Phase generated carrier demodulation method based on two-parameter estimation

Abstract

The invention provides a phase generated carrier demodulation method based on two-parameter estimation. The method comprises the following steps of: firstly, realizing estimation of a C value by extracting an amplitude ratio of a carrier frequency multiplication component in an interference signal frequency spectrum and combining a Bessel function characteristic; then, carrying out operation processing by utilizing a first frequency multiplication signal and a second frequency multiplication signal to extract carrier phase delay theta c; and finally, eliminating the influence through dynamic phase compensation. According to the demodulation method provided by the invention, the nonlinear drift of the modulation depth parameter C and the synchronous estimation and compensation of the carrier phase disturbance signal theta c can be realized, the cross interference error in the traditional demodulation system is effectively inhibited, the phase demodulation robustness is remarkably improved, and the harmonic nonlinear distortion is effectively inhibited.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of interferometric fiber sensing, in particular to a phase generated carrier demodulation method based on double parameter estimation. BACKGROUND

[0002] In the field of interferometric fiber sensing, the phase generated carrier (PGC) demodulation technology as a classical phase detection method has been applied to the extraction of phase information of the output signal of the fiber interferometer for a long time. The traditional PGC algorithm injects a high-frequency carrier signal into the sensing system, and realizes phase demodulation by using carrier modulation combined with quadrature demodulation.

[0003] However, the traditional phase generated carrier demodulation algorithm has the following inherent defects: firstly, the carrier modulation depth is nonlinearly coupled with the demodulation result, which causes the phase demodulation accuracy to be significantly restricted by the modulation coefficient drift; secondly, the harmonic interference suppression mechanism is imperfect, and second-order harmonic distortion is easily generated in a strong noise environment; and thirdly, the dynamic range and sensitivity are mutually restricted, and it is difficult to balance the high-frequency signal response and weak signal detection requirements. For example, the traditional differential cross-multiplication (PGC-DCM) algorithm is sensitive to the fluctuation of the modulation depth C value, and the dynamic range is limited due to the need for complex integral circuits in hardware implementation. The PGC-Arctan-DSM algorithm introduces a differential self-multiplication operation on the basis of the traditional arctangent demodulation, and eliminates the light intensity disturbance by self-multiplication and ratio operation of the two quadrature components, which to some extent makes up for the defects of the traditional algorithm that is disturbed by the C value and has a limited harmonic suppression ability for large amplitude signals. However, the PGC-Arctan-DSM algorithm needs to strictly match the reference signal phase, and the harmonic suppression ability for large amplitude signals is limited. c The PGC single differential division algorithm proposed in the document “An Improved PGC Demodulation Algorithm Based on Fiber Laser Hydrophone” is not robust to carrier phase delay, and the linearity of the demodulation result is limited by the high-order approximation condition of the Bessel function. In actual application, the modulation depth C value drift and the carrier phase delay θ c coupling, and the dynamic range is limited, which makes it difficult to meet the high-precision detection requirements in complex scenarios such as deep-sea high pressure and multi-channel multiplexing. SUMMARY

[0004] The present application proposes a phase generated carrier demodulation method based on double parameter estimation to solve the technical defects of the coupling between the modulation depth parameter C drift and the carrier phase delay θ c The present application aims to realize the synchronous estimation and compensation of the nonlinear drift of the modulation depth parameter C and the carrier phase disturbance signal by constructing a dynamic cooperative compensation mechanism, effectively suppress the cross interference error in the traditional demodulation system, significantly improve the robustness of the phase demodulation, and effectively suppress the harmonic nonlinear distortion.

[0005] The application is realized by the following technical scheme, the application provides a phase generated carrier demodulation method based on double parameter estimation, the method comprises:

[0006] Firstly, the amplitude ratio of carrier frequency components in the frequency spectrum of the interference signal output by the fiber interferometer is extracted, and the estimation of C value is realized by combining the characteristics of Bessel function;

[0007] Then, the carrier phase delay θ is extracted by using the operation processing of the first and second frequency components. c ;

[0008] Finally, the influence is eliminated by dynamic phase compensation.

[0009] Further, under the phase generated carrier PGC external modulation mode, the input interference signal is:

[0010]

[0011] Wherein, A = I1 + I2 and is a modulation term, C is the carrier amplitude, also known as the modulation depth, ω o is the modulation angular frequency; contains the measured signal and environmental noise, which is a signal in the form of sine and cosine D represents the amplitude of the measured signal, ω s is the angular frequency of the measured signal, represents the phase containing the influence of external noise; is the measured signal; θ c represents the phase delay.

[0012] Further, the modulated interference signal is rewritten as:

[0013]

[0014]

[0015] Wherein, J k (C) is the kth order Bessel function of the first kind, J even is the even order component of Bessel function, J odd is the odd order component of Bessel function.

[0016] Further, after the interference signal V is mixed with the reference signal with frequency ω0 and amplitude H and the reference signal with frequency 2ω0 and amplitude H respectively, and then respectively passes through the low pass filter LPF, two mutually orthogonal cosine terms and sine terms are obtained, and the signal is expressed by the following expression:

[0017]

[0018] The signal expression obtained by dividing V1 and V2 is:

[0019]

[0020] Further, the modulation depth estimation C value is compensated for parameters, specifically: in the case of a given C value, the frequency amplitude ratio at even multiple carrier frequencies 2k1, 2k2 is The frequency amplitude ratio at odd multiple carrier frequencies 2k3-1, 2k4-1 is The ratio at respective internal frequencies is a constant, and by the characteristic that the odd and even frequency amplitude ratios are constants, the C estimation value is obtained, and then the C estimation value is compensated for parameters.

[0021] Further, a pair of parameter estimation functions is set as:

[0022]

[0023] Where F f＝x is the spectrum amplitude of the interference signal at a frequency of x, represents the estimation value of the modulation depth C value, and the modulation depth C is also called the carrier amplitude;

[0024] The frequency amplitude ratio function curve and The frequency amplitude ratio function and are non-monotonic functions, and according to the known actual spectrum amplitude F f＝x , E1 and E2 are calculated, and the estimation value of the corresponding modulation depth C value is obtained by comparing the E1 and E2 values with the frequency amplitude ratio function curve

[0025] Further, the modulation depth estimation value of the signal is pre-compensated for parameters.

[0026] Further, the estimation value θ c of the carrier phase delay is compensated for parameters, specifically: the interference signal V with a phase delay is mixed with a sine signal of the modulation frequency base frequency, and after filtering, the quadrature signal expression is:

[0027]

[0028] The above two signals are differentiated to obtain the signal expression:

[0029]

[0030] ​Square P1 and P1', square Q1 and Q1', and get the signal expression:

[0031]

[0032]

[0033] Finally, the estimated value of the carrier phase delay is:

[0034] Where sign(x) is a sign function, when x>0, sign(x)=1; when x<0, sign(x)=-1; when x=0, sign(x)=0; the expression exists The term is to keep the estimated θ c The same as The same as

[0035] Further, the carrier phase delay of the signal The estimated value θ c Pre-compensate the parameters.

[0036] Further, the carrier phase delay of the estimated value θ c The parameter is corrected; specifically, V3 is subjected to an inverse tangent operation to obtain the final signal θ(t):

[0037]

[0038] Wherein, In fact, θ(t) contains And a correction term:

[0039] V 修正 Is subjected to a tangent transformation:

[0040]

[0041] The final signal expression θ(t) obtained after demodulation is:

[0042]

[0043] The application also provides an electronic device, including a memory and a processor, the memory stores a computer program, and the processor realizes the steps of the phase generation carrier demodulation method based on double parameter estimation when executing the computer program.

[0044] The application also provides a computer readable storage medium for storing computer instructions, and the computer instructions realize the steps of the phase generation carrier demodulation method based on double parameter estimation when executed by a processor.

[0045] Advantages of the present application:

[0046] 1. The method of the present application realizes accurate estimation and compensation of the modulation depth C value and carrier phase delay θ c ;

[0047] 2. Under the complex condition of C value and carrier phase delay θ c , the method of the present application can still maintain high-precision demodulation, verifying its strong robustness. BRIEF DESCRIPTION OF DRAWINGS

[0048] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only a part of the present application, and other drawings can be obtained by those skilled in the art without any creative effort on the basis of the provided drawings.

[0049] Figure 1 The schematic diagram of the phase generation carrier demodulation method based on double parameter estimation according to the present application.

[0050] Figure 2 The schematic diagram of the quadrature signal before parameter compensation in the demodulation method.

[0051] Figure 3 The schematic diagram of the quadrature signal after parameter compensation in the demodulation method.

[0052] Figure 4 The graph of SNR index changing with C value under different demodulation algorithms.

[0053] Figure 5 The graph of SNR index changing with θ c value under different demodulation algorithms. DETAILED DESCRIPTION

[0054] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without any creative effort belong to the protection scope of the present application.

[0055] In combination with Figures 1-5The application provides a phase-generated carrier demodulation method based on double-parameter estimation, which comprises the following steps: firstly, estimating the value of C by extracting the amplitude ratio of the carrier frequency component in the frequency spectrum of the interference signal output by the fiber interferometer and combining the characteristics of the Bessel function; then extracting the carrier phase delay θ by using the operation processing of the first and second frequency components; and finally, eliminating the influence by dynamic phase compensation. c

[0056] Specifically, under the phase-generated carrier PGC external modulation mode, the input interference signal is as follows:

[0057]

[0058] wherein A=I1+I2 and is a modulation term, C is the carrier amplitude, ω o is the modulation angular frequency; contains the to-be-detected signal and the environmental noise influence, and is a signal in the form of sine and cosine D represents the amplitude of the to-be-detected signal, ω s is the angular frequency of the to-be-detected signal, represents the phase containing the external influence of the noise; is the to-be-detected signal; and θ c represents the phase delay.

[0059] After the modulation of the interference signal, the interference signal is rewritten by the Bessel function expansion as follows:

[0060]

[0061] wherein J k (C) is the k-th order first-type Bessel function, J even is the even-order component of the Bessel function, and J odd is the odd-order component of the Bessel function.

[0062] After the interference signal V is mixed with the reference signal with the frequency ω0 and the amplitude H and the reference signal with the frequency 2ω0 and the amplitude H, respectively, and then respectively passes through the low-pass filter LPF, two mutually orthogonal cosine terms and sine terms are obtained, and the signal is expressed by the following expression:

[0063]

[0064] The division operation is performed on V1 and V2, and the signal expression obtained is as follows:

[0065]

[0066] ​In actuality, various factors can cause the C value to drift or jitter, causing nonlinear distortion of the demodulation signal; meanwhile, when the carrier phase delay θ c The demodulation result of the signal can also be distorted to different degrees, so in the present application, both factors are considered comprehensively, and both are eliminated and compensated for before the arctangent operation.

[0067] The modulation depth estimation C value is parameter compensated, specifically: in the case of a given C value, the frequency amplitude ratio at even multiple carrier frequencies 2k1, 2k2 is The frequency amplitude ratio at odd multiple carrier frequencies 2k3-1, 2k4-1 is The ratio at respective internal frequencies is a constant, and by the characteristic that the odd and even frequency amplitude ratios are constants, the C estimation value is obtained, and then the C estimation value is parameter compensated.

[0068] Because the frequency amplitude ratio function and are non-monotonic functions, one function value can correspond to multiple C value solutions, in order to solve this problem, the present application sets a pair of parameter estimation functions as:

[0069]

[0070] Where F f＝x is the spectrum amplitude of the interference signal at a frequency of x, represents the estimation value of the modulation depth C value, and the modulation depth C is also called the carrier amplitude;

[0071] The frequency amplitude ratio function curve and The frequency amplitude ratio function and are non-monotonic functions, according to the known actual spectrum amplitude F f＝x , E1 and E2 are calculated, and the estimation value of the corresponding modulation depth C value is obtained by comparing the E1 and E2 values with the frequency amplitude ratio function curve

[0072] The modulation depth estimation value of the signal is further parameter compensated in advance.

[0073] The estimation value of the carrier phase delay θ c is parameter compensated, the C value is estimated by the modulation depth estimation algorithm and eliminated, and before the arctangent operation, the carrier phase delay θ c is also estimated and offset. Specifically: the interference signal V with a phase delay is mixed with the sine and cosine signals of the modulation frequency base frequency, and after filtering, the quadrature signal expression is:​​

[0074]

[0075] The signal expression is obtained by differentiating the above two signals:

[0076] The signal expression is obtained by squaring P1 and P1' respectively and squaring Q1 and Q1' respectively:

[0077]

[0078]

[0079] The estimated value of the carrier phase delay is finally obtained as:

[0080] Where sign(x) is a sign function, sign(x) = 1 when x > 0, sign(x) = -1 when x < 0, and sign(x) = 0 when x = 0. The expression has

[0081] The term is to keep the estimated θ c The same as ;

[0082] The estimated value of the carrier phase delay of the signal is further pre-compensated for parameters. c The estimated value of the carrier phase delay of the signal

[0083] The modulation depth estimation value C and the estimated value of the carrier phase delay θ c are modified for parameters; specifically, V3 is arctangent operated to obtain the final signal θ(t):

[0084]

[0085] Where, In fact, θ(t) contains and a correction term:

[0086] V 修正 is tangent transformed:

[0087]

[0088] The final signal expression θ(t) obtained after demodulation is:

[0089]

[0090] It can be seen that the expression contains linear and nonlinear terms, where, The signal to be measured With environmental noise D represents the amplitude of the signal to be measured, ω s is the angular frequency of the signal to be measured. After high-pass filtering (HPF) processing, the signal to be measured The demodulation of the signal is realized.

[0091] Embodiment

[0092] This embodiment is based on the phase modulation model of Michelson interferometric fiber hydrophone, and a phase generation carrier demodulation method based on double parameter estimation is proposed. Specifically, the following steps are included:

[0093] Step 1, input the sound signal V. AD sampling frequency F s = 125 MHz, modulation frequency f o = 5 MHz, modulation depth C = 2.63 rad, signal to be measured frequency f s = 1 kHz, amplitude D = 3 rad, initial phase Add-30dB Gaussian white noise as environmental noise.

[0094] Step 2, the modulated interference signal is expanded by Bessel function,

[0095]

[0096] Step 3, after mixing the interference signal V with the reference signal with frequency ω0 and 2ω0 respectively, and then passing through low-pass filter (LPF), two mutually orthogonal cosine terms and sine terms are obtained. Divide V1 and V2 to obtain the signal expression:

[0097]

[0098] Step 4, modulation depth estimation C value parameter compensation. In the modulation depth estimation model based on Bessel function expansion, when there is no phase delay, set the spectral amplitude of the interference signal at different frequency positions: The estimated functions E1 and E2 are calculated as 1.923 and 5.310 respectively. Comparing the estimated function values with the estimated function curve and The estimated value of the modulation depth C value can be obtained is 2.6300, is 2.6299, the deviation of the two estimated values from the actual value 2.63 is extremely small, and this method theoretically realizes the estimation of the C value.

[0099] Further, the modulation depth estimation value of the signal is pre-compensated.

[0100] Step 5, estimation value θ of carrier phase delay c is pre-compensated. Other simulation parameters remain unchanged, and the C value is set to the optimal value 2.63 rad, and the θ C value is 0.2π rad.

[0101] Further, the interference signal V with the phase delay is mixed with the sine and cosine signals of the modulation frequency base frequency, and the quadrature signal expression after filtering is:

[0102]

[0103] Further, the two signals are differentiated to obtain the signal expression:

[0104]

[0105] Further, the square sum of P1 and P1' and the square sum of Q1 and Q1' are obtained, respectively, to obtain the signal expression:

[0106]

[0107] Further, the carrier phase delay estimation in the interference signal is obtained through the sliding average processing, and the value is close to the carrier phase delay 0.2π rad set in the simulation.

[0108] Step 6, estimation value θ of modulation depth estimation C value and carrier phase delay c is pre-compensated, and the quadrature signal diagrams before and after the parameter compensation are shown in Figure 2 and Figure 3 After the parameter compensation, the relative error between the estimation value of the arctangent operation result and the actual value is less than 0.2%, which is extremely small and can be ignored. The demodulation is almost not affected by the change of the final demodulation θ c value, and the result is still the sine wave form of the input waveform, and the demodulation waveform has not been obviously distorted, and the to-be-measured signal is successfully restored.

[0109] In order to highlight the demodulation advantages of the method of the application, the demodulation SNR of the method of the application is compared and verified with the demodulation SNR of the traditional demodulation algorithm and two kinds of mainstream improved algorithms. It can be known from Figure 4 that when the C value changes, the SNR of the demodulation of the method of the application is between 50 and 60 dB, and the average SNR is about 55 dB, which is higher than the SNR value of the demodulation results of the other three algorithms; when the C value is set to 2.63 rad, the θ c ​​When the value of C fluctuates in the range of 0-2π, the demodulation results of the four algorithms are compared as shown in the following table: Figure 5 As shown in the table, θ c When the value of C changes, the SNR curves of the demodulation of the four algorithms all appear "dip" at the phases of 0.5π and 1.5π, and the SNR of the method of the application is between 60-70dB except for the special phase, which is higher than that of the other three demodulation algorithms, indicating that the demodulation method proposed in the application is superior to the traditional demodulation algorithm and the two mainstream improved algorithms, and the defects of the traditional demodulation algorithm affected by the value of C and θ c are improved.

[0110] The application further provides an electronic device comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the phase generation carrier demodulation method based on double parameter estimation when executing the computer program.

[0111] The application further provides a computer readable storage medium for storing computer instructions, wherein the computer instructions implement the steps of the phase generation carrier demodulation method based on double parameter estimation when executed by a processor.

[0112] The memory in the embodiments of the present application can be a volatile memory or a nonvolatile memory, or can include both volatile and nonvolatile memory. Among them, the nonvolatile memory can be a read only memory (ROM), a programmable ROM (PROM), an erasable programmable ROM (EPROM), an electrically EPROM (EEPROM), or a flash memory. The volatile memory can be a random access memory (RAM) used as an external cache. By way of example, and not limitation, many forms of RAM can be used, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous dynamic RAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchlink DRAM (SLDRAM), and direct rambus RAM (DRRAM). It is noted that the memory of the methods described herein is intended to include, but not be limited to, these and any other suitable types of memory.

[0113] In the above embodiments, all or part of the methods can be implemented by software, hardware, firmware, or any combination thereof. When implemented by software, all or part of the methods can be implemented in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of the present application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The computer instructions can be stored in a computer-readable storage medium or transferred from one computer-readable storage medium to another computer-readable storage medium, for example, the computer instructions can be transferred from one website, computer, server, or data center to another website, computer, server, or data center through wired (such as coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (such as infrared, wireless, microwave, etc.) manner. The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device such as a server, data center, etc. that includes one or more available media sets. The available media can be magnetic media (such as floppy disk, hard disk, magnetic tape), optical media (such as high-density digital video disc (DVD)), or semiconductor media (such as solid state disc (SSD)), etc.

[0114] In the implementation process, each step of the above method can be completed by integrated logic circuit of hardware in the processor or instruction in the form of software. The steps of the method disclosed in the embodiments of the present application can be directly embodied as hardware processor execution, or executed by combination of hardware and software modules in the processor. The software module can be located in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, register, and other mature storage media in the art. The storage medium is located in the memory, and the processor reads the information in the memory and combines the hardware to complete the steps of the above method. To avoid repetition, it will not be described in detail here.

[0115] It should be noted that the processor in the embodiments of the present application can be an integrated circuit chip with a signal processing capability. In the implementation process, each step of the method embodiments can be completed by the integrated logic circuit of hardware in the processor or the instructions in the form of software. The processor mentioned above can be a general processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components. The disclosed methods, steps and logic block diagrams in the embodiments of the present application can be implemented or executed. The general processor can be a microprocessor or the processor can also be any conventional processor. The steps of the method disclosed in combination with the embodiments of the present application can be directly embodied as a hardware code processor for execution, or a combination of hardware and software modules in the code processor for execution. The software module can be located in a random access memory, a flash memory, a read only memory, a programmable read only memory or an electrically erasable programmable memory, a register or other mature storage medium in the art. The storage medium is located in the memory, and the processor reads the information in the memory, and combines the hardware to complete the steps of the above method.

[0116] The above describes in detail the phase generation carrier demodulation method based on double parameter estimation. The principle and implementation of the present application are described by using specific examples. The above embodiment is only used to help understand the method of the present application and its core idea. For those skilled in the art, according to the idea of the present application, the specific implementation and application range will be changed. In summary, the content of the specification should not be understood as a limitation of the present application.

Claims

1. A phase generation carrier demodulation method based on two-parameter estimation, characterized in that, The method includes: First, the C value is estimated by extracting the amplitude ratio of the carrier frequency harmonic component in the spectrum of the interference signal output by the fiber optic interferometer and combining it with the characteristics of the Bessel function. Then, the carrier phase delay θ is extracted using first and second harmonic frequency harmonic signal processing. c ; Finally, its effects are eliminated through dynamic phase compensation.

2. The method according to claim 1, characterized in that, The input interference signal under the PGC external modulation mode with added phase-generated carrier: Where A = I1 + I2 and For the modulation term, C is the carrier amplitude, also known as the modulation depth, and ωo is the modulation angular frequency; Including the influence of the signal under test and environmental noise, it is a signal in sine and cosine form. D represents the amplitude of the signal to be measured, ω s The angular frequency of the signal to be measured. This is represented as the phase, which includes external noise and influences. θ is the signal to be measured. c This indicates a phase delay.

3. The method according to claim 2, characterized in that, The modulated interference signal, expanded using Bessel functions, is rewritten as follows: Among them, J k (C) is the k-th order Bessel function of the first kind, J even J is the even-order component of the Bessel function. odd For the odd-order components of the Bessel function.

4. The method according to claim 3, characterized in that, After mixing the interference signal V with reference signals of frequency ω0 and amplitude H and frequency 2ω0 and amplitude H respectively, and then passing it through a low-pass filter LPF, two mutually orthogonal cosine and sine terms are obtained. The signal is expressed by the following expression: The signal expression obtained by dividing V1 and V2 is as follows:

5. The method according to claim 4, characterized in that, The modulation depth estimation C value is used for parameter compensation, specifically: given the C value, the frequency amplitude ratio at even-numbered carrier frequencies 2k1 and 2k2 is... The frequency amplitude ratio at odd multiples of carrier frequencies 2k3-1 and 2k4-1 is The ratios to their respective internal frequencies are all constants. Using the characteristic that the amplitude ratios of odd and even octave frequencies are constant, an estimated value of C is obtained. Then, the... Perform parameter compensation for the C estimate.

6. The method according to claim 5, characterized in that, Set a pair of parameter estimation functions as follows: Where F f＝x Let x be the spectral amplitude of the interference signal at frequency x. This represents an estimated value of the modulation depth C, which is also known as the carrier amplitude. Plot the frequency-amplitude ratio function curve and Frequency-amplitude ratio function and It is a non-monotonic function, based on the known actual spectral amplitude F f＝x E1 and E2 are calculated, and by comparing the values ​​of E1 and E2 with the frequency amplitude ratio function curve, the estimated value of the corresponding modulation depth C is obtained. Further analysis of the signal modulation depth estimate Perform parameter compensation in advance.

7. The method according to claim 6, characterized in that, The estimated value of carrier phase delay θ c Parameter compensation is performed, specifically: the interference signal V with phase delay is mixed with the sine and cosine signals of the fundamental frequency modulation frequency, and after filtering, the orthogonal signal expression is obtained as follows: Differentiating the two signals yields the signal expression: By summing the squares of P1P′1 and Q1Q′1 respectively, we obtain the signal expression: The final estimated value of the carrier phase delay is: Where sign(x) is the sign function, when x>0, sign(x)=1; when x<0, sign(x)=-1; When x = 0, sign(x) = 0; this expression exists. The term is to preserve the estimated θ c Positive and negative values same; Further analysis of the signal The estimated value of the carrier phase delay θ c Perform parameter compensation in advance.

8. The method according to claim 7, characterized in that, The modulation depth estimation value C and the estimated carrier phase delay θ c Parameter correction is performed; specifically, the arctangent of V3 is used to obtain the final signal θ(t): in, In fact, θ(t) contains Sum with a correction term: For V 修正 Perform tangent transformation: The final demodulated signal expression θ(t) is:

9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1-8.

10. A computer-readable storage medium for storing computer instructions, characterized in that, When the computer instructions are executed by the processor, they implement the steps of the method according to any one of claims 1-8.

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