CN115727890A - Method for correcting homodyne symmetric demodulation errors through space ellipse fitting - Google Patents
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Abstract
The invention discloses a method for correcting homodyne symmetric demodulation errors by fitting a space ellipse, which comprises the steps of integrally processing three paths of output data of an optical fiber 3X 3coupler as a three-dimensional space ellipse, fitting out a general equation of a plane where the ellipse is located by adopting a least square method, establishing a new three-dimensional coordinate space by using the plane and a normal line thereof, converting an original three-dimensional coordinate space ellipse into a new three-dimensional coordinate space to obtain a two-dimensional plane ellipse, fitting out the general equation of the two-dimensional plane ellipse by adopting the least square method, obtaining a fitting coordinate of the original three-dimensional space ellipse by utilizing the relation of the new three-dimensional coordinate space and the old three-dimensional coordinate space, and respectively obtaining a direct current component, an alternating current component coefficient and a phase error of the three paths of output data by utilizing the maximum value and the minimum value of the three components of the fitting coordinate of the original three-dimensional space ellipse, thereby correcting errors of homodyne symmetric demodulation calculation. The method is different from the traditional method for processing two paths of output data, more objectively obtains the system error of the optical fiber sensing system, and is less influenced by the random noise of the system.
Description
Technical Field
The invention relates to the technical field of signal processing of an optical fiber sensing system, in particular to a method for correcting homodyne symmetric demodulation errors through space ellipse fitting.
Background
The optical fiber interference sensing technology is widely applied to the fields of seismic acoustic wave detection, sonar early warning, pipeline gas leakage monitoring and the like due to the advantages of high sensitivity, weak signal detection and the like. A homodyne symmetric demodulation algorithm (NPS algorithm) based on an optical fiber 33coupler is a commonly used algorithm for extracting a phase signal of an optical fiber interference sensing system, but because of factors such as a splitting ratio and a phase error of the 33coupler in the optical fiber interference sensing system, a sensitivity error of a photoelectric detector, other noise of the system and the like, the accuracy of the NPS algorithm for extracting the phase signal of the system is influenced [ ZHao Z Q, demokan M S, macAlpine M.Impulse modulation scheme for fiber optical interference using an asynchronous 33coupler [ J ]. Journal of light Technology,1997,15 (11): 9-2068 ].
The homodyne symmetric demodulation calculation of a modified optical fiber interference sensing system is widely concerned, wherein a common method mainly comprises a piezoelectric ceramic (PZT) modulation method, the method is characterized in that PZT periodic vibration signals are added in the optical fiber interference sensing system, then the maximum value and the minimum value of three interference signals are respectively extracted, and the direct current component coefficient and the alternating current component coefficient [ Li Rizhong ] are calculated and obtained, and the DFB optical fiber laser hydrophone key technology research [ D ]. Wuhan: china university of science and technology, 2014 67-93 ], this method increases the hardware cost of the system and cannot correct the phase error of the three-way interference signal. A two-dimensional ellipse fitting parameter estimation method is also a commonly used method, two paths of signals of three paths of interference signals are randomly selected to form a Lissajous two-dimensional ellipse graph, relevant parameters [ Liu Juncheng, zhang Zichao, residual waves, and the like ] of homodyne symmetric demodulation are corrected after fitting, polarization analysis and processing [ J ] photonics newspaper, 2019, 48 (1): 15-24 ] in the demodulation process of a 33coupler are not considered integrally, the method is not influenced by noise in fact, and error correction parameters obtained by fitting different two paths of signals have deviation. Three interference signals are considered integrally, three-dimensional space ellipse parameter estimation is a method which is more consistent with system objective, wherein a three-dimensional ellipse is converted into a two-dimensional ellipse by matrix singular value decomposition, the problem of three-dimensional ellipse fitting is well solved, but the calculation amount is large [ Zhang Huayong, wang Liwei, shi Qingping, and the like ].
Disclosure of Invention
The invention provides a method for correcting homodyne symmetric demodulation errors through space ellipse fitting, which aims to solve the problems of low accuracy, large calculation amount and high hardware cost in the prior art for correcting the demodulation errors.
The invention provides a method for correcting homodyne symmetric demodulation errors by space ellipse fitting, which comprises the following steps:
step 1: acquiring three paths of output data of the optical fiber 3x3 optical fiber coupler, constructing an ellipse of a three-dimensional space by taking the three paths of output data as three-dimensional coordinate components in a three-dimensional space coordinate system, and recording a current three-dimensional space coordinate system as an original three-dimensional space coordinate system;
step 2: fitting a general equation of a plane where an ellipse of a three-dimensional space is located by adopting a least square method, constructing a new three-dimensional space coordinate system by using the plane where the ellipse of the three-dimensional space is located and a normal line of the plane, and constructing a coordinate conversion relation between the new three-dimensional space coordinate system and an original three-dimensional space coordinate system;
and step 3: converting the ellipse of the three-dimensional space into a new three-dimensional space coordinate system to obtain an ellipse of a two-dimensional plane, wherein two coordinate components form the ellipse of the two-dimensional plane, and the third coordinate component fluctuates slightly up and down around the average value under the influence of noise;
and 4, step 4: fitting a general equation of the ellipse of the two-dimensional plane by adopting a least square method, and obtaining the fitting quantity of two coordinate components of the ellipse of the two-dimensional plane according to the general equation of the ellipse of the two-dimensional plane;
and 5: obtaining fitting quantities of three coordinate components of the ellipse of the original three-dimensional space according to the fitting quantities of two coordinate components of the ellipse of the two-dimensional plane in the new three-dimensional space, the average value of the third coordinate component and the coordinate conversion relation between the new three-dimensional space coordinate system and the original three-dimensional space coordinate system;
step 6: and respectively acquiring direct current components, alternating current components and phase errors of three paths of output data of the 3x3 optical fiber coupler according to the maximum value and the minimum value of the three components in the fitting quantity of the ellipse of the original three-dimensional space, and finishing correction of homodyne symmetric demodulation calculation errors.
Further, a general equation of a plane where an ellipse of a three-dimensional space is fitted by using a least square method is as follows:
Ax+By+Cz+1＝0
a, B, C is the undetermined coefficient of the plane equation, and x, y and z are the coordinates of the ellipse of the original three-dimensional space.
Further, a coordinate conversion relation between the new three-dimensional space coordinate system and the original three-dimensional space coordinate system is constructed as follows:
wherein, I 1 、I 2 、I 3 The three-way output data of the optical fiber coupler corresponds to the coordinate, I 'of the original three-dimensional space coordinate system' 1 、I' 2 、I′ 3 And A, B, C are undetermined coefficients of the plane equation respectively for the coordinates of the new three-dimensional space coordinate system corresponding to the coordinates of the original three-dimensional space coordinate system after conversion.
Further, the general equation for fitting an ellipse of a two-dimensional plane by using the least square method is:
b 1 x 2 +b 2 y 2 +b 3 xy+b 4 x+b 5 y+1＝0
wherein, b 1 ～b 5 Respectively, undetermined coefficients of an elliptic general equation.
Further, the specific method of step 6 is:
respectively acquiring current components, alternating current component coefficients and phase errors of the three signals by the following formulas:
D＝(I f_max +I f_min )/2
a＝(I f_max -I f_min )/2
θ 2,1 ＝arccos[(I f2 -D 2 )/a 2 ]+2π/3
θ 3,1 ＝arccos[(I f3 -D 3 )/a 3 ]+4π/3
wherein D is a current component; a is an alternating current component coefficient; theta 2,1 The phase error between the second signal and the first path of signal; theta 3,1 The phase error between the third path of signal and the first path of signal; i is f_max Is the maximum value of the fitted quantity; i is f_min Is the minimum value of the fitted quantity; i is f2 Calculating the corresponding second path of signal fitting quantity when the maximum value of the first path of signal fitting quantity is calculated; i is f3 The third path of signal fitting quantity corresponding to the maximum value of the first path of signal fitting quantity is calculated.
The invention has the beneficial effects that:
the invention relates to a method for correcting homodyne symmetric demodulation errors by space ellipse fitting, which is characterized in that three paths of output data are considered integrally, an ellipse model of the three paths of output data is constructed, an ellipse in a three-dimensional coordinate system is converted by adopting a space coordinate conversion mode, fitting quantity is obtained by a fitting method, and finally parameters required by error correction are obtained according to the fitting quantity.
Drawings
The features and advantages of the present invention will be more clearly understood by reference to the accompanying drawings, which are illustrative and not to be construed as limiting the invention in any way, and in which:
FIG. 1 is a flow chart of an embodiment of the present invention;
FIG. 2 is a two-dimensional ellipse of an embodiment of the present invention;
FIG. 3 is a fitting curve of a two-dimensional ellipse according to an embodiment of the present invention;
FIG. 4 is a graph of values in an embodiment of the present invention;
FIG. 5 is a fitting curve in an embodiment of the invention;
FIG. 6 is an ellipse of a three-dimensional space in an embodiment of the present invention;
fig. 7 is a fitted curve of an ellipse in three dimensions in an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention will be further elucidated with reference to the following specific examples. It will be understood by those skilled in the art that these examples are given for the purpose of illustration only and are not intended to limit the scope of the invention, which is defined in the claims appended hereto as modified by various equivalents thereto.
The invention provides a method for correcting homodyne symmetric demodulation errors by fitting a space ellipse, which comprises the following steps:
step 1: acquiring three paths of output data of the optical fiber 3X3 optical fiber coupler, wherein output light intensity signals are respectively as follows:
I 1 ＝D 1 +a 1 cos(θ) (1)
I 2 ＝D 2 +a 2 cos(θ-2π/3+Δθ 2,1 ) (2)
I 3 ＝D 3 +a 3 cos(θ-4π/3+Δθ 3,1 ) (3)
under the noise-free state of an ideal optical fiber interference sensing system, the splitting ratio of the 3 × 3 optical fiber coupler is 1 1 ＝D 2 ＝D 3 The coefficient of the AC component is the same as a 3 ＝a 3 ＝a 3 The phase difference is 2 pi/3, wherein the phase error is theta 2,1 ＝θ 3,1 ＝0。
In an actual optical fiber interference sensing system, due to the existence of system errors and noise, direct current component systems and alternating current component systems of three signals are different, phase difference also deviates from 2 pi/3, and further homodyne symmetric demodulation has errors, and D needs to be solved 1 、D 2 、D 3 、a 1 、a 2 、a 3 、θ 2,1 、θ 3,1 To I 1 、I 2 And I 3 And correcting, and then performing homodyne symmetric demodulation calculation, so that the phase calculation precision of the optical fiber interference sensing system is improved.
Three paths of output data are used as three-dimensional coordinate components in a three-dimensional space coordinate system to construct an ellipse of a three-dimensional space, and the current three-dimensional space coordinate system is marked as an original three-dimensional space coordinate system;
data acquisition card acquires I 1(i) 、I 2(i) And I 3(i) In the three-dimensional space o-xyz, if they are respectively used as coordinate components, an ellipse L in the three-dimensional space shown in fig. 6 is formed 1 ；
And 2, step: ellipse L 1 Because of being influenced by noise, the edge is irregular, and needs to be fitted, and the general equation of the plane where the ellipse of the three-dimensional space is fitted by adopting the least square method is as follows:
Ax+By+Cz+1＝0 (4)
constructing a new three-dimensional space coordinate system o '-x' y 'z' and a coordinate conversion relation between the new three-dimensional space coordinate system and the original three-dimensional space coordinate system according to the plane of the ellipse of the three-dimensional space and the normal of the plane, wherein the conversion relation formula is as follows:
and step 3: converting the ellipse of the three-dimensional space into a new three-dimensional space coordinate system according to a general equation of a plane where the ellipse of the three-dimensional space is located and a coordinate conversion relation between the new three-dimensional space coordinate system and an original three-dimensional space coordinate system to obtain an ellipse of a two-dimensional plane;
the three-dimensional ellipse L in the o-xyz space can be expressed by the formula (5) 1 Into a two-dimensional ellipse L in o '-x' y 'z' space 2 Two-dimensional ellipse L 2 As shown in FIG. 2, L 2 Is I' 1(i) 、I' 2(i) 。
And 4, step 4: fitting a general equation of the ellipse of the two-dimensional plane by adopting a least square method, and obtaining fitting quantities of three coordinate components of the ellipse of the two-dimensional plane according to the general equation of the ellipse of the two-dimensional plane;
performing least square fitting on the two-dimensional ellipse L2 to obtain I' 1(i) 、I' 2(i) Of fitting amount I' f1(i) 、I' f2(i) 。I′ 3(i) L 'was taken because it fluctuated with a small amplitude above and below the mean value thereof under the influence of noise' 3(i) As its fitted quantity I' f3(i) The fitted curves are shown in fig. 3 and 5.
And 5: acquiring fitting quantities of three coordinate components of the ellipse of the three-dimensional space according to the fitting quantities of the three coordinate components of the ellipse of the two-dimensional plane and the coordinate conversion relation between the new three-dimensional space coordinate system and the original three-dimensional space coordinate system;
according to the fitting quantity of three coordinate components of the ellipse of the two-dimensional plane, the three-dimensional ellipse L in the o-xyz space can be obtained by combining the formula (6) 1 Three components I 1(i) 、I 2(i) And I 3(i) Fitting quantity of (I) f1(i) 、I f2(i) And I f3(i) As shown in fig. 7.
Step 6: respectively acquiring direct current components, alternating current components and phase errors of three paths of output data of the 3x3 optical fiber coupler according to the maximum value and the minimum value of the three components in the fitting quantity of the ellipse of the original three-dimensional space, and finishing correction of homodyne symmetric demodulation calculation errors;
respectively search for I f1(i) 、I f2(i) And I f3(i) Is marked as I f1_max 、I f2_max 、I f3_max And I f1_min 、I f2_min 、I f3_min Then, the following formulas (1) to (3) can be obtained:
D 1 ＝(I f1_max +I f1_min )/2 (9)
a 1 ＝(I f1_max -I f1_min )/2 (10)
D 2 ＝(I f2_max +I f2_min )/2 (11)
a 2 ＝(I f2_max -I f2_min )/2 (12)
D 3 ＝(I f3_max +I f3_min )/2 (13)
a 3 ＝(I f3_max -I f3_min )/2 (14)
note I f1_max The other two corresponding coordinate components are respectively I f2 、I f3 If the value θ in the expressions (1) to (3) is 0, I can be obtained first from the expressions (2) and (3) f2 、D2、a 2 、I f3 、D3、a 3 Then, the phase error theta is calculated 2,1 、θ 3,1 The concrete formula is as follows:
θ 2,1 ＝arccos[(I f2 -D 2 )/a 2 ]+2π/3
θ 3,1 ＝arccos[(I f3 -D 3 )/a 3 ]+4π/3
the process of the invention is illustrated below by way of example:
simulation I 1 、I 2 、I 3 The following were used:
I 1 ＝4+2cos(θ)+ε (15)
I 2 ＝5+3cos(θ-2π/3+0.6)+ε (16)
I 3 ＝6+6cos(θ-4π/3+0.8)+ε (17)
where θ =12cos (2 π t), t is time, ε is Gaussian white noise.
The dc component, the ac component coefficient, and the phase error in equations (15) to (17) are solved by the present invention.
Establishing an o-xyz space, wherein the original three-dimensional space elliptical coordinate is as follows: I.C. A 1 、I 2 、I 3 The diagram of the three-dimensional space ellipse is shown in fig. 5, and a general equation of a plane where the three-dimensional ellipse is located by using a least square method is as follows:
-0.1435x-0.0247y-0.0504z+1＝0 (17)
further, in the formulas (7) and (8), theta is obtained 1 ＝-2.6854，θ 2 = 1.1985, and is substituted into equation (5), a two-dimensional plane ellipse in o-x ' y ' z ' space can be obtained, as shown in fig. 2, and the ellipse is fitted by using the least square method to obtain a general equation:
0.0668x 2 +0.1230y 2 +0.1513xy+0.6481x+0.8721y+1＝0 (18)
the average value of I'3 (I) is-6.4859.
From formulae (18) and I' 3(i) The average value of (a) and the equation (6) can be fitted to obtain the fitting amount of the original three-dimensional space ellipse L1, as shown in fig. 6.
Thus, D1, D2, D3, a are calculated by the expressions (9) to (14) 1 、a 2 、a 3 、θ 2,1 、θ 3,1 Table 1 below: correction parameter one obtained by space ellipse fittingThe look-up of a table is carried out,
TABLE 1
The correction parameters found in table 1 are substantially identical to the parameters preset in equations (15) - (17), thereby indicating that the spatial ellipse fitting is feasible to correct the homodyne symmetric demodulation error.
Although the embodiments of the present invention have been described in conjunction with the accompanying drawings, those skilled in the art may make various modifications and variations without departing from the spirit and scope of the invention, and such modifications and variations fall within the scope defined by the appended claims.
Claims (5)
1. A method for correcting homodyne symmetric demodulation errors through space ellipse fitting is characterized by comprising the following steps:
step 1: acquiring three paths of output data of the optical fiber 3x3 optical fiber coupler, constructing an ellipse of a three-dimensional space by taking the three paths of output data as three-dimensional coordinate components in a three-dimensional space coordinate system, and marking the current three-dimensional space coordinate system as an original three-dimensional space coordinate system;
and 2, step: fitting a general equation of a plane where an ellipse of a three-dimensional space is located by adopting a least square method, constructing a new three-dimensional space coordinate system by using the plane where the ellipse of the three-dimensional space is located and a normal line of the plane, and constructing a coordinate conversion relation between the new three-dimensional space coordinate system and an original three-dimensional space coordinate system;
and step 3: converting the ellipse of the three-dimensional space into a new three-dimensional space coordinate system to obtain an ellipse of a two-dimensional plane, wherein two coordinate components form the ellipse of the two-dimensional plane, and the third coordinate component fluctuates slightly up and down around the average value under the influence of noise;
and 4, step 4: fitting a general equation of the ellipse of the two-dimensional plane by adopting a least square method, and obtaining the fitting quantity of two coordinate components of the ellipse of the two-dimensional plane according to the general equation of the ellipse of the two-dimensional plane;
and 5: obtaining fitting quantities of three coordinate components of the ellipse of the original three-dimensional space according to the fitting quantities of two coordinate components of the ellipse of the two-dimensional plane in the new three-dimensional space, the average value of the third coordinate component and the coordinate conversion relation between the new three-dimensional space coordinate system and the original three-dimensional space coordinate system;
step 6: and respectively acquiring direct current components, alternating current components and phase errors of three paths of output data of the 3x3 optical fiber coupler according to the maximum value and the minimum value of the three components in the fitting quantity of the ellipse of the original three-dimensional space, and finishing correction of homodyne symmetric demodulation calculation errors.
2. The method for correcting homodyne symmetric demodulation errors by space ellipse fitting according to claim 1, wherein a general equation of a plane where an ellipse of a three-dimensional space is fitted by a least square method is as follows:
Ax+By+Cz+1＝0
a, B, C is the undetermined coefficient of the plane equation, and x, y and z are the coordinates of the ellipse of the original three-dimensional space.
3. The method for correcting homodyne symmetric demodulation errors through spatial ellipse fitting according to claim 1 or 2, characterized in that a coordinate transformation relation between a new three-dimensional space coordinate system and an original three-dimensional space coordinate system is constructed as follows:
wherein, I 1 、I 2 、I 3 The three-way output data of the optical fiber coupler corresponds to the coordinate, I 'of the original three-dimensional space coordinate system' 1 、I' 2 、I' 3 And A, B, C are undetermined coefficients of the plane equation respectively for the coordinates of the new three-dimensional space coordinate system corresponding to the coordinates of the original three-dimensional space coordinate system after conversion.
4. The method for correcting homodyne symmetric demodulation errors by spatial ellipse fitting of claim 1, wherein the general equation for fitting the ellipse of the two-dimensional plane by the least squares method is as follows:
b 1 x 2 +b 2 y 2 +b 3 xy+b 4 x+b 5 y+1＝0
wherein, b 1 ～b 5 Respectively, are undetermined coefficients of an elliptic general equation.
5. The method for correcting homodyne symmetric demodulation errors by spatial ellipse fitting according to claim 1, wherein the specific method in the step 6 is as follows:
respectively acquiring current components, alternating current component coefficients and phase errors of the three signals by the following formulas:
D＝(I f_max +I f_min )/2
a＝(I f_max -I f_min )/2
θ 2,1 ＝arccos[(I f2 -D 2 )/a 2 ]+2π/3
θ 3,1 ＝arccos[(I f3 -D 3 )/a 3 ]+4π/3
wherein D is a current component; a is an alternating current component coefficient; theta 2,1 The phase error between the second signal and the first path of signal; theta 3,1 The phase error between the third path of signal and the first path of signal; i is f_max Is the maximum value of the fitted quantity; i is f_min Is the minimum value of the fitted quantity; i is f2 To calculateThe corresponding second path of signal fitting quantity when the first path of signal fitting quantity is maximum; i is f3 The third path of signal fitting quantity corresponding to the maximum value of the first path of signal fitting quantity is calculated.
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| CN115994403B (en) * | 2023-03-22 | 2023-06-23 | 中国水利水电第七工程局有限公司 | Pile casing checking method, device and equipment based on three-dimensional circle center fitting |
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