtain a linear equation coefficient, and then a cosecant curve of the ADS-B track is obtained through a transformation between a rectangular coordinate system and a polar coordinate system.
3. The method for error correction of a radar system according to claim 1, wherein in step S1, a curve corresponding to the radar track is curve-fitted in a polar coordinate system for the acquired radar track, so as to obtain a cosecant curve of the radar track.
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