CN106546961A - A kind of variable step constrains total least square spatial registration algorithm - Google Patents
A kind of variable step constrains total least square spatial registration algorithm Download PDFInfo
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- CN106546961A CN106546961A CN201610603059.9A CN201610603059A CN106546961A CN 106546961 A CN106546961 A CN 106546961A CN 201610603059 A CN201610603059 A CN 201610603059A CN 106546961 A CN106546961 A CN 106546961A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/40—Means for monitoring or calibrating
Abstract
The invention discloses a kind of variable step constrains total least square spatial registration algorithm：Given initial estimate and the initial step length factor, put iterative steps for 1；Calculate Hessian matrixes and gradient vector；Estimate is calculated using formula；Whether inspection iterative steps are a certain constant value for setting, and final estimate is then exported if being, the present invention constrains subjective general well-being by the variable step based on ECEF（ECEF‑VCTLS）Systematic error is estimated, the step factor constrained in subjective general well-being is allowed to change with the change of step number, can not only accurate estimating system error, and reduce convergence step number and improve the stability after convergence, so as to improve the performance of target following positioning.
Description
Technical field
The present invention relates to a kind of spatial registration algorithm, more particularly to a kind of variable step constraint total least square spatial registration
Algorithm, belongs to radar data processing technology field.
Background technology
It is well known that in modern detection system, single-sensor or single base detection system such as radar cannot meet height
The demand of precision, and two kinds of errors are primarily present in multisensor or many base detection systems：Random error and system are missed
Difference.Different according to the origin of systematic error, the systematic error of radar network can be divided mainly into following a few classes：What is positioned is uncertain
Property, antenna direction deviation, space coordinate conversion model bias and inaccurate apart from clock rate.Error registration is then by these
The key technology that error is minimized.Spatial registration is the spacial alignment part in data prediction, and it includes Coordinates calibration, form
Specification is aligned, and is to solve to detect same target between two identical sensor different carriers and different sensors different carriers
Data synthetic method, be the important component part of whole data fusion.
Based on constraint total least square (ECEF-CTLS) algorithm of ECEF coordinate systems, it analyzes coefficient matrix and sight
The restriction relation of direction finding amount disturbance, reduces impact of the noise to registration result by additional interference matrix, therefore in noise ratio
When larger, reasonable registration result can be also obtained, be a kind of relatively effective error registration algorithm, but the method meeting
Anomalous differences is produced, registration result still can be made to be a greater impact.For this problem, this paper presents in ECEF coordinate systems
Under variable step constraint total least square.The algorithm changes with the change of step number by step factor, reduces abnormal mistake
Poor impact, so as to reduce convergence step number, improves the stability after convergence, effectively improves the property of target following positioning
Energy.
The content of the invention
The technical problem to be solved is overall there is provided a kind of constraint of variable step for the deficiency of background technology
Least square spatial registration algorithm.
The present invention is employed the following technical solutions to solve above-mentioned technical problem
A kind of variable step constrains total least square spatial registration algorithm, specifically comprises the steps of：
Step 1, setting initial estimate and the initial step length factor, put iterative steps for 1；
Step 2, calculates Hessian matrix HsnWith gradient vector Tn, specifically it is calculated as follows：
Wherein,For the estimate of target location vector, n is iterations, and β is estimate, ajFor j-th component of β,For observation vector, F is coefficient square
Battle array, L are vector,Length；
Step 3, calculates vectorial estimate using iterative formula, is specifically calculated as follows：
Wherein, β is vector, and n is iterations, and μ is step factor, μ0For the initial step length factor, k is iterative steps, and p is
Constant.
Step 4, checks whether iterative steps are the constant value for setting, and is to export final vectorial estimate.
The further preferred scheme of total least square spatial registration algorithm is constrained as a kind of variable step of the invention, in step
In rapid 3, calculating is iterated using Newton algorithms.
The further preferred scheme of total least square spatial registration algorithm is constrained as a kind of variable step of the invention, in step
In rapid 3, after algorithmic statement, the adjusting step of very little should be all kept to reach the steady output rate noise of very little, according to this step
Long Adjustment principle, gives the expression formula of step-length：
In formula, μ is step factor, μ0For the initial step length factor, k is step number, and p is constant.
The further preferred scheme of total least square spatial registration algorithm is constrained as a kind of variable step of the invention, it is described
P is 2
The present invention adopts above technical scheme compared with prior art, with following technique effect：
The present invention constrains subjective general well-being (ECEF-VCTLS) to systematic error by the variable step based on ECEF
Estimated, allow the step factor constrained in subjective general well-being to change with the change of step number, can not only be accurate
Estimating system error, and reduce convergence step number and improve the stability after convergence, it is fixed so as to improve target following
The performance of position.
Description of the drawings
Fig. 1 is the relation curve of step-length and step number when p takes 2,4,5,6,7；
Fig. 2 is the radial distance estimation of deviation based on ECEF-CTLS and ECEF-VCTLS of radar A；
Fig. 3 is that the azimuth angle deviation based on ECEF-CTLS and ECEF-VCTLS of radar A is estimated；
Fig. 4 is that the pitch angle deviation based on ECEF-CTLS and ECEF-VCTLS of radar A is estimated；
Fig. 5 is the radial distance estimation of deviation based on ECEF-CTLS and ECEF-VCTLS of radar B；
Fig. 6 is that the azimuth angle deviation based on ECEF-CTLS and ECEF-VCTLS of radar B is estimated；
Fig. 7 is that the pitch angle deviation based on ECEF-CTLS and ECEF-VCTLS of radar B is estimated.
Specific embodiment
Below in conjunction with the accompanying drawings technical scheme is described in further detail：
A kind of variable step constrains total least square spatial registration algorithm, specifically comprises the steps of：
Step 1, setting initial estimate and the initial step length factor, put iterative steps for 1；
Step 2, calculates Hessian matrixes and gradient vector；
In ECEF coordinate systems, the ECEF coordinates of radar A and B are made to be respectively (xAs,yAs,zAs) and (xBs,yBs,zBs), thunder
Geographical coordinate up to A and B is respectively (LA,λA,HA) and (LB,λB,HB).At the k moment, Fig. 2 is radar A based on ECEF-CTLS
With the radial distance estimation of deviation of ECEF-VCTLS；Fig. 3 is the azimuth based on ECEF-CTLS and ECEF-VCTLS of radar A
Estimation of deviation；Fig. 4 is that the pitch angle deviation based on ECEF-CTLS and ECEF-VCTLS of radar A is estimated；Fig. 5 is the base of radar B
In the radial distance estimation of deviation of ECEF-CTLS and ECEF-VCTLS；Fig. 6 is radar B based on ECEF-CTLS and ECEF-
The azimuth angle deviation of VCTLS is estimated；Fig. 7 is that the pitch angle deviation based on ECEF-CTLS and ECEF-VCTLS of radar B is estimated；
The radial distance of radar A and B, azimuth and angle of pitch system deviation are β=[Δ rA,ΔθA,ΔηA,ΔrB,Δ
θB,ΔηB] ', ψ (k)=[r "A(k),θ″A(k),η″A(k),r″B(k),θ″B(k),η″B(k)] ' represent when only considering system deviation
Radar A and B is to the radial distance of target, azimuth and pitching angle measurements.So target is in radar A and the local coordinate of radar B
Rectangular co-ordinate in system is represented by
(x ' can be obtained in the same mannerBl,y′Bl,z′Bl).By Coordinate Conversion, the rectangular co-ordinate in local coordinate system is transformed into
Have in ECEF coordinate systems：
Wherein spin matrixX can be obtained in the same mannertB(k) and TB。
Coordinate of the target in the ECEF coordinate systems of radar A and B is made to carry out subtracting each other having：
First order Taylor expansion (linearizing) is carried out to formula (3)
In formula, ψ ' (k) (is missed comprising systematic error and random measurement to the measured value of target at the kth moment for radar A and B
Difference, is not corrected)；Initial estimations of the β ' for system deviation, under conditions of no any prior information, it can be assumed that β '=
[0,0,0,0,0,0]′。
For same target, discounting for the impact of random observation noise, f (ψ (k), β)=[0,0,0] ', then make：
λ (k) β=λ (k) β '-f (ψ ' (k), β ') (5)
In formula, λ (k) is the matrix of known parameters, and its expression formula is：Wherein
L can be obtained in the same mannerB(k)。
Then for k moment (step number), formula (14) is represented by X β=Y, wherein
X=[λ (1), λ (2) ..., λ (k)] ' (6)
Y=[λ (1) β '-f (ψ ' (1), β '), λ (2) β '-f (ψ ' (2), β '), ..., λ (k) β '-f (ψ ' (k), β ')] '
(7)
As the estimate of actual angle is constantly present error with actual value, therefore X and Y in formula (17) cannot be obtained
Can only obtain the matrix by noise jammingWithWhen therefore solving the formula using least square, the solution for obtaining no longer is optimum
, but it is devious.
It is not difficult to find after careful observation, the noise component(s) of X and Y not statistical iteration, in order to obtain the relation between them, institute
To make
In formula, (wA,nA,mA) and (wB,nB,mB) be respectively the oblique distance of radar A and B, azimuth and the angle of pitch with chance error
Difference,WithIt is respectively its real measurement (comprising random error).
Following Taylor launches to be considered to formula (8)：
So in the case where noise higher order term is ignored, following equation can be obtained：
F1, F2, F3, F4, F5, F6And F7The specific derivation of equation is referred to pertinent literature.
As can be seen that the noise pollution suffered by matrix X and Y is from noise vector E from (10) formula, then can be with
It is translated into following constraint total least square problem：
In pertinent literature, the restricted problem of formula (11) has been converted into unconfined problem, in order to without loss of generality, no
The length of harm order vector β is L=6, ajFor j-th component of vectorial β, then have Connect
OrderTherefore unconstrained problem is represented by
Therefore, gradient vector TnWith the Hessian matrix Hs of formula (12)nIt is expressed as
In formula,
Step 3, calculates estimate using formula；
Because (12) formula is the nonlinear function with regard to β, have no idea directly to be solved, so we adopt Newton
Algorithm is iterated calculating, and iterative formula is as follows：
In formula, μ is step factor.
So far we have been presented for constraining subjective general well-being, but the algorithm can produce anomalous differences, to fixed
Position result has large effect, so reducing impact of the anomalous differences to positioning result herein by the adjusting step factor, walks
Long Adjustment principle is according to document：In initial convergence phase, step-length should be than larger, to there is convergence rate faster；And
After algorithmic statement, the adjusting step of very little should be all kept to reach the steady output rate noise of very little.Adjusted according to this step-length
Principle, this article give Sigmoid function New variable step-size LMSs：
In formula, α is the constant of control function shape, and β is the constant of control function span, and e (n) is error, μ (n)
It is the parameter (step factor) of control stability and convergence rate.This algorithm simultaneously obtains convergence rate faster and less steady
State error.And this does not meet the applied environment of spatial registration, so the principle adjusted according to applied environment and step-length, is given herein
The variable step constraint subjective general well-being based on Poisson distribution is gone out：
In formula, μ0For the initial step length factor, k is step number, and p is constant, and it is step size mu and step number when p takes different value that figure one is
Relation curve, as shown in figure 1, as p=2 and p=4, though the bottom form of curve is more gentler than during p=5, receipts can be reduced
Slow down one's steps number, but this shows that μ has been zero, you can cause larger stable state mistuning noise when step number is 10 or 20.As p=6 and
During p=7, the bottom form of curve is more sharp than the bottom form of curve during p=5, it means that when step number is 40 or so
(now algorithm has reached or will reach stable state), μ changes still very greatly, reduces convergence rate.Therefore choosing p=5 herein is
The variable step formula of this paper algorithms, can obtain convergence rate faster and less stable state mistuning noise simultaneously.
Step 4, checks whether iterative steps are a certain constant value for setting, and final estimate is then exported if being.
Claims (4)
1. a kind of variable step constrains total least square spatial registration algorithm, it is characterised in that：Specifically comprise the steps of：
Step 1, setting initial estimate and the initial step length factor, put iterative steps for 1；
Step 2, calculates Hessian matrix HsnWith gradient vector Tn, specifically it is calculated as follows：
Wherein,For the estimate of target location vector, n is iterations, and β is estimate, ajFor j-th component of β,For observation vector, F is coefficient square
Battle array, L are vector,Length；
Step 3, calculates vectorial estimate using iterative formula, is specifically calculated as follows：
Wherein, β is vector, and n is iterations, and μ is step factor, μ0For the initial step length factor, k is iterative steps, and p is constant.
Step 4, checks whether iterative steps are the constant value for setting, and is to export final vectorial estimate.
2. a kind of variable step according to claim 1 constrains total least square spatial registration algorithm, it is characterised in that：
In step 3, calculating is iterated using Newton algorithms.
3. a kind of variable step according to claim 1 constrains total least square spatial registration algorithm, it is characterised in that：
In step 3, after algorithmic statement, the adjusting step of very little should all be kept to reach the steady output rate noise of very little, root
According to this step-length Adjustment principle, the expression formula of step-length is given：
In formula, μ is step factor, μ0For the initial step length factor, k is step number, and p is constant.
4. a kind of variable step according to claim 3 constrains total least square spatial registration algorithm, it is characterised in that：Institute
P is stated for 2.
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| CN108021095A (en) * | 2017-12-14 | 2018-05-11 | 哈尔滨工业大学 | A kind of hyperspace profile errors method of estimation based on confidence region algorithm |
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Application publication date: 20170329 |