CN109839620A - A kind of least square method for estimating radar system error for combining ADS-B - Google Patents
A kind of least square method for estimating radar system error for combining ADS-B Download PDFInfo
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Abstract
The present invention provides a kind of least square method for estimating radar system error for combining ADS-B, it is related to radar information processing technical field, first by two-coordinate radar and ADS-B to target joint observation, then ADS-B is measured from geographic coordinate system and is transformed into radar local rectangular coordinate system, establish unified registration space；Secondly on the basis of the sampling time of radar track, interpolation is carried out to ADS-B track, constructs new ADS-B track；Simultaneously according to 3 σ principles, the outlier of radar track is rejected；Then the linear equation of radar track and ADS-B track is calculated separately using straight line fitting, and calculates the angle of two straight lines, recycles the course angular data of angle compensation radar track；Radar system error is finally estimated using least-squares algorithm.The present invention can more effectively estimate radar system error；After proposing method registration process, the average inclined range error and azimuth angle error of radar track data reduce 71.7% and 52.7% respectively.
Description
Technical field
The present invention relates to radar information processing technical field more particularly to a kind of least square radar systems for combining ADS-B
System error estimation.
Background technique
In radar network composite, radar system error estimation is the matter of utmost importance of multi-sensor multi-target tracking, is closed with track
Premised on connection is mutual.The measurement error of electronic skyscreen mainly includes the error of two kinds of forms: random error and systematic error with
Chance error difference can be filtered out using various filtering methods.Systematic error is a kind of deterministic type error, is difficult to pass through filtering method
Processing, needs to estimate it, recycles estimated value to compensate or be registrated radar measurement, can reduce or eliminate it
It influences.The presence of systematic error can reduce the precision of tracking result, cause tracking root-mean-square error more much larger than theoretical value；Seriously
When cause more radar measurements from same target to be associated with failure, or even generate a plurality of track, it is difficult to formed it is unified, accurately with
Track situation.Therefore in radar network composite, how to solve radar system error estimation problem and improve the essence of systematic error estimation
Degree is one of the key points and difficulties in multi-sensor multi-target tracking field.
Existing method generally assume that radar system error be fixed value, mainly include real-time accuracy control (RTQC) algorithm,
Least square (LS) algorithm, Generalized Least Square (GLS) algorithm, the GLS algorithm (EFEC-GLS) based on ECEF coordinate system,
Maximum likelihood (ML) algorithm is augmented (ED) algorithm and their improved method.But the above method is deposited in practical radar network composite
In following characteristic and defect:
(1) systematic error of different radars is generally different, or even differs greatly；
(2) radar range is remoter, and measurement error is bigger；
(3) since the sampling instant of different radars is different, the sampling period (or sampling interval) is larger, it is contemplated that target flight
Speed is fastly and the uncertainty of target trajectory often introduces newly when causing to radar track progress time adjustment
Error.Therefore, the measurement error that radar measurement data include in practice is generally large.In such case, it is contemplated that above-mentioned
Estimation method is built upon mostly on least square model, and the shadow of systematic error second order or higher order term is had ignored in calculating process
It rings, so that the estimated accuracy of these methods also will receive very big influence in practice.
In view of systematic error estimation and track association it is mutual premised on, in the prior art combine plot-track Association Algorithm solve simultaneously
Certainly systematic error estimation problem.It such as proposes a kind of more radar robust Data Associations based on referring to topological characteristic, can solve
Certainly more radar track related questions under the influence of systematic error；It is proposed a kind of robust Data Association based on distance measurement,
The robust track association problem being able to solve in the complex environment of sensor time-varying error, heavy dense targets and multiple target；It is based on
Gaussian random vector statistical property proposes more radar robust plot-track Association Algorithms of the space base of a kind of suitable complex environment etc..But
It is that above-mentioned algorithm complexity is high, is subject to certain restrictions in engineer application.
In fact, if it is known that the actual position of target, then radar system error estimation procedure will be greatly simplified.It examines
The advantages of considering ADS-B, Li Pengfei, wait scholars propose " based on multi straight fusion radar system error calibration algorithm grind
Study carefully ", from the angle of graphics, propose a kind of Radar Calibration error (FL) algorithm based on multi straight fusion.Although FL method letter
It is single practical, but it still needs further improvement for its estimated accuracy.
For this purpose, combining tracking platform based on two-coordinate radar and ADS-B herein, in " the radar system based on multi straight fusion
Error demarcated method of uniting is studied " on the basis of, while considering tradition based on the systematic error estimation method of LS model to measurement
The more sensitive feature of data, the application propose a kind of least square method for estimating radar system error for combining ADS-B.It proposes
Method is pre-processed first against the characteristics of radar measurement and ADS-B metric data, then estimates radar system using LS algorithm
System error is finally verified using validity and feasibility of the measured data experiment to the method for proposition.
Based on this, thus this case generates.
Summary of the invention
In order to solve drawbacks described above existing in the prior art, the present invention provides a kind of least squares for combining ADS-B
Method for estimating radar system error can more effectively estimate radar system error, improve estimated accuracy.
To achieve the goals above, the technical solution adopted by the present invention is as follows:
A kind of least square method for estimating radar system error for combining ADS-B, includes the following steps:
Step S100 two-coordinate radar and ADS-B constitute target joint observation with a two-coordinate radar and ADS-B
Multi-Sensor Tracking system measures the inclined range of same cooperative target, azimuth, obtains radar track and ADS- respectively
B track；
Step S200 radar track and ADS-B track pre-process；
Wherein, step S200 includes
The ADS-B geographic coordinate system measured is transformed into the partial, right angle centered on radar by the conversion of step S210 coordinate
Coordinate system establishes unified registration space；
Step S220 temporal registration carries out interpolation, construction to ADS-B track on the basis of the sampling time of radar track
New ADS-B track；
Step S230 rejects the outlier of radar track, rejects the outlier in radar track data using 3 σ criterion；
The compensation of step S240 radar bearing angle error: radar track and ADS-B track are calculated separately using straight line fitting
Linear equation, and the angle of two straight lines is calculated, recycle the course angular data of angle compensation radar track；
Step S300 is based on least-squares algorithm and estimates radar system error.
It is further preferred that the ADS-B geographic coordinate system measured is transformed into centered on radar in the step S210
Local rectangular coordinate system after, then ADS-B metric data is converted into polar coordinates from rectangular co-ordinate, finally by radar measurement and
ADS-B measurement conversion is to plane right-angle coordinate, if (xi′,yi') and (ri,θi) it is respectively that radar measurement or ADS-B are measured
Polar coordinates and rectangular co-ordinate, then finally obtain
Further, in the step S220, with the sampling instant sequence of radar track dataOn the basis of, to ADS-
B track data carries out interpolation, and interpolating sequence obtained by calculation is as new ADS-B track data, use and radar sampling
Moment tR,iTwo adjacent ADS-B measure zA,j、zA,j+1(tA,j<tR,i<tA,j+1) calculate interpolation:
Wherein,
In formula, tA,j、tA,j+1For corresponding zA,j、zA,j+1Sampling instant.
Further, in the step S230, comprising the following steps:
Step S231 is according to the metric data collection of radar trackEstimated using least-square fitting approach
Straight lineEquation:
Step S232 calculates each radar measurement zR,iTo straight lineDistance:
Step S233 calculates standard deviation:
Wherein,
Step S234 works as d according to 3 σ criterionR,i>3σR,lWhen, then zR,iFor outlier, need to delete from radar track data set
It removes, and updates the metric data collection of radar track；Otherwise, continue to retain the measurement；
Step S235 utilizes the data set updated, again fitting a straight line equation；
Step S236 repeats step b-e, until the data set being updated all meets 3 σ criterion.
Further, radar track and the corresponding linear equation of ADS-B track are calculated using least square fitting:
Then the angle of two straight lines, and the thick value that the angle is estimated as radar bearing angle error are calculated:
The bearing data of radar track is finally repaid using the thick value complement:
θ′R,i=θR,i+ΔθR, 0 (11)
Further, if radar track data and ADS-B track data are after pretreatment, (rR,i,θR,i) and (rA,i,
θA,i) respectively indicate tiThe polar coordinates that radar measurement and ADS-B of the moment target T in radar polar coordinate system measure, (x 'R,i,
y′R,i) and (x 'A,i,y′A,i) it is respectively their rectangular co-ordinates in radar rectangular coordinate system, Δ rR、ΔθRIt is the oblique of radar respectively
System of distance error and azimuth system error, available according to (1) formula if ignoring the influence with error in measurement:
Because of Δ rR、ΔθRIt is micro, if ignoring their second order term, formula (12) be can simplify are as follows:
In view of ADS-B systematic error is very small with respect to radar system error, ignore ADS-B systematic error here, by it
Actual position as target position, it may be assumed that
By (x 'R,i,y′R,i) and (x 'A,i,y′A,i) geometrical relationship known to:
It can be obtained by identity deformation:
It enablesβ=[Δ rR,ΔθR]T,Then (16) formula matrix
Form can indicate are as follows:
Zi=Hiβ (17)
For M different metric data of radar track, can be obtained according to formula (17):
[Z1,Z2,…HM]T=[H1,H2,…HM]Tβ (18)
Enable H=[H1,H2,…HM]T, Z=[Z1,Z2,…ZM]T, then (19) formula can further indicate that are as follows:
Z=H β (20)
Since (20) formula is overdetermination, can be obtained using the least square estimation method solution:
β=(HTH-1)HTZ (21)。
The working principle of the invention: the advantages of analyzing legacy system error registration method herein and deficiency.It is basic herein
On, for two-coordinate radar systematic error estimation problem, propose a kind of least square radar system error estimation for combining ADS-B
Method.In proposition method, the metric data of radar track and ADS-B track is pre-processed first, including pass through coordinate
Unified registration space is established in conversion, and new ADS-B track is constructed by interpolation, is carried out at rejecting to the outlier of radar track
Reason, and the course angle of radar track data is compensated.After pretreatment, the error of metric data can reduce.So
Afterwards, radar system error is estimated using least-squares algorithm.
The present invention is able to achieve following technical effect:
(1) present invention opposite traditional line approximating method and least square method proposes that method can more effectively, accurately
Estimate radar system error, improves estimated accuracy.
(2) present invention is after proposing method registration process, the average inclined range error of radar track data and azimuth
Error reduces 71.7% and 52.7% respectively.
(3) algorithm used in the present invention is simply uncomplicated, is more widely applied the present invention.
Detailed description of the invention
Fig. 1 is two-coordinate radar and ADS-B joint observation model；
Fig. 2 is the sampling instant of two-coordinate radar and ADS-B；
Fig. 3 is two-coordinate radar and ADS-B track data；
Fig. 4 is the sampling instant of two-coordinate radar and ADS-B；
Fig. 5 is pretreated radar track and ADS-B track data；
Radar track after Fig. 6 registration；
Radar track after the registration of the part Fig. 7；
Fig. 8 inclined range error；
Fig. 9 azimuth angle error.
Specific embodiment
In order to make the attainable technical effect of technological means of the invention and its institute, more perfect exposure can be become apparent from,
Following embodiment is hereby provided, and is described in detail as follows in conjunction with attached drawing:
1, two-coordinate radar and ADS-B joint observation model construction
As shown in Figure 1, in two-coordinate radar and ADS-B joint observation model, with a two-coordinate radar and ADS-B structure
At Multi-Sensor Tracking system, the inclined range of same target, azimuth are measured.In order to estimate that the system of radar is missed
Difference, the generally multipair measurement according to radar and ADS-B to same cooperative target, estimate radar system error, then again
Radar measurement is registrated using estimated value.
In order to facilitate processing, radar and the ADS-B track obtained are briefly referred to as radar track herein and ADS-B navigates
Mark；Simultaneously, it is assumed that radar track and ADS-B track have been subjected to thick association process, are that two kinds of sensors of same cooperative target navigate
Mark, and target moves in a straight line.Although target moves in the sky has uncertainty, sensor track is generally curvilinear motion,
But if within the relatively short time, it is contemplated that the inertia of target flight, it is easy to which sensor track is split into difference
The rectilinear path of period.In addition, it is contemplated that can be using airline carriers of passengers as cooperative target, airline carriers of passengers is in stabilized flight process
In, there are a large amount of rectilinear path sections.Therefore, above-mentioned hypothesis is also feasible in practice.
2, radar and the pretreatment of ADS-B track number
In view of (radar local coordinate system and geographical coordinate is respectively adopted in the coordinate system of radar track and ADS-B track
System), sampling instant is different and the influence of singular value, it is necessary first to they are pre-processed.
(1) coordinate is converted
Since ADS-B metric data uses geographical coordinate, in order to which the metric data to radar and ADS-B carries out at unified
Reason, needs that the local rectangular coordinate system that ADS-B metric data is transformed into centered on radar is first set (λA,i,φA,i,hA,i) be
The geographical coordinate that ADS-B is measured, then corresponding local coordinate are as follows:
[xA,i,yA,i,zA,i]T=D (λR,φR)[P(λA,i,φA,i,hA,i)-P(λR,φR,hR)] (1)
Here, (λR,φR,hR) be radar site geographical coordinate, D (λR,φR)、P(λR,φR,hR) can be respectively under
Two formula of face calculates:
Wherein,For the eccentricity of the earth, re=6356.752km is earth short axle
Radius, Re=6378.137km is earth major axis radius
Since two-coordinate radar is only capable of obtaining the inclined range and azimuth information of target, some subsequent steps are needed in radar
Polar coordinate system handles data, it is therefore desirable to which ADS-B metric data is converted into polar coordinates from right angle seat.If (rA,i,θA,i,hA,i)
(xA,i,yA,i,zA,i) it is that ADS-B measures polar coordinates and rectangular co-ordinate in radar local coordinate system respectively, then
Here be that the inclined range measured for two-coordinate radar and azimuth are registrated, it is only necessary to radar measurement and
The inclined range and azimuth that ADS-B is measured carry out processing and facilitate processing in order to subsequent, still need to radar measurement and ADS- further
B measurement conversion is to plane right-angle coordinate, if (x 'i,y′i) and (ri,θi) it is respectively the pole seat that radar measurement or ADS-B are measured
Mark and rectangular co-ordinate, then
Hereinafter, the rectangular co-ordinate that the radar measurement or ADS-B being related to measure is that is calculated by (5) formula
(2) temporal registration
In practice, when radar and ADS-B are monitored target, sampling instant is approximate period.Generally,
ADS-B sampling instant is more more dense than radar.Fig. 2 provides the sampling instant of radar in practice and the same a collection of target of ADS-B tracking, can
To find out that the ADS-B sampling interval is smaller than radar.The processing of subsequent radar data and accurate estimation radar system are missed for convenience
Difference, here with the sampling instant sequence of radar track dataOn the basis of, interpolation is carried out to ADS-B track data, passes through meter
Obtained interpolating sequence is subsequently used for estimation radar system error as new ADS-B track data.
It is 1s/ times approximate since the ADS-B sampling interval is small in specific Interpolation Process, it assume that target single thus
Sampling interval moves with uniform velocity, using with radar sampling moment tR,iTwo adjacent ADS-B measure zA,j、zA,j+1(tA,j<tR,i<
tA,j+1) calculate interpolation:
Wherein,
In formula, tA,j、tA,j+1For corresponding zA,j、zA,j+1Sampling instant.
(3) outlier is handled
In radar data treatment process, combined influence or effect due to a variety of accidentalia, radar measurement data set
In usually contain the data of some substantial deviation target true values, usually by this part, abnormal data is known as outlier or exceptional value is wild
Value can seriously affect model parameter optimal estimation of the precision based on Least Square Theory of radar system error estimation, optimal line
Property all very sensitive to outlier such as filtering algorithm for this purpose, rejecting the outlier in radar track data using 3 σ criterion:
1) according to the metric data collection of radar trackStraight line is estimated using least-square fitting approach
Equation:
2) each radar measurement z is calculatedR,iTo straight lineDistance:
3) standard deviation is calculated:
Wherein,
4) according to 3 σ criterion, work as dR,i>3σR,lWhen, then zR,iIt for outlier, needs to delete from radar track data set, and more
The metric data collection of new radar track；Otherwise, continue to retain the measurement；
5) data set updated is utilized, again fitting a straight line equation；
6) step 2) -5 is repeated), until the data set being updated all meets 3 σ criterion.
(4) radar bearing angle error compensates
In view of systematic error estimation algorithm is more sensitive to error in measurement, in order to more accurately estimate that radar system is missed
Difference estimates the thick value of radar bearing angle error first here, then compensates to radar bearing angular data and assumes that target is done directly
Line movement calculates radar track and the corresponding straight line side of ADS-B track using least square fitting (i.e. formula (9) and formula (10))
Journey:
Then the angle of two straight lines, and the thick value that the angle is estimated as radar bearing angle error are calculated:
The bearing data of radar track is finally repaid using the thick value complement:
θ′R,i=θR,i+ΔθR, 0 (15)
3, the radar system error estimation based on least square
If radar track data and ADS-B track data are after pretreatment, (rR,i,θR,i) and (rA,i,θA,i) difference table
Show tiThe polar coordinates that radar measurement and ADS-B of the moment target T in radar polar coordinate system measure, (x 'R,i,y′R,i) and
(x′A,i,y′A,i) it is respectively their rectangular co-ordinates in radar rectangular coordinate system, Δ rR、ΔθRIt is the inclined range system of radar respectively
If system error and azimuth system error ignore the influence with error in measurement, available according to (5) formula:
Because of Δ rR、ΔθRIt is micro, if ignoring their second order term, formula (16) be can simplify are as follows:
In view of ADS-B systematic error is very small with respect to radar system error, ignore ADS-B systematic error here, by it
Actual position as target position, it may be assumed that
By (x 'R,i,y′R,i) and (x 'A,i,y′A,i) geometrical relationship known to:
It can be obtained by identity deformation:
It enablesβ=[Δ rR,ΔθR]T,Then (20) formula matrix
Form can indicate are as follows:
Zi=Hiβ (21)
For M different metric data of radar track, can be obtained according to formula (21):
[Z1,Z2,…HM]T=[H1,H2,…HM]Tβ (22)
Enable H=[H1,H2,…HM]T, Z=[Z1,Z2,…ZM]T, then (22) formula can further indicate that are as follows:
Z=H β (23)
Since (23) formula is overdetermination, can be obtained using the least square estimation method solution:
β=(HTH-1)HTZ (24)
4, measured data is tested
In order to verify the performance of proposition method, three kinds of system error approach are compared using measured data, including base
In the systematic error estimation method (FL) of straight line fitting, the systematic error estimation method (LS) based on least square and it is based on
The least square systematic error estimation method (FL-LS) of straight line fitting.
(1) measured data experiment and analysis
Measured data is from aerial with a collection of radar track of cooperative target and the metric data of ADS-B track, target
Approximate straight line motion in the sky, as shown in Figure 3, wherein radar track includes 27 sampled points, and ADS-B track includes 105 and adopts
Sampling point, corresponding sampling instant as shown in Figure 4 first sit ADS-B track data from geography to estimate radar system error
Mark system is transformed into the local coordinate system of radar, and radar track data are transformed into radar rectangular co-ordinate from radar polar coordinate system
System.
By conversion after radar track and ADS-B track metric data as shown in Figure 3 from the figure 3, it may be seen that despite the presence of
Systematic error, but all APPROXIMATE DISTRIBUTION is in the two sides of corresponding straight line for the metric data of radar track and ADS-B track, especially
For ADS-B track this is because ADS-B data set is based on GPS, positioning accuracy is high, can satisfy radar and estimates to systematic error
The requirement of meter.Therefore, the angle of straight line can be corresponded to by calculating radar track and ADS-B track, as radar bearing
The thick value of angle systematic error estimation, for compensating the azimuth of radar track data.By Fig. 3 and Fig. 4 it can be seen from ADS-B
Track sampling instant is more more dense than radar in order to be registrated to radar track, needs the metric data sampling instant with radar track
On the basis of, ADS-B track is calculated in the interpolation at corresponding moment, and the interpolating sequence being calculated is recycled to construct new ADS-B boat
The metric data of mark, for estimate radar system error after interpolation processing, the sampling of new ADS-B track and radar track
Moment is identical, and sampling number is also 27.
Fig. 5 provides the new ADS-B track and radar track data by temporal interpolation, and to new ADS-B track data
After straight line fitting, the angle that two straight lines can be calculated is fitting a straight line with radar track data
161.7mrad, for compensating the azimuth of radar track data, by the compensated new radar track data in azimuth also as schemed
Shown in 5.As shown in Figure 5, for radar track and ADS-B track, all APPROXIMATE DISTRIBUTION is in the two sides of fitting a straight line, by azimuth
The radar track data of compensation are sat in system between plane closer to ADS-B track.
Fig. 6 is using the radar track after systematic error registration it will be appreciated from fig. 6 that being estimated using tri- kinds of FL, LS and FL-LS
Radar track after meter method registration is all very close to ADS-B track, it was demonstrated that three kinds of system error estimations are all effective.
In order to further compare the performance of three kinds of methods, Fig. 7 lists the measurement of three kinds of radar tracks of the 5th to the 9th sampling instant
Data.It as can be seen from Figure 7, according to being successively from small to large is registrated via FL-LS, LS and FL respectively to ADS-B track points distance
Radar track afterwards is finally FL method to illustrate the estimated accuracy highest of FL-LS method, followed by LS method.
In order to more intuitively compare the performance of three kinds of methods, Fig. 8 and Fig. 9 provide the radar track after three kinds of registrations respectively and exist
Each moment inclined range evaluated error and azimuth evaluated error as shown in Figure 8, in most of sampling instant, FL-LS method
Inclined range registration effect is better than LS method and FL method, and LS method is better than FL method again.It similarly, can also be with by Fig. 9
Same conclusion is obtained, azimuth registration performance is successively from low to high: FL method, LS method and tri- kinds of FL-LS method estimations
Method significantly reduces azimuth angle error.Particularly, although FL method azimuth estimated result ratio LS method is slightly poor,
It is very close, to also illustrate from the angle analysis and estimation radar system error of graphics to be also a kind of simple, effective side
Method provides a kind of good thinking further to solve radar system error estimation problem later.
Finally, that table 1 gives three kinds of systematic error estimations as a result, table 2 provides the mean error of radar track after registration
(using ADS-B track data as true value).It is similar with the analysis result of above system error performance, as shown in Figure 2, either oblique
In distance or azimuth, the performance of three kinds of estimation methods is successively FL-LS method, LS method and FL method from high to low.Needle
Azimuthal error, three kinds of system error estimations can significantly improve azimuthal precision of radar track.In order to fixed
Amount illustrates the precise manner of radar track after registration, defines inclined range performance parameter and azimuth registration performance indicator respectively:
Wherein, εr、εr0The inclined range mean error of radar track and radar track is averaged before being registrated after being respectively registrated
Error, εθ、εθ0The azimuth of the azimuth mean error of radar track and the preceding radar track of registration is averagely missed after being respectively registrated
Difference, ηr、ηθIt is defined as registration performance indicator
On this basis, table 3 gives the registration performance indicator situation of three kinds of estimation methods, more intuitive, quantitatively analyze
As shown in Table 3, after registration process, FL-LS method, LS method can significantly reduce radar to their registration performance
The inclined range mean error of track, and FL-LS method is better than LS method, reduces 84.1%.FL method to the oblique of radar track
The improvement of range averaging error is unobvious, and effect is bad, only reduces 0.2%. in addition, three kinds of methods can significantly reduce radar boat
The azimuth mean error of mark, wherein FL-LS method is best, followed by LS method, is finally FL method.FL method navigates to radar
The azimuth mean error of mark reduces 71.7.Therefore, either to inclined range or azimuth, FL-LS method matches parasexuality
It can be best.
1 systematic error estimation result of table (unit: m, mrad)
The mean error (unit: m, mrad) of 2 radar track of table
Table 3 is registrated performance indicator
(2) experimental result discussion
Above-mentioned actual measurement experiment is sufficiently compared the performance of three kinds of system error estimation algorithms and is analyzed it is found that according to matching
Parasexuality can the sequence from secondary to excellent be successively FL method, LS method and FL-LS method, FL method from the angle of graphics,
Method realizes simple, explicit physical meaning, provides a kind of very good solution thinking for radar system error estimation.Although the side FL
Method has preferable estimation effect for azimuth system estimation error, but also for the estimated accuracy of inclined range systematic error
Wait improve.In addition, FL method is moved in a straight line dependent on target, and target trajectory has uncertainty in practice, because
This its application scenarios is also subject to certain restrictions.For this purpose, the adaptability and crudity of FL method it still needs further improvement different scenes
Property.
Similarly, the advantages of FL-LS method is based on FL method, and there is also FL methods and insufficient still FL-LS method
The compensated radar track data in azimuth are further handled using least-squares algorithm；Opposite FL method, systematic error are estimated
Meter performance is greatly improved, especially for inclined range systematic error.Although LS method also uses least-squares algorithm to handle
Radar track data, but its performance to be inferior to FL-LS method this be primarily due to LS method processing data be the original boat of radar
Mark data, and the processing of FL-LS method is the compensated radar track data in azimuth.Obviously, the original track data packet of radar
The error contained radar track data more compensated than azimuth are much bigger；And in least-squares estimation modeling process, ignore
The second order term of systematic error (see (16) formula and (17) formula) and higher order term, actually their information for also including systematic error,
It will affect the estimated accuracy of systematic error, especially when systematic error is larger.This just illustrates least-squares estimation algorithm pair
The application condition of metric data is sensitive.When therefore, using least-squares estimation algorithm estimated sensor systematic error, to measurement number
It is necessary according to pretreatment or error compensation processing is carried out.
In addition, being directed to although FL method is not so good as LS method and FL-LS method to the effect that radar system error is estimated
The effect of azimuth system estimation error and LS method are very close, and corresponding azimuth registration performance indicator is 32.6% He
33.0%. it is also highly effective that this explanation, which carrys out analyte sensors systematic error from the angle of graphics, and its method is simply real
With, it is readily appreciated that.Certainly, FL method relys more on the motion model of metric data and target, but there are also very big for algorithm design
Room for promotion, to solve the problems, such as that systematic error estimation provides a kind of good thinking.
In conclusion three kinds of methods are all built upon on the basis of radar system error fixation, target movement is not accounted for
The factors such as uncertain of influence and radar and ADS-B observation time to systematic error estimation, so above-mentioned three kinds of methods exist
In follow-up study, it is also necessary to by measured data, these problems further be analyzed and be handled.
The above content is combine the preferred embodiment of the present invention to made by provided technical solution further specifically
It is bright, and it cannot be said that the present invention specific implementation be confined to it is above-mentioned these explanation, for the common skill of the technical field of the invention
For art personnel, without departing from the inventive concept of the premise, a number of simple deductions or replacements can also be made, all should be considered as
It belongs to the scope of protection of the present invention.
Claims (6)
1. a kind of least square method for estimating radar system error for combining ADS-B, which comprises the steps of:
Step S100 two-coordinate radar and ADS-B are to target joint observation, the more biographies constituted with a two-coordinate radar and ADS-B
Sensor tracking system measures the inclined range of same cooperative target, azimuth, obtains radar track and ADS-B boat respectively
Mark；
Step S200 radar track and ADS-B track pre-process；
Wherein, step S200 includes
The ADS-B geographic coordinate system measured is transformed into the local rectangular coordinates centered on radar by the conversion of step S210 coordinate
System, establishes unified registration space；
Step S220 temporal registration is carried out interpolation to ADS-B track, is constructed new on the basis of the sampling time of radar track
ADS-B track；
Step S230 rejects the outlier of radar track, rejects the outlier in radar track data using 3 σ criterion；
The compensation of step S240 radar bearing angle error: the straight line of radar track and ADS-B track is calculated separately using straight line fitting
Equation, and the angle of two straight lines is calculated, recycle the course angular data of angle compensation radar track；
Step S300 is based on least-squares algorithm and estimates radar system error.
2. a kind of least square method for estimating radar system error for combining ADS-B as described in claim 1, feature exist
In: in the step S210, the ADS-B geographic coordinate system measured is transformed into the local rectangular coordinate system centered on radar
Afterwards, then by ADS-B metric data from rectangular co-ordinate polar coordinates are converted into, finally by radar measurement and ADS-B measurement conversion to flat
Face rectangular coordinate system, if (x 'i,y′i) and (ri,θi) it is respectively polar coordinates and rectangular co-ordinate that radar measurement or ADS-B are measured,
Then finally obtain
3. a kind of least square method for estimating radar system error for combining ADS-B as claimed in claim 2, feature exist
In: in the step S220, with the sampling instant sequence of radar track dataOn the basis of, ADS-B track data is carried out
Interpolation, interpolating sequence obtained by calculation as new ADS-B track data, using with radar sampling moment tR,iAdjacent
Two ADS-B measure zA,j、zA,j+1(tA,j<tR,i<tA,j+1) calculate interpolation:
Wherein,
In formula, tA,j、tA,j+1For corresponding zA,j、zA,j+1Sampling instant.
4. a kind of least square method for estimating radar system error for combining ADS-B as claimed in claim 3, feature exist
In: in the step S230, comprising the following steps:
Step S231 is according to the metric data collection of radar trackStraight line is estimated using least-square fitting approach
Equation:
Step S232 calculates each radar measurement zR,iTo straight lineDistance:
Step S233 calculates standard deviation:
Wherein,
Step S234 works as d according to 3 σ criterionR,i>3σR,lWhen, then zR,iFor outlier, need to delete from radar track data set, and
Update the metric data collection of radar track；Otherwise, continue to retain the measurement；
Step S235 utilizes the data set updated, again fitting a straight line equation；
Step S236 repeats step b-e, until the data set being updated all meets 3 σ criterion.
5. a kind of least square method for estimating radar system error for combining ADS-B as claimed in claim 4, feature exist
In: radar track and the corresponding linear equation of ADS-B track are calculated using least square fitting:
Then the angle of two straight lines, and the thick value that the angle is estimated as radar bearing angle error are calculated:
The bearing data of radar track is finally repaid using the thick value complement:
θ′R,i=θR,i+ΔθR, 0 (11)。
6. a kind of least square method for estimating radar system error for combining ADS-B as claimed in claim 5, feature exist
In: radar track data and ADS-B track data are set after pretreatment, (rR,i,θR,i) and (rA,i,θA,i) respectively indicate tiWhen
Carve the polar coordinates that radar measurement and ADS-B of the target T in radar polar coordinate system measure, (x 'R,i,y′R,i) and (x 'A,i,y′A,i)
Respectively their rectangular co-ordinates in radar rectangular coordinate system, Δ rR、ΔθRIt is the inclined range systematic error and orientation of radar respectively
Angle systematic error, available according to (1) formula if ignoring the influence with error in measurement:
Because of Δ rR、ΔθRIt is micro, if ignoring their second order term, formula (12) be can simplify are as follows:
In view of ADS-B systematic error is very small with respect to radar system error, ignore ADS-B systematic error here, as
The actual position of target position, it may be assumed that
By (x 'R,i,y′R,i) and (x 'A,i,y′A,i) geometrical relationship known to:
It can be obtained by identity deformation:
It enablesβ=[Δ rR,ΔθR]T,The then form of (16) formula matrix
It can indicate are as follows:
Zi=Hiβ (17)
For M different metric data of radar track, can be obtained according to formula (17):
[Z1,Z2,…HM]T=[H1,H2,…HM]Tβ (18)
Enable H=[H1,H2,…HM]T, Z=[Z1,Z2,…ZM]T, then (19) formula can further indicate that are as follows:
Z=H β (20)
Since (20) formula is overdetermination, can be obtained using the least square estimation method solution:
β=(HTH-1)HTZ (21)
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