CN111754970B - Photoacoustic signal noise reduction system and noise reduction method thereof - Google Patents
Photoacoustic signal noise reduction system and noise reduction method thereof Download PDFInfo
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- G10K—SOUND-PRODUCING DEVICES; METHODS OR DEVICES FOR PROTECTING AGAINST, OR FOR DAMPING, NOISE OR OTHER ACOUSTIC WAVES IN GENERAL; ACOUSTICS NOT OTHERWISE PROVIDED FOR
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Abstract
The invention provides a photoacoustic signal noise reduction system and a noise reduction method thereof, wherein the photoacoustic signal noise reduction system comprises an input signal processing unit, a reference signal generating unit, a phase-sensitive detecting unit, a low-pass filtering unit, a Kalman filtering unit and an output signal processing unit; the input signal processing unit pre-amplifies an input photoacoustic signal and then sends the input photoacoustic signal to the phase-sensitive detection unit; the reference signal generating unit generates two paths of reference signals with phase difference; the phase-sensitive detection unit is used for respectively compositing the output photoacoustic signals after the pre-amplification with two paths of reference signals to generate two paths of detection output signals, and the two paths of detection output signals are sent to the low-pass filtering unit to eliminate a high-frequency part; then output to the Kalman filtering unit; and after receiving the output value of the low-pass filter, the Kalman filtering unit further performs Kalman filtering noise reduction, and outputs a filtering noise reduction result to the output signal processing unit.
Description
Technical Field
The invention relates to the technical field of photoacoustic signal detection and processing, in particular to a photoacoustic signal noise reduction system and a noise reduction method thereof.
Background
Along with the gradual entering of the times of high voltage and large power grids in the power industry, the reliability requirement on the fault diagnosis technology of power equipment is higher and higher, so that the accuracy requirement on the detection of the concentration of dissolved gas in oil is higher and higher. The concentration of dissolved gas in the transformer oil is detected by the photoacoustic spectroscopy technology, and analysis of different gas concentration ratios is a main method for judging potential operation faults of the transformer at present. The principle of detecting the gas concentration by the photoacoustic spectroscopy technology is shown in fig. 1, and the main structure of the detection device comprises an excitation light source, an acousto-optic cell, a signal detection part and the like. The method comprises the steps of irradiating a beam of monochromatic light with adjustable frequency to gas in a photoacoustic cell, enabling the gas to absorb light energy to transit from a ground state to an excited state, immediately de-exciting the gas in a heat energy release mode, enabling the released heat energy to generate periodic heating to surrounding media according to the modulation frequency of the light, and accordingly enabling the media to generate periodic pressure fluctuation. However, the signal is inevitably mixed with strong environmental noise and circuit noise, and the phase-locked amplifier is used for extracting the signal to reduce noise, which is the main method for the current photoacoustic signal noise reduction treatment, when the gas concentration is low or the on-line monitoring system is in a very bad natural environment, the high voltage and the high current of the transformer generate strong magnetic field to have larger interference on the signal, so that the very weak photoacoustic signal is mixed with strong noise, and the traditional phase-locked amplifier is difficult to filter out the high-efficiency photoacoustic signal, therefore, the signal processing method is difficult to meet the requirement on the detection precision of low-concentration gas.
Disclosure of Invention
In view of the above, the present invention proposes a photoacoustic signal noise reduction system and a noise reduction method thereof that can combine a kalman filter and a lock-in amplifier, enhance noise reduction capability, and not increase a time constant.
In one aspect, the invention provides a photoacoustic signal noise reduction system, which comprises an input signal processing unit, a reference signal generating unit, a phase-sensitive detecting unit, a low-pass filtering unit, a Kalman filtering unit and an output signal processing unit; the output end of the input signal processing unit and the output end of the reference signal generating unit are respectively connected with the input end of the phase-sensitive detecting unit in a signal manner; the output end of the phase-sensitive detection unit is in signal connection with the input end of the low-pass filtering unit, and the output end of the low-pass filtering unit is in signal connection with the input end of the Kalman filtering unit; the output end of the Kalman filtering unit is in signal connection with the input end of the output signal processing unit; wherein:
an input signal processing unit for pre-amplifying the input photoacoustic signal and then transmitting the pre-amplified photoacoustic signal to a phase-sensitive detection unit;
the reference signal generating unit generates a reference signal and directly sends the reference signal into the phase-sensitive detecting unit, and the reference signal is phase-shifted and then sent into the phase-sensitive detecting unit;
the phase-sensitive detection unit is used for respectively compositing the pre-amplified output photoacoustic signals with the reference signals and the phase-shifted reference signals to generate two paths of detection output signals, and the two paths of detection output signals are sent to the low-pass filtering unit;
the low-pass filtering unit filters the two paths of detection output signals generated by the phase-sensitive detection unit respectively and outputs the two paths of detection output signals to the Kalman filtering unit;
after receiving the output value of the low-pass filter, the Kalman filtering unit further carries out Kalman filtering noise reduction and outputs a filtering noise reduction result to the output signal processing unit;
and the output signal processing unit performs addition operation according to the results output by the two paths of Kalman filtering units to obtain the amplitude of the photoacoustic signal to be detected, and back-calculates the gas concentration in the acousto-optic cell.
On the basis of the technical scheme, preferably, the phase-sensitive detection unit is used for performing proportional operation on the pre-amplified input photoacoustic signal and the reference signal after phase shift respectively to obtain two paths of detection output signals; the reference signal and the phase-shifted reference signal are orthogonal sinusoidal signals.
Further preferably, the phase-sensitive detection unit includes a first digital multiplier and a second digital multiplier, and the pre-amplified input photoacoustic signal and the reference signal are input into the first digital multiplier; the pre-amplified input photoacoustic signal and the phase-shifted reference signal are input into a second digital multiplier, and the outputs of the two digital multipliers are both led into a low-pass filtering unit.
Further preferably, the low-pass filtering unit is an FIR filter or an IIR filter.
On the other hand, the invention also provides a noise reduction method of the photoacoustic signal noise reduction system, which comprises the following steps:
s1: the photoacoustic signal excited in the acousto-optic cell is preamplified by an input signal processing unit to obtain a preamplified output photoacoustic signal S i (t)，C is the amplitude of the signal and,for signal phase, ω is angular frequency, +.>An initial phase at time t=0; n is n i (t) is a chaotic white noise;
s2: pre-amplified output photoacoustic signal S i (t) inputting the phase-sensitive detection unit, and compositing the phase-sensitive detection unit with the reference signal generated by the reference signal generation unit and the phase-shifted reference signal to obtain two paths of detection output signals, wherein the two paths of detection output signals are respectively:
wherein a (t) is time-varying noise superimposed in the amplitude after extracting a signal of known frequency; s is S r (t) is a known frequency signal, sin ωt and cos ωt in the formula; nT is the width of the fourier time window; n is the fundamental wave cycle number; a (t) is much smaller than n i (t), and A (t) > c;
s3: the low-pass filter unit filters and outputs two paths of detection output signals generated by the phase-sensitive detection unit, eliminates high-frequency components except cut-off frequency, and outputs Y after the photoacoustic signals of each path are processed by the low-pass filter 1 Or Y 2 The method comprises the following steps:
a' (t) is a low-pass filtered noise component;
s4: output Y of photoacoustic signal processed by low-pass filter 1 Or Y 2 For inputting the output value into the Kalman filtering unit, performing Kalman filtering noise reduction, and continuously predicting and correcting the output value by using the Kalman filtering unit to further reduce the superimposed noise: let the effective value processed by the low-pass filter be X' (t),the superimposed noise isThen there is a low pass filter output Y at time t 1 Or Y 2 The method comprises the following steps of: x (t) =x (t) +w (t);
let the effective value of the output obtained by measurement be Z (t), the measurement error be V (t), Z (t) =x (t) +v (t); w (t) and V (t) are both Gaussian noise parts varying with time, and the variances of W (t) and V (t) are respectivelyCovariance (covariance)Based on the output X (t) of the low-pass filter at time t, the estimated value X (t+1) of the output of the low-pass filter at time t+1 is solved as follows:
the next time forecast value: x (t+1) | (t) =x (t);
covariance matrix prediction is: p (t+1) | (t) =p (t) +w (t);
the state update is:
x (t+1) =x (t+1) | (t) +k (t+1) [ Z (t+1) -X (t+1) | (t) ]; k (t+1) is Kalman gain;
the covariance matrix is updated as: p (t+1) = [1-K (t+1) ] P (t+1) | (t);
the effective value after the Kalman filtering unit filters and reduces noise is as follows:
w '(t) is output noise after noise reduction by the Kalman filtering unit, and W' (t) < W (t); the noise intensity contained in the effective value is further reduced;
s5: the output signal processing unit calculates the amplitude of the acousto-optic signal by addition according to the result of Kalman filtering noise reduction, and further calculates the concentration of the acousto-optic cell gas; the relationship between photoacoustic signal and gas concentration is: u (u) λ ＝aσ λ I λ C cell ；
Wherein u is λ For the intensity of the photoacoustic signal excited in the photoacoustic cell, a is the proportionality coefficient, σ λ Is the absorption coefficient of the gas at wavelength λ; i λ Is the intensity of the incident light at wavelength λ; c (C) cell Is the cell constant of the photoacoustic cell; the excitation light is monochromatic laser or infrared light, and sigma is different according to the change of gas concentration λ And will follow the change.
Compared with the prior art, the photoacoustic signal noise reduction system and the photoacoustic signal noise reduction method provided by the invention have the following beneficial effects:
(1) According to the invention, the low-pass filter unit and the Kalman filter unit are sequentially added after the existing phase-locked amplifier is processed, so that the noise reduction capability can be enhanced without increasing the time constant, and weak photoacoustic signals can be reliably amplified, thereby facilitating the subsequent detection;
(2) Compared with the existing signal detection processing system, when the noise is at the same level, the invention can reduce the work load of the lock-in amplifier by setting the cut-off frequency of the higher low-pass filtering unit;
(3) The Kalman filtering unit can prevent signal distortion from generating singular values, so that the stability of an online monitoring system is improved;
(4) The mean value and covariance of the Kalman filtering unit have linear transitivity, the output value at each moment is recorded into the posterior estimated value at the next moment through multiplication, and the posterior estimated value at the moment contains the information of all the previous measured values through continuous multiplication and iteration, so that the system error is reduced.
Drawings
In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic diagram of a photoacoustic spectroscopy technique for detecting gas concentration;
FIG. 2 is a block diagram of a photoacoustic signal noise reduction system and a noise reduction method thereof according to the present invention;
FIG. 3 is a schematic diagram of noise reduction effect of a conventional signal noise reduction method;
fig. 4 is a schematic diagram of a noise reduction effect of a photoacoustic signal noise reduction system and a noise reduction method thereof according to the present invention;
FIG. 5 is a schematic diagram of the time delay corresponding to the lower cut-off frequency when the prior signal extraction method achieves the same noise reduction effect of the invention;
fig. 6 is a schematic diagram illustrating a filtering effect of a photoacoustic signal noise reduction system and a noise reduction method thereof according to the present invention.
Detailed Description
The following description of the embodiments of the present invention will clearly and fully describe the technical aspects of the embodiments of the present invention, and it is apparent that the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, are intended to fall within the scope of the present invention.
As shown in fig. 2, the present invention provides a photoacoustic signal noise reduction system, comprising an input signal processing unit, a reference signal generating unit, a phase-sensitive detecting unit, a low-pass filtering unit, a kalman filtering unit and an output signal processing unit; wherein:
an input signal processing unit for pre-amplifying the input photoacoustic signal and then transmitting the pre-amplified photoacoustic signal to a phase-sensitive detection unit;
the reference signal generating unit generates a reference signal and directly sends the reference signal into the phase-sensitive detecting unit, and the reference signal is phase-shifted and then sent into the phase-sensitive detecting unit;
the phase-sensitive detection unit is used for respectively compositing the pre-amplified output photoacoustic signals with the reference signals and the phase-shifted reference signals to generate two paths of detection output signals, and the two paths of detection output signals are sent to the low-pass filtering unit;
the low-pass filtering unit filters the two paths of detection output signals generated by the phase-sensitive detection unit respectively and outputs the two paths of detection output signals to the Kalman filtering unit;
after receiving the output value of the low-pass filter, the Kalman filtering unit further carries out Kalman filtering noise reduction and outputs a filtering noise reduction result to the output signal processing unit;
the output signal processing unit performs addition operation according to the results output by the two paths of Kalman filtering units to obtain the amplitude of the photoacoustic signal to be detected, and reversely calculates the gas concentration in the acousto-optic cell;
the output end of the input signal processing unit and the output end of the reference signal generating unit are respectively connected with the input end of the phase-sensitive detecting unit in a signal manner; the output end of the phase-sensitive detection unit is in signal connection with the input end of the low-pass filtering unit, and the output end of the low-pass filtering unit is in signal connection with the input end of the Kalman filtering unit; the output end of the Kalman filtering unit is in signal connection with the input end of the output signal processing unit; and the output signal processing unit performs subsequent processing to obtain the concentration information of the gas so as to facilitate subsequent analysis.
In the invention, the phase-sensitive detection unit performs proportional operation on the pre-amplified input photoacoustic signal and the reference signal after phase shift to obtain two paths of detection output signals; the reference signal and the phase-shifted reference signal are orthogonal sinusoidal signals. The phase-sensitive detection unit comprises a first digital multiplier and a second digital multiplier, and the input photoacoustic signal and the reference signal after the pre-amplification are input into the first digital multiplier; the pre-amplified input photoacoustic signal and the phase-shifted reference signal are input into a second digital multiplier, and the outputs of the two digital multipliers are both led into a low-pass filtering unit.
Further, the low-pass filtering unit is an FIR filter or an IIR filter.
In addition, the invention also provides a noise reduction method of the photoacoustic signal noise reduction system, which comprises the following steps:
s1: the photoacoustic signal excited in the acousto-optic cell is preamplified by an input signal processing unit to obtain a preamplified output photoacoustic signal S i (t)，C is the signal amplitude, < >>For signal phase, ω is angular frequency, +.>An initial phase at time t=0; n is n j (t) is a chaotic white noise; the directly input photoacoustic signal to be detected is weak and needs to be amplified, so that the working requirement of the phase-sensitive monitoring unit is met.
S2: pre-amplified output photoacoustic signal S i (t) inputting into a phase-sensitive detection unit, and compositing with the reference signal generated by the reference signal generation unit and the phase-shifted reference signal to obtain two paths of detection output signals, S r (t) is a known frequency signal, here orthogonalized sin ωt and cos ωt; according to the correlation principle, S i (t) and S r The ideal output result of (t) multiplication is:
however, when the actually detected gas concentration is low, the noise power is too high relative to the weak photoacoustic signal, so that the extracted photoacoustic signal still has strong noise; s is S i (t) and S r The actual result of (t) multiplication is:
wherein a (t) is time-varying noise superimposed in the amplitude after extracting a signal of known frequency; s is S r (t) is a known frequency signal, i.e., sibωt and cos ωt in the formula; nT is FourierThe width of the time window; n is the fundamental wave cycle number; a (t) is much smaller than n i (t), and A (t) > C.
S3: the low-pass filter unit filters and outputs two paths of detection output signals generated by the phase-sensitive detection unit, eliminates high-frequency components except cut-off frequency, and outputs Y after the photoacoustic signals of each path are processed by the low-pass filter 1 Or Y 2 The method comprises the following steps:
a' (t) is a low-pass filtered noise component;
if Y is to be 1 And Y 2 Directly accumulating to obtain the amplitude of the acousto-optic signal to be measured by subsequent calculation, wherein the amplitude comprises an A '(t) noise part, and when C > A' (t), the A (t) is negligible; when the gas concentration is low, A (t) can cause the amplitude of an acousto-optic signal to be detected to generate larger fluctuation to generate errors, which is not beneficial to the monitoring and maintenance of the power transformer; therefore, further noise reduction measures need to be introduced; according to the noise reduction principle of the low-pass filter, the signal-to-noise ratio of an output signal can be improved by reducing the cut-off frequency, but the time constant can be increased, so that great time delay is caused, when the photoacoustic signal is very weak, the extremely low cut-off frequency is required to obtain the output value of the low-pass filter meeting the requirement, and the calculation result can be obtained after a long time is required, and the real-time requirement of on-line monitoring is not met; at the same time, a lower cut-off frequency affects the load of the phase-locked amplification of the phase-sensitive detection unit. Therefore, the invention further adopts a Kalman filtering unit to perform further noise reduction treatment.
S4: output Y of photoacoustic signal processed by low-pass filter 1 Or Y 2 Inputting the corrected output value into a Kalman filtering unit, carrying out Kalman filtering noise reduction, and continuously predicting a corrected output value by using the Kalman filtering unit to further reduce the superimposed noise: let the effective value processed by the low-pass filter be X' (t),the superimposed noise isThen there is a low pass filter output Y at time t 1 Or Y 2 The transformation is as follows: x (t) =x' (t) +w (t);
let the effective value of the output obtained by measurement be Z (t), the measurement error be V (t), Z (t) =x (t) +v (t); w (t) and V (t) are both Gaussian noise parts varying with time, and the variances of W (t) and V (t) are respectivelyCovariance (covariance)Based on the output X (t) of the low-pass filter at time t, the estimated value X (t+1) of the output of the low-pass filter at time t+1 is solved as follows:
the next time forecast value: x (t+1) | (t) =x (t);
covariance matrix prediction is: p (t+1) | (t) =p (t) +w (t);
the state update is:
x (t+1) =x (t+1) | (t) +k (t+1) [ Z (t+1) -X (t+1) | (t) ]; k (t+1) is Kalman gain;
the covariance matrix is updated as: p (t+1) = [1-K (t+1) ] P (t+1) | (t);
the effective value after the Kalman filtering unit filters and reduces noise is as follows:
w '(t) is output noise after noise reduction by the Kalman filtering unit, and W' (t) < W (t); the noise intensity contained in the effective value is further reduced;
the mean value and covariance of the Kalman filtering unit have linear transitivity, the output value at each moment is recorded into the posterior estimated value at the next moment through multiplication, and the posterior estimated value at the moment contains the information of all the previous measured values through continuous multiplication and iteration, so that the system error is reduced. On the other hand, the invention can prevent the signal distortion from generating singular values, improve the stability of an on-line monitoring system, and save the hardware resources of the system compared with the reduction of the cut-off frequency of a low-pass filter. The Kalman filter unit is a Kalman filter.
S5: the output signal processing unit further calculates the concentration of the gas in the acousto-optic tank according to the result of Kalman filtering noise reduction; the relationship between photoacoustic signal and gas concentration is: u (u) λ ＝aσ λ I λ C coll ；
Wherein u is λ For the intensity of the photoacoustic signal excited in the photoacoustic cell, a is the proportionality coefficient, σ λ Is the absorption coefficient of the gas at wavelength λ; i λ Is the intensity of the incident light at wavelength λ; c (C) cell Is the cell constant of the photoacoustic cell; the excitation light is monochromatic laser or infrared light, and sigma is different according to the change of gas concentration λ And will follow the change.
Cell constant C of acousto-optic cell cell The photoacoustic conversion capability of the acousto-optic cell is determined, the smaller the radius of the resonant cavity of the acousto-optic cell is, the larger the length is, the larger the cell constant is, but the radius of the resonant cavity cannot be too small, so that the difficulty of light beam collimation can be increased, and the acousto-optic cell is manufactured by actually selecting materials with good heat conduction performance and small gas adsorptivity.
As shown in fig. 3-5, fig. 3 illustrates a schematic diagram of noise reduction effect of the existing signal noise reduction method; FIG. 4 is a schematic diagram showing the noise reduction effect of the signal noise reduction method of the present invention; fig. 5 shows a schematic time delay diagram corresponding to a lower cut-off frequency when the equivalent noise reduction effect of the present invention is achieved by the conventional signal extraction method.
FIG. 6 is a pair C 2 H 2 The concentration monitoring result shows that the concentration comparison of the existing noise reduction method and the noise reduction method respectively shows that the noise reduction system and the noise reduction method have smoother and more stable detection results.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, alternatives, and improvements that fall within the spirit and scope of the invention.
Claims (5)
1. A photoacoustic signal noise reduction system, characterized by: the device comprises an input signal processing unit, a reference signal generating unit, a phase-sensitive detecting unit, a low-pass filtering unit, a Kalman filtering unit and an output signal processing unit; the output end of the input signal processing unit and the output end of the reference signal generating unit are respectively connected with the input end of the phase-sensitive detecting unit in a signal manner; the output end of the phase-sensitive detection unit is in signal connection with the input end of the low-pass filtering unit, and the output end of the low-pass filtering unit is in signal connection with the input end of the Kalman filtering unit; the output end of the Kalman filtering unit is in signal connection with the input end of the output signal processing unit; wherein:
an input signal processing unit for pre-amplifying the input photoacoustic signal and then transmitting the pre-amplified photoacoustic signal to a phase-sensitive detection unit;
the reference signal generating unit generates a reference signal and directly sends the reference signal into the phase-sensitive detecting unit, and the reference signal is phase-shifted and then sent into the phase-sensitive detecting unit;
the phase-sensitive detection unit is used for respectively compositing the pre-amplified output photoacoustic signals with the reference signals and the phase-shifted reference signals to generate two paths of detection output signals, and the two paths of detection output signals are sent to the low-pass filtering unit;
the low-pass filtering unit filters the two paths of detection output signals generated by the phase-sensitive detection unit respectively and outputs the two paths of detection output signals to the Kalman filtering unit;
after receiving the output value of the low-pass filter, the Kalman filtering unit further carries out Kalman filtering noise reduction and outputs a filtering noise reduction result to the output signal processing unit;
and the output signal processing unit performs addition operation according to the results output by the two paths of Kalman filtering units to obtain the amplitude of the photoacoustic signal to be detected, and back-calculates the gas concentration in the acousto-optic cell.
2. A photoacoustic signal noise reducing system according to claim 1, wherein: the phase-sensitive detection unit is used for performing proportional operation on the pre-amplified input photoacoustic signal and the reference signal after phase shift to obtain two paths of detection output signals; the reference signal and the phase-shifted reference signal are orthogonal sinusoidal signals.
3. A photoacoustic signal noise reducing system according to claim 2, wherein: the phase-sensitive detection unit comprises a first digital multiplier and a second digital multiplier, and the input photoacoustic signal and the reference signal after the pre-amplification are input into the first digital multiplier; the pre-amplified input photoacoustic signal and the phase-shifted reference signal are input into a second digital multiplier, and the outputs of the two digital multipliers are both led into a low-pass filtering unit.
4. A photoacoustic signal noise reducing system according to claim 2, wherein: the low-pass filtering unit is an FIR filter or an IIR filter.
5. A noise reduction method of a photoacoustic signal noise reduction system is characterized by comprising the following steps of: the method comprises the following steps:
s1: the photoacoustic signal excited in the acousto-optic cell is preamplified by an input signal processing unit to obtain a preamplified output photoacoustic signal S i (t)，C is the signal amplitude, < >>For signal phase, ω is angular frequency, +.>An initial phase at time t=0; n is n i (t) is a chaotic white noise;
s2: pre-amplified output photoacoustic signal S i (t) inputting the signals into a phase-sensitive detection unit, and compositing the signals with the reference signals generated by the reference signal generation unit and the reference signals after phase shift to obtain two paths of detection output signals, namely：
Wherein a (t) is time-varying noise superimposed in the amplitude after extracting a signal of known frequency; s is S r (t) is a known frequency signal, sin ωt and cos ωt in the formula; nT is the width of the fourier time window; n is the fundamental wave cycle number; a (t) is much smaller than n i (t), and A (t) > C;
s3: the low-pass filter unit filters and outputs two paths of detection output signals generated by the phase-sensitive detection unit, eliminates high-frequency components except cut-off frequency, and outputs Y after the photoacoustic signals of each path are processed by the low-pass filter 1 Or Y 2 The method comprises the following steps:
a' (t) is a low-pass filtered noise component;
s4: output Y of photoacoustic signal processed by low-pass filter 1 Or Y 2 Inputting the noise into a Kalman filtering unit, carrying out Kalman filtering and reducing noise, and continuously predicting and correcting an output value by using the Kalman filtering unit to further reduce the superimposed noise: let the effective value processed by the low-pass filter be X (t),the superimposed noise isThen there is a low pass filter output Y at time t 1 Or Y 2 The transformation is as follows: x (t) =x' (t) +w (t);
let the effective value of the output obtained by measurement be Z (t), and measure the errorV (t), Z (t) =x (t) +v (t); w (t) and V (t) are both Gaussian noise parts varying with time, and the variances of W (t) and V (t) are respectivelyCovariance (covariance)Based on the output X (t) of the low-pass filter at time t, the estimated value X (t+1) of the output of the low-pass filter at time t+1 is solved as follows:
the next time forecast value: x (t+1) | (t) =x (t);
covariance matrix prediction is: p (t+1) | (t) =p (t) +w (t);
the state update is:
x (t+1) =x (t+1) | (t) +k (t+1) [ Z (t+1) -X (t+1) | (t) ]; k (t+1) is Kalman gain;
the covariance matrix is updated as: p (t+1) = [1-K (t+1) ] P (t+1) | (t);
the effective values after the Kalman filtering unit is discussed to filter and reduce noise are as follows:
w '(t) is output noise after noise reduction by the Kalman filtering unit, and W' (t) < W (t); the noise intensity contained in the effective value is further reduced;
s5: the output signal processing unit calculates the amplitude of the acousto-optic signal by addition according to the result of Kalman filtering noise reduction, and further calculates the concentration of the acousto-optic cell gas; the relationship between photoacoustic signal and gas concentration is: u (u) λ ＝aσ λ I λ C cell ；
Wherein u is λ For the intensity of the photoacoustic signal excited in the photoacoustic cell, a is the proportionality coefficient, σ λ Is the absorption coefficient of the gas at wavelength λ; i λ Is the intensity of the incident light at wavelength λ; c (C) cell Is the cell constant of the photoacoustic cell; the excitation light is monochromatic laser or infrared light, and sigma is different according to the change of gas concentration λ And will follow the change.
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