CN108319567A - A kind of spatial target posture estimation uncertainty calculation method based on Gaussian process - Google Patents
A kind of spatial target posture estimation uncertainty calculation method based on Gaussian process Download PDFInfo
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Abstract
The invention discloses a kind of, and the spatial target posture based on Gaussian process estimates that uncertainty calculation method, specific steps include as follows：S1 dimensions extend：Two-dimensional posture is extended on three-dimensional sphere and is indicated；S2 Gauss estimation procedures：Estimate to obtain the relationship of the mean value and variance and desired value and desired value uncertainty of the desired value of test set by Gauss；S3 derives the uncertainty for calculating yaw angle and pitch angle：According to the mean value, the variance and the desired value uncertainty, the corresponding uncertainty of analysis of two-dimensional posture yaw angle θ and pitch angle β.The present invention provides a kind of, and the spatial target posture based on Gaussian process estimates uncertainty calculation method, it is derived by variance and calculates corresponding uncertainty, uncertainty will be prompted to the confidence level of prediction result, by analyzing uncertainty, determine the accuracy of its corresponding Attitude estimation, it picks out result with a low credibility and carries out secondary interpretation, to reduce erroneous judgement.
Description
Technical field
The present invention relates to digital image processing field, more particularly to a kind of extraterrestrial target based on Gaussian process
Attitude estimation uncertainty calculation method.
Background technology
Vision system is widely used in each application field of aerospace：Landing, position and the posture of view-based access control model are estimated
Meter, in-orbit adaptive, satellite identification etc., the Attitude estimation of wherein view-based access control model be realize these applications key technology it
One.
The Attitude estimation method of view-based access control model is broadly divided into two classes：Method based on 3D models and the side based on 2D models
Method.Method based on 3D models needs the 3D models of the extraterrestrial target object of priori, and should include structure, shape
Abundant information including shape, texture etc., but accurately 3D models hardly result in practice.Method based on 2D models is tasted
Examination directly restores posture information from image sequence or single image, these methods are based on monocular or binocular vision, but most of
It is required for camera calibration or carries out optical markings on target aircraft, while when imaging sensor distance objective aircraft is far
When, the method based on binocular vision may be invalid.General Attitude estimation method only gives in corresponding error range
Accuracy rate can not confirm the confidence level of prediction result without other reference informations, can not further confirm the standard of Attitude estimation
Exactness.
Therefore, how to provide it is a kind of Attitude estimation carried out by Gaussian process, in the mean value for the predicted value for obtaining posture
Corresponding variance is obtained simultaneously, is derived by variance and calculates corresponding uncertainty, what uncertainty will be prompted to prediction result can
Reliability determines the accuracy of its corresponding Attitude estimation, picks out result with a low credibility by analyzing uncertainty
Secondary interpretation is carried out, the spatial target posture estimation uncertainty calculation method based on Gaussian process to reduce erroneous judgement is ability
The problem of field technique personnel's urgent need to resolve.
Invention content
In view of this, the present invention provides a kind of, the spatial target posture based on Gaussian process estimates uncertainty calculation side
Method carries out Attitude estimation by Gaussian process, obtains corresponding variance while the mean value for the predicted value for obtaining posture, pass through
Variance, which derives, calculates corresponding uncertainty, and uncertainty will be prompted to the confidence level of prediction result, by being carried out to uncertainty
Analysis, determines the accuracy of its corresponding Attitude estimation, picks out result with a low credibility and carries out secondary interpretation, is missed with reducing
Sentence.
To achieve the goals above, the present invention provides the following technical solutions：
A kind of spatial target posture estimation uncertainty calculation method based on Gaussian process, specific steps include as follows：
S1 dimensions extend：Two-dimensional posture is extended on three-dimensional sphere and is indicated；
S2 Gauss estimation procedures：Estimate to obtain by Gauss the desired value of test set mean value and variance and desired value with
The relationship of desired value uncertainty；
S3 derives the uncertainty for calculating yaw angle and pitch angle：According to the mean value, the variance and the desired value
Uncertainty, the corresponding uncertainty of analysis of two-dimensional posture yaw angle θ and pitch angle β.
Through the above technical solutions, the technique effect of the present invention：Attitude estimation is carried out by Gaussian process, is obtaining posture
Predicted value mean value while obtain corresponding variance, pass through variance and derive and calculate corresponding uncertainty, uncertainty will
The confidence level of prompt prediction result determines the accuracy of its corresponding Attitude estimation, selects by analyzing uncertainty
Go out result with a low credibility and carry out secondary interpretation, to reduce erroneous judgement.
Preferably, in a kind of above-mentioned spatial target posture estimation uncertainty calculation method based on Gaussian process,
In the S1 dimensions extension, specifically formula is as follows：
y1=cos θ cos β
y2=sin θ cos β
y3=sin θ (1)
y1, y2, y3Corresponding uncertainty uses Δ y respectively1, Δ y2, Δ y3It indicates.
Through the above technical solutions, the technique effect of the present invention：Two-dimensional posture (yaw angle θ and pitch angle β) is expanded
It is indicated on to three-dimensional spherical surface, the uncertainty to calculate yaw angle and pitch angle is prepared.
Preferably, in a kind of above-mentioned spatial target posture estimation uncertainty calculation method based on Gaussian process,
The S2 Gausses estimation procedure, specific steps include：
S21：Definition X is training set, X*For test set, the data amount check of training set and test set is N, and y is training set X
The predictive equation of corresponding desired value, Gaussian process regression model is：
S22：Mean value is obtained by the predictive equation (2)With variance cov (f*)；Also assume that test set X*It is corresponding
Desired value Normal Distribution, the then mean valueIt is test set X*The mean value of corresponding desired value normal distribution, for normal state
Distribution, mean value maximum probability, we use mean valueRepresent the desired value predicted；The variance of normal distribution is bigger, illustrates it
Distribution more disperses, more inaccurate with mean value characterization actual value (the objective value for wanting estimation), otherwise is characterized with mean value real
Actual value is more accurate, so passing through cov (f*) may indicate that the uncertainty degree of estimation, we are using standard deviation as uncertainty
Measurement；S23：By training set X and test set X*Corresponding three desired value y with training set X respectively1, y2, y3, it is input to three
A Gauss regression model carries out attitude prediction, obtains three class mean μ1, μ2, μ3And variances sigma1, σ2, σ3Test set X is corresponded to respectively*'s
Desired value mean value and the relationship of variance and desired value and desired value uncertainty are as follows：
Through the above technical solutions, the technique effect of the present invention：The desired value mean value and variance of test set are obtained, and is determined
Relationship between desired value and desired value uncertainty.
Preferably, in a kind of above-mentioned spatial target posture estimation uncertainty calculation method based on Gaussian process,
The mean value is calculated in the S22With the variance cov (f*) formula it is as follows：
Through the above technical solutions, the technique effect of the present invention：Mean value and the side of desired value are determined by formula (4) (5)
Difference.
Preferably, in a kind of above-mentioned spatial target posture estimation uncertainty calculation method based on Gaussian process,
Calculate the mean valueWith the variance cov (f*) specifically, by square of the isotropism range measurement with unit magnitude
Index covariance function K (X, X ') it is defined as follows：
K (x, x ')=exp {-(x-x ')T(ell2I)-1(x, x ') } (6)
Wherein x and x ' is two data points, and I is the unit matrix with dimension, parameter ell with data set2It is characteristic length；
K (X, X) is the covariance matrix that using formula (6) all training points are carried out with N × N-dimensional that assessment is calculated, K (X*,X*)、K
(X*,X)、K(X,X*) and K (X, X) similarly calculate；It is variance of the additive noise in regression model, passes through cross validation reality
It tests and is selected.
Through the above technical solutions, the technique effect of the present invention：Mean value and variance to calculate desired value provide basis, really
Determine K (X*,X*)、K(X*,X)、K(X,X*) and K (X, X) computational methods.
Preferably, in a kind of above-mentioned spatial target posture estimation uncertainty calculation method based on Gaussian process,
The S3, which is derived, to be calculated the uncertainty specific steps of yaw angle and includes：The uncertainty Δ θ for calculating yaw angle θ first, passes through
Known to formula (1)
θ=g (y3)=arcsin (y3) (7)
Differential is carried out to formula (7), its differential formulas can be obtained：
Differential dy represents the variation of y, also illustrates that the uncertainty of y, so dy is regarded as Δ y, then the uncertainty Δ of θ
θ is calculated by formula (8)；The uncertainty Δ θ of further yaw angle θ：
Through the above technical solutions, the technique effect of the present invention：Pass through the pass between desired value and desired value uncertainty
System determines the uncertainty Δ θ of yaw angle θ.
Preferably, in a kind of above-mentioned spatial target posture estimation uncertainty calculation method based on Gaussian process,
The S3, which is derived, to be calculated the uncertainty specific steps of pitch angle and includes：Known to formula (1)
Differential is carried out to formula (10), is obtained
The uncertainty Δ β of pitch angle β can be calculated by following formula：
By formula (1) but by：
The complete formula for then calculating the uncertainty Δ β of pitch angle β is as follows：
Through the above technical solutions, the technique effect of the present invention：Pass through the pass between desired value and desired value uncertainty
System determines the uncertainty Δ β of pitch angle β.
It can be seen via above technical scheme that compared with prior art, the present disclosure provides one kind being based on Gauss mistake
The spatial target posture of journey estimates uncertainty calculation method, carries out Attitude estimation by Gaussian process, is obtaining the pre- of posture
Corresponding variance is obtained while the mean value of measured value, is derived by variance and calculates corresponding uncertainty, and uncertainty will be prompted to
The confidence level of prediction result determines the accuracy of its corresponding Attitude estimation, picking out can by analyzing uncertainty
The low result of reliability carries out secondary interpretation, to reduce erroneous judgement.
Description of the drawings
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technology description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this
The embodiment of invention for those of ordinary skill in the art without creative efforts, can also basis
The attached drawing of offer obtains other attached drawings.
Fig. 1 attached drawings are the flow chart of the present invention；
Fig. 2 attached drawings are the absolute error and uncertainty comparison diagram of the angle of drift of the present invention；
Fig. 3 attached drawings are the absolute error and uncertainty comparison diagram of the pitch angle of the present invention.
Specific implementation mode
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation describes, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other
Embodiment shall fall within the protection scope of the present invention.
The embodiment of the invention discloses a kind of, and the spatial target posture based on Gaussian process estimates uncertainty calculation method,
Attitude estimation is carried out by Gaussian process, corresponding variance, the side of passing through are obtained while the mean value for the predicted value for obtaining posture
Difference, which derives, calculates corresponding uncertainty, and uncertainty will be prompted to the confidence level of prediction result, by dividing uncertainty
Analysis, determines the accuracy of its corresponding Attitude estimation, picks out result with a low credibility and carries out secondary interpretation, to reduce erroneous judgement.
A kind of spatial target posture estimation uncertainty calculation method based on Gaussian process, which is characterized in that specific step
Suddenly include as follows：
S1 dimensions extend：Two-dimensional posture is extended on three-dimensional sphere and is indicated；
S2 Gauss estimation procedures：Estimate to obtain by Gauss the desired value of test set mean value and variance and desired value with
The relationship of desired value uncertainty；
S3 derives the uncertainty for calculating yaw angle and pitch angle：According to the mean value, the variance and the desired value
Uncertainty, the corresponding uncertainty of analysis of two-dimensional posture yaw angle θ and pitch angle β.
In order to advanced optimize above-mentioned technical proposal, in the S1 dimensions extension, specifically formula is as follows：
y1=cos θ cos β
y2=sin θ cos β
y3=sin θ (1)
y1, y2, y3Corresponding uncertainty uses Δ y respectively1, Δ y2, Δ y3It indicates.
In order to advanced optimize above-mentioned technical proposal, the S2 Gausses estimation procedure, specific steps include：S21：Define X
For training set, X*For test set, the data amount check of training set and test set is N, and y is the corresponding desired values of training set X, Gauss
The predictive equation of process regression model is：
S22：Mean value is obtained by the predictive equation (2)With variance cov (f*)；Also assume that test set X*It is corresponding
Desired value Normal Distribution, the then mean valueIt is test set X*The mean value of corresponding desired value normal distribution, for normal state
Distribution, mean value maximum probability, we use mean valueRepresent the desired value predicted；The variance of normal distribution is bigger, illustrates it
Distribution more disperses, more inaccurate with mean value characterization actual value (the objective value for wanting estimation), otherwise is characterized with mean value real
Actual value is more accurate, so passing through cov (f*) may indicate that the uncertainty degree of estimation, we are using standard deviation as uncertainty
Measurement；S23：By training set X and test set X*Corresponding three desired value y with training set X respectively1, y2, y3, it is input to three
A Gauss regression model carries out attitude prediction, obtains three class mean μ1, μ2, μ3And variances sigma1, σ2, σ3Test set X is corresponded to respectively*'s
Desired value mean value and the relationship of variance and desired value and desired value uncertainty are as follows：
In order to advanced optimize above-mentioned technical proposal, the mean value is calculated in the S22With the variance cov (f*)
Formula is as follows：
In order to advanced optimize above-mentioned technical proposal, the mean value is calculatedWith the variance cov (f*) specifically, will have
There is square index covariance function K (X, X ') of the isotropism range measurement of unit magnitude to be defined as follows：
K (x, x ')=exp {-(x-x ')T(ell2I)-1(x, x ') } (6)
Wherein x and x ' is two data points, and I is the unit matrix with dimension, parameter ell with data set2It is characteristic length；
K (X, X) is the covariance matrix that using formula (6) all training points are carried out with N × N-dimensional that assessment is calculated, K (X*,X*)、K
(X*,X)、K(X,X*) and K (X, X) similarly calculate；It is variance of the additive noise in regression model, passes through cross validation reality
It tests and is selected.
In order to advanced optimize above-mentioned technical proposal, the S3 derives the uncertainty specific steps packet for calculating yaw angle
It includes：The uncertainty Δ θ for calculating yaw angle θ first, by formula (1)
θ=g (y3)=arcsin (y3) (7)
Differential is carried out to formula (7), its differential formulas can be obtained：
Differential dy represents the variation of y, also illustrates that the uncertainty of y, so dy is regarded as Δ y, then the uncertainty Δ of θ
θ is calculated by formula (8)；The uncertainty Δ θ of further yaw angle θ：
In order to advanced optimize above-mentioned technical proposal, the S3 derives the uncertainty specific steps packet for calculating pitch angle
It includes：Known to formula (1)
Differential is carried out to formula (10), can be obtained
The uncertainty Δ β of pitch angle β can be calculated by following formula：
By formula (1) but by：
The complete formula for then calculating the uncertainty Δ β of pitch angle β is as follows：
It can achieve the effect that Attitude estimation accuracy rate is significantly promoted by the way that two-dimensional attitude is expanded to three-dimensional, the present invention
Corresponding uncertainty calculation method is derived into explanation, so as on the basis of high-accuracy for the credible of result
Degree is further analyzed.It can learn that the absolute error of predicted value and actual value is bigger as shown in Figure 2,3, correspond to result
Uncertainty is bigger.
Each embodiment is described by the way of progressive in this specification, the highlights of each of the examples are with other
The difference of embodiment, just to refer each other for identical similar portion between each embodiment.For device disclosed in embodiment
For, since it is corresponded to the methods disclosed in the examples, so description is fairly simple, related place is said referring to method part
It is bright.
The foregoing description of the disclosed embodiments enables those skilled in the art to implement or use the present invention.
Various modifications to these embodiments will be apparent to those skilled in the art, as defined herein
General Principle can be realized in other embodiments without departing from the spirit or scope of the present invention.Therefore, of the invention
It is not intended to be limited to the embodiments shown herein, and is to fit to and the principles and novel features disclosed herein phase one
The widest range caused.
Claims (7)
1. a kind of spatial target posture based on Gaussian process estimates uncertainty calculation method, which is characterized in that specific steps
Including as follows：
S1 dimensions extend：Two-dimensional posture is extended on three-dimensional sphere and is indicated；
S2 Gauss estimation procedures：Estimate to obtain the mean value and variance and desired value and target of the desired value of test set by Gauss
It is worth the relationship of uncertainty；
S3 derives the uncertainty for calculating yaw angle and pitch angle：It is not true according to the mean value, the variance and the desired value
Fixed degree, the corresponding uncertainty of analysis of two-dimensional posture yaw angle θ and pitch angle β.
2. a kind of spatial target posture based on Gaussian process according to claim 1 estimates uncertainty calculation method,
It is characterized in that, in the S1 dimensions extension, specifically formula is as follows：
y1=cos θ cos β
y2=si θ cos β
y3=sin θ (1)
y1, y2, y3Two-dimensional posture target yaw angle θ and pitch angle β are extended to the three-dimensional calculating done to convert, originally two
Thus dimension label yaw angle θ and pitch angle β are expanded into three-dimensional, referred to as desired value.
3. a kind of spatial target posture based on Gaussian process according to claim 1 estimates uncertainty calculation method,
It is characterized in that, the S2 Gausses estimation procedure, specific steps include：
S21：Definition X is training set, X*For test set, the data amount check of training set and test set is N, and y is that training set X is corresponded to
Desired value, according to given X to y model, and assume y obey joint normal distribution, then the prediction of Gaussian process regression model
Equation is：
S22：Mean value is obtained by the predictive equation (2)With variance cov (f*)；The mean valueIt is to represent the mesh predicted
Scale value, the variance cov (f*) show uncertainty；
S23：By training set X and test set X*Corresponding three desired value y with training set X respectively1, y2, y3, it is input to three height
This regression model carries out attitude prediction, obtains test set X*Three class mean μ1, μ2, μ3And variances sigma1, σ2, σ3And desired value and mesh
The relationship of scale value uncertainty is as follows：
y1, y2, y3Corresponding uncertainty uses Δ y respectively1, Δ y2, Δ y3It indicates.
4. a kind of spatial target posture based on Gaussian process according to claim 3 estimates uncertainty calculation method,
It is characterized in that, calculating the mean value in the S22It is as follows with the formula of the variance cov (f*)：
5. a kind of spatial target posture based on Gaussian process according to claim 4 estimates uncertainty calculation method,
It is characterized in that, calculating the mean valueSpecifically with the variance cov (f*), by the isotropism distance with unit magnitude
Square index covariance function K (X, X ') measured is defined as follows：
K (x, x ')=exp {-(x-x ')T(ell2I)-1(x, x ') } (6)
Wherein x and x ' is two data points, and I is the unit matrix with dimension, parameter ell with data set2It is characteristic length；K (X,
X) it is the covariance matrix that using formula (6) all training points are carried out with N × N-dimensional that assessment is calculated, K (X*, X*), K
(X*, X), K (X, X*) and K (X, X) are similarly calculated；It is variance of the additive noise in regression model, passes through cross validation reality
It tests and is selected.
6. a kind of spatial target posture based on Gaussian process according to claim 1 estimates uncertainty calculation method,
It is characterized in that, the uncertainty specific steps that the S3 derives calculating yaw angle include：The uncertain of yaw angle θ is calculated first
Δ θ is spent, by formula (1)
θ=g (y3)=arcsin (y3) (7)
Differential is carried out to formula (7), obtains its differential formulas：
The uncertainty Δ θ of θ is calculated by formula (8)；The uncertainty Δ θ of further yaw angle θ：
7. a kind of spatial target posture based on Gaussian process according to claim 1 estimates uncertainty calculation method,
It is characterized in that, the uncertainty specific steps that the S3 derives calculating pitch angle include：Known to formula (1)
Differential is carried out to formula (10), is obtained
The uncertainty Δ β of pitch angle β is calculated by following formula：
By formula (1) and know：
The complete formula for then calculating the uncertainty Δ β of pitch angle β is as follows：
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Application publication date: 20180724 |