Gain Kalman filtering denoising method and system for Brillouin optical time domain reflection signals

Abstract

The invention relates to the technical field of distributed optical fiber sensing, and provides a gain Kalman filtering denoising method and system for a Brillouin optical time domain reflection signal, and the method comprises the steps: initializing Kalman filter parameters which comprise a state transition matrix, a control matrix, an observation matrix, a process noise variance and a priori estimation covariance; performing prior state estimation on the Brillouin optical time domain reflection signal according to the state transition matrix, the control matrix and the control input quantity, and calculating a prior estimation covariance according to the state transition matrix and the process noise variance; dynamically adjusting the observation noise variance based on the dynamic relationship between the observation noise variance and the Kalman gain in combination with the original noise power and the Brillouin scattering light signal power; updating the Kalman gain by using the priori estimation covariance, the observation matrix and the dynamically adjusted observation noise variance, and updating the system state estimation and error covariance by using the Kalman gain and the observation variable; and outputting the filtered and denoised Brillouin optical time domain reflection signal.

Description

Technical Field

[0001] This invention relates to the field of distributed optical fiber sensing technology, and in particular to a gain Kalman filtering denoising method and system for Brillouin optical time-domain reflectometry signals. Background Technology

[0002] Brillouin optical time-domain reflectometry (BOTDR) distributed fiber optic sensing systems have demonstrated significant application value in fields such as structural health monitoring due to their high sensitivity and distributed dynamic measurement capabilities. However, BOTDR signals are highly susceptible to multiple interferences during actual detection processes, including external environmental disturbances and inherent noise from hardware devices, such as laser frequency shift / phase noise and attenuation noise caused by fiber refractive index inhomogeneity. This leads to a significant reduction in the system's signal-to-noise ratio, severely impacting the accuracy of subsequent event detection and identification. To improve signal quality, existing technologies mainly employ two types of denoising schemes: one is the multiple superposition averaging method. Although this method can suppress random noise through statistical averaging, it suffers from inherent drawbacks such as low efficiency, poor real-time performance, and saturation of denoising effect after the number of superpositions exceeds a threshold. The other is the traditional Kalman filter algorithm, which uses a fixed-gain filtering mechanism. While suitable for linear time-invariant systems, it lacks adaptive adjustment capability when facing strong nonlinear noise generated during BOTDR dynamic measurements. It struggles to effectively filter out complex noise components strongly coupled with the signal, resulting in insufficient smoothness and a tendency to lose key characteristic information of vibration events. Therefore, there is an urgent need for an efficient denoising method that can dynamically adapt to the nonlinear noise characteristics of the BOTDR system and significantly improve the signal-to-noise ratio while preserving the effective information of the signal. Summary of the Invention

[0003] To address the aforementioned shortcomings, the present invention aims to propose a gain Kalman filter denoising method and system for Brillouin optical time-domain reflectometry signals. The goal is to achieve adaptive optimization of the filter gain by constructing a dynamic adjustment relationship between the observation noise variance and the Kalman gain, thereby effectively filtering out nonlinear noise in the signal, significantly improving the signal-to-noise ratio and smoothness, and enhancing the denoising effect and the system's dynamic adaptability.

[0004] To achieve this objective, the present invention adopts the following technical solution: The gain-Kalman filtering denoising method for Brillouin optical time-domain reflectometry signals includes the following steps: S1: Initialize the Kalman filter parameters, including the state transition matrix, control matrix, observation matrix, process noise variance, and prior estimate covariance; S2: Based on the state transition matrix, the control matrix, and the control input, perform prior state estimation on the Brillouin optical time-domain reflection signal, and calculate the prior estimation covariance based on the state transition matrix and the process noise variance; S3: Based on the dynamic relationship between observation noise variance and Kalman gain, combined with the original noise power and Brillouin scattered light signal power, the observation noise variance is dynamically adjusted. S4: Update the Kalman gain using the prior estimated covariance, observation matrix, and the dynamically adjusted observation noise variance; then update the system state estimate and error covariance using the Kalman gain and observation variables. S5: Output the filtered and denoised Brillouin optical time-domain reflectometry signal.

[0005] Preferably, the initialization operation in step S1 is performed based on the noise level of the Brillouin optical time-domain reflectometry signal.

[0006] Preferably, step S2 includes: Prior state estimation is performed on the Brillouin optical time-domain reflection signal to obtain the prior state estimate at the current time. The following relation is satisfied: ; in, Represents the state transition matrix. This represents the prior state estimate from the previous time step. Represents the control matrix. Indicates the control input quantity; Calculate the prior estimate of covariance at the current time. The following relation is satisfied: ; in, Represents the state transition matrix, This represents the prior estimate error covariance at the previous time step. This represents the variance of process noise.

[0007] Preferably, in step S3, dynamically adjusting the observation noise variance includes calculating the observation noise variance at the current time. The following relation is satisfied: ; in, Indicates the original noise power level. Indicates Kalman gain, Indicates the power level of the Brillouin scattered light signal. Represents the observation matrix. It represents the change in state.

[0008] Preferably, step S4 includes: Update Kalman gain The following relation is satisfied: ; in, This represents the prior estimate of covariance. Represents the observation matrix. This represents the dynamically adjusted variance of the observation noise. Updating the system state estimate using Kalman gain and observed variables The following relation is satisfied: ; in, This represents the prior state estimate. Indicates Kalman gain, Represents the observed variable. Represents the observation matrix; Update error covariance The following relation is satisfied: ; in, Represents the identity matrix. Represents the observation matrix. This represents the prior estimate of the covariance.

[0009] A gain-Kalman filter denoising system for Brillouin optical time-domain reflectometry signals includes: The initialization module is used to initialize the Kalman filter parameters, including the state transition matrix, control matrix, observation matrix, process noise variance, and prior estimate covariance. The signal prediction module is used to perform prior state estimation on the Brillouin optical time-domain reflection signal based on the state transition matrix, the control matrix and the control input, and to calculate the prior estimation covariance based on the state transition matrix and the process noise variance. The noise adjustment module is used to dynamically adjust the observation noise variance based on the dynamic relationship between the observation noise variance and the Kalman gain, combined with the original noise power and the Brillouin scattered light signal power. The state update module is used to update the Kalman gain using the prior estimated covariance, the observation matrix, and the dynamically adjusted observation noise variance, and then use the Kalman gain and the observation variables to update the system state estimate and error covariance. The signal output module is used to output the filtered and denoised Brillouin optical time-domain reflectometry signal.

[0010] Preferably, in the initialization module, the initialization operation is performed based on the noise level of the Brillouin optical time-domain reflectometry signal.

[0011] Preferably, the signal prediction module is further used for: Prior state estimation is performed on the Brillouin optical time-domain reflection signal to obtain the prior state estimate at the current time. The following relation is satisfied: ; in, Represents the state transition matrix. This represents the prior state estimate from the previous time step. Represents the control matrix. Indicates the control input quantity; Calculate the prior estimate of covariance at the current time. The following relation is satisfied: ; in, Represents the state transition matrix, This represents the prior estimate error covariance at the previous time step. This represents the variance of process noise.

[0012] Preferably, in the noise adjustment module, dynamically adjusting the observation noise variance includes calculating the observation noise variance at the current moment. The following relation is satisfied: ; in, Indicates the original noise power level. Indicates Kalman gain, Indicates the power level of the Brillouin scattered light signal. Represents the observation matrix. It represents the change in state.

[0013] Preferably, the state update module includes: Update Kalman gain The following relation is satisfied: ; in, This represents the prior estimate of covariance. Represents the observation matrix. This represents the dynamically adjusted variance of the observation noise. Updating the system state estimate using Kalman gain and observed variables The following relation is satisfied: ; in, This represents the prior state estimate. Indicates Kalman gain, Represents the observed variable. Represents the observation matrix; Update error covariance The following relation is satisfied: ; in, Represents the identity matrix. Indicates Kalman gain, Represents the observation matrix. This represents the prior estimate of the covariance.

[0014] One of the above technical solutions has the following advantages or beneficial effects: This invention initializes the core parameters of the Kalman filter based on the signal-noise characteristics, establishing a benchmark for subsequent adaptive adjustment. Then, it performs prior state estimation and covariance prediction to construct a system state evolution framework. Furthermore, it introduces real-time feedback of the original noise power and the Brillouin scattering signal power to dynamically adjust the observation noise variance, making it no longer a fixed constant but adaptively changing with the local characteristics of the signal, thereby driving the Kalman gain to optimize and adjust accordingly. Based on this, the Kalman gain is recalculated using the updated observation noise variance, and the system state estimate is corrected using the observation residuals, synchronously updating the error covariance for closed-loop feedback to the next prediction cycle. Finally, it outputs a denoised signal optimized through multiple iterations. In summary, the above process enables the filter to match the nonlinear distribution characteristics of noise in the Brillouin optical time-domain reflection signal in real time. It automatically enhances the gain to suppress high-frequency noise when abrupt events occur, while maintaining stability and smoothness in the steady segment. This effectively avoids under-filtering or over-smoothing problems caused by fixed gain, and significantly enhances the robustness to complex environmental noise and the dynamic adaptability of the system. It can achieve effective filtering of nonlinear noise and comprehensive improvement of overall signal quality while preserving the effective vibration information of the signal. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0016] Figure 1 This is a flowchart of the gain Kalman filtering denoising method for Brillouin optical time-domain reflectometry signals provided in this embodiment of the invention; Figure 2 This is a schematic diagram of the gain Kalman filter denoising system for Brillouin optical time-domain reflectometry signals provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of the Kalman filtering implementation process provided in an embodiment of the present invention; Figure 4 This is a schematic diagram of the denoising results of a traditional Brillouin optical time-domain reflectometry signal using a fixed-gain Kalman filter. Figure 5This is a schematic diagram of the denoising result of the gain Kalman filter denoising method for Brillouin optical time-domain reflectometry provided in this embodiment of the invention; Figure 6 This is a schematic diagram comparing the noise reduction performance evaluation indicators under different noise conditions provided in the embodiments of the present invention. Detailed Implementation

[0017] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0018] In this invention, the terms "comprising," "including," or any other variations thereof are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0019] Gain Kalman filtering denoising method for Brillouin optical time-domain reflectometry signals, such as Figure 1 As shown, a preferred embodiment of the present invention includes the following steps: S1: Initialize the Kalman filter parameters, including the state transition matrix, control matrix, observation matrix, process noise variance, and prior estimate covariance; It should be noted that the state transition matrix is ​​a mathematical matrix describing the evolution of the system state at different times. In the Brillouin optical time-domain reflectometry system, it is used to characterize the dynamic transmission characteristics of the fiber optic sensing signal during its spatiotemporal propagation. The control matrix is ​​a transformation matrix that maps the control input to the state space, used to model the influence of external stimuli on the system state. The observation matrix is ​​a transformation matrix connecting the real state and the observed data. In the BOTDR system, it is reflected as the photoelectric conversion relationship from the Brillouin scattered light signal to the actual detected electrical signal. The process noise variance is a statistical parameter that quantifies the intensity of random disturbances in the dynamic process of the system, reflecting the state uncertainty caused by laser phase noise, ambient temperature fluctuations, etc. The prior estimation covariance is an error metric matrix that characterizes the degree of deviation between the estimated state value and the true value. Its initial value setting directly affects the convergence speed and stability of the filter. These parameters constitute the core framework of the Kalman filter algorithm. Their physical meaning and specific values ​​directly determine the accuracy and dynamic response capability of BOTDR signal denoising. The Kalman filter implementation process is as follows: Figure 3 As shown.

[0020] S2: Based on the state transition matrix, the control matrix, and the control input, perform prior state estimation on the Brillouin optical time-domain reflection signal, and calculate the prior estimation covariance based on the state transition matrix and the process noise variance; It should be noted that prior state estimation is an intermediate calculation result used to predict the current state by combining the posterior estimate from the previous moment with the system dynamic model. Essentially, it involves time-recursion of the Brillouin optical time-domain reflection signal distribution characteristics along the fiber, based on state transition laws. The control input is a known excitation signal characterizing the influence of external forces on the system; in a BOTDR system, this might correspond to temperature control commands or strain loading signals. The prior estimation covariance calculation propagates the estimation error from the previous moment through matrix operations and adds the influence of current process noise to obtain a measure of uncertainty in the prediction stage. The calculation result directly reflects the degree of dependence on the measured value in state prediction. This step achieves time-domain prediction of the signal through state equations, providing a benchmark for subsequent measurement updates.

[0021] Understandably, the prior estimation step simulates the physical evolution of the signal from time k-1 to time k. In a Brillouin optical time-domain reflectometry system, as the light pulse propagates in the optical fiber, the Brillouin frequency shift at each spatial point is affected by the thermal conduction and mechanical coupling effects of the strain field at adjacent points, exhibiting spatiotemporal correlation. The state transition matrix is ​​a mathematical tool for quantifying this spatiotemporal correlation. Through matrix operations, the signal distribution characteristics of the previous time step can be mapped to the current time step, forming a reasonable state prediction. Simultaneously, the inclusion of process noise variance ensures that the prediction covariance accurately reflects the decrease in prediction reliability caused by random environmental disturbances, preventing the filter from over-relying on model predictions and ignoring actual observation information, thus achieving a balance between model accuracy and environmental adaptability.

[0022] S3: Based on the dynamic relationship between observation noise variance and Kalman gain, combined with the original noise power and Brillouin scattered light signal power, the observation noise variance is dynamically adjusted. It should be noted that observation noise variance is a statistical measure describing the degree of deviation between sensor observations and the true state. In the BOTDR system, it reflects random errors introduced by the measurement link, such as electronic noise of the photodetector and quantization noise of analog-to-digital conversion. Kalman gain is a core adjustment factor that determines the strength of observation correction and the weight of model prediction reliability. The larger the value, the more the filter trusts the observation data, and the smaller the value, the more it trusts the model prediction. The raw noise power level is a statistical indicator of the background noise collected when no signal is applied, which can be obtained through dark current testing or calibration without light input. The Brillouin scattering light signal power level is the effective signal strength containing sensing information and is directly related to fiber strain and temperature changes. The state change quantity is the difference vector of state estimates between adjacent time steps, reflecting the degree of dynamic change of the signal.

[0023] Understandably, traditional Kalman filtering, due to its fixed observation noise variance, results in a essentially constant Kalman gain throughout the filtering process, making it unsuitable for adapting to the time-varying characteristics of nonlinear noise in BOTDR signals. When a sudden strain event occurs at a point in the fiber, the signal power abruptly changes, accompanied by strong nonlinear noise. The fixed gain, unable to provide immediate enhancement, is powerless to suppress the noise during this abrupt change. Conversely, in stable signal segments, the fixed gain may over-correct, leading to excessive smoothing. This step introduces signal power and state change variables to construct a dynamic noise variance, achieving real-time gain optimization. In summary: when signal power increases and state changes drastically, the formula... Increasing the term leads to an increase in the variance of the observation noise, which in turn suppresses the Kalman gain. To avoid excessive amplification of sudden noise; when the signal is stable, The noise variance is reduced, and the gain is moderately increased to enhance the denoising effect. This reverse adjustment mechanism forms a negative feedback closed loop, enabling the filter to automatically match the local signal-to-noise ratio characteristics of the signal.

[0024] S4: Update the Kalman gain using the prior estimated covariance, observation matrix, and the dynamically adjusted observation noise variance; then update the system state estimate and error covariance using the Kalman gain and observation variables. It should be noted that the observed variable is the raw, noisy signal obtained by the BOTDR system through photoelectric detection and data acquisition, including Brillouin frequency shift information and various interference noises; the error covariance is a matrix that quantifies the uncertainty of the state estimate, and its update process reflects the filter's self-evaluation and correction of its own estimation accuracy. Step S4 includes two core operations: Kalman gain update calculates the optimal weighting coefficient by comparing the prior estimation uncertainty with the observation uncertainty, and the dynamically adjusted observation noise variance gives the gain adaptive characteristics; state estimation update feeds back the observation residual (the difference between the actual observation and the prior estimate) to the state vector according to the Kalman gain ratio, realizing the approximation of the predicted value to the true value; and error covariance update uses the gain to shrink the prior covariance, reflecting the improvement in estimation accuracy after the introduction of observation information.

[0025] S5: Output the filtered and denoised Brillouin optical time-domain reflectometry signal.

[0026] It should be noted that the output denoised signal is the system state estimate obtained in step S4. This output signal has filtered out most of the nonlinear noise, retaining the signal abrupt changes caused by the actual stress or temperature events. The output format can be a digital signal sequence, waveform data file, or real-time display curve. This signal can be directly used for subsequent applications such as event localization, strain inversion, or temperature reconstruction. Output operations can be implemented using electronic communication methods such as memory writing, bus transmission, or interface transmission. After outputting the filtered and denoised Brillouin optical time-domain reflectometry signal, the following can be obtained: Figure 5 The denoising results shown are illustrated in the image. The denoising results corresponding to the traditional method are as follows: Figure 4 As shown, combined with Figure 4 , 5 From points 6 and 7, we can draw the following conclusions: A performance comparison between the traditional gain Kalman filter denoising effect and the dynamically adjusted gain Kalman filter denoising effect proposed in this invention shows that, with other parameters remaining constant, the dynamically adjusted gain Kalman filter denoising effect (i.e., ...) is significantly better. Figure 6 The improved effect) is better than the traditional fixed-gain Kalman filter for noise reduction. Figure 6 The original solution is better, with a higher signal-to-noise ratio, stronger noise immunity, smoother denoised signals, and can effectively denoise the nonlinear noise of the system.

[0027] Preferably, the initialization operation in step S1 is performed based on the noise level of the Brillouin optical time-domain reflectometry signal.

[0028] It should be noted that noise magnitude refers to the quantitative characterization of the interference intensity experienced by the Brillouin optical time-domain reflectometry signal during detection. It encompasses the statistical characteristics of various components, including environmental background noise, laser phase noise, photodetector electronic noise, and analog-to-digital conversion quantization noise, and is typically measured using metrics such as noise power spectral density, root mean square (RMS), or signal-to-noise ratio (SNR). This parameter directly affects the Kalman filter's initial assessment of system uncertainties and determines the baseline setting for the process noise variance and prior estimate covariance. If the noise magnitude is underestimated, the filter will over-rely on model predictions, leading to insufficient observation correction; if it is overestimated, the filter will over-rely on observation data, weakening its dynamic tracking capability.

[0029] Understandably, the initialization operation is performed based on the noise level, addressing the issue that fixed initialization cannot adapt to dynamic measurement environments. Different noise environments require differentiated filter parameter configurations. When the noise is high, the initial values ​​of the process noise variance and the prior estimate covariance are appropriately increased, giving the filter strong robustness from the initial stage and preventing divergence caused by over-reliance on model predictions due to excessively small parameters. When the noise is low, these parameters are correspondingly decreased to improve the filter's sensitivity to weak signals and avoid excessive smoothing that results in the loss of details. This adaptive initialization mechanism allows the filter to match the actual noise level from the first cycle, shortening the convergence time and improving stability. The above operations adjust the initial uncertainty based on real-time noise characteristics, laying a good foundation for subsequent dynamic gain adjustment and overcoming the initial performance degradation problem caused by the mismatch between static initialization and the actual noise environment in traditional methods.

[0030] Preferably, step S2 includes: Prior state estimation is performed on the Brillouin optical time-domain reflection signal to obtain the prior state estimate at the current time. The following relation is satisfied: ; in, Represents the state transition matrix. This represents the prior state estimate from the previous time step. Represents the control matrix. Indicates the control input quantity; Calculate the prior estimate of covariance at the current time. The following relation is satisfied: ; in, Represents the state transition matrix, This represents the prior estimate error covariance at the previous time step. This represents the variance of process noise.

[0031] It should be noted that the prior state estimate This is a prediction of the state using a system dynamic model before current observation data is obtained; this value forms the baseline for subsequent observation corrections. State transition matrix. To achieve a linear evolution mapping of the state vector from the previous time step to the current time step, the values ​​of its elements are determined based on the physical propagation characteristics of the Brillouin optical time-domain reflection signal. Typically, a diagonal matrix close to the identity matrix is ​​chosen to reflect the spatiotemporal continuity of the fiber optic sensing signal. Control matrix The weights describing the influence of external control inputs on the system state, typically corresponding to the effect coefficients of temperature or stress modulation on the Brillouin frequency shift in distributed fiber optic sensing scenarios. Control input quantity. This represents the controllable external variable applied to the system at the previous moment, which is typically a zero vector in a BOTDR monitoring system without active control. Prior estimation error covariance. The uncertainty of the state estimate at the previous time step is quantified, and its diagonal elements reflect the variance of the estimation errors of each state component. Process noise variance. This matrix characterizes the statistical properties of the deviation between the system model and the actual physical process. It is typically a diagonal matrix, with its diagonal elements set according to the fluctuations in fiber optic environmental factors, and their values ​​generally ranging from [value range missing]. to Between. Prior estimate of covariance. It is a measure of uncertainty in the output of the prediction stage. Its calculation integrates the model propagation uncertainty and process noise, providing a basis for the prediction confidence of Kalman gain calculation.

[0032] Understandably, the prior state estimation formula extrapolates the optimal estimate from the previous time step using the evolutionary laws of a linear system. It applies the state transition matrix to historical states and superimposes the influence of control inputs to generate the predicted value for the current time step. This mechanism allows the filter to form reasonable expectations before observations arrive, avoiding instability caused by relying entirely on observation data. The prior estimation covariance formula uses matrix similarity transformations... To achieve forward propagation of uncertainty, the estimation error covariance from the previous time step is mapped to the current time step according to the state transition relationship, and the process noise variance is added. To reflect the accumulation of model errors, the covariance matrix is ​​appropriately increased over time to accurately characterize the time decay characteristics of prediction confidence. and By collaboratively constructing prediction benchmarks and confidence metrics, necessary intermediate variables are provided for subsequent dynamic gain adjustments, ensuring that observation corrections are based on scientific predictions, thereby improving the filter's ability to track dynamic changes in Brillouin optical temporal reflection signals.

[0033] Preferably, in step S3, dynamically adjusting the observation noise variance includes calculating the observation noise variance at the current time. The following relation is satisfied: ; in, Indicates the original noise power level. Indicates Kalman gain, Indicates the power level of the Brillouin scattered light signal. Represents the observation matrix. It represents the change in state.

[0034] It should be noted that the original noise power level The system's floor noise power, obtained through offline calibration or prior statistics, characterizes the inherent noise intensity generated by hardware devices against a constant environmental background. This value serves as the lower bound of the dynamic observation noise variance, ensuring... Not lower than the system's physical limits. Brillouin scattering light signal power level. This refers to the average power of the Brillouin scattering signal at the current moment or within a local sliding window. It is calculated using statistical observation data and reflects the local intensity characteristics of the signal. (State change quantity) Defined as the difference vector between prior state estimates at adjacent time steps, i.e. This vector captures abrupt changes in the signal along the time or spatial dimensions. Observation matrix To achieve a linear mapping from the state space to the observation space, in the case of direct observation, take the identity matrix and its transpose. Used for covariance propagation calculation. Absolute value operation. Ensure that the adjustment amount is non-negative to avoid the physical inconsistency of negative variance in the observation noise. and The product term constitutes the core of the dynamic adjustment, among which Provide feedback intensity, Quantify the amplitude of signal fluctuations; the two drive each other synergistically. As the local signal-to-noise ratio changes, the fixed observation noise variance in the traditional Kalman filter is transformed into a time-varying parameter, enabling the filter to adapt to different environments.

[0035] Understandably, step S3 establishes a closed-loop coupling relationship between the observation noise variance and the Kalman gain through real-time feedback of the original noise power and the Brillouin scattered light signal power, thereby achieving dynamic adjustment. That is, when strain or a sudden temperature change occurs at a certain location in the optical fiber, the change in state... Significantly increased, leading to The term increases, which in turn increases the variance of dynamic observation noise. Increase; according to the Kalman gain formula Increase the gain that forces the next cycle Automatic reduction suppresses excessive smoothing of abrupt changes by the filter, preserving signal edge information. Conversely, in stable signal segments, Approaching zero By maintaining a small observation noise variance and keeping the Kalman gain at an appropriate size to achieve effective noise reduction, the above mechanism enables the observation noise model to respond in real time to the local features of the signal, allowing the filter to distinguish between real events and random noise, avoiding under-filtering or over-smoothing problems caused by fixed observation noise, and enhancing the ability to suppress nonlinear noise.

[0036] Preferably, step S4 includes: Update Kalman gain The following relation is satisfied: ; in, This represents the prior estimate of covariance. Represents the observation matrix. This represents the dynamically adjusted variance of the observation noise. Updating the system state estimate using Kalman gain and observed variables The following relation is satisfied: ; in, This represents the prior state estimate. Indicates Kalman gain, Represents the observed variable. Represents the observation matrix; Update error covariance The following relation is satisfied: ; in, Represents the identity matrix. Indicates Kalman gain, Represents the observation matrix. This represents the prior estimate of the covariance.

[0037] It should be noted that the Kalman gain This is a weighting coefficient that balances the confidence level between model predictions and observed data; its value determines the smoothness and response speed of the filtered output. Prior estimation of covariance. The uncertainty characterizing the predicted state is calculated during the prediction phase. Observation matrix. and its transpose Achieve a two-way mapping between the state space and the observation space. Transform the state uncertainty into the observation space. Dynamically adjusted observation noise variance. Step S3 performs real-time calculations to reflect the current local observation quality. The combined model uncertainty and observation uncertainty are physically represented as the total variance of the observation residuals. Observation variables This is a vector of actual measured values ​​including noise; in a BOTDR system, it represents the Brillouin scattered light power distribution output by the photodetector. Observation residuals. Quantify the difference between actual and predicted observations, including changes in the actual signal and noise components. Identity matrix. It is a square matrix with 1s on the main diagonal and 0s on the rest, maintaining dimensional consistency, and the error covariance is... The residual uncertainty of the updated state estimate is quantified and used for prediction propagation in the next period.

[0038] Understandably, step S4 involves achieving optimal fusion of prediction and observation using dynamically adjusted Kalman gain. First, the Kalman gain is calculated based on the prior estimated covariance and the dynamic observation noise variance. The Kalman gain automatically adapts to the local signal-to-noise ratio: during signal stability... Smaller, relatively larger gain, fully trusting the observational data to suppress noise; in abrupt change segments Increasing the gain automatically decreases it, suppressing the interference of observation noise on state estimation. Then, the observation residuals are calculated and multiplied by the Kalman gain. This product term reflects the correction amount of the observation information to the predicted state; the gain magnitude controls the correction strength, achieving smooth updates. Finally, the error covariance is updated through... Factoring reduces prior covariance, reflecting the reduction in uncertainty after the introduction of new observation information. The above mechanism ensures that the filter achieves an adaptive optimal balance between prediction and observation under dynamic gain drive, avoiding under-filtering or over-smoothing problems caused by fixed gain.

[0039] Gain Kalman filter denoising system for Brillouin optical time-domain reflectometry signals, such as Figure 2 As shown, it includes: The initialization module is used to initialize the Kalman filter parameters, including the state transition matrix, control matrix, observation matrix, process noise variance, and prior estimate covariance. The signal prediction module is used to perform prior state estimation on the Brillouin optical time-domain reflection signal based on the state transition matrix, the control matrix and the control input, and to calculate the prior estimation covariance based on the state transition matrix and the process noise variance. The noise adjustment module is used to dynamically adjust the observation noise variance based on the dynamic relationship between the observation noise variance and the Kalman gain, combined with the original noise power and the Brillouin scattered light signal power. The state update module is used to update the Kalman gain using the prior estimated covariance, the observation matrix, and the dynamically adjusted observation noise variance, and then use the Kalman gain and the observation variables to update the system state estimate and error covariance. The signal output module is used to output the filtered and denoised Brillouin optical time-domain reflectometry signal.

[0040] This embodiment implements a gain Kalman filter denoising method and its implementation process for Brillouin optical time-domain reflectometry signals. Please refer to the above embodiments, which will not be repeated here.

[0041] Preferably, in the initialization module, the initialization operation is performed based on the noise level of the Brillouin optical time-domain reflectometry signal.

[0042] Preferably, the signal prediction module is further used for: Prior state estimation is performed on the Brillouin optical time-domain reflection signal to obtain the prior state estimate at the current time. The following relation is satisfied: ; in, Represents the state transition matrix. This represents the prior state estimate from the previous time step. Represents the control matrix. Indicates the control input quantity; Calculate the prior estimate of covariance at the current time. The following relation is satisfied: ; in, Represents the state transition matrix, This represents the prior estimate error covariance at the previous time step. This represents the variance of process noise.

[0043] Preferably, in the noise adjustment module, dynamically adjusting the observation noise variance includes calculating the observation noise variance at the current moment. The following relation is satisfied: ; in, Indicates the original noise power level. Indicates Kalman gain, Indicates the power level of the Brillouin scattered light signal. Represents the observation matrix. It represents the change in state.

[0044] Preferably, the state update module includes: Update Kalman gain The following relation is satisfied: ; in, This represents the prior estimate of covariance. Represents the observation matrix. This represents the dynamically adjusted variance of the observation noise. Updating the system state estimate using Kalman gain and observed variables The following relation is satisfied: ; in, This represents the prior state estimate. Indicates Kalman gain, Represents the observed variable. Represents the observation matrix; Update error covariance The following relation is satisfied: ; in, Represents the identity matrix. Indicates Kalman gain, Represents the observation matrix. This represents the prior estimate of the covariance.

[0045] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "illustrative embodiment," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0046] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A gain-Kalman filtering denoising method for Brillouin optical time-domain reflectometry signals, characterized in that, Includes the following steps: S1: Initialize the Kalman filter parameters, including the state transition matrix, control matrix, observation matrix, process noise variance, and prior estimate covariance; S2: Based on the state transition matrix, the control matrix, and the control input, perform prior state estimation on the Brillouin optical time-domain reflection signal, and calculate the prior estimation covariance based on the state transition matrix and the process noise variance; S3: Based on the dynamic relationship between observation noise variance and Kalman gain, combined with the original noise power and Brillouin scattered light signal power, the observation noise variance is dynamically adjusted. S4: Update the Kalman gain using the prior estimated covariance, observation matrix, and the dynamically adjusted observation noise variance; then update the system state estimate and error covariance using the Kalman gain and observation variables. S5: Output the filtered and denoised Brillouin optical time-domain reflectometry signal.

2. The dynamic gain Kalman filter denoising method for Brillouin optical time-domain reflectometry signals according to claim 1, characterized in that, The initialization operation in step S1 is performed based on the noise level of the Brillouin optical time-domain reflectometry signal.

3. The dynamic gain Kalman filter denoising method for Brillouin optical time-domain reflectometry signals according to claim 1, characterized in that, Step S2 includes: Prior state estimation is performed on the Brillouin optical time-domain reflection signal to obtain the prior state estimate at the current time. The following relation is satisfied: ； in, Represents the state transition matrix. This represents the prior state estimate from the previous time step. Represents the control matrix. Indicates the control input quantity; Calculate the prior estimate of covariance at the current time. The following relation is satisfied: ； in, Represents the state transition matrix, This represents the prior estimate error covariance at the previous time step. This represents the variance of process noise.

4. The dynamic gain Kalman filter denoising method for Brillouin optical time-domain reflectometry signals according to claim 1, characterized in that, In step S3, dynamically adjusting the observation noise variance includes calculating the observation noise variance at the current time. The following relation is satisfied: ； in, Indicates the original noise power level. Indicates Kalman gain, Indicates the power level of the Brillouin scattered light signal. Represents the observation matrix. It represents the change in state.

5. The dynamic gain Kalman filter denoising method for Brillouin optical time-domain reflectometry signals according to claim 1, characterized in that, Step S4 includes: Update Kalman gain The following relation is satisfied: ； in, This represents the prior estimate of covariance. Represents the observation matrix. This represents the dynamically adjusted variance of the observation noise. Updating the system state estimate using Kalman gain and observed variables The following relation is satisfied: ； in, This represents the prior state estimate. Indicates Kalman gain, Represents the observed variable. Represents the observation matrix; Update error covariance The following relation is satisfied: ； in, Represents the identity matrix. Represents the observation matrix. This represents the prior estimate of the covariance.

6. A gain Kalman filter denoising system for Brillouin optical time-domain reflectometry signals, characterized in that, include: The initialization module is used to initialize the Kalman filter parameters, including the state transition matrix, control matrix, observation matrix, process noise variance, and prior estimate covariance. The signal prediction module is used to perform prior state estimation on the Brillouin optical time-domain reflection signal based on the state transition matrix, the control matrix and the control input, and to calculate the prior estimation covariance based on the state transition matrix and the process noise variance. The noise adjustment module is used to dynamically adjust the observation noise variance based on the dynamic relationship between the observation noise variance and the Kalman gain, combined with the original noise power and the Brillouin scattered light signal power. The state update module is used to update the Kalman gain using the prior estimated covariance, the observation matrix, and the dynamically adjusted observation noise variance, and then use the Kalman gain and the observation variables to update the system state estimate and error covariance. The signal output module is used to output the filtered and denoised Brillouin optical time-domain reflectometry signal.

7. The dynamic gain Kalman filter denoising system for Brillouin optical time-domain reflectometry signals according to claim 1, characterized in that, In the initialization module, the initialization operation is performed based on the noise level of the Brillouin optical time-domain reflectometry signal.

8. The dynamic gain Kalman filter denoising system for Brillouin optical time-domain reflectometry signals according to claim 1, characterized in that, The signal prediction module is also used for: Prior state estimation is performed on the Brillouin optical time-domain reflection signal to obtain the prior state estimate at the current time. The following relation is satisfied: ； in, Represents the state transition matrix. This represents the prior state estimate from the previous time step. Represents the control matrix. Indicates the control input quantity; Calculate the prior estimate of covariance at the current time. The following relation is satisfied: ； in, Represents the state transition matrix, This represents the prior estimate error covariance at the previous time step. This represents the variance of process noise.

9. The dynamic gain Kalman filter denoising system for Brillouin optical time-domain reflectometry signals according to claim 1, characterized in that, In the noise adjustment module, dynamically adjusting the observation noise variance includes calculating the observation noise variance at the current moment. The following relation is satisfied: ； in, Indicates the original noise power level. Indicates Kalman gain, Indicates the power level of the Brillouin scattered light signal. Represents the observation matrix. It represents the change in state.

10. The dynamic gain Kalman filter denoising system for Brillouin optical time-domain reflectometry signals according to claim 1, characterized in that, The state update module includes: Update Kalman gain The following relation is satisfied: ； in, This represents the prior estimate of covariance. Represents the observation matrix. This represents the dynamically adjusted variance of the observation noise. Updating the system state estimate using Kalman gain and observed variables The following relation is satisfied: ； in, This represents the prior state estimate. Indicates Kalman gain, Represents the observed variable. Represents the observation matrix; Update error covariance The following relation is satisfied: ； in, Represents the identity matrix. Indicates Kalman gain, Represents the observation matrix. This represents the prior estimate of the covariance.

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