CN111220158B - Line spectrum target motion parameter estimation method based on time azimuth history chart - Google Patents
Line spectrum target motion parameter estimation method based on time azimuth history chart Download PDFInfo
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Abstract
A line spectrum target motion parameter estimation method based on a time azimuth history chart belongs to the field of target motion parameter estimation. The invention solves the problem that the existing target motion parameter estimation method can not provide the course information of the target or the nearest passing time of the artificially and subjectively observed target is inaccurate. The method is based on the azimuth estimation result of the traditional detection equipment, and the nearest passing time, the course, the nearest passing distance and the motion track information of the target are obtained by using a method of two times of generalized Radon transformation. Different from the previous method for extracting the target motion parameter information on the time-frequency graph result and the problem that the target course information cannot be obtained, and also different from other existing methods for extracting the target parameter on the time-azimuth course, the method needs to predict the latest passing time of the target, and the method can obtain the latest passing time of the target through the first Radon transformation, thereby solving the problem of inaccurate artificial observation in the past. The invention can be applied to the estimation of the motion parameters of the target.
Description
Technical Field
The invention belongs to the field of target motion parameter estimation, and particularly relates to a line spectrum target motion parameter estimation method based on a time and azimuth history chart.
Background
In the ocean acoustic target detection equipment, a plurality of pieces of equipment only have target detection and direction finding functions, can provide information on the existence and the direction of a target, and do not have the motion parameter information estimation capabilities of target course, distance, nearest passing distance and the like. If the motion parameters of the target can be estimated on the basis of the direction finding result of the traditional equipment, the method can greatly help to judge the motion situation of the linear course moving target relative to the detection point, and the functions of the traditional detection equipment can be expanded.
At present, the main researches on the feature extraction of target motion parameters are as follows: the study on the university of Harbin engineering, target motion analysis based on STFT-Hough transformation (hereinafter referred to as "document 1"); yanjuan, Huijinging, etc. utilize low frequency sound pressure interference spectrum to estimate the target motion parameters, the university of Harbin's college (hereinafter referred to as literature 2); yurt 36191, huijinging, invar, huijian and royal silk, target motion parameter estimation and passive distance measurement based on waveguide invariants, acoustic science and report (hereinafter referred to as document 3).
Document 3 discloses a method for estimating a target motion parameter and passively ranging based on a waveguide invariant, which is described in the literature to know that a time-frequency analysis LOFAR spectrum measurement result and Hough transformation are used to perform parameter estimation on a distance-velocity ratio of a target and the waveguide invariant, then Hough transformation is performed on a time-azimuth process to obtain heading information of the target, and finally the result measured by two receiving points is used to obtain distance information of the target. The method in document 3, like documents 1 and 2, requires that the latest passing time of a known target be assumed in advance, and requires that a person observe and obtain the parameter from a LOFAR chart, so that the inaccuracy of human subjective observation exists.
Disclosure of Invention
The invention aims to solve the problem that the existing target motion parameter estimation method cannot provide the course information of a target or the passing time of a target is not accurate in artificial subjective observation, and provides a line spectrum target motion parameter estimation method based on a time azimuth history chart.
The technical scheme adopted by the invention for solving the technical problems is as follows: a line spectrum target motion parameter estimation method based on a time and azimuth history map comprises the following steps:
step one, reading a time azimuth process chart formed by the movement of a line spectrum target to obtain a time azimuth process matrix R (t, theta); judging whether the target passes through the left side or the right side of the measuring system according to the time azimuth process matrix R (t, theta);
step two, performing first generalized Radon transformation on the time azimuth history matrix R (t, theta) according to the judgment result of the step one to obtain the latest passing time t of the target 0 ；
Step three, according to the latest passing time t obtained in the step two 0 Performing generalized Radon transformation on the time azimuth history matrix R (t, theta) for the second time to obtain a heading angle theta 0 And a transformation parameter space matrix of velocity to nearest passing distance ratio k, wherein: k is the ratio of the target movement speed to the nearest passing distance;
according to the course angle theta 0 Solving the course angle theta of the target by the transformation parameter space matrix of the sum speed and the nearest passing distance ratio k 0 And a ratio k of the target movement speed to the nearest passing distance;
step four, solving the moving speed v of the target, and then calculating the nearest passing distance r of the target by utilizing the ratio k obtained in the step three 0 ；
And step five, reversely deducing the motion track of the target by using the results obtained in the step two to the step four.
The invention has the beneficial effects that: the invention provides a line spectrum target motion parameter estimation method based on a time azimuth process diagram, which estimates the motion parameters of a target on the basis of direction and frequency measurement results of traditional detection equipment, gives the motion trail of the target, expands the functions of underwater sound detection equipment only capable of measuring direction and frequency, and can be used for judging the motion situation of the target passing through a detection system in the coming and going directions or detecting the main course of a passing ship near a flight path. Most of acoustic targets such as ships and warships contain rich line spectrum information, so that the speed measurement method provided by the invention can be used for obtaining the movement speed of the target so as to obtain a track. The invention can be combined with the non-line spectrum target to obtain the track information of the target under the condition that the movement speed of the target can be obtained by using the existing method.
The method is based on the azimuth estimation result of the traditional detection equipment, and the nearest passing time, the heading, the nearest passing distance and the motion track information of the target are obtained by using a method of two times of generalized Radon transformation. Different from the previous method for extracting the target motion parameter information on the time-frequency graph result and the problem that the target course information cannot be obtained, and also different from other existing methods for extracting the target parameter on the time-azimuth course, the method needs to predict the latest passing time of the target, and the method can obtain the latest passing time of the target through the first Radon transformation, thereby solving the problem of inaccurate artificial observation in the past.
Drawings
FIG. 1 is a flow chart of a method for estimating line spectrum target motion parameters based on a time azimuth history chart according to the present invention;
FIG. 2 is a geometric model diagram of the motion of a left-hand pass object;
FIG. 3 is a geometric model diagram of the motion of the right-hand pass object;
FIG. 4 is a time bearing history plot of a left-hand pass through target;
FIG. 5 is a time bearing history plot of a right-hand pass through the target;
FIG. 6 is a left side passage t 0 And a k-domain Radon transformation result graph;
FIG. 7 is a right side passage t 0 And k-domain Radon transformation result graph;
FIG. 8 is the left hand side through Θ 0 And k-domain Radon transformation result graph;
FIG. 9 is the right side through Θ 0 And a k-domain Radon transformation result graph;
FIG. 10 is a diagram of the simulated time-frequency analysis result of a line spectrum target time-frequency diagram;
FIG. 11 is a diagram of the simulation frequency measurement result of a line spectrum target time-frequency diagram;
wherein: t represents time and f represents frequency;
FIG. 12 is a diagram of left-side pass object motion trajectory estimation results;
fig. 13 is a diagram of the right-side passage target motion trajectory estimation result.
Detailed Description
The first embodiment is as follows: as shown in fig. 1, a method for estimating a line spectrum target motion parameter based on a time and azimuth history chart according to this embodiment includes the following steps:
step one, reading a time azimuth process chart formed by the movement of a line spectrum target to obtain a time azimuth process matrix R (t, theta); judging whether the target passes through the left side or the right side of the measuring system according to the time azimuth process matrix R (t, theta);
step two, performing first generalized Radon transformation (Radon transformation) on the time azimuth history matrix R (t, theta) according to the judgment result of the step one to obtain the latest passing time t of the target 0 ；
Step three, obtaining the latest passing time t according to the step two 0 Performing generalized Radon transformation on the time and azimuth history matrix R (t, theta) for the second time to obtain a course angle theta 0 And a transformation parameter space matrix of velocity to nearest passing distance ratio k, wherein: k is the ratio of the target movement speed to the nearest passing distance;
according to the course angle theta 0 Solving the course angle theta of the target by the transformation parameter space matrix of the sum speed and the nearest passing distance ratio k 0 And a ratio k of the target movement speed to the nearest passing distance;
step four, solving the moving speed v of the target, and then calculating the nearest passing distance r of the target by utilizing the ratio k obtained in the step three 0 ；
And step five, reversely deducing the motion track of the target by using the results obtained in the step two to the step four.
The embodiment is a method for estimating target motion parameters by using a generalized Radon transformation method based on a time and azimuth history map, is suitable for targets sailing in a straight line on the sea, and can obtain the heading information and the ratio information of the motion speed and the nearest passing distance of the targets. On the basic layer, the line spectrum Doppler information of the line spectrum target is utilized to obtain the target motion speed information, and then the motion track of the target relative to the detection equipment can be reversely deduced.
The second embodiment is as follows: the first difference between the present embodiment and the specific embodiment is: the specific process of the step one is as follows:
as shown in fig. 2 and fig. 3, a left-hand coordinate system is established by using the north-east coordinate system with the position of the measurement system as the origin O, wherein: the positive direction of the x axis points to the true north direction of the geodetic coordinates, and the positive direction of the y axis points to the true east direction of the geodetic coordinates;
measuring a time and azimuth process chart formed by the movement of a line spectrum target by using a measuring system to obtain a time and azimuth process matrix R (t, theta), wherein: theta is the azimuth angle of the target, and t is time;
the adopted time azimuth process is the time azimuth process under a geodetic coordinate system measured by an acoustic detection system;
and if the target azimuth angle theta gradually becomes larger along with the time t, the target is considered to pass through the left side of the measuring system, otherwise, if the target azimuth angle theta gradually becomes smaller along with the time t, the target is considered to pass through the right side of the measuring system.
Regardless of the 0 ° and 360 ° angle jumps, if the azimuth angle is gradually increased with time, the target is considered to be left-side passed, and if the change law of the azimuth angle is gradually decreased with time, the target is considered to be right-side passed. According to the conventional definition of the horizontal azimuth angle, the value range is usually between 0 and 359 degrees, and if the value is larger than or smaller than the angle, the value is left for 360 degrees. When the left side and the right side of the target pass through, if the angle exceeds the value range and is subjected to remainder operation, namely the angle jumps, the jump of more than 360 degrees is carried out, the jumped angle is added with 360 degrees, and the jump of less than 0 degree is carried out, so that the angle is subtracted with 360 degrees to ensure that the angle is continuous, and then the law of increasing or decreasing the angle is judged.
For example, the heading angle is 30 °, the moving speed of the target is 10m/s, the nearest passing distance is 100m, the nearest passing time is 200s, and the time-azimuth history chart results of the target passing through the left side and the right side of the detection system respectively are shown in fig. 4 and fig. 5.
Observing the results of fig. 4 and 5, it can be found that, except that the left side has a jump of more than 360 ° through the azimuth angle of the model target, the jump angle can be added to 360 ° in the judgment, and the target can be easily judged to be gradually increased along with the time after the processing. And the right-side passing model obviously has gradually reduced angles under the condition of the same parameters of course angle, speed and the like.
Target course angle theta 0 The angle of the clockwise deviation between the moving course of the line spectrum target and the positive direction of the x axis is the north east deviation angle; according to the time and azimuth history chart measured by the existing detection equipment, a time and azimuth history matrix R (t, theta) can be actually written. The adopted time azimuth process is the time azimuth process under a geodetic coordinate system measured by an acoustic detection system.
Let θ be the azimuth of the target, also defined as the positive clockwise deviation from the x-axis, r 0 Defining t as the nearest passing distance of the target, namely the nearest distance between the target track and the detection system, and the nearest passing time 0 The time corresponding to the time when the target passes through the nearest distance moment from the measurement time. The motion model of the target passing through the measuring platform in a straight line is shown in fig. 2 and fig. 3, and the direction finding result has a larger relation with whether the target passes through the left side or the right side of the platform. And respectively establishing mathematical models aiming at the left side motion model and the right side motion model. According to the geometric relationship, the relationship between the orientation measurement result of the left-side passing motion model and the core mathematical model of the course angle and time is as follows:
θ＝arctan[k(t-t 0 )]+Θ 0 -90
the core mathematical model relation of the orientation measurement result of the right-side passing motion model and the course angle and time is as follows:
θ＝90-arctan[-k(t-t 0 )]+Θ 0
when the target passes right above the measuring point, the direction-finding result has azimuth jump, and the k value is infinite, so the method is not suitable for the situation that the target passes right above the measuring point, which is a small probability event in practice.
The third concrete implementation mode: the second embodiment is different from the first embodiment in that: the specific process of the second step is as follows:
the Radon transform is mathematically an integral transform, and the generalized Radon transform in two dimensions can be understood as performing line integral processing on a value corresponding to a point on a curve along a certain curve rule in a plane to obtain a transform result in which another domain contains parameters affecting the curve rule. The common Radon transform in the traditional sense mainly has the forms of straight line, parabola, hyperbola, etc. It is derived from the foregoing mathematical model that when the nearest transit time of the target is known, the relationship of the target's azimuth time history to the parameters of the ratio of the navigation angle to the speed distance is the tangent tan transform. The generalized Radon transform curve integration form used here is shown as integrating points on the tangent tan function curve. While when the last pass time is unknown, the transform domain scan parameter for integration may be set to t 0 And k value, at which three scan parameters appear, Radon transform cannot be directly performed, but recently by time t 0 Corresponding azimuth angle theta 0 (t 0 ) Angle theta with course 0 (t 0 ) Is relevant, the left-side passing time relation is as follows:
Θ 0 ＝θ 0 (t 0 )-270
the right-side passage time relationship is as follows:
Θ 0 ＝θ 0 (t 0 )-90
θ 0 (t 0 ) With t of each scan 0 Obtaining azimuth corresponding to time, t for scanning 0 The azimuth output value at the moment is maximized to obtain the azimuth theta corresponding to the maximum value 0 (t 0 ) I.e. is t 0 The azimuth angle corresponding to the time.
Defining the ratio of the target movement speed to the nearest passing distance as k;
if the target passes through the left side of the measurement system, performing first generalized Radon transformation on the time azimuth history matrix R (t, theta) to obtain k sumTarget recent passage time t 0 Is transformed to a parameter space matrix U 1 (k,t 0 )；
Wherein: n is the discrete time number, i represents the ith of N discrete times, t (i) is the ith discrete time value, theta 0 (t 0 ) For the target at the latest passing time t 0 The corresponding target azimuth angle, R (-) represents Radon transformation;
according to a transformation parameter space matrix U 1 (k,t 0 ) Selecting the abscissa corresponding to the maximum k value as the latest passing time t 0 ；
If the target passes through the right side of the measurement system, performing first generalized Radon transformation on the time azimuth history matrix R (t, theta) to obtain k and the latest passing time t of the target 0 Of transformation parameter space matrix U' 1 (k,t 0 )；
According to a transformation parameter space matrix U' 1 (k,t 0 ) Selecting the abscissa corresponding to the maximum k value as the latest passing time t 0 。
Generalized Radon transform is performed using the time azimuth history of fig. 4 and 5 to obtain t of fig. 6 and 7 0 And a transformation result map of the k-domain.
As shown in fig. 6 and 7, the abscissa time in the graph represents the scanning amount of the latest passing time of the target, and the abscissa value corresponding to the maximum value position is t 0 Value, t in the figure 0 Is 200 s.
The time azimuth history chart measured by general equipment is a two-dimensional matrix which can be regarded as an image, and the generalized Radon transformation of the image processing method can be used for extracting the regular line characteristics in the image and mapping the line characteristics into a point of a transformation parameter space. The characteristic of an azimuth line in a target azimuth time history of linear navigation near a detection device is a tangent curve, Radon transformation in the traditional sense is mainly used for extracting motion models such as straight lines, circles, parabolas and hyperbolas, and the idea of generalized Radon transformation is applied to extracting the tangent curve on a time azimuth history diagram.
The fourth concrete implementation mode: the third difference between the present embodiment and the specific embodiment is that: the third step comprises the following specific processes:
if the target passes through the left side of the measurement system, performing second generalized Radon transformation on the time and azimuth history matrix R (t, theta) to obtain a heading angle theta 0 Transformation parameter space matrix U of sum velocity and nearest passing distance ratio k 2 (k,Θ 0 )；
Then U will be 2 (k,Θ 0 ) The abscissa value corresponding to the maximum value position in the range is used as the target course angle theta 0 Will U 2 (k,Θ 0 ) The longitudinal coordinate value corresponding to the maximum position in the target is used as the ratio k of the movement speed of the target to the nearest passing distance;
if the target passes through the right side of the measuring system, performing generalized Radon transformation on the time and azimuth course matrix R (t, theta) for the second time to obtain a course angle theta 0 And a transformation parameter space matrix U 'of the ratio k' 2 (k,Θ 0 )；
Then U 'will be' 2 (k,Θ 0 ) The abscissa value corresponding to the maximum value position in the range is used as the target course angle theta 0 Prepared from U' 2 (k,Θ 0 ) The ordinate value corresponding to the maximum position in the target is used as the ratio k of the movement speed of the target to the nearest passing distance.
The result of performing the second generalized Radon transform on the results of fig. 4 and 5 is shown in fig. 8 and 9.
Selecting the abscissa and ordinate corresponding to the maximum position in fig. 8 and 9, where the abscissa is the target heading angle Θ 0 The ordinate value corresponds to a ratio k of the moving speed of the target to the closest passing distance.
The fifth concrete implementation mode is as follows: the fourth difference between this embodiment and the specific embodiment is that: the specific process of the step four is as follows:
there are several existing methods for obtaining the velocity of movement of objects, including non-line spectral objects, that can be used in conjunction with the present invention. The method for measuring the speed of the ship line spectrum target by using the line spectrum Doppler phenomenon is only provided. Acoustic targets such as ships and the like often contain rich line spectrum information due to the functions of propellers, main engines and auxiliary engines.
When radial relative motion exists between the target and the receiving point, the line spectrum generates a Doppler frequency shift phenomenon, the Doppler frequency shift is related to the radial motion speed and the central frequency of the target, the target speed can be estimated by measuring the line spectrum two-way Doppler frequency shift of the straight-ahead flight target in the approaching and departing processes, and the central frequency is f 0 Has a Doppler shift Deltaf and a moving speed v in a relationship of
Thus, can obtain
And c is the sound velocity in water, can be measured by a sound velocity gradiometer, and can be 1500m/s under an unknown condition. Center frequency f of line spectrum 0 Equal to the target most recent transit time t 0 The corresponding line spectral frequency.
The method comprises the following steps of measuring the line spectrum frequency f of a target in real time by using a time-frequency analysis or frequency measurement method, and calculating the Doppler frequency offset delta f according to the line spectrum frequency f:
Δf＝f-f 0
wherein: f. of 0 Target recent transit time t 0 The corresponding line spectrum frequency;
then calculating the target motion speed v according to the Doppler frequency offset delta f;
wherein: c is the speed of sound in water;
calculating the nearest passing distance r of the target according to the ratio k of the target movement speed to the nearest passing distance 0 。
Therefore, the larger the absolute value of the Doppler frequency shift delta f is in actual processing, the more accurate the measured speed is, and the larger the Doppler frequency shift is when the target distance is far away, so that the moment when the target distance is far away can be selected as much as possible to measure the Doppler frequency shift and measure the speed in actual use. And obtaining the target motion speed by using a speed calculation formula after measuring the Doppler frequency offset.
Fig. 10 is a time-frequency analysis result of a 300Hz target line spectrum measured by simulation under the same motion parameters as fig. 4 and fig. 5, and fig. 11 is a result of frequency measurement of the time-frequency result at each moment.
The sixth specific implementation mode: the fifth embodiment is different from the fifth embodiment in that: the concrete process of the fifth step is as follows:
and after the parameters are obtained, the motion trail of the target can be calculated. Coordinate information of the target in a northeast coordinate system centered on the measurement system is obtained.
The coordinate of the target at the closest passing distance is (x) 0 ,y 0 ) If the target is passing from the left side of the measurement system, (x) 0 ,y 0 ) The calculation formula of (c) is:
x 0 ＝r 0 cos(θ 0 (t 0 )+270)
y 0 ＝r 0 sin(θ 0 (t 0 )+270)
if the target is passing from the right side of the measurement system, (x) 0 ,y 0 ) The calculation formula of (2) is as follows:
x 0 ＝r 0 cos(θ 0 (t 0 )+90)
y 0 ＝r 0 sin(θ 0 (t 0 )+90)
the motion trajectory of the target in the northeast coordinate system is:
from this, it is derived to obtain the motion trajectory (x, y) of the target, and the simulation conditions are set according to fig. 4 and 5, and the result of estimating the motion trajectory of the target is shown in fig. 12 and 13.
Fig. 12 and 13 show "" curves as actual motion trajectories of targets, "o" curves as estimated trajectory results, and "" positions of measurement systems, i.e., coordinate origin positions.
The above-described calculation examples of the present invention are merely to explain the calculation model and the calculation flow of the present invention in detail, and are not intended to limit the embodiments of the present invention. It will be apparent to those skilled in the art that other variations and modifications of the present invention can be made based on the above description, and it is not intended to be exhaustive or to limit the invention to the precise form disclosed, and all such modifications and variations are possible and contemplated as falling within the scope of the invention.
Claims (4)
1. A line spectrum target motion parameter estimation method based on a time azimuth process map is characterized by comprising the following steps:
step one, reading a time azimuth process chart formed by the movement of a line spectrum target, and obtaining a time azimuth process matrix R (t, theta), wherein: theta is the azimuth angle of the target, and t is time; judging whether the target passes through the left side or the right side of the measuring system according to the time azimuth process matrix R (t, theta);
step two, performing first generalized Radon transformation on the time azimuth history matrix R (t, theta) according to the judgment result of the step one to obtain the latest passing time t of the target 0 ；
Step three, obtaining the latest passing time t according to the step two 0 Performing generalized Radon transformation on the time azimuth history matrix R (t, theta) for the second time to obtain a heading angle theta 0 And a transformation parameter space matrix of velocity to nearest passing distance ratio k, wherein: k is the ratio of the target movement speed to the nearest passing distance;
according to the course angle theta 0 Solving the course angle theta of the target by the transformation parameter space matrix of the sum speed and the nearest passing distance ratio k 0 And a ratio k of the target movement speed to the nearest passing distance;
step four, solving the moving speed v of the target, and then calculating the nearest passing distance r of the target by utilizing the ratio k obtained in the step three 0 ；
The specific process of the step four is as follows:
measuring the line spectrum frequency f of the target in real time, and calculating the Doppler frequency offset delta f according to the line spectrum frequency f:
Δf＝f-f 0
wherein: f. of 0 Target recent passage time t 0 The corresponding line spectrum frequency;
then calculating the target motion speed v according to the Doppler frequency offset delta f;
wherein: c is the speed of sound in water;
calculating the nearest passing distance r of the target according to the ratio k of the target movement speed to the nearest passing distance 0 ；
Step five, reversely deducing the motion trail of the target by using the results obtained in the step two to the step four;
the concrete process of the step five is as follows:
the coordinate of the target at the closest passing distance is (x) 0 ,y 0 ) If the target is passing from the left side of the measurement system then (x) 0 ,y 0 ) The calculation formula of (2) is as follows:
x 0 ＝r 0 cos(θ 0 (t 0 )+270)
y 0 ＝r 0 sin(θ 0 (t 0 )+270)
wherein r is 0 Is the closest passing distance of the target, theta 0 (t 0 ) For the target at the latest passing time t 0 Corresponding target azimuth, t 0 Is the target recent transit time;
if the target is passing from the right side of the measurement system, (x) 0 ,y 0 ) The calculation formula of (2) is as follows:
x 0 ＝r 0 cos(θ 0 (t 0 )+90)
y 0 ＝r 0 sin(θ 0 (t 0 )+90)
the motion trajectory of the target in the northeast coordinate system is:
2. the method for estimating the motion parameters of the line spectrum target based on the time and azimuth history map according to claim 1, wherein the specific process of the first step is as follows:
and taking the position of the measuring system as a coordinate origin O, and establishing a left-hand coordinate system by adopting the northeast coordinate, wherein: the positive direction of the x axis points to the true north direction of the geodetic coordinates, and the positive direction of the y axis points to the true east direction of the geodetic coordinates;
measuring a time azimuth process chart formed by the movement of a line spectrum target by using a measuring system to obtain a time azimuth process matrix R (t, theta), wherein: theta is the azimuth angle of the target, and t is time;
and if the target azimuth angle theta gradually becomes larger along with the time t, the target is considered to pass through the left side of the measuring system, otherwise, if the target azimuth angle theta gradually becomes smaller along with the time t, the target is considered to pass through the right side of the measuring system.
3. The method for estimating the motion parameters of the line spectrum target based on the time azimuth history chart according to claim 2, wherein the specific process of the second step is as follows:
defining the ratio of the target movement speed to the nearest passing distance as k;
if the target passes through the left side of the measurement system, performing first generalized Radon transformation on the time azimuth history matrix R (t, theta) to obtain k and the latest passing time t of the target 0 Is transformed to a parameter space matrix U 1 (k,t 0 )；
Wherein: n is the discrete time number, i represents the ith of N discrete times, t (i) is the ith discrete time value, theta 0 (t 0 ) For the target at the latest passing time t 0 The corresponding target azimuth angle, R (-) represents Radon transformation;
according to a transformation parameter space matrix U 1 (k,t 0 ) Selecting the abscissa corresponding to the maximum k value as the latest passing time t 0 ；
If the target passes through the right side of the measurement system, performing first generalized Radon transformation on the time azimuth history matrix R (t, theta) to obtain k and the latest passing time t of the target 0 Of transformation parameter space matrix U' 1 (k,t 0 )；
According to a transformation parameter space matrix U' 1 (k,t 0 ) Selecting the abscissa corresponding to the maximum k value as the latest passing time t 0 。
4. The method for estimating the motion parameters of the line spectrum target based on the time azimuth history chart according to claim 3, wherein the specific process of the third step is as follows:
if the target is passing from the left side of the measurement system, to the time bearingPerforming generalized Radon transformation on the course matrix R (t, theta) for the second time to obtain a course angle theta 0 Transformation parameter space matrix U of sum velocity and nearest passing distance ratio k 2 (k,Θ 0 )；
Then U will be 2 (k,Θ 0 ) The abscissa value corresponding to the maximum value position in the range is used as the target course angle theta 0 Will U is 2 (k,Θ 0 ) The longitudinal coordinate value corresponding to the maximum position in the target image is used as a ratio k of the target movement speed to the nearest passing distance;
if the target passes through the right side of the measurement system, performing second generalized Radon transformation on the time and azimuth history matrix R (t, theta) to obtain a heading angle theta 0 And a transformation parameter space matrix U 'of the ratio k' 2 (k,Θ 0 )；
Then U 'will be' 2 (k,Θ 0 ) The abscissa value corresponding to the maximum value position in the range is used as the target course angle theta 0 Prepared from U' 2 (k,Θ 0 ) And taking the ordinate value corresponding to the maximum value position in the target image as the ratio k of the target movement speed to the nearest passing distance.
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