CN101308206B - Circumferential track mobile target tracking method under white noise background - Google Patents
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Abstract
The invention provides a circle trajectory maneuvering target tracking method under white noise. The method firstly measures the location of a maneuvering target based on the three-station time-difference-of-arrival (TDOA) principle and then chooses a part of points from measuring points to form a section of arc which is equally divided and paired according to the principle of symmetry, so as to get the intersection point of the perpendicular bisector of a chord corresponding to the paired arc and filter the intersection point by three steps, and the mean coordinates of intersection points in an intersection point set will be the estimated value of the circle center, finally, a Kalman filtering method is used to filter the measuring track and calculate the root mean square error. The invention can estimate the moving track of the circle trajectory maneuvering target under white noise and reduce the amount and time of calculation.
Description
Technical field
The present invention relates to the circular path maneuvering target tracking method under a kind of white noise background, belong to the passive detection field.
Background technology
In traditional aviation electronics, radar is as the major equipment of airborne detection system, just be subjected to increasing challenge, various airborne and alarm equipments ground all can be made alarm to the radar emission signal, inappropriate start mode is exposed to self under enemy's the antiaircraft fire possibly, we can say that an effective way that improves aircraft survivability is exactly to reduce the probability that the radar emission signal is intercepted and captured by the enemy, in this sense, the effective means that addresses this problem just based on the appearance of the passive radar of passive detection technology.Passive detection be by the electromagnetic wave signal of detection of a target radiation or scattering find, analyze, identification, tracking target because working method is hidden, be difficult for being found that by enemy's reconnaissance system the detection of a target has apart from advantage, can win long pre-warning time.Along with the avionic development of a new generation, the passive detection technology more and more is subject to people's attention as important field in the aviation electronics, the passive detection technology is applied in the Lock on as an important means of electronic countermeasure, and USAF has been that the ALR-69RWR receivers that more than 30 countries use install " low-cost fast accurately positioning function " additional; Israel and Russia have also begun to install additional passive detection equipment on early warning plane, complex apparatus is exactly a Passive Detention System in the aviation electronics of the 4th generation opportunity of combat F22 of the U.S., it can be followed the tracks of radiation target outside 460km, lock onto target outside 220km.We can say that passive detection has become requisite detection means in the aviation electronics of new generation.
Target following is an important topic in passive detection field, in recent years the focus of always paying close attention to for people; The tracking of maneuvering target then is one of them research emphasis.The method of passive detection is a lot, as: survey methods such as time difference location, direction finding location, survey Doppler shift location, because the influence of factors such as noise and measuring error, certainly existing positioning error, must adopt reasonable method that locator data is carried out Filtering Estimation, at the different kinetic characteristic of target, method of estimation is also different, and general motion model has CV model, CA model, Singer model and " current " model etc. at present.The CV model can be adopted for circumference maneuvering target at the uniform velocity, but different, before application model, the motor-driven center of target, the i.e. center of circle must be at first determined the target of circular motion with rectilinear motion.
A kind of string perpendicular bisector of propositions such as J.A.ROECKER intersection point method of average obtains the suboptimum estimation technique of motor-driven central point, and the method for estimation of this central point is simple, but when noise increased a little, the central point that obtains can obviously depart from actual value, causes than large deviation.This method is obtained the perpendicular bisector of any 2 lines on the circular arc earlier, utilizes the coordinate of the average of these perpendicular bisector intersection points as motor-driven center again.When n point arranged on the circular arc, the intersection point number of all perpendicular bisectors was k (k-2)/4 (k=n (n-1)) under maximum situations, if n=10 then need calculate 1980 number of hits, obviously calculated amount is excessive.Generally speaking, owing to measure the existence of noise, each intersection point number that calculates might be inequality, causes computing time unequal and can't predict; On the other hand, when noise was big, the estimated value error at motor-driven center is bigger, three kinds of situations mainly occur: one, the part intersection point was offset to the protruding side of circular arc, two, the part intersection point obviously depart from arc the perpendicular bisector of corresponding string, three, indivedual intersection point distance of each point to the arc is obviously bigger than normal or less than normal.
Though classical least square method is optimum method of estimation under square error, but calculated amount is big under the more situation of measurement point, and need find the solution nonlinear equation, cause growing computing time and not restraining sometimes, therefore be unfavorable for the Fast estimation at circular path center, be subjected to certain restriction in actual applications.
Summary of the invention
The object of the present invention is to provide the circular path maneuvering target tracking method under a kind of white noise background; this method is that calculated amount is little; take the circular path maneuvering target tracking method under the few white noise background of resource; this method can be carried out Fast estimation to the center of circle of circular path maneuvering target; compare with least square method; under the identical condition of evaluated error, reduced the calculation amount, shortened computing time, thereby can realize quick tracking the circular path maneuvering target.
The method that the present invention proposes is surveyed time-of-arrival loaction to three stations and is obtained the position data of target as measurement point, one section arc that selected part point constitutes in measurement point, principle according to symmetry is carried out continuous five equilibrium and pairing to arc, obtain the intersection point of perpendicular bisector of string of the arc correspondence of pairing, all intersection points have constituted the intersection point set, filter with the intersection point in three step of the time-division pair set, the average of last resulting intersection point is the estimated value at round track center, after obtaining the center of circle, utilizing hybrid coordinate is method, target trajectory is carried out Kalman filtering, obtain the estimated value of target trajectory, according to the estimated value geometric locus of tracking target that draws, and calculate root-mean-square error, the error bright tracking effect of novel more is good more.This method is compared with the center of circle that estimates with least square method, and last tracking error is identical, but the used time shortens greatly.
Method provided by the invention is divided into following ten steps:
Step 1: survey time difference principle with three research stations maneuvering target is positioned;
If T
0For target transmits the time, r
iBe the distance of target and i research station, c is the light velocity, t
iFor signal by the time of target to the research station, (x
i, y
i) be the position of research station, (x y), carries out Continuous Observation and calculating to target, just can obtain the position measurement point data of target then can to obtain the target location according to formula 1;
r
1 2＝(x-x
1)
2+(y-y
1)
2
r
2 2＝(x-x
2)
2+(y-y
2)
2
r
3 2＝(x-x
3)
2+(y-y
3)
2
Step 2: the standard deviation of input measurement point data, measuring error and desired evaluated error d;
If counter variable i=0, the measure dot number of j circular path of input reaches desired error d according to this, and one section arc note that described j measurement point constitutes is made a[i * j+1, (i+1) * j], wherein variable j is a single measurement point sample drawn number, j=2
N+ 1, N is an exponent number, and is relevant with the sum M of measurement point on the circular path, and N satisfies 2
N+ 1＜＜M;
Step 3: to the described arc of step 2 carry out partition to and calculate intersection point;
The described arc of step 2 is divided equally into two parts, and note is done respectively
With
Again with arc a
1And a
2Divide equally and be a
11, a
12, a
21, a
22, the rest may be inferred, up to being divided into arc
(i
h=1,2, h=1......N), then all arcs constitute binary tree structure; This binary tree structure is a total N+1 layer from top to bottom, all chooses centrosymmetric two the pairing string perpendicular bisector of arc intersection points as alternative point for each layer, for example for the n=3 layer, chooses (a
11, a
22) and (a
12, a
21) these two sections arcs match, the rest may be inferred, up to the n=N+1 layer; Obtain all be made into right arc the perpendicular bisector equation of corresponding string, obtain the intersection point of two perpendicular bisectors of each centering again, all intersection points constitute the intersection point S set, the equation of find intersection as formula (2) to shown in the formula (7):
Wherein, x
1, y
1, x
3, y
3Be the coordinate of two end points on the arc, x
2, y
2Be point coordinate in the arc,
It is the perpendicular bisector intersecting point coordinate of two sections strings;
Step 4: filtering is at the intersection point of arc projection one side;
Concrete grammar is: with intersecting point coordinate and arc a[i * j+1 in the described intersection point S set of step 3, (i+1) * j] middle point coordinate bring the equation of the pairing string of arc a respectively into, the symbolization determining method determines that the mid point of intersection point among the S and arc lays respectively at the homonymy or the heteropleural of string, the symbol decision method is meant by the symbol of the result of calculation behind the substitution equation judges homonymy or heteropleural relation, be arranged in homonymy then from this point of described intersection point S set filtering, heteropleural then keeps this point, and S set becomes S1;
Wherein the expression formula of the string of arc correspondence is as shown in Equation (8):
Wherein, x
1, y
1, x
2, y
2Coordinate for the end points of arc;
Step 5: filtering is apart from the bigger intersection point of arc two-end-point range difference;
Concrete grammar is: calculate that each puts the range difference of arc two-end-point in the set of described intersection point, when range difference greater than given threshold value d
1The time, this point of filtering from intersection point S set 1 then, S set 1 becomes S2; d
1Initial value can elect desired evaluated error d as, if described intersection point S set 2 is empty, then need increase d
1Value, recomputate step 5;
Step 6: the mean value of filtering distance of each point to the arc is greater than given threshold value d
2Intersection point;
For all intersection points, obtain the average value mu of the distance of each point on the arc respectively
k(k=1......2
N-1), these mean values as sample, is obtained sample average μ and standard deviation sigma, make d
2=σ, when | μ-μ
k|＞d
2The time, then from intersection point S set 2, filtering out k intersection point, S set 2 becomes S3; d
2Initial value can elect the evaluated error d of expectation as, if described intersection point S set 3 is empty, then need increase d
2Value, recomputate step 6;
Step 7: calculate the mean value of intersection point in the described intersection point S set 3, be the estimated value at circular path center;
With the mean value of intersection point in the described intersection point S set 3 that obtains estimated value as circle track center;
Step 8: judge whether that all measure dot number are according to all importing;
Make i=i+1, if i * (2
N+ 1)＜and M, then continue step 2, otherwise finish;
Step 9: the track that estimates the center of circle is carried out Kalman filtering, obtain the estimated value of target trajectory;
The coordinate of Kalman filtering is the polar coordinate system at current goal place, the transfer equation of this coordinate system and rectangular coordinate system as shown in Equation (9):
(9)
Wherein, x, y be tracing point rectangular coordinate system in coordinate, x
0, y
0Be current center of circle estimated value, r, θ are the coordinate of tracing point in polar coordinate system;
Step 10: according to the estimated value pursuit path of target that draws, and weigh the effect of tracking with the track root-mean-square error that calculates, the track root-mean-square error is more little, and tracking effect is good more.
The invention has the advantages that:
(1) compare with the center of circle of adopting least square method to estimate, under the identical condition of last tracking error, the used time shortens greatly;
(2) compare with the center of circle of adopting least square method to estimate, computation complexity reduces;
(3) in polar coordinate system, carry out Kalman filtering, can avoid the nonlinear filtering computing in rectangular coordinate system, reduced calculated amount.
Description of drawings
Fig. 1 is the method for the invention process flow diagram;
Fig. 2 is arc five equilibrium of the present invention and matching method synoptic diagram;
Fig. 3 is for being used for the aircraft flight track synoptic diagram of example with the inventive method;
Fig. 4 for obtain with the inventive method circle track centre coordinate to flight path filtering after the axial Error Graph of x;
Fig. 5 for obtain with least square method circle track centre coordinate to flight path filtering after the axial Error Graph of x.
Embodiment
The present invention is described in further detail below in conjunction with drawings and Examples.
As shown in Figure 1, be the method for the invention process flow diagram.
The first step, survey time difference principle with three research stations maneuvering target is positioned, obtain the position measurement of target;
Second step, input measurement point data, the standard deviation of measuring error and desired evaluated error;
The 3rd step, that the arc that the measurement point of input is constituted carries out partition is right, and calculates the intersection point S set;
The 4th step, point coordinate in the coordinate of each point in the intersection point S set and the corresponding arc is brought into formula (8) respectively, according to the jack per line filtering, the principle that contrary sign keeps, filtering obtains intersection point S set 1 at the intersection point of arc projection one side;
The 5th step, calculate that each puts the range difference of arc two-end-point in the described intersection point S set 1, when range difference greater than threshold value d
1The time, this point of filtering from intersection point S set 1 then, S set 1 becomes S2, d
1Initial value get desired evaluated error d, judge that whether intersection point S set 2 is empty, as be sky, then need increase d
1Value, recomputate the range difference that each puts the arc two-end-point, until till S2 is not empty set;
The 6th step, for all intersection points among the S2, obtain the average value mu of this distance of each point to the arc respectively
k, these mean values as sample, are obtained sample average μ and standard deviation sigma, make d
2=σ, when | μ-μ
k|＞d
2The time, then from intersection point S set 2, filtering out k intersection point, S set 2 becomes S3; d
2Initial value get desired evaluated error d, if described intersection point S set 3 is empty, then need increase d
2Value, recomputate this step, be not empty set up to S3;
The 7th goes on foot, obtains the mean value of intersecting point coordinate in the described intersection point S set 3, is the estimated value at circular path center;
The 8th step, judge whether all measure dot number according to all importing, if all input then end, otherwise would get back to step 2;
The 9th the step, the track that estimates the center of circle is carried out Kalman filtering, obtain the estimated value of target trajectory;
The tenth step, according to the estimated value pursuit path of target that draws, and weigh the effect of tracking with the track root-mean-square error that calculates, the track root-mean-square error is more little, tracking effect is good more.
As shown in Figure 2, be arc five equilibrium of the present invention and matching method synoptic diagram, a of top layer is that the measure dot number of input is according to the arc that constitutes, second layer a
1And a
2Be a to be divided equally form two sections arcs that obtain, in like manner, four sections arcs of the 3rd layer are to a
1And a
2Cut apart, and the like, be the input data of N for exponent number, constitute the binary tree structure of N+1 layer altogether, wherein the string of two of each bifurcated sections arc correspondences constitutes a pair ofly, is the input data of N for exponent number, altogether 2
N-1 pair of string.
A kind of aircraft provided by the invention is done the example of the trajectory diagram of circular flight, and the flying quality and the measuring error of aircraft are as follows: suppose that aircraft is the center of circle with (20,20) when 0≤t≤30s, it is motor-driven that 2km is that radius is done circumference; When 30≤t≤54.5s, aircraft is the center of circle with (27,20), and it is motor-driven that 5km is that radius is done circumference; When 54.5s≤t≤66s, aircraft is the center of circle with (27,13), and it is motor-driven that 2km is that radius is done circumference, and wherein t is the time; The time T if target transmits
0The site coordinate of=0, three research stations is respectively (0,0), (0,20), (30,0), and the observation cycle of establishing flight path is 0.5s, the measuring error dx=dy=0.5km under the cartesian coordinate system.
At first application of formula (1) obtains the position measurement of aircraft, shown in the discrete dotted line of Fig. 3, imports k=1 then, and k * (2
N+ 1) measure dot number of individual circular path is according to N=5 and anticipation error d=1km;
To carry out partition right according to constituting arc to described measure dot number, obtains 31 pairs altogether, calculates the intersection point of perpendicular bisector of the string of every pair of arc correspondence, obtains intersection point and gather;
Filter according to the method antinode intersection of sets point of step 4, get intersection point set to the end to step 6;
Intersection point in the pair set is averaged, and obtains the estimated value of circle center;
Make k=k+1, continue the operation of step 2, to the last obtain the coordinate at three round track centers.
Following table is to utilize the comparison to the estimated result of described example of this paper method and least square method:
Table 1
As can be seen from Table 1, method provided by the invention is similar to the error of circle track center estimation with least square method, and the average error that the present invention estimates the circle track is 1.664, and the average error that least square method is estimated is 1.444; But from computing time, method provided by the invention is much smaller than least square method.
After obtaining center of circle estimated value, the target measurement track is carried out filtering, obtain filtered target trajectory curve, shown in Fig. 3 continuous lines with Kalman filtering method.
Ask the root-mean-square error of filtered target trajectory at last, Fig. 4 and Fig. 5 carry out the axial trajectory error comparison diagram of filtered x to track behind the round track centre coordinate that obtains of the present invention and least square method, Fig. 4 obtains behind the circle track centre coordinate the axial Error Graph of x after the flight path filtering with the inventive method, Fig. 5 obtains behind the circle track centre coordinate the axial Error Graph of x after the flight path filtering with least square method, two curves are arranged on each figure, above one be the root-mean-square error of measurement data, below one be the root-mean-square error of the estimated value of track on the x direction, as can be seen, no matter be the present invention or least square method, the trajectory error after the estimation is all less than the measured value error; The average of the track x direction root-mean-square error after the present invention and least square method estimation is near 0.3, fluctuation range is from 0.2-0.4, and least square method also has at some some place jumps, the result shows: the error of method of estimation to circumference maneuvering target track following time the to circle track center that the present invention proposes is similar to least square method, but as seen from Table 1, the present invention computing time that circle track center is estimated is much smaller than least square method.
Claims (4)
1. the circular path maneuvering target tracking method under the white noise background, it is characterized in that: this method comprises following step:
Step 1: survey time difference principle with three research stations maneuvering target is positioned, establish counter variable i=0;
Step 2: the standard deviation of input measurement point data, measuring error and desired evaluated error;
The measure dot number of j circular path of input reaches desired error d according to this, and one section arc note that described j measurement point constitutes is made arc a[i * j+1, (i+1) * j], wherein variable j is a single measurement point sample drawn number, j=2
N+ 1, N is an index, and is relevant with the sum M of measurement point on the circular path, and N satisfies 2
N+ 1＜＜M;
Step 3: to the described arc a[i * j+1 of step 2, (i+1) * j] carry out partition to and calculate intersection point;
To the described arc a[i * j+1 of step 2, (i+1) * j] to carry out partition according to the method for symmetry right: with the described arc a[i * j+1 of step 2, (i+1) * and j] be divided equally into two parts, note is done respectively
With
N is an index, again with arc a
1And a
2Divide equally and be a
11, a
12, a
21, a
22, the rest may be inferred, up to being divided into arc
i
h=1,2, h=1......N, then all arcs constitute binary tree structure; This binary tree structure is a total N+1 layer from top to bottom, all chooses centrosymmetric two the pairing string perpendicular bisector of arc intersection points as alternative point for each layer; Obtain all be made into right arc the perpendicular bisector equation of corresponding string, obtain the intersection point of the perpendicular bisector of every pair of pairing string of arc again, all intersection points constitute the intersection point S set;
Step 4: filtering is at arc a[i * j+1, (i+1) * j] intersection point of a protruding side;
With intersecting point coordinate and arc a[i * j+1 in the described intersection point S set of step 3, (i+1) * j] mid point substitution arc a[i * j+1 respectively, (i+1) * and j] equation of pairing string, the symbolization determining method is determined intersection point and the arc a[i * j+1 among the S, (i+1) * j] mid point lay respectively at the homonymy or the heteropleural of string, be arranged in homonymy then from this point of described intersection point S set filtering, heteropleural then keeps this point, and S set becomes S1;
Step 5: filtering is apart from arc a[i * j+1, (i+1) * j] intersection point that the two-end-point range difference is bigger;
Calculate that each puts arc a[i * j+1 in the described intersection point S set 1, (i+1) * j] range difference of two-end-point, when range difference greater than given threshold value d
1The time, this point of filtering from intersection point S set 1 then, S set 1 becomes S set 2;
d
1Initial value elect desired evaluated error d as, if described intersection point S set 2 is empty, then need increase d
1Value, recomputate step 5;
Step 6: filtering is to arc a[i * j+1, (i+1) * j] go up the absolute value of difference of the mean value of distance of each point and sample average greater than the intersection point of given threshold value;
For all intersection points, obtain arc a[i * j+1 respectively, (i+1) * and j] go up the average value mu of the distance of each point
k, k=1......2
N-1, these mean values as sample, are obtained sample average μ and standard deviation sigma, when | μ-μ
k|＞d
2The time, then from intersection point S set 2, filtering out k intersection point, S set 2 becomes S3;
d
2Initial value elect desired evaluated error d as, if described intersection point S set 3 is empty, then need increase d
2Value, recomputate step 6;
Step 7: calculate the mean value of intersection point in the described intersection point S set 3, be the estimated value at circular path center;
With the mean value of intersection point in the described intersection point S set 3 that obtains estimated value as circle track center;
Step 8: judge whether that all measure dot number are according to all importing;
Make i=i+1, if i * (2
N+ 1)＜and M, M is the sum of the measurement point on the circular path, then continues step 2, otherwise finishes;
Step 9: the track that estimates the center of circle is carried out Kalman filtering, obtain the estimated value of target trajectory;
Step 10:, and weigh the effect of tracking with the track root-mean-square error that calculates according to the estimated value pursuit path of target that draws.
2. the circular path maneuvering target tracking method under a kind of white noise background according to claim 1; it is characterized in that described the pairing according to symmetrical manner of step 3 is meant: the mid point with the measurement point track of current input is symmetric points, and it is one group that the string of symmetry spatially that will be positioned at the symmetric points both sides is joined.
3. the circular path maneuvering target tracking method under a kind of white noise background according to claim 1; it is characterized in that the described symbol decision method of step 4 is meant intersection point and middle point coordinate respectively behind the equation of substitution string; if two results are jack per line then are homonymy that contrary sign then is a heteropleural.
4. the circular path maneuvering target tracking method under a kind of white noise background according to claim 1 is characterized in that the described Kalman filtering of step 9 is to carry out under polar coordinate system.
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| CN102589549B (en) * | 2011-12-22 | 2017-09-29 | 中国人民解放军海军航空工程学院 | Three station direction cross positioning track algorithm in terrestrial coordinate system space |
| CN103869279B (en) * | 2014-02-27 | 2017-01-25 | 杭州电子科技大学 | Multi-target positioning tracking method with multiple sensor platforms |
| CN104363461B (en) * | 2014-11-04 | 2017-12-22 | 中国科学技术大学 | The error concealing method of frame of video and apply its video encoding/decoding method |
| CN104950286A (en) * | 2015-06-10 | 2015-09-30 | 哈尔滨工业大学 | Optimal inflection point determining method under single passive radar limiting condition |
| CN107271974B (en) * | 2017-06-08 | 2020-10-20 | 中国人民解放军海军航空大学 | Space-time error solving method based on stable angular points |
| CN112147574B (en) * | 2020-09-25 | 2022-02-01 | 四川九洲电器集团有限责任公司 | Multi-station positioning algorithm verification method and simulation system |
| CN112581279B (en) * | 2020-12-25 | 2024-03-19 | 深圳市富途网络科技有限公司 | Ordering method of desktop financial software and related products |
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