CN109447133B - SVR algorithm-based method for eliminating position information outliers - Google Patents

SVR algorithm-based method for eliminating position information outliers Download PDF

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CN109447133B
CN109447133B CN201811182293.4A CN201811182293A CN109447133B CN 109447133 B CN109447133 B CN 109447133B CN 201811182293 A CN201811182293 A CN 201811182293A CN 109447133 B CN109447133 B CN 109447133B
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张涛
王帅
翁铖铖
杨阳
袁杰
张硕骁
魏宏宇
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Abstract

The invention discloses a method for eliminating position information outliers based on an SVR algorithm. And then constructing an SVR regression model and determining parameters of the SVR model to be constructed. And then, calculating the relative position of the AUV by a pure distance method and substituting the condition parameters of the AUV at the current moment into the SVR model to obtain position prediction. And finally, determining whether the calculated position value is a wild value or not by setting the confidence level, if the difference value is greater than the set confidence level, rejecting the current calculated value, and returning to calculate the position value at the next moment, otherwise, keeping the value. The invention realizes the preprocessing of position measurement data in underwater sound positioning, reduces the error generated by a outlier and is beneficial to the subsequent filtering processing.

Description

SVR algorithm-based method for eliminating position information outliers
Technical Field
The invention relates to the field of a method for removing position information outliers, in particular to a method for removing position information outliers based on an SVR algorithm.
Background
The pure distance method in the USBL system carries out position information resolving and positioning by measuring distances at a plurality of positions and combining AUV course information. The initial position p of the AUV, the vertical distance d between the AUV and the underwater sound source emitter, the course speed v and the course angle of the AUV
Figure GDA0003077214840000011
To make a real-time solution to the position of the AUV. When positioning is carried out by the USBL, positioning errors are inevitably generated due to the influence of factors such as underwater noise, reverberation, sound propagation multi-path effect, Doppler effect and sound velocity nonlinear distribution, so that the AUV navigation positioning accuracy is influenced. Sometimes 1% to 5% or even as much as 10% to 20% of the data severely shifts the true target value and becomes outliers.
In practical engineering application, when a pure distance method is used for positioning and resolving the AUV, due to the reasons of a measurement system or data transmission and the like, outliers can appear in measured data, if the outliers are not screened, the outliers can be directly applied to Kalman filtering for correction, errors existing in state estimation cannot be corrected, but the filter system can be unstable, and filtering divergence can be caused in serious cases. Therefore, the measurement information is preprocessed, and the positioning error and the filtering divergence caused by the outlier can be reduced.
In order to solve the above problems, researchers have proposed many methods for removing outliers. The method comprises a outlier rejection method based on least square, an outlier rejection method based on polynomial fitting and an outlier rejection method based on Kalman filtering. These methods can reject outliers to some extent, but if the parameters are not well selected, it is likely that the data processing results will be too distorted to be convincing or will not reach the result of effectively rejecting outliers.
Disclosure of Invention
In order to solve the above problems, the invention provides a method for removing a position information field value based on an SVR algorithm, the thought of the SVR algorithm is to adopt a structure risk minimization principle to replace the traditional experience risk minimization principle, map a sample to a high-dimensional kernel space, map a nonlinear problem to a linear problem of the high-dimensional space, so as to perform linear regression in a high-dimensional feature space, and further remove the position field value caused by various errors in underwater sound positioning by using the SVR algorithm, and the invention provides the method for removing the position information field value based on the SVR algorithm, which comprises the following steps:
(1) acquiring historical position resolving data of the AUV at one moment before the current moment for the positions of the AUV at different moments to obtain a training data set, wherein the data set at each moment comprises existing condition data including the vertical distance d between the AUV and an underwater sound source emitter, the course speed v of the AUV and a course angle
Figure GDA0003077214840000012
And solved forA position value;
(2) constructing an SVR regression model, determining regular parameters and Gaussian kernel parameters of the SVR model to be constructed, then training each training data set to finally obtain a corresponding support vector regression SVR model, and being capable of predicting the position of the AUV at the current moment;
(3) according to the vertical distance difference d, the course speed v and the course angle of the AUV at the current moment
Figure GDA0003077214840000021
Calculating the absolute position of the AUV by a pure distance method;
(4) and using a support vector regression model to pre-obtain the position prediction value at the next moment. Namely the vertical distance difference d, the course speed v and the course angle of the AUV at the current moment
Figure GDA0003077214840000022
Inputting the SVR model in the step 2 to obtain a predicted value of the AUV position at the current moment;
(5) and judging whether the difference value between the position calculation value of the AUV obtained by the pure distance method at the next moment and the position value predicted by the SVR meets the condition, if so, the calculated position value is available, otherwise, the value is eliminated and recalculated.
In a further improvement of the present invention, in step 1, the training sample set obtained is:
S＝{(xi，yi)，i＝1，2，...，l}；
wherein
Figure GDA0003077214840000023
Is a state parameter at the ith time, which is a factor affecting the position of the AUV, yiAnd e R is the position solution value of the model sample output, namely the ith moment.
In a further improvement of the present invention, in the step 2, the SVR regression model is constructed by:
f(x)＝ωTφ(xi)+b
where b is the offset and phi is the non-linear mapping. The purpose of model training is to calculate the optimal parameter omegaTAnd b, equivalent to solving the solution of the following convex quadratic programming problem:
Figure GDA0003077214840000024
constraint conditions
Figure GDA0003077214840000025
In the formula, C is greater than 0 and is a penalty coefficient, the tolerance of the sample points exceeding the maximized boundary is represented, the larger C is, the larger the penalty of the sample with large error is, otherwise, the higher tolerance of the sample with large error is represented, and the generalization capability of the C changeable model is adjusted; ε is the insensitive loss function; xii，
Figure GDA0003077214840000026
Is the relaxation variable. With the lagrange multiplier method, the original problem translates into the following dual problem:
Figure GDA0003077214840000027
constraint conditions
Figure GDA0003077214840000028
In the formula, Qij＝φ(xi)Tφ(xj)＝K(xi，xj) Where K () is a kernel function, explicit use of the non-linear mapping phi () can be avoided by the kernel function, thereby avoiding the dimensionality disaster, alphai，
Figure GDA0003077214840000029
To solve the above dual problem, the regression function that is sought can be rewritten as:
Figure GDA0003077214840000031
wherein x is a factor affecting the position of the AUV; x is the number ofiThe factors influencing the position of the ith sample in the l samples; k (x)iAnd x) is a kernel function, the adopted kernel function is a radial basis function, and the RBF kernel function is shown as the following formula:
K(x，y)＝exp|-γ·||x-y||2|
where γ is the width of the kernel function.
In a further improvement of the present invention, the step 3 of calculating the position formula of the AUV by using the pure distance method refers to:
Figure GDA0003077214840000032
in the formula (I), the compound is shown in the specification,
Figure GDA0003077214840000033
Figure GDA0003077214840000034
Figure GDA0003077214840000035
Figure GDA0003077214840000036
x3＝X0
y3＝Y0
wherein the sound source emitter psIs known as (X)0，Y0)，p1，p2，p3Three points on the AUV flight path, three points and psAre each r1，r2，r3。t13，t23Distribution is AUV from p1Position to p3Time sum of location p2Is positioned top3The time of the location.
In a further improvement of the present invention, in the step 5, the judging whether the position solution value and the position prediction value satisfy a condition specifically includes: setting a confidence degree delta, wherein a position solution value obtained at the time t is p (t), and a position predicted value obtained at the time t is
Figure GDA0003077214840000037
When p (t) satisfies:
(1)
Figure GDA0003077214840000038
when p (t) is accepted;
(2)
Figure GDA0003077214840000039
when p (t) is the wild value, the wild value is removed, and p (t) is recalculated;
the value of delta is selected based on the accuracy characteristic of the location and the confidence interval.
The invention relates to a method for eliminating a position information field value based on an SVR algorithm. And obtaining a model by extracting the position information training sample data of the AUV at the previous moment. Has important application value for practical engineering application. Compared with other methods, the method does not depend on design experience, and is more convenient. The method provided by the invention realizes the preprocessing of the positioning position data, can effectively eliminate the outlier and reduce the error and the filtering divergence caused by the outlier. Facilitating the subsequent filtering process.
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FIG. 1 is a flow chart of the method for eliminating the location information outliers based on the SVR algorithm.
Detailed Description
The invention is described in further detail below with reference to the following detailed description and accompanying drawings:
the invention provides a method for eliminating position information field values based on an SVR algorithm, which adopts the idea of adopting a structure risk minimization principle to replace the traditional experience risk minimization principle, maps samples to a high-dimensional kernel space, maps nonlinear problems to linear problems of the high-dimensional space, and performs linear regression in the high-dimensional feature space, thereby eliminating the position field values caused by various errors in underwater sound positioning by utilizing the SVR algorithm.
Step 1, firstly, training data are obtained, historical position resolving data of 4 moments before the current moment are obtained for positions of AUVs at different moments, and a training data set is obtained. Wherein the data set at each moment comprises the existing condition data including the vertical distance d between the AUV and the underwater sound source emitter, the heading speed v of the AUV and the heading angle
Figure GDA0003077214840000041
And resolving the calculated position value. The training sample set was obtained as follows:
S＝{(xi，yi)，i＝1，2，3，4}
wherein
Figure GDA0003077214840000042
For model sample input, i.e. factors affecting the position of the AUV, yiAnd e R is the position solution value of the model sample output, namely the ith moment.
Step 2, constructing an SVR regression model, determining the regular parameters and Gaussian kernel parameters of the SVR model to be constructed, then training each training data set to finally obtain a corresponding support vector regression SVR model, and constructing a linear regression function, wherein the specific form of the function is as follows:
f(x)＝ωTφ(xi)+b
where b is the offset. The purpose of model training is to calculate the optimal parameter omegaTAnd b, equivalent to solving the solution of the following convex quadratic programming problem:
Figure GDA0003077214840000043
constraint conditions
Figure GDA0003077214840000044
In the formula, C is greater than 0 and is a penalty coefficient, the tolerance of the sample points exceeding the maximized boundary is represented, the larger C is, the larger the penalty of the sample with large error is, otherwise, the higher tolerance of the sample with large error is represented, and the generalization capability of the C changeable model is adjusted; ε is the insensitive loss function; xii，
Figure GDA0003077214840000045
Is the relaxation variable. With the lagrange multiplier method, the original problem translates into the following dual problem:
Figure GDA0003077214840000046
constraint conditions are as follows:
Figure GDA0003077214840000051
in the formula, alphai，
Figure GDA0003077214840000052
Is the solution of the dual problem, so in the dual optimization problem, only the solution alpha is requirediAnd
Figure GDA0003077214840000053
the amount of calculation is reduced. Solving the dual optimization problem to obtain alphaiAnd
Figure GDA0003077214840000054
the solution of (1). Qij＝φ(xi)Tφ(xj)＝K(xi，xj) The kernel function is a radial basis function, and the RBF kernel function is shown as follows:
K(x，y)＝exp|-γ·||x-y||2|
γ is the width of the kernel function. The regression function that is sought can be rewritten as:
Figure GDA0003077214840000055
wherein x is a factor affecting the position of the AUV; x is the number ofiIs the factor affecting the position of the ith sample among the l samples. The form of the trained SVR model thus obtained is:
Figure GDA0003077214840000056
in the dual optimization problem, two parameters C and γ need to be selected, and an optimal model can be obtained by selecting the optimal values of C and γ. By making the training sample S { (x)t-iP (t-i)), i ═ 1, 2, 3, 4}, where
Figure GDA0003077214840000057
Solution parameter alpha of the substitution modeliAnd
Figure GDA0003077214840000058
in the process, the optimal C and gamma are found by adopting a GA algorithm, wherein the mean square error generated when the SVR model is trained is used as a fitness function of the GA algorithm. Thus, a well-trained SVR model can be obtained.
Step 3, according to the vertical distance difference d, the course speed v and the course angle of the AUV at the current moment
Figure GDA0003077214840000059
The absolute position of the AUV is solved by the pure distance method. The position formula for resolving the AUV by the pure distance method is as follows:
Figure GDA00030772148400000510
in the formula (I), the compound is shown in the specification,
Figure GDA00030772148400000511
Figure GDA00030772148400000512
Figure GDA00030772148400000513
Figure GDA00030772148400000514
x3＝X0
y3＝Y0
wherein the sound source emitter psIs known as (X)0，Y0，)，p1，p2，p3Three points on the AUV flight path, three points and psAre each r1，r2，r3。t13。t23Distribution is AUV from p1Position to p3Time sum of location p2Position to p3The time of the location.
And 4, using a support vector regression model to obtain a position predicted value at the next moment in advance. Namely the state parameter of AUV at the current moment
Figure GDA0003077214840000061
Namely, the vertical distance difference, the course speed and the SVR model in the step 2 are input to obtain the predicted value of the AUV position at the current moment, namely the predicted value of the position at the current moment
Figure GDA0003077214840000062
Step 5, judging whether the difference value between the position calculation value of the AUV at the next moment and the position value predicted by the SVR meets the condition or not, setting the confidence level delta, wherein the position calculation value obtained at the moment t is p (t), and the position prediction value obtained at the moment t is p (t)
Figure GDA0003077214840000063
When p (t) satisfies:
(1)、
Figure GDA0003077214840000064
when p (t) is accepted;
(2)、
Figure GDA0003077214840000065
when p (t) is the outlier, it is removed and p (t) is recalculated.
The value of delta is selected based on the accuracy characteristic of the location and the confidence interval. The accuracy of the model is related to the selection of the delta value, and the selection of the appropriate delta value is an important condition for obtaining a good model effect. A reasonable threshold value (0.4-0.8m/s) is selected through priori knowledge, and more than 97% of outlier points can be removed.
The purpose of the invention is realized as follows:
in underwater acoustic positioning, for the position information of the calculated AUV, because the AUV has weak maneuverability and small acceleration, the AUV usually runs at a constant speed in a certain direction at a certain stable speed, the position information does not change too much in a short time, and the position of the AUV at the next moment can be predicted by using the previous position data in the running process of the AUV. Outliers are usually generated from error values generated in the transmission process, successive observation points of the position information can be regarded as continuously changed, and outlier elimination is performed by using a data reasonableness test criterion in combination with a statistical model. In order to effectively eliminate the outlier problem caused by various errors in positioning, the invention provides a position information outlier elimination method based on support vector regression. The support vector machine adopts a structural risk minimization principle to replace a traditional empirical risk minimization principle, and can well solve the problems of small samples, nonlinearity and high dimensionality. Compared with the traditional learning mode, the method has the advantages that the local minimum problem does not exist, the generalization capability is strong, and the method does not depend on the quantity and quality of samples excessively. The method predicts the next position change of the AUV through a support vector regression model, selects historical data from the existing position information data set, predicts the position of the AUV at the next moment, and eliminates the calculated position information outlier by subtracting the position from the calculated position.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention in any way, but any modifications or equivalent variations made according to the technical spirit of the present invention are within the scope of the present invention as claimed.

Claims (4)

1. A method for eliminating position information outliers based on an SVR algorithm is characterized by comprising the following steps:
(1) acquiring historical position resolving data of the AUV at one moment before the current moment for the positions of the AUV at different moments to obtain a training data set, wherein the data set at each moment comprises existing condition data including the vertical distance d between the AUV and an underwater sound source emitter, the course speed v of the AUV and a course angle
Figure FDA0003077214830000011
And solving the calculated position value;
(2) constructing an SVR regression model, determining regular parameters and Gaussian kernel parameters of the SVR model to be constructed, then training each training data set to finally obtain a corresponding support vector regression SVR model, and being capable of predicting the position of the AUV at the current moment;
in the step (2), the SVR regression model is constructed by:
f(x)＝ωTφ(xi)+b
wherein b is offset, phi is nonlinear mapping, and the purpose of model training is to calculate optimal parameter omegaTAnd b, equivalent to solving the solution of the following convex quadratic programming problem:
Figure FDA0003077214830000012
constraint conditions are as follows:
Figure FDA0003077214830000013
wherein C > 0 is a penalty coefficient and represents the tolerance of the sample point exceeding the maximum boundary, and the larger C represents the larger errorThe larger the sample punishment is, otherwise, the higher tolerance is shown to the sample with large error, and the generalization capability of the model can be changed by adjusting C; ε is the insensitive loss function; xii，
Figure FDA0003077214830000014
For relaxing variables, the original problem is transformed into the following dual problem using the lagrange multiplier method:
Figure FDA0003077214830000015
constraint conditions are as follows:
Figure FDA0003077214830000016
in the formula, Qij＝φ(xi)Tφ(xj)＝K(xi，xj) Where K () is a kernel function by which explicit use of the non-linear mapping phi () can be avoided, thereby avoiding dimensional disasters, ai，
Figure FDA0003077214830000017
To solve the above dual problem, the regression function that is sought can be rewritten as:
Figure FDA0003077214830000018
wherein x is a factor affecting the position of the AUV; x is the number ofiThe factors influencing the position of the ith sample in the l samples; k (x)iAnd x) is a kernel function, the adopted kernel function is a radial basis function, and the RBF kernel function is shown as the following formula:
K(x，y)＝exp|-γ·||x-y||2}
wherein γ is the width of the kernel function;
(3) according to the vertical distance d between the AUV and the underwater sound source emitter at the current moment, the course speed v and the course angle of the AUV
Figure FDA0003077214830000021
Calculating the absolute position of the AUV by a pure distance method;
(4) using a support vector regression model to pre-obtain a position predicted value at the next moment, namely the vertical distance d between the AUV at the current moment and the underwater sound source emitter, the course speed v and the course angle of the AUV
Figure FDA0003077214830000022
Inputting the SVR model in the step (2) to obtain a predicted value of the AUV position at the current moment;
(5) and judging whether the difference value between the position calculation value of the AUV obtained by the pure distance method at the next moment and the position value predicted by the SVR meets the condition, if so, the calculated position value is available, otherwise, the value is eliminated and recalculated.
2. The removing method of the location information outlier based on the SVR algorithm as claimed in claim 1, wherein: in the step (1), the obtained training sample set is:
S＝{(xi，yi)，i＝1，2，...，l}；
wherein
Figure FDA0003077214830000023
Is a state parameter at the ith time, which is a factor affecting the position of the AUV, yiAnd e R is the position solution value of the model sample output, namely the ith moment.
3. The removing method of the location information outlier based on the SVR algorithm as claimed in claim 1, wherein: the step (3) of calculating the position formula of the AUV by using a pure distance method refers to:
Figure FDA0003077214830000024
in the formula (I), the compound is shown in the specification,
Figure FDA0003077214830000025
Figure FDA0003077214830000026
Figure FDA0003077214830000027
Figure FDA0003077214830000028
x3＝X0
y3＝Y0
wherein the sound source emitter psIs known as (X)0，Y0)，p1，p2，p3Three points on the AUV flight path, three points and psAre each r1，r2，r3，t13，t23Distribution is AUV from p1Position to p3Time sum of location p2Position to p3The time of the location.
4. The removing method of the location information outlier based on the SVR algorithm as claimed in claim 1, wherein: in the step (5), the determining whether the position solution value and the position prediction value satisfy a condition specifically includes: setting a confidence degree delta, wherein a position solution value obtained at the time t is p (t), and a position predicted value obtained at the time t is
Figure FDA0003077214830000029
When p (t) satisfies:
(1)
Figure FDA0003077214830000032
when p (t) is accepted;
(2)
Figure FDA0003077214830000031
when p (t) is the wild value, the wild value is removed, and p (t) is recalculated;
the value of delta is selected based on the accuracy characteristic of the location and the confidence interval.
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