CN113688908B - Bluetooth indoor propagation model correction method based on twin support vector regression machine - Google Patents

Bluetooth indoor propagation model correction method based on twin support vector regression machine Download PDF

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CN113688908B
CN113688908B CN202110983720.4A CN202110983720A CN113688908B CN 113688908 B CN113688908 B CN 113688908B CN 202110983720 A CN202110983720 A CN 202110983720A CN 113688908 B CN113688908 B CN 113688908B
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顾斌杰
曹杰
潘丰
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Chongqing Tailewei Technology Co ltd
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Abstract

The invention relates to a Bluetooth signal indoor propagation model correction method based on an online epsilon type twin support vector regression machine. The method reduces the time for updating the model, improves the real-time performance of correcting the indoor propagation model of the Bluetooth signal, has higher prediction precision, is more suitable for the deployment of terminal equipment with limited memory, and provides an effective method for correcting the indoor propagation model on site by using portable terminal equipment.

Description

Bluetooth indoor propagation model correction method based on twin support vector regression machine
Technical Field
The invention relates to the technical field of Bluetooth indoor positioning, in particular to a Bluetooth signal indoor propagation model correction method based on an online epsilon type twin support vector regression machine.
Background
At present, along with the rapid development of the internet of things and mobile communication technology, the demand for indoor accurate positioning is also increasing. The complexity of the indoor environment causes significant interference and impact on the propagation process of the wireless signals, and thus GPS technology cannot be used for indoor positioning. Based on ranging algorithm and ranging independent algorithm are two common types of indoor positioning algorithm. The method has certain requirements on hardware based on a ranging algorithm but has higher positioning accuracy, and mainly represents RSSI, TOA, TDOA and AOA.
Currently, various RSSI-based indoor positioning algorithms generally use some common indoor propagation models to fit the relationship between the distance and the bluetooth signal strength RSSI, and model parameters in the positioning algorithms are often derived from empirical values or fit to the overall environment. However, factors such as multi-path propagation of radio signals and nonlinear time-varying characteristics introduced by the motion of positioning nodes or surrounding scatterers are main characteristics of a mobile communication channel, and the characteristics are not only main reasons influencing communication quality, but also main factors causing fitting errors of indoor propagation models. Therefore, the interference of factors such as complicated indoor environment layout and narrow space on the RSSI measurement is not fully considered from the empirical value or the model parameter fitting to the whole environment, so that the final positioning accuracy is limited and the method is difficult to adapt to different scenes.
Therefore, in order to improve the accuracy, a signal transmitter and a signal receiver need to be erected for signal simulation test, and collected data is input into corresponding tool software for data processing, model correction and signal prediction. The existing equipment is large in size, the testing equipment and the data processing and analyzing equipment are independent and need to be processed separately, results cannot be obtained in real time in the testing process, and the requirement on the capability of a design engineer is high, so that the working efficiency is low, and a large amount of manpower and material resources need to be consumed.
Disclosure of Invention
Therefore, the technical problem to be solved by the present invention is to overcome the above technical problems, and to provide a bluetooth signal indoor propagation model correction method based on an online epsilon type twin support vector regression machine, which is based on the online epsilon type twin support vector regression machine and improves the efficiency of bluetooth signal indoor propagation model correction by saving effective information in the training process.
In order to solve the technical problem, the invention provides a bluetooth signal indoor propagation model correction method based on an online epsilon type twin support vector regression machine, which comprises the following steps:
s10: a signal receiver is used for collecting the Bluetooth signal strength RSSI of a signal transmitter for multiple times at the kth sampling point, and mean value filtering is carried out to obtain a logarithmic distance loss model r of the Bluetooth signal strength RSSI k ＝RSSI(d k )＝RSSI(d 0 )+10wlg(d k /d 0 ) Wherein d is k Denotes the distance of the sample point from the signal transmitter, the subscript k denotes the number, RSSI (d) k ) Representing a distance d to the signal transmitter k Signal receiver of (2) collected Bluetooth signal strength, d 0 Representing the close distance to the signal transmitter, w represents the weight of the model, let d 0 ＝1m，y k ＝r k ，x k ＝10lg(d k ) B = RSSI (1), yielding a linear model y k ＝wx k + b, training sample is (x) k ,y k )；
S20: and comparing the root mean square error of the training value and the predicted value of the y value in the training sample with a set threshold, if the root mean square error of the training value and the predicted value of the y value is greater than or equal to the threshold, utilizing the training sample to correct and update the Bluetooth signal indoor propagation model based on the online epsilon type twin support vector regression, and going to the step S10, if the root mean square error of the training value and the predicted value of the y value is less than the threshold, stopping correcting and updating the Bluetooth signal indoor propagation model based on the online epsilon type twin support vector regression.
In one embodiment of the invention, the updating, by using the training sample, the correction of the bluetooth signal indoor propagation model based on the online epsilon type twin support vector regression comprises the following steps:
let the set of training samples be T, which is divided into S 1 、R 1 、E 1 Three sets of where S 1 Set of vectors for boundary support of lower-bound insensitive function, R 1 To reserve a set of support vectors, E 1 A set of vectors is supported for errors.
In one embodiment of the invention, the updating, by using the training sample, the correction of the bluetooth signal indoor propagation model based on the online epsilon type twin support vector regression comprises the following steps:
t is further divided into S 2 、R 2 、E 2 Three sets of where S 2 Supporting a set of vectors for the boundaries of upper-bound insensitive functions, R 2 To reserve a set of support vectors, E 2 A set of vectors is supported for errors.
In one embodiment of the invention, the updating, by using the training sample, the correction of the bluetooth signal indoor propagation model based on the online epsilon type twin support vector regression comprises the following steps:
s21: reading training samples (x) k ,y k )；
S22: when k =1, c is set 1 、c 2 、c 3 、ε 1 And epsilon 2 A value of (b), wherein c 1 、c 2 Is a penalty constant, c 3 Is a regularization constant, ε 1 、ε 2 Is an insensitive constant; initializing linear model parametersLet b 1 ＝b 2 ＝w 1 ＝w 2 =0, wherein b 1 、b 2 To be offset, w 1 、w 2 Is a weight; then, the initial M is calculated from the formula (1) -1 ；
When k ≠ 1, M is updated by equation (2) -1 When is coming into contact with
Figure GDA0003521777380000031
When it is time, V is updated by equation (3) 1 When is coming into contact with
Figure GDA0003521777380000032
When the V is updated by the formula (4) 2 ；
Figure GDA0003521777380000033
Wherein, g k ＝[1,x k ]I is a unit matrix of corresponding dimension;
M -1 ＝M -1 -ZZ T /J (2)
Figure GDA0003521777380000034
Figure GDA0003521777380000035
wherein, the first and the second end of the pipe are connected with each other,
Figure GDA0003521777380000036
J＝1+g k Z，
Figure GDA0003521777380000037
Figure GDA0003521777380000038
is a row vector g i ,i∈S 1 A composed matrix, Z 1 ′＝V 1 Z 1 ，
Figure GDA0003521777380000039
Figure GDA00035217773800000310
Is a row vector g i ,i∈S 2 A composed matrix, Z 2 ′＝V 2 Z 2 ，
Figure GDA00035217773800000311
S23: calculation of α from equations (5) and (6) k And gamma k ：
α k ＝y k -(L T L) -1 L T l 1 (5)
γ k ＝(L T L) -1 L T l 2 -y k (6)
Wherein alpha is k And gamma k Respectively represent training samples (x) k ,y k ) Lagrange multipliers in the lower bound insensitive function and the upper bound insensitive function,
Figure GDA00035217773800000312
G＝[e,X]e is a column vector with the corresponding dimension elements all being 1, X = [ X = 1 ,x 2 ,...,x k-1 ] T ，l 1 ＝G(ZZ T /J)G T (Y-α)，l 2 ＝G(ZZ T /J)G T (Y+γ)，Y＝[y 1 ,y 2 ,...,y k-1 ] T Alpha is a group of i I ∈ T, a column vector consisting of γ i I belongs to a column vector consisting of T;
s24: let α = [ α = T ,α k ] T ，γ＝[γ T ,γ k ] T ，
Figure GDA00035217773800000313
Y＝[Y T ,y k ] T T = T { k }; when in use
Figure GDA00035217773800000314
When the time is over, the time is updated by the formula (7) -formula (9)
Figure GDA00035217773800000315
Figure GDA00035217773800000316
Is formed by alpha i ,i∈S 1 A column vector of components; when in use
Figure GDA00035217773800000317
When the time is over, the time is updated by the formula (10) -formula (12)
Figure GDA00035217773800000318
Figure GDA00035217773800000319
Is formed by gamma i ,i∈S 2 A column vector of components;
u 1 ＝M -1 G T (Y-α) (7)
H 1 ＝Y-(Gu 1 -ε 1 e) (8)
Figure GDA00035217773800000320
u 2 ＝M -1 G T (Y+γ) (10)
H 2 ＝(Gu 2 +ε 2 e)-Y (11)
Figure GDA00035217773800000321
wherein H 1 A column vector H representing the boundary distance components from the training samples in the T set to the lower-bound insensitive function 2 A column vector consisting of the boundary distances from the training samples in the T set to the upper-bound insensitive function,
Figure GDA00035217773800000322
is S 1 A column vector composed of the boundary distances corresponding to the training samples in the set,
Figure GDA00035217773800000323
is S 2 A column vector consisting of boundary distances corresponding to training samples in the set;
s25: recalculating H from equation (7) -equation (8) 1 Then screening the abnormal sample set F 1 ，t 1(i) Is represented by F 1 A target value adjusted by a Lagrange multiplier of an ith sample in the set;
for S 1 Samples in the set, if α i Not more than 0, transferred into F 1 Set and t 1(i) ＝c 1 (ii) a If α is i ≥c 1 Is moved into F 1 Set and t 1(i) =0, and the inverse matrix V needs to be updated by equation (13) 1 ；
For R 1 Sample in the set, if H 1(i) Less than or equal to 0, transferring into F 1 Set and t 1(i) ＝c 1 ；
For E 1 Sample in the set, if H 1(i) Not less than 0, shift-in F 1 Set and t 1(i) ＝0；
For training sample (x) k ,y k ) If H is H 1(k) ≥0,α k If not less than 0, then move into R 1 Gathering; if H 1(k) ＝0,0＜α k ＜c 1 Then move into S 1 The inverse matrix V is collected and updated by equation (14) 1 (ii) a If H 1(k) ≤0,α k ＝c 1 Then move into E 1 Gathering; otherwise, when alpha is k Not more than 0, transferred into F 1 Set and t 1(k) ＝c 1 (ii) a When alpha is k ≥c 1 Is moved into F 1 Set and t 1(k) =0; when 0 < alpha k ＜c 1 If H is H 1(k) < 0, move into F 1 Set and t 1(k) ＝c 1 If H is H 1(k) > 0, into F 1 Set and t 1(k) ＝0；
Figure GDA0003521777380000041
Wherein the subscript t denotes a shift out of S 1 The samples of the set, the subscript \ tt representing the elements of the t rows and t columns of the deletion matrix, the subscript x representing the full index of the row or column;
Figure GDA0003521777380000042
wherein the content of the first and second substances,
Figure GDA0003521777380000043
Q＝GMG T ；
s26: recalculating H from equation (10) -equation (11) 2 Then screening the abnormal sample set F 2 ，t 2(i) Is represented by F 2 The target value of the lagrange multiplier adjustment of the ith sample;
for S 2 Samples in the set, if γ i Not more than 0, transferred into F 2 Set and t 2(i) ＝c 2 (ii) a If gamma is i ≥c 2 Is moved into F 2 Set and t 2(i) =0, and the inverse matrix V needs to be updated by equation (15) 2 ；
For R 2 Samples in the set, if H 2(i) Not more than 0, transferred into F 2 Set and t 2(i) ＝c 2 ；
For E 2 Samples in the set, if H 2(i) Not less than 0, shift-in F 2 Set and t 2(i) ＝0；
For sample (x) k ,y k ) If H is H 2(k) ≥0,γ k If not less than 0, then move into R 2 Gathering; if H 2(k) ＝0,0＜γ k ＜c 2 Then move into S 2 The inverse matrix V is collected and updated by equation (16) 2 (ii) a If H 2(k) ≤0,γ k ＝c 2 Then move into E 2 Gathering; otherwise, when gamma is k Not more than 0, transferred into F 2 Set and t 2(k) ＝c 2 (ii) a When gamma is k ≥c 2 Is moved into F 2 Set and t 2(k) =0; when 0 < gamma k ＜c 2 If H is H 2(k) < 0, move into F 2 Set and t 2(k) ＝c 2 If H is H 2(k) > 0, into F 2 Set and t 2(k) ＝0；
Figure GDA0003521777380000044
Wherein the subscript t denotes a shift out of S 2 A sample of the collection;
Figure GDA0003521777380000045
wherein the content of the first and second substances,
Figure GDA0003521777380000046
s27: from the respective equations (17) and (18)
Figure GDA0003521777380000047
Then, the maximum step length eta is calculated from the formula (19) to the formula (26) max ；
If it is used
Figure GDA0003521777380000048
Then the corresponding sample is represented by F 1 Set shift into S 1 Is aggregated and V is updated by equation (14) 1 ；
If it is not
Figure GDA0003521777380000051
Then the corresponding sample is represented by F 1 Set shift into R 1 Gathering;
if it is not
Figure GDA0003521777380000052
Then the corresponding sample is represented by F 1 Set move-in E 1 Gathering;
if it is not
Figure GDA0003521777380000053
Then the corresponding sample is represented by S 1 Set shift into R 1 Set or E 1 Set, determined by Lagrange multiplier of corresponding sample, and update V by equation (13) 1 ；
If it is not
Figure GDA0003521777380000054
Then the corresponding sample is represented by R 1 Set migration S 1 Is aggregated and V is updated by equation (14) 1 ；
If it is not
Figure GDA0003521777380000055
Then the corresponding sample is represented by E 1 Set shift into S 1 Is aggregated and V is updated by equation (14) 1 ；
Then, order
Figure GDA0003521777380000056
Repeating (7) to F 1 Stopping iteration when the set is empty;
Figure GDA0003521777380000057
Figure GDA0003521777380000058
wherein, t 1 Is composed of t 1(i) ,i∈F 1 The column vector of the component is composed of,
Figure GDA0003521777380000059
Figure GDA00035217773800000510
Figure GDA00035217773800000511
Figure GDA00035217773800000512
Figure GDA00035217773800000513
Figure GDA00035217773800000514
Figure GDA00035217773800000515
Figure GDA00035217773800000516
Figure GDA00035217773800000517
wherein h is 1 (i)，
Figure GDA0003521777380000061
t 1(i) And alpha i Are each H 1 ，
Figure GDA0003521777380000062
t 1 And the ith element of α;
Figure GDA0003521777380000063
Figure GDA0003521777380000064
and
Figure GDA0003521777380000065
are respectively F 1 The ith sample in the set is shifted into S 1 Set of R 1 Set sum E 1 Step size of the set;
Figure GDA0003521777380000066
is S 1 Moving the ith sample in the set into R 1 Set or E 1 A step size of the set;
Figure GDA0003521777380000067
is R 1 Set shift into S 1 Step size of the set;
Figure GDA0003521777380000068
is E 1 Set shift into S 1 Step size of the set;
Figure GDA0003521777380000069
and
Figure GDA00035217773800000610
are respectively composed of
Figure GDA00035217773800000611
And
Figure GDA00035217773800000612
a column vector of components;
s28: from the respective equations (27) and (28)
Figure GDA00035217773800000613
Then, equation (29) -equation (36) calculates the maximum step η' max ；
If it is not
Figure GDA00035217773800000614
Then the corresponding sample is represented by F 2 Set shift into S 2 Is aggregated and V is updated by equation (16) 2 ；
If it is not
Figure GDA00035217773800000615
Then the corresponding sample is represented by F 2 Set shift into R 2 Gathering;
if it is not
Figure GDA00035217773800000616
Then the corresponding sample is represented by F 2 Set migration E 2 Gathering;
if it is not
Figure GDA00035217773800000617
Then the corresponding sample is represented by S 2 Set shift into R 2 Set or E 2 Set, determined by the Lagrange multiplier of the corresponding sample, and update V by equation (15) 2 ；
If it is used
Figure GDA00035217773800000618
Then the corresponding sample is represented by R 2 Set shift into S 2 Is aggregated and V is updated by equation (16) 2 ；
If it is not
Figure GDA00035217773800000619
Then the corresponding sample is represented by E 2 Set shift into S 2 Is collected and V is updated by equation (16) 2 ；
Then, let
Figure GDA00035217773800000620
Repeating (8) to F 2 Stopping iteration when the set is empty;
Figure GDA00035217773800000621
Figure GDA00035217773800000622
wherein, t 2 Is composed of t 2(i) ,i∈F 2 The column vector of the component(s) is,
Figure GDA00035217773800000623
Figure GDA00035217773800000624
Figure GDA00035217773800000625
Figure GDA00035217773800000626
Figure GDA00035217773800000627
Figure GDA0003521777380000071
Figure GDA0003521777380000072
Figure GDA0003521777380000073
Figure GDA0003521777380000074
wherein h is 2 (i)，
Figure GDA0003521777380000075
t 2(i) And gamma i Are each H 2 ，
Figure GDA0003521777380000076
d 2 And the ith element of γ;
Figure GDA0003521777380000077
Figure GDA0003521777380000078
and
Figure GDA0003521777380000079
are respectively F 2 The ith sample in the set is shifted into S 2 Set of R 2 Set sum E 2 Step size of the set;
Figure GDA00035217773800000710
is S 2 Moving the ith sample in the set into R 2 Set or E 2 A step size of the set;
Figure GDA00035217773800000711
is R 2 Set shift into S 2 Step size of the set;
Figure GDA00035217773800000712
is E 2 Set shift into S 2 Step size of the set;
Figure GDA00035217773800000713
and
Figure GDA00035217773800000714
are respectively composed of
Figure GDA00035217773800000715
Figure GDA00035217773800000716
And
Figure GDA00035217773800000717
a column vector of components;
s29: calculating the solution u of the updated model from equations (7) and (10) 1 And u 2 And store M -1 Parameter u of lower bound insensitive function 1 ，α，V 1 Set R 1 、S 1 、E 1 And the parameter u of the upper bound insensitive function 2 ，γ，V 2 Set R 2 、S 2 、E 2 。
Compared with the prior art, the technical scheme of the invention has the following advantages:
the invention saves the effective information in the training process, gradually and iteratively adjusts the Lagrange multiplier of the training sample in each updating process, so that the Lagrange multiplier meets the KKT condition, the model updating speed in the correction process is improved, the method is more suitable for the deployment of terminal equipment with limited memory, and an effective method is provided for the field correction of the indoor propagation model by using the portable terminal equipment.
Drawings
In order that the present invention may be more readily and clearly understood, reference will now be made in detail to the present invention, examples of which are illustrated in the accompanying drawings.
FIG. 1 is a flow chart of a Bluetooth signal indoor propagation model correction method based on an online epsilon type twin support vector regression machine.
FIG. 2 is a graph of a predicted result of a Bluetooth signal indoor propagation model based on an online epsilon type twin support vector regression machine.
FIG. 3 is a diagram of predicted output residuals of a Bluetooth signal indoor propagation model based on an online epsilon type twin support vector regression.
Detailed Description
The present invention is further described below in conjunction with the following figures and specific examples so that those skilled in the art may better understand the present invention and practice it, but the examples are not intended to limit the present invention.
Referring to fig. 1, the present invention provides a bluetooth signal indoor propagation model calibration method based on an online epsilon type twin support vector regression, including the following steps:
s10: collecting the Bluetooth signal strength RSSI of the signal transmitter for multiple times by using a signal receiver at the kth sampling point, and carrying out mean value filtering to obtain a logarithmic distance loss model r of the Bluetooth signal strength RSSI k ＝RSSI(d k )＝RSSI(d 0 )+10wlg(d k /d 0 ) Wherein d is k Indicating the distance of the sample point from the signal transmitter, subscript k indicating the number, RSSI (d) k ) Representing a distance d to the signal transmitter k Signal receiver of (2) collected Bluetooth signal strength, d 0 Representing the close distance to the signal transmitter, w represents the weight of the model, let d 0 ＝1m，y k ＝r k ，x k ＝10lg(d k ) B = RSSI (1), yielding a linear model y k ＝wx k + b, training sample is (x) k ,y k )；
S20: and comparing the root mean square error of the training value and the predicted value of the y value in the training sample with a set threshold, if the root mean square error of the training value and the predicted value of the y value is greater than or equal to the threshold, utilizing the training sample to correct and update the Bluetooth signal indoor propagation model based on the online epsilon type twin support vector regression, and going to the step S10, if the root mean square error of the training value and the predicted value of the y value is less than the threshold, stopping correcting and updating the Bluetooth signal indoor propagation model based on the online epsilon type twin support vector regression.
In one embodiment of the invention, the updating, by using the training sample, the correction of the bluetooth signal indoor propagation model based on the online epsilon type twin support vector regression comprises the following steps:
let the set of training samples be T, which is divided into S 1 、R 1 、E 1 Three sets of where S 1 Set of vectors for boundary support of lower-bound insensitive function, R 1 To reserve a set of support vectors, E 1 A set of vectors is supported for errors.
In one embodiment of the invention, the updating, by using the training sample, the correction of the bluetooth signal indoor propagation model based on the online epsilon type twin support vector regression comprises the following steps:
t is further divided into S 2 、R 2 、E 2 Three sets of where S 2 Supporting a set of vectors for the boundaries of upper-bound insensitive functions, R 2 To reserve a set of support vectors, E 2 A set of vectors is supported for errors.
In one embodiment of the invention, the updating, by using the training sample, the correction of the bluetooth signal indoor propagation model based on the online epsilon type twin support vector regression comprises the following steps:
s21: reading training samples (x) k ,y k )；
S22: when k =1, c is set 1 、c 2 、c 3 、ε 1 And ε 2 A value of (b), wherein c 1 、c 2 Is a penalty constant, c 3 Is a regularization constant, ε 1 、ε 2 Is an insensitive constant; initialize the parameters of the linear model, let b 1 ＝b 2 ＝w 1 ＝w 2 =0, wherein b 1 、b 2 To be biased, w 1 、w 2 Is a weight; then, the initial M is calculated from the formula (1) -1 ；
When k ≠ 1, M is updated by equation (2) -1 When is coming into contact with
Figure GDA0003521777380000091
When it is time, V is updated by equation (3) 1 When is coming into contact with
Figure GDA0003521777380000092
When it is time, V is updated by equation (4) 2 ；
Figure GDA0003521777380000093
Wherein, g k ＝[1,x k ]I is a unit matrix of corresponding dimension;
M -1 ＝M -1 -ZZ T /J (2)
Figure GDA0003521777380000094
Figure GDA0003521777380000095
wherein, the first and the second end of the pipe are connected with each other,
Figure GDA0003521777380000096
J＝1+g k Z，
Figure GDA0003521777380000097
Figure GDA0003521777380000098
is a row vector g i ,i∈S 1 A composed matrix, Z 1 ′＝V 1 Z 1 ，
Figure GDA0003521777380000099
Figure GDA00035217773800000910
Is a row vector g i ,i∈S 2 A composed matrix, Z 2 ′＝V 2 Z 2 ，
Figure GDA00035217773800000911
S23: calculation of α from equations (5) and (6) k And gamma k ：
α k ＝y k -(L T L) -1 L T l 1 (5)
γ k ＝(L T L) -1 L T l 2 -y k (6)
Wherein alpha is k And gamma k Respectively represent training samples (x) k ,y k ) Lagrange multipliers in the lower bound insensitive function and the upper bound insensitive function,
Figure GDA00035217773800000912
G＝[e,X]e is a column vector with the corresponding dimension elements all being 1, X = [ X = 1 ,x 2 ,...,x k-1 ] T ，l 1 ＝G(ZZ T /J)G T (Y-α)，l 2 ＝G(ZZ T /J)G T (Y+γ)，Y＝[y 1 ,y 2 ,...,y k-1 ] T Alpha is a group of i I ∈ T, a column vector consisting of γ i I belongs to a column vector consisting of T;
s24: let alpha = [ alpha ] T ,α k ] T ，γ＝[γ T ,γ k ] T ，
Figure GDA00035217773800000913
Y＝[Y T ,y k ] T T = T { k }; when in use
Figure GDA00035217773800000914
When the time is over, the time is updated by the formula (7) -formula (9)
Figure GDA00035217773800000915
Figure GDA00035217773800000916
Is formed by alpha i ,i∈S 1 A column vector of components; when in use
Figure GDA00035217773800000917
When the time is over, the time is updated by the formula (10) -formula (12)
Figure GDA00035217773800000918
Figure GDA00035217773800000919
Is formed by gamma i ,i∈S 2 A column vector of components;
u 1 ＝M -1 G T (Y-α) (7)
H 1 ＝Y-(Gu 1 -ε 1 e) (8)
Figure GDA00035217773800000920
u 2 ＝M -1 G T (Y+γ) (10)
H 2 ＝(Gu 2 +ε 2 e)-Y (11)
Figure GDA0003521777380000101
wherein H 1 A column vector H representing the boundary distance components from the training samples in the T set to the lower-bound insensitive function 2 A column vector consisting of the boundary distances from the training samples in the T set to the upper-bound insensitive function,
Figure GDA0003521777380000102
is S 1 A column vector composed of the boundary distances corresponding to the training samples in the set,
Figure GDA0003521777380000103
is S 2 A column vector consisting of boundary distances corresponding to training samples in the set;
s25: recalculating H from equation (7) -equation (8) 1 Then screening an abnormal sample set F 1 ，t 1(i) Is represented by F 1 A target value adjusted by a Lagrange multiplier of an ith sample in the set;
for S 1 Samples in the set, if α i Not more than 0, transferred into F 1 Set and t 1(i) ＝c 1 (ii) a If α is i ≥c 1 Is moved into F 1 Set and t 1(i) =0, and the inverse matrix V needs to be updated by equation (13) 1 ；
For R 1 Sample in the set, if H 1(i) Not more than 0, transferred into F 1 Set and t 1(i) ＝c 1 ；
For E 1 Sample in the set, if H 1(i) Not less than 0, shift-in F 1 Set and t 1(i) ＝0；
For training sample (x) k ,y k ) H if H 1(k) ≥0,α k If not less than 0, then move into R 1 Gathering; if H 1(k) ＝0,0＜α k ＜c 1 Then move into S 1 Inverse integration and updating by equation (14)Matrix V 1 (ii) a If H 1(k) ≤0,α k ＝c 1 Then move into E 1 Gathering; otherwise, when alpha is k Not more than 0, transferred into F 1 Set and t 1(k) ＝c 1 (ii) a When alpha is k ≥c 1 Is moved into F 1 Set and t 1(k) =0; when 0 < alpha k ＜c 1 If H is H 1(k) < 0, move into F 1 Set and t 1(k) ＝c 1 If H is H 1(k) > 0, into F 1 Set and t 1(k) ＝0；
Figure GDA0003521777380000104
Wherein the subscript t denotes the removal of S 1 The samples of the set, the subscript \ tt representing the elements of the t rows and t columns of the deletion matrix, the subscript x representing the full index of the row or column;
Figure GDA0003521777380000105
wherein the content of the first and second substances,
Figure GDA0003521777380000106
Q＝GMG T ；
s26: recalculating H from equation (10) -equation (11) 2 Then screening the abnormal sample set F 2 ，t 2(i) Is represented by F 2 The target value of the lagrange multiplier adjustment of the ith sample;
for S 2 Samples in the set, if γ i Not more than 0, transferred into F 2 Set and t 2(i) ＝c 2 (ii) a If gamma is i ≥c 2 Is moved into F 2 Set and t 2(i) =0, and the inverse matrix V needs to be updated by equation (15) 2 ；
For R 2 Samples in the set, if H 2(i) Not more than 0, transferred into F 2 Set and t 2(i) ＝c 2 ；
For E 2 In a collectionIf H is a sample of 2(i) Not less than 0, shift-in F 2 Set and t 2(i) ＝0；
For sample (x) k ,y k ) If H is H 2(k) ≥0,γ k If not less than 0, then move into R 2 Gathering; if H 2(k) ＝0,0＜γ k ＜c 2 Then move into S 2 The inverse matrix V is collected and updated by equation (16) 2 (ii) a If H 2(k) ≤0,γ k ＝c 2 Then move into E 2 Gathering; otherwise, when γ k Not more than 0, transferred into F 2 Set and t 2(k) ＝c 2 (ii) a When gamma is k ≥c 2 Is moved into F 2 Set and t 2(k) =0; when 0 < gamma k ＜c 2 If H is H 2(k) < 0, move into F 2 Set and t 2(k) ＝c 2 H if H 2(k) > 0, into F 2 Set and t 2(k) ＝0；
Figure GDA0003521777380000107
Wherein the subscript t denotes a shift out of S 2 A sample of the collection;
Figure GDA0003521777380000111
wherein the content of the first and second substances,
Figure GDA0003521777380000112
s27: from the respective equations (17) and (18)
Figure GDA0003521777380000113
Then, the maximum step length eta is calculated from the formula (19) to the formula (26) max ；
If it is not
Figure GDA0003521777380000114
Then the corresponding sample is represented by F 1 Set shift into S 1 Are combined and represented by(14) Update V 1 ；
If it is not
Figure GDA0003521777380000115
Then the corresponding sample is represented by F 1 Set shift into R 1 Gathering;
if it is not
Figure GDA0003521777380000116
Then the corresponding sample is represented by F 1 Set move-in E 1 Gathering;
if it is not
Figure GDA0003521777380000117
Then the corresponding sample is represented by S 1 Set shift into R 1 Set or E 1 Set, determined by the Lagrange multiplier of the corresponding sample, and update V by equation (13) 1 ；
If it is not
Figure GDA0003521777380000118
Then the corresponding sample is represented by R 1 Set migration S 1 Is aggregated and V is updated by equation (14) 1 ；
If it is not
Figure GDA0003521777380000119
Then the corresponding sample is represented by E 1 Set shift into S 1 Is aggregated and V is updated by equation (14) 1 ；
Then, order
Figure GDA00035217773800001110
Repeating (7) to F 1 Stopping iteration when the set is empty;
Figure GDA00035217773800001111
Figure GDA00035217773800001112
wherein, t 1 Is composed of t 1(i) ,i∈F 1 The column vector of the component(s) is,
Figure GDA00035217773800001113
Figure GDA00035217773800001114
Figure GDA00035217773800001115
Figure GDA00035217773800001116
Figure GDA00035217773800001117
Figure GDA00035217773800001118
Figure GDA0003521777380000121
Figure GDA0003521777380000122
Figure GDA0003521777380000123
wherein h is 1 (i)，
Figure GDA0003521777380000124
t 1(i) And alpha i Are each H 1 ，
Figure GDA0003521777380000125
t 1 And the ith element of α;
Figure GDA0003521777380000126
Figure GDA0003521777380000127
and
Figure GDA0003521777380000128
are respectively F 1 The ith sample in the set is shifted into S 1 Set of R 1 Set and E 1 Step size of the set;
Figure GDA0003521777380000129
is S 1 Moving the ith sample in the set into R 1 Set or E 1 Step size of the set;
Figure GDA00035217773800001210
is R 1 Set migration S 1 Step size of the set;
Figure GDA00035217773800001211
is E 1 Set shift into S 1 A step size of the set;
Figure GDA00035217773800001212
and
Figure GDA00035217773800001213
are respectively composed of
Figure GDA00035217773800001214
And
Figure GDA00035217773800001215
a column vector of components;
s28: from the respective equations (27) and (28)
Figure GDA00035217773800001216
Then, equation (29) -equation (36) calculates the maximum step η' max ；
If it is used
Figure GDA00035217773800001217
Then the corresponding sample is represented by F 2 Set shift into S 2 Is aggregated and V is updated by equation (16) 2 ；
If it is not
Figure GDA00035217773800001218
Then the corresponding sample is represented by F 2 Set shift into R 2 Gathering;
if it is not
Figure GDA00035217773800001219
Then the corresponding sample is represented by F 2 Set move-in E 2 Gathering;
if it is not
Figure GDA00035217773800001220
Then the corresponding sample is represented by S 2 Set shift into R 2 Set or E 2 Set, determined by Lagrange multiplier of corresponding sample, and update V by equation (15) 2 ；
If it is not
Figure GDA00035217773800001221
Then the corresponding sample is represented by R 2 Set shift into S 2 Is collected and V is updated by equation (16) 2 ；
If it is used
Figure GDA00035217773800001222
Then the corresponding sample is represented by E 2 Set shift into S 2 Is aggregated and V is updated by equation (16) 2 ；
Then, order
Figure GDA00035217773800001223
Repeating (8) until F 2 Stopping iteration when the set is empty;
Figure GDA00035217773800001224
Figure GDA00035217773800001225
wherein, t 2 Is composed of t 2(i) ,i∈F 2 The column vector of the component is composed of,
Figure GDA00035217773800001226
Figure GDA00035217773800001227
Figure GDA00035217773800001228
Figure GDA00035217773800001229
Figure GDA0003521777380000131
Figure GDA0003521777380000132
Figure GDA0003521777380000133
Figure GDA0003521777380000134
Figure GDA0003521777380000135
wherein h is 2 (i)，
Figure GDA0003521777380000136
t 2(i) And gamma i Are each H 2 ，
Figure GDA0003521777380000137
d 2 And the ith element of γ;
Figure GDA0003521777380000138
Figure GDA0003521777380000139
and
Figure GDA00035217773800001310
are respectively F 2 The ith sample in the set is shifted into S 2 Set of R 2 Set sum E 2 Step size of the set;
Figure GDA00035217773800001311
is S 2 The ith sample in the set is moved into R 2 Set or E 2 Step size of the set;
Figure GDA00035217773800001312
is R 2 Set shift into S 2 Step size of the set;
Figure GDA00035217773800001313
is E 2 Set shift into S 2 Step size of the set;
Figure GDA00035217773800001314
and
Figure GDA00035217773800001315
are respectively composed of
Figure GDA00035217773800001316
Figure GDA00035217773800001317
And
Figure GDA00035217773800001318
a column vector of components;
s29: the solution u of the updated model is calculated from equations (7) and (10) 1 And u 2 And save M -1 Parameter u of lower bound insensitive function 1 ，α，V 1 Set R 1 、S 1 、E 1 And the parameter u of the upper bound insensitive function 2 ，γ，V 2 Set R 2 、S 2 、E 2 。
The invention saves the effective information in the training process, gradually and iteratively adjusts the Lagrange multiplier of the training sample in each updating process to ensure that the Lagrange multiplier meets the KKT condition, improves the updating speed of the model in the correction process, is more suitable for the deployment of terminal equipment with limited memory, and provides an effective method for the field correction of the indoor propagation model by using the portable terminal equipment.
The following describes in detail a bluetooth signal indoor propagation model correction method based on an online epsilon type twin support vector regression provided by the present invention with an embodiment.
The effectiveness of the invention is explained by adopting the method for correcting the Bluetooth signal indoor propagation model based on the online epsilon type twin support vector regression machine and combining a specific example of correcting the Bluetooth signal propagation model between a transmitting device and a receiving device. Fixing a Bluetooth signal transmitting device, then selecting 50 different sampling points from near to far, acquiring 10 RSSI values at each sampling point by using a Bluetooth signal receiving device to carry out mean filtering to obtain the more stable RSSI value of the sampling point, recording the distance between the Bluetooth signal transmitting device and the receiving device, thereby obtaining 50 data samples, and selecting 40 samples as training samples and 10 samples as testing samples. The specific implementation mode is as follows:
initializing various parameters, setting C 1 ＝C 2 ＝2 10 ，ε 1 ＝ε 2 ＝0.01，C 3 ＝2 -5 And correcting the indoor propagation model of the Bluetooth signal in an online updating mode, then storing the corrected model parameters, and directly substituting the corrected model parameters into test data to obtain the predicted values of the RSSI (received signal strength indicator) of the Bluetooth signals at different distances.
As can be seen from the attached figures 2 and 3, the RSSI value of the Bluetooth signal strength predicted by the Bluetooth signal indoor propagation model based on the online epsilon type twin support vector regression machine has better prediction accuracy.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
It should be understood that the above examples are only for clarity of illustration and are not intended to limit the embodiments. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. And obvious variations or modifications of the invention may be made without departing from the spirit or scope of the invention.

Claims (1)

1. A Bluetooth signal indoor propagation model correction method based on an online epsilon type twin support vector regression machine is characterized by comprising the following steps:
s10: a signal receiver is used for collecting the Bluetooth signal strength RSSI of a signal transmitter for multiple times at the kth sampling point, and mean value filtering is carried out to obtain a logarithmic distance loss model r of the Bluetooth signal strength RSSI k ＝RSSI(d k )＝RSSI(d 0 )+10wlg(d k /d 0 ) Wherein d is k Denotes the distance of the sample point from the signal transmitter, the subscript k denotes the number, RSSI (d) k ) Representing a distance d to the signal transmitter k Signal receiver of (2) collected Bluetooth signal strength, d 0 Representing the close distance to the signal transmitter, w represents the weight of the model, let d 0 ＝1m，y k ＝r k ，x k ＝10lg(d k ) B = RSSI (1), yielding a linear model y k ＝wx k + b, training sample is (x) k ,y k )；
S20: comparing the root mean square error of the training value and the predicted value of the y value in the training sample with a set threshold, if the root mean square error of the training value and the predicted value of the y value is greater than or equal to the threshold, utilizing the training sample to correct and update the Bluetooth signal indoor propagation model based on the online epsilon type twin support vector regression machine, and going to the step S10, if the root mean square error of the training value and the predicted value of the y value is less than the threshold, stopping correcting and updating the Bluetooth signal indoor propagation model based on the online epsilon type twin support vector regression machine;
let the set of training samples be T, which is divided into S 1 、R 1 、E 1 Three sets of where S 1 Set of vectors for boundary support of lower-bound insensitive function, R 1 To reserve a set of support vectors, E 1 Supporting a set of vectors for errors; t is further divided into S 2 、R 2 、E 2 Three sets of where S 2 Supporting a set of vectors for the boundaries of upper-bound insensitive functions, R 2 To reserve a set of support vectors, E 2 Supporting a set of vectors for errors;
the method for correcting and updating the Bluetooth signal indoor propagation model based on the online epsilon type twin support vector regression by using the training samples comprises the following steps:
s21: reading training samples (x) k ,y k )；
S22: when k =1, c is set 1 、c 2 、c 3 、ε 1 And ε 2 A value of (b), wherein c 1 、c 2 Is a penalty constant, c 3 Is a regularization constant, ε 1 、ε 2 Is an insensitive constant; initialize the parameters of the linear model, let b 1 ＝b 2 ＝w 1 ＝w 2 =0, wherein b 1 、b 2 To be biased, w 1 、w 2 Is a weight; then, the initial M is calculated from the formula (1) -1 ；
When k ≠ 1, M is updated by equation (2) -1 When is coming into contact with
Figure FDA0003537221580000011
When the V is updated by the formula (3) 1 When is coming into contact with
Figure FDA0003537221580000012
When the V is updated by the formula (4) 2 ；
Figure FDA0003537221580000013
Wherein, g k ＝[1,x k ]I is a unit matrix of the corresponding dimension;
M -1 ＝M -1 -ZZ T /J (2)
V 1 ＝V 1 +Z′ 1 Z′ 1 T /J′ 1 (3)
V 2 ＝V 2 +Z′ 2 Z′ 2 T /J′ 2 (4)
wherein the content of the first and second substances,
Figure FDA0003537221580000021
J＝1+g k Z，
Figure FDA0003537221580000022
Figure FDA0003537221580000023
is a row vector g i ,i∈S 1 Matrix of composition, Z' 1 ＝V 1 Z 1 ，
Figure FDA0003537221580000024
Figure FDA0003537221580000025
Is a row vector g i ,i∈S 2 Matrix of composition, Z' 2 ＝V 2 Z 2 ，
Figure FDA0003537221580000026
S23: byFormula (5) and formula (6) calculate α k And gamma k ：
α k ＝y k -(L T L) -1 L T l 1 (5)
γ k ＝(L T L) -1 L T l 2 -y k (6)
Wherein alpha is k And gamma k Respectively represent training samples (x) k ,y k ) Lagrange multipliers in the lower bound insensitive function and the upper bound insensitive function,
Figure FDA0003537221580000027
e is a column vector with all 1's of the corresponding dimension elements, X = [ X = 1 ,x 2 ,...,x k-1 ] T ，l 1 ＝G(ZZ T /J)G T (Y-α)，l 2 ＝G(ZZ T /J)G T (Y+γ)，Y＝[y 1 ,y 2 ,...,y k-1 ] T Alpha is a group of i I ∈ T, a column vector consisting of γ i I belongs to a column vector consisting of T;
s24: let alpha = [ alpha ] T ,α k ] T ，γ＝[γ T ,γ k ] T ，
Figure FDA0003537221580000028
Y＝[Y T ,y k ] T T = T { k }; when in use
Figure FDA0003537221580000029
When the time is over, the time is updated by the formula (7) -formula (9)
Figure FDA00035372215800000210
Figure FDA00035372215800000217
Is formed by alpha i ,i∈S 1 A column vector of components; when the temperature is higher than the set temperature
Figure FDA00035372215800000211
When the time is over, the time is updated by the formula (10) -formula (12)
Figure FDA00035372215800000212
Figure FDA00035372215800000218
Is formed by gamma i ,i∈S 2 A column vector of components;
u 1 ＝M -1 G T (Y-α) (7)
H 1 ＝Y-(Gu 1 -ε 1 e) (8)
Figure FDA00035372215800000213
u 2 ＝M -1 G T (Y+γ) (10)
H 2 ＝(Gu 2 +ε 2 e)-Y (11)
Figure FDA00035372215800000214
wherein H 1 A column vector H composed of boundary distances from the training samples in the T set to the lower-bound insensitive function 2 A column vector consisting of the boundary distances from the training samples in the T set to the upper-bound insensitive function,
Figure FDA00035372215800000215
is S 1 A column vector composed of the boundary distances corresponding to the training samples in the set,
Figure FDA00035372215800000216
is S 2 A column vector consisting of boundary distances corresponding to training samples in the set;
s25: is represented by formula (7) -formula(8) Recalculating H 1 Then screening an abnormal sample set F 1 ，t 1(i) Is represented by F 1 The target value of the Lagrange multiplier adjustment of the ith sample in the set;
for S 1 Samples in the set, if α i Not more than 0, transferred into F 1 Set and t 1(i) ＝c 1 (ii) a If α is i ≥c 1 Is moved into F 1 Set and t 1(i) =0, and the inverse matrix V needs to be updated by equation (13) 1 ；
For R 1 Samples in the set, if H 1(i) Not more than 0, transferred into F 1 Set and t 1(i) ＝c 1 ；
For E 1 Samples in the set, if H 1(i) Not less than 0, shift-in F 1 Set and t 1(i) ＝0；
For training sample (x) k ,y k ) If H is present 1(k) ≥0,α k =0, then move into R 1 Gathering; if H is 1(k) ＝0,0＜α k ＜c 1 Then move into S 1 The inverse matrix V is collected and updated by equation (14) 1 (ii) a If H is present 1(k) ≤0,α k ＝c 1 Then move into E 1 Gathering; otherwise, when alpha is k Less than or equal to 0, transferring into F 1 Set and t 1(k) ＝c 1 (ii) a When alpha is k ≥c 1 Is moved into F 1 Set and t 1(k) =0; when 0 < alpha k ＜c 1 If H is present 1(k) < 0, move into F 1 Set and t 1(k) ＝c 1 If H is present 1(k) > 0, transfer into F 1 Set and t 1(k) ＝0；
Figure FDA0003537221580000031
Wherein the subscript t denotes a shift out of S 1 The samples of the set, the subscript \ tt representing the elements of the t rows and t columns of the deletion matrix, the subscript x representing the full index of the row or column;
Figure FDA0003537221580000032
wherein the content of the first and second substances,
Figure FDA0003537221580000033
Q＝GMG T ；
s26: recalculating H from equation (10) -equation (11) 2 Then screening the abnormal sample set F 2 ，t 2(i) Is represented by F 2 The target value of the lagrange multiplier adjustment of the ith sample;
for S 2 Samples in the set, if γ i Not more than 0, transferred into F 2 Set and t 2(i) ＝c 2 (ii) a If gamma is equal to i ≥c 2 Is moved into F 2 Set and t 2(i) =0, and the inverse matrix V needs to be updated by equation (15) 2 ；
For R 2 Samples in the set, if H 2(i) Not more than 0, transferred into F 2 Set and t 2(i) ＝c 2 ；
For E 2 Samples in the set, if H 2(i) Not less than 0, shift-in F 2 Set and t 2(i) ＝0；
For sample (x) k ,y k ) If H is 2(k) ≥0,γ k If not less than 0, then move into R 2 Gathering; if H is present 2(k) ＝0,0＜γ k ＜c 2 Then move into S 2 The inverse matrix V is collected and updated by equation (16) 2 (ii) a If H is present 2(k) ≤0,γ k ＝c 2 Then move into E 2 Gathering; otherwise, when γ k Not more than 0, transferred into F 2 Set and t 2(k) ＝c 2 (ii) a When gamma is equal to k ≥c 2 Is moved into F 2 Set and t 2(k) =0; when 0 < gamma k ＜c 2 If H is present 2(k) < 0, move into F 2 Set and t 2(k) ＝c 2 If H is present 2(k) > 0, into F 2 Set and t 2(k) ＝0；
Figure FDA0003537221580000034
Wherein the subscript t denotes the removal of S 2 A sample of the collection;
Figure FDA0003537221580000035
wherein the content of the first and second substances,
Figure FDA0003537221580000036
s27: from the respective equations (17) and (18)
Figure FDA0003537221580000037
Then, the maximum step length eta is calculated from the formula (19) to the formula (26) max ；
If it is not
Figure FDA0003537221580000038
Then the corresponding sample is represented by F 1 Set shift into S 1 Is aggregated and V is updated by equation (14) 1 ；
If it is not
Figure FDA0003537221580000039
Then the corresponding sample is represented by F 1 Set shift into R 1 Gathering;
if it is not
Figure FDA00035372215800000310
Then the corresponding sample is represented by F 1 Set move-in E 1 Gathering;
if it is used
Figure FDA00035372215800000311
Then the corresponding sample is represented by S 1 Set shift into R 1 Set or E 1 Set, determined by Lagrange multiplier of corresponding sample, and updated by equation (13)V 1 ；
If it is not
Figure FDA0003537221580000041
Then the corresponding sample is represented by R 1 Set shift into S 1 Is aggregated and V is updated by equation (14) 1 ；
If it is not
Figure FDA0003537221580000042
Then the corresponding sample is represented by E 1 Set shift into S 1 Is aggregated and V is updated by equation (14) 1 ；
Then, order
Figure FDA0003537221580000043
Repeating (7) to F 1 Stopping iteration when the set is empty;
Figure FDA0003537221580000044
Figure FDA0003537221580000045
wherein, t 1 Is composed of t 1(i) ,i∈F 1 The column vector of the component is composed of,
Figure FDA0003537221580000046
Figure FDA0003537221580000047
Figure FDA0003537221580000048
Figure FDA0003537221580000049
Figure FDA00035372215800000410
Figure FDA00035372215800000411
Figure FDA00035372215800000412
Figure FDA00035372215800000413
Figure FDA00035372215800000414
wherein h is 1 (i)，
Figure FDA00035372215800000415
t 1(i) And alpha i Are each H 1 ，
Figure FDA00035372215800000416
t 1 And the ith element of α;
Figure FDA00035372215800000417
Figure FDA00035372215800000418
and
Figure FDA00035372215800000419
are respectively F 1 The ith sample in the set is shifted into S 1 Set of R 1 Set sum E 1 A step size of the set;
Figure FDA00035372215800000420
is S 1 Moving the ith sample in the set into R 1 Set or E 1 A step size of the set;
Figure FDA00035372215800000421
is R 1 Set migration S 1 Step size of the set;
Figure FDA00035372215800000422
is E 1 Set shift into S 1 Step size of the set;
Figure FDA00035372215800000423
and
Figure FDA00035372215800000424
are respectively composed of
Figure FDA00035372215800000425
And
Figure FDA0003537221580000051
a column vector of components;
s28: from the respective equations (27) and (28)
Figure FDA0003537221580000052
Then, equation (29) -equation (36) calculates the maximum step η' max ；
If it is not
Figure FDA0003537221580000053
Then the corresponding sample is represented by F 2 Set shift into S 2 Is collected and V is updated by equation (16) 2 ；
If it is used
Figure FDA0003537221580000054
Then the corresponding sample is represented by F 2 Set shift into R 2 Gathering;
if it is used
Figure FDA0003537221580000055
Then the corresponding sample is represented by F 2 Set migration E 2 Gathering;
if it is used
Figure FDA0003537221580000056
Then the corresponding sample is represented by S 2 Set shift into R 2 Set or E 2 Set, determined by the Lagrange multiplier of the corresponding sample, and update V by equation (15) 2 ；
If it is not
Figure FDA0003537221580000057
Then the corresponding sample is represented by R 2 Set shift into S 2 Is aggregated and V is updated by equation (16) 2 ；
If it is not
Figure FDA0003537221580000058
Then the corresponding sample is represented by E 2 Set shift into S 2 Is collected and V is updated by equation (16) 2 ；
Then, let
Figure FDA0003537221580000059
Repeating (8) until F 2 Stopping iteration when the set is empty;
Figure FDA00035372215800000510
Figure FDA00035372215800000511
wherein, t 2 Is composed of t 2(i) ,i∈F 2 The column vector of the component is composed of,
Figure FDA00035372215800000512
Figure FDA00035372215800000513
Figure FDA00035372215800000514
Figure FDA00035372215800000515
Figure FDA00035372215800000516
Figure FDA00035372215800000517
Figure FDA00035372215800000518
Figure FDA0003537221580000061
Figure FDA0003537221580000062
wherein h is 2 (i)，
Figure FDA0003537221580000063
t 2(i) And gamma i Are each H 2 ，
Figure FDA0003537221580000064
d 2 And the ith element of γ;
Figure FDA0003537221580000065
Figure FDA0003537221580000066
and
Figure FDA0003537221580000067
are respectively F 2 The ith sample in the set is shifted into S 2 Set of R 2 Set sum E 2 Step size of the set;
Figure FDA0003537221580000068
is S 2 The ith sample in the set is moved into R 2 Set or E 2 Step size of the set;
Figure FDA0003537221580000069
is R 2 Set shift into S 2 Step size of the set;
Figure FDA00035372215800000610
is E 2 Set shift into S 2 A step size of the set;
Figure FDA00035372215800000611
and
Figure FDA00035372215800000612
are respectively composed of
Figure FDA00035372215800000613
Figure FDA00035372215800000614
And
Figure FDA00035372215800000615
a column vector of components;
s29: calculating the solution u of the updated model from equations (7) and (10) 1 And u 2 And store M -1 Parameter u of lower bound insensitive function 1 ，α，V 1 Set R 1 、S 1 、E 1 And the parameter u of the upper bound insensitive function 2 ，γ，V 2 Set R 2 、S 2 、E 2 。
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