CN112084741B - Digital all-pass filter design method based on hybrid particle swarm algorithm - Google Patents
Digital all-pass filter design method based on hybrid particle swarm algorithm Download PDFInfo
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Abstract
The invention discloses a method for designing a digital all-pass filter based on a hybrid particle swarm algorithm, which comprises the steps of firstly constructing a phase frequency response of a digital all-pass filter based on second order cascade connection according to design requirements, and then constructing a cost function based on a target phase frequency response and an error value formed by the phase frequency response of the digital all-pass filter and the target phase frequency response; and finally, searching a global optimal solution in a value range by using a particle swarm algorithm of global search to obtain a rough solution, triggering from the rough solution, and performing accurate search by using a Levenbergmarquardt algorithm to optimize the positions of poles of all second-order all-pass filters, so that the mean square error minimization of the phase-frequency response of the designed all-pass filters and the target phase-frequency response is realized, and the design of filter coefficients is realized.
Description
Technical Field
The invention belongs to the technical field of all-pass filters, and particularly relates to a digital all-pass filter design method based on a hybrid particle swarm algorithm.
Background
In practice, when a signal is transmitted in a system, a certain phase distortion, especially a nonlinear distortion of the phase, may be generated, and different phase shifts may be added to signals of different frequencies, which may have a large influence on the output of the system, and in a severe case, the signal may be distorted. Compensation of the phase is an essential part for systems where strict linearity of the phase is required. The all-pass filter can change the phase characteristics of signals and effectively solve the problem of phase nonlinear distortion. The all-pass filter has the same gain for all frequency components input in the system, does not attenuate signals of any frequency, but changes the phase characteristics of the input signal. The all-pass filter plays an important role in application occasions such as phase compensation, group delay equalization and the like to meet the requirement of a system on linear phase-frequency response.
The design problem of the digital all-pass filter can be reduced to the problem of nonlinear optimization, and the traditional design algorithms include swarm intelligence optimization algorithms, such as Particle Swarm Optimization (PSO), and gradient-based nonlinear optimization algorithms, such as levenberg marquardt algorithm (LM). However, in the optimization process of designing the digital all-pass filter, the optimization speed of the PSO algorithm is obviously reduced after the global optimal solution is approached, and even the PSO algorithm is premature. The LM algorithm belongs to an unconstrained optimization problem, although the LM algorithm has a high optimization speed, the designed digital all-pass filter is easy to be unstable due to the fact that the optimization range is not limited, and besides, the LM algorithm is very sensitive to the initial value of optimization iteration.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a digital all-pass filter design method based on a hybrid particle swarm algorithm, which converts the design problem of filter coefficients into the problem of nonlinear function optimization and then searches and optimizes the filter coefficients from rough to precise by using different optimization algorithms so as to realize the design of the filter coefficients.
In order to achieve the above object, the present invention provides a method for designing a digital all-pass filter based on a hybrid particle swarm algorithm, which is characterized by comprising the following steps:
(1) Constructing a phase frequency response of a digital all-pass filter based on second-order cascade connection;
(1.1) according to actual requirements, setting the order N of the digital all-pass filter, wherein N is an even number, the number of second-order sections of the corresponding digital all-pass filter is N/2, and then the Z domain expression H (Z) of the cascaded digital all-pass filter is as follows:
wherein H n (Z) Z-domain expression representing nth order digital all-pass filter, a n1 、a n2 Is the coefficient of the nth order digital all-pass filter;
(1.2) setting the pole of the nth second order section as
M n 、θ n The modulus and phase angle of the nth second order pole are shown as the poles of the N-order digital all-pass filter
Define variable U = [ M = 1 ,θ 1 ,M 2 ,θ 2 ,…,M n ,θ n ,…,M N/2 ,θ N/2 ]The phase-frequency response of the digital all-pass filter
Expressed as:
wherein ω = [ ω = ] 1 ,ω 2 ,…,ω l ,…,ω L ]，ω l The angular frequency of the digital all-pass filter is L, and the number of sampled frequency points is L;
(2) Constructing a cost function of the digital all-pass filter;
let the target phase-frequency response of the digital all-pass filter be phi goal (ω) the phase frequency response of the digital all-pass filter
Has a phase frequency response phi with respect to the target goal (omega) error value constructed cost function phi error (U) is represented as:
(3) Searching a cost function phi by utilizing a particle swarm algorithm error (U) a global optimal solution;
(3.1) setting the population number S of the particle swarm algorithm and the maximum iteration number K of the particle swarm algorithm;
(3.2) initializing the particle group
To ensure the stability of each second order section of the digital all-pass filter, the process of initializing each particle in the population needs to be satisfied
Rho is a constant slightly less than 1;
(3.3) updating and iterating the particle swarm;
(3.3.1) calculating the updating speed of each particle;
wherein, V s k Is the velocity of the s-th particle after the k-th update, C 1 And C 2 Respectively corresponding to the acceleration factor, r 1 And r 2 Is [0,1 ]]Random number of inner, zb s And gb is the historical optimal solution of the S-th particle and the global optimal solution of the particle swarm composed of the S particles respectively;
(3.3.2) updating the particle position;
wherein χ (·) is a defining function;
(3.3.3) calculating the iterated particles
Of (2) a cost function
And updating the historical optimal solution zb of the s-th particle according to the following formula s And a global optimal solution gb of a particle swarm of S particles;
(3.4) repeating the step (3.3), and iterating for K times in total to obtain a final global optimal solution gb;
(4) Carrying out local optimal solution by utilizing a Levenberg Marquardt algorithm;
(4.1) setting the total iteration number K of the Levenberg Marquardt algorithm max ，k＝1,2,…,K max Initialization k =1;
(4.2) calculating an iteration starting point X of the Levenberg Marquardt algorithm 0 ＝[x 1 ,θ 1 ,x 2 ,θ 2 ,…,x n ,θ n ,…,x N/2 ,θ N/2 ]Wherein, in the step (A),
(4.3) calculating X after the k iteration k Phase frequency response phi of corresponding digital all-pass filter design (ω,X)；
(4.4) calculating X after the k iteration k Corresponding residual vector R k ；
R k ＝φ design (ω,X k )-φ goal (ω) (9)
(4.5) calculating X after the k iteration k A corresponding cost function value;
φ error (X k )＝R k ·R k T (10)
(4.6) calculating X after the k iteration k Corresponding Accord matrix J k Blackplug matrix H k ＝J k T J k And diagonal matrix D k ＝diag{H k }；
(4.7) calculating an update vector after the kth iteration;
Δ k ＝(H k +λ·D k ) -1 ·J k ·R k (11)
(4.8) calculating a new vector X after the k iteration new ＝X k +Δ k And a corresponding cost function value phi error (X new ) Then compare phi error (X new ) Phi and phi error (X k ) If is phi error (X new )＜φ error (X k ) Then let X k+1 ＝X new And λ = λ/v; if phi is error (X new )≥φ error (X k ) Then let X k+1 ＝X k And λ = λ × v; wherein, lambda and v are integers, lambda > v;
(4.9) circularly executing the steps (4.3) to (4.8) to sum up to K max Then, the iteration end point X is finally obtained final ；
(5) Inverse mapping;
x is to be final The pole vector is then substituted into the following equation to obtain the final pole vector U final ；
(6) According to the pole vector U final Calculating the coefficient of a digital all-pass filter;
and finishing the design of the all-pass filter.
The invention aims to realize the following steps:
the invention relates to a digital all-pass filter design method based on a hybrid particle swarm algorithm, which comprises the steps of firstly constructing a phase-frequency response of a digital all-pass filter based on second order cascade connection according to design requirements, and then constructing a cost function based on a target phase-frequency response and an error value formed by the phase-frequency response of the digital all-pass filter and the target phase-frequency response; and finally, searching a global optimal solution in a value range by using a particle swarm algorithm of global search to obtain a rough solution, triggering from the rough solution, and performing accurate search by using a Levenbergmarquardt algorithm to optimize the positions of poles of all second-order all-pass filters, so that the mean square error minimization of the phase-frequency response of the designed all-pass filters and the target phase-frequency response is realized, and the design of filter coefficients is realized.
Meanwhile, the method for designing the digital all-pass filter based on the hybrid particle swarm optimization further has the following beneficial effects:
(1) Although the Levenberg Marquardt algorithm can realize the optimal solution search, the Levenberg Marquardt algorithm has high dependency on an initial value and weak searching capability on a global optimal solution. The particle swarm algorithm has global search capability, finds a global optimal region, but has the problem of local extremum, and can only find a rough value of a global optimal solution. Therefore, the Levenberg Marquardt algorithm and the particle swarm algorithm are combined, so that the global optimal rough solution can be searched, and the global optimal precise solution can also be searched;
(2) The stability of the all-pass filter is guaranteed during design, parameters are constrained during searching of an optimal solution, the unconstrained problem of the Levenbergmarquardt algorithm needs to be converted into a constrained problem, and the result of the Levenbergmarquardt algorithm is converted into a filter stable interval through a mapping function so as to guarantee the stability of the designed filter.
Drawings
FIG. 1 is a flow chart of a method for designing a digital all-pass filter based on a hybrid particle swarm optimization according to the present invention;
FIG. 2 is a block diagram of an N-order all-pass filter system based on a two-stage cascade structure;
FIG. 3 is a map of when an all-pass filter is stable, where FIG. 3 (a) is the stable pole region; FIG. 3 (b) is a mapping function curve; FIG. 3 (c) is the stable pole mode length and phase angle; FIG. 3 (d) is the mapped document interval.
Detailed Description
The following description of the embodiments of the present invention is provided in order to better understand the present invention for those skilled in the art with reference to the accompanying drawings. It is to be expressly noted that in the following description, a detailed description of known functions and designs will be omitted when it may obscure the subject matter of the present invention.
Examples
FIG. 1 is a flow chart of a method for designing a digital all-pass filter based on a hybrid particle swarm optimization.
In this embodiment, as shown in fig. 1, the method for designing a digital all-pass filter based on a hybrid particle swarm optimization of the present invention includes the following steps:
s1, constructing a phase frequency response of a digital all-pass filter based on second-order cascade connection;
s1.1, the expression of the N-order (N is an even number) all-pass digital filter in the time domain is expressed by a constant coefficient linear difference equation as follows:
and (2) a system function expression is used in a z domain, namely a system function H (z) obtained by performing z change on the time domain expression in (1) is as follows:
factorizing the numerator denominator of the formula (2) respectively, and forming a second-order factorization form of the numerator denominator, as shown in fig. 2, so as to implement the cascade structure of the digital filter, and then the Z-domain expression H (Z) of the digital all-pass filter having N/2 second-order cascades is:
wherein H n (Z) Z-domain expression representing the nth order digital all-pass filter, a n1 、a n2 Is the coefficient of the nth order digital all-pass filter;
s1.2, because the pole-zero position of the all-pass filter is in one-to-one correspondence with the frequency response of the all-pass filter, the formula (3) can be rewritten into the expression form of the pole-zero
Wherein xi is k And xi k * The pole of the kth second order node, is the conjugate sign,
is the real part operation.
The cascade structure adopts a form of second-order combination, can realize various cascade orders, and does not influence the realization of the all-pass filter; by changing the coefficient of each second order section, the zero pole is flexibly and visually adjusted, so that the frequency response is convenient to adjust; meanwhile, the expansion of the filter order can be realized only by increasing the number of the cascade of the second order sections.
Let the pole of the nth second stage be
M n 、θ n The modulus and phase angle of the nth second order pole are shown as the poles of the N-order digital all-pass filter
Define variable U = [ M = 1 ,θ 1 ,M 2 ,θ 2 ,…,M n ,θ n ,…,M N/2 ,θ N/2 ]The phase-frequency response of the digital all-pass filter
Expressed as:
wherein ω = [ ω = [ [ ω ]) 1 ,ω 2 ,…,ω l ,…,ω L ]，ω l The angular frequency of the digital all-pass filter is shown, and L is the number of sampled frequency points;
s2, constructing a cost function of the digital all-pass filter;
let the target phase-frequency response of the digital all-pass filter be phi goal (ω) the phase frequency response of the digital all-pass filter
Has a phase frequency response phi with respect to the target goal Cost function phi constructed by error value of (omega) error (U) is represented as:
in order to make the designed all-pass filter have the best approximation effect, the cost function phi is error The value of (U) is small enough to make the frequency response of the designed filter as consistent as possible with the frequency response of the target filter. Since equation (5) is a non-linear expression for vector U, we can minimize φ error The problem of (U) translates into a mathematical problem of non-linear optimization.
In order to solve the problem of nonlinear optimization in the formula (6), the invention provides a filter design method based on a hybrid particle swarm algorithm, which fully utilizes the global search capability of the particle swarm algorithm and the local search capability of the Levenbergmarquardt algorithm to realize the optimization of the formula (6), and comprises the following specific processes:
s3, utilizing particlesGroup algorithm for finding cost function phi error (U) a global optimal solution;
s3.1, setting the population number S of the particle swarm algorithm and the maximum iteration number K of the particle swarm algorithm;
s3.2, initializing particle swarm
To ensure the stability of each second order section of the digital all-pass filter, the process of initializing each particle in the population needs to be satisfied
Rho is a constant slightly less than 1, and the calculation of the global optimal solution of the all-pass filter is realized under the constraint condition;
s3.3, particle swarm updating and iteration are carried out;
s3.3.1, calculating the updating speed of each particle;
wherein, V s k Is the speed of the s-th particle after the kth update, C 1 And C 2 Respectively corresponding to the acceleration factor, r 1 And r 2 Is [0,1 ]]Random number of inner, zb s And gb is the historical optimal solution of the S-th particle and the global optimal solution of the particle swarm composed of the S particles respectively;
s3.3.2, updating the particle position;
wherein, χ (·) is a limiting function, and is obtained by limiting the modulus U.M of the second order section pole of the filter n The stability of the designed filter is ensured, and the expression of χ (-) is as follows:
s3.3.3, calculating the iterated particles
Cost function of
And updating the historical optimal solution zb of the s-th particle according to the following formula s And a global optimal solution gb of a particle swarm of S particles;
s3.4, repeating the step S3.3, and iterating for K times in total to obtain a final global optimal solution gb;
s4, performing local optimal solution by utilizing a Levenberg Marquardt algorithm;
and after the optimization iteration of the particle swarm optimization is completed, the global optimal solution gb obtained by the particle swarm optimization is brought into the Levenbergmarquardt optimization for further accurate search. However, since the levenberg marquardt algorithm is an unconstrained algorithm, finding the optimal solution directly using the levenberg marquardt algorithm will likely result in the mode length M of the filter poles n And the stability interval of the all-pass filter is exceeded, which causes the instability of the filter. Therefore, in order to ensure the stability of each second order section of the all-pass filter, a constrained optimization problem needs to be converted into an unconstrained optimization problem.
Defining a mapping function
As shown in fig. 3 (b), for an arbitrary x n (value range- ∞ x n + ∞) of M n The value is between 0 and 1, and because the function is a monotonically increasing functionThere is a one-to-one mapping relationship between x to F (x), so F (x) n ) Presence of an inverse function F -1 (M n ) The expression is F -1 (M n )＝ln(M n /(1-M n ))。F -1 (M n ) Mapping values between (0, 1) to the entire real space, while F (x) can be achieved n ) Mapping from the entire real space to the range of (0, 1) can be achieved.
For the cascade-type all-pass filter, in order to ensure the stability of each second order section, the module value of the pole should be smaller than ρ, as shown in fig. 3 (a). Converting the second order stability interval into the pole modulus M n And pole phase θ n Is a coordinate axis, as shown in FIG. 3 (c), when M is present n Has a value range of (0, rho)]To pole modulus M n By an inverse function F -1 (M n ) Is mapped to variable x n After, x n The value range of (a) is expanded to the whole real number space, as shown in fig. 3 (d), the problem of converting the unconstrained problem into the constrained problem is realized, meanwhile, the value of the whole real number space can be mapped between 0 and 1 through a mapping function, and a one-to-one correspondence relationship exists, so that the stability of the second order section of each all-pass filter is ensured.
The Levenbergmarquardt algorithm is a nonlinear least square algorithm, and the algorithm can modify parameters during execution to combine the advantages of the Gauss-Newton algorithm and the gradient descent method and improve the defects of the Gauss-Newton algorithm and the gradient descent method. According to the size of lambda, the step length is switched between Newton method step length and gradient descent method step length, and the specific optimization process is as follows:
s4.1, setting the total iteration number K of the Levenberg Marquardt algorithm max ，k＝1,2,…,K max Initialization k =1;
s4.2, calculating iteration starting point X of Levenberg Marquardt algorithm 0 ＝[x 1 ,θ 1 ,x 2 ,θ 2 ,…,x n ,θ n ,…,x N/2 ,θ N/2 ]Wherein, in the step (A),
at this time x n The value range of (1) can ensure the stability of the designed all-pass filter within the range of (-infinity, + ∞); thus, the pole value space mapping U → X of the all-pass filter is also completed;
s4.3, calculating X after k iteration k Phase frequency response of corresponding digital all-pass filter
S4.4, calculating X after k iteration k Corresponding residual vector R k ；
R k ＝φ design (ω,X k )-φ goal (ω) (13)
S4.5, calculating X after the kth iteration k A corresponding cost function value;
φ error (X k )＝R k ·R k T (14)
s4.6, calculating X after k iteration k Corresponding Accord matrix J k Blackplug matrix H k ＝J k T J k And diagonal matrix D k ＝diag{H k }；
S4.7, calculating an update vector after the kth iteration;
Δ k ＝(H k +λ·D k ) -1 ·J k ·R k (15)
s4.8, calculating a new vector X after the kth iteration new ＝X k +Δ k And a corresponding cost function value phi error (X new ) Then compare phi error (X new ) Phi (phi) and phi (phi) error (X k ) If phi is greater than error (X new )＜φ error (X k ) Then let X k+1 ＝X new And λ = λ/v; if phi is error (X new )≥φ error (X k ) Then let X k+1 ＝X k And λ = λ × v; wherein λ =10000,v =10;
s4.9, circularly executing the steps S4.3-S4.8 to sum up to K max Then, the iteration end point X is finally obtained final ；
S5, space inverse mapping;
mixing X final The pole vector is then substituted into the following equation to obtain the final pole vector U final ；
S6, according to the pole vector U final Calculating the coefficient of a digital all-pass filter;
and completing the design of the all-pass filter.
Although illustrative embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, and various changes may be made apparent to those skilled in the art as long as they are within the spirit and scope of the present invention as defined and defined by the appended claims, and all matters of the invention which utilize the inventive concepts are protected.
Claims (2)
1. A digital all-pass filter design method based on a hybrid particle swarm algorithm is characterized by comprising the following steps:
(1) Constructing a phase frequency response of a digital all-pass filter based on second-order cascade connection;
(1.1) according to actual requirements, setting the order N of the digital all-pass filter, wherein N is an even number, the number of second-order sections of the corresponding digital all-pass filter is N/2, and then the Z domain expression H (Z) of the cascaded digital all-pass filter is as follows:
wherein H n (Z) Z-domain expression representing the nth order digital all-pass filter, a n1 、a n2 Is the coefficient of the nth order digital all-pass filter;
(1.2) setting the pole of the nth second-order section as
M n 、θ n The magnitude and phase angle of the nth second order pole are used to represent the pole of the N-order digital all-pass filter as
Define variable U = [ M = 1 ,θ 1 ,M 2 ,θ 2 ,…,M n ,θ n ,…,M N/2 ,θ N/2 ]The phase frequency response of the digital all-pass filter
Expressed as:
wherein ω = [ ω = [ [ ω ]) 1 ,ω 2 ,…,ω l ,…,ω L ]L is the number of the sampled frequency points;
(2) Constructing a cost function of the digital all-pass filter;
let the target phase-frequency response of the digital all-pass filter be phi goal (ω) the phase frequency response of the digital all-pass filter
Has a phase frequency response phi with respect to the target goal (omega) error value constructed cost function phi error (U) is represented as:
(3) Searching a cost function phi by utilizing a particle swarm algorithm error (U) a global optimal solution;
(3.1) setting the population number S of the particle swarm algorithm and the maximum iteration number K of the particle swarm algorithm;
(3.2) initializing the particle group
To ensure the stability of each second order section of the digital all-pass filter, the initialization process of each particle in the population needs to be satisfied
Rho is a constant slightly less than 1;
(3.3) particle swarm updating and iteration;
(3.3.1) calculating the updating speed of each particle;
wherein, the first and the second end of the pipe are connected with each other,
is the velocity of the s-th particle after the k-th update, C 1 And C 2 Respectively corresponding to the acceleration factor, r 1 And r 2 Is [0,1 ]]Random number of inner, zb s And gb is the historical optimal solution of the S-th particle and the global optimal solution of the particle swarm composed of the S particles respectively;
(3.3.2) updating the particle position;
wherein χ (·) is a defining function;
(3.3.3) calculating iterated particles
Of (2) a cost function
And updating the historical optimal solution zb of the s-th particle according to the following formula s And a global optimal solution gb of a particle swarm of S particles;
(3.4) repeating the step (3.3), and iterating for K times in total to obtain a final global optimal solution gb;
(4) Carrying out local optimal solution by utilizing a Levenberg Marquardt algorithm;
(4.1) setting the total iteration number K of the Levenberg Marquardt algorithm max ，k＝1,2,…,K max Initializing k =1;
(4.2) calculating iteration starting point X of Levenberg Marquardt algorithm 0 ＝[x 1 ,θ 1 ,x 2 ,θ 2 ,…,x n ,θ n ,…,x N/2 ,θ N/2 ]Wherein, in the step (A),
(4.3) calculating X after the k iteration k Phase frequency response phi of corresponding digital all-pass filter design (ω,X)
(4.4) calculating X after the k iteration k Corresponding residual vector R k ；
R k ＝φ design (ω,X k )-φ goal (ω) (9)
(4.5) calculating X after the k iteration k A corresponding cost function value;
φ error (X k )＝R k ·R k T (10)
(4.6) calculating X after the kth iteration k Corresponding Accord matrix J k Black plug matrix H k ＝J k T J k And diagonal matrix D k ＝diag{H k }；
(4.7) calculating an update vector after the kth iteration;
Δ k ＝(H k +λ·D k ) -1 ·J k ·R k (11)
(4.8) calculating a new vector X after the k iteration new ＝X k +Δ k And a corresponding cost function value phi error (X new ) Then compare phi error (X new ) Phi and phi error (X k ) If phi is greater than error (X new )＜φ error (X k ) Then let X k+1 ＝X new And λ = λ/v; if phi is error (X new )≥φ error (X k ) Then let X k+1 ＝X k And λ = λ × v; wherein, lambda and v are integers, lambda > v;
(4.9) circularly executing the steps (4.3) to (4.8) to sum up to K max Then, the iteration end point X is finally obtained final ；
(5) And inverse mapping;
x is to be final The pole vector is then substituted into the equation final ；
(6) According to the pole vector U final Calculating the coefficient of a digital all-pass filter;
and completing the design of the all-pass filter.
2. The method according to claim 1, wherein the expression of the limiting function χ (-) is:
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| TW201019595A (en) * | 2008-11-07 | 2010-05-16 | Univ Shu Te | Design method of recursive all-pass digital filter |
| CN106921365A (en) * | 2017-02-28 | 2017-07-04 | 西安电子科技大学 | A kind of method for being designed with limit for length's impulse response wave digital lowpass filter |
| CN111585658A (en) * | 2020-05-25 | 2020-08-25 | 电子科技大学 | Frequency overlapping band phase compensation method of bandwidth alternating sampling system |
-
2020
- 2020-09-11 CN CN202010952125.XA patent/CN112084741B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| TW201019595A (en) * | 2008-11-07 | 2010-05-16 | Univ Shu Te | Design method of recursive all-pass digital filter |
| CN106921365A (en) * | 2017-02-28 | 2017-07-04 | 西安电子科技大学 | A kind of method for being designed with limit for length's impulse response wave digital lowpass filter |
| CN111585658A (en) * | 2020-05-25 | 2020-08-25 | 电子科技大学 | Frequency overlapping band phase compensation method of bandwidth alternating sampling system |
Non-Patent Citations (3)
| Title |
|---|
| Hybrid of Particle Swarm and Levenberg Marquardt Optimization in Neural Network Model for Rainfall Prediction;Budi Warsito等;《Journal of Physics: Conference Series》;20191231;1-6 * |
| Hybrid Particle Swarm Optimization for Multi-Sensor Data Fusion;Hyunseok Kim等;《Sensors 2018》;20180824;1-12 * |
| 基于参数化模型的近红外干涉图相位校正方法;吴雪梅;《山东化工》;20190923;第48卷;62-63 * |
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