An adaptive filtering method for SERF atom gyroscope

Abstract

This invention relates to the field of signal processing for spin-free exchange-relaxed (SERF) atomic gyroscopes, specifically an adaptive filtering method for SERF atomic gyroscopes. Addressing the issues of multi-source noise coupling interference (optical, thermal, magnetic, etc.) and time-varying noise statistical characteristics in the output signal of SERF atomic gyroscopes, this invention proposes a signal processing method combining multi-source noise modeling and adaptive filtering. First, based on an improved genetic algorithm, multiple types of random errors, including quantization noise, angle random walk, bias instability, rate random walk, rate ramp, Markov noise, and sinusoidal noise, are jointly modeled to obtain the characteristic parameters of each noise component as prior knowledge. Second, discrete wavelet transform is used to perform multi-scale decomposition and threshold denoising on the original gyroscope signal, achieving effective separation of useful signals and high-frequency noise. Based on this, a time-varying state-space model is constructed, and an adaptive Kalman filter algorithm is used to estimate and compensate for various random error components in the original signal online. Finally, the compensated signal is output. This invention can improve the long-term stability of the SERF atomic gyroscope output signal and has good engineering application value.

Description

Technical Field

[0001] This invention relates to the field of signal processing for SERF inertial measurement units, specifically a multi-noise modeling adaptive filtering method for SERF atomic gyroscopes. This method is suitable for multi-source time-varying noise suppression and output signal optimization of high-precision SERF atomic gyroscopes and can be applied to fields such as deep-sea exploration, deep space exploration, and high-precision inertial navigation. Background Technology

[0002] The SERF atomic gyroscope achieves ultra-high precision measurement of angular velocity based on the atomic spin effect, with a theoretical sensitivity of up to 10. -8 o The / s level represents the core direction of next-generation high-precision inertial measurement technology, and is widely used in fields such as deep-sea exploration, deep space exploration, and high-precision inertial navigation. The measurement accuracy of SERF atomic gyroscopes directly depends on the quality of the output signal, but they are inevitably subject to coupling interference from multiple sources during operation. Furthermore, the statistical characteristics of each noise component dynamically change with the working environment (temperature, magnetic field), device status (pump optical power, gas chamber temperature), and motion conditions, exhibiting time-varying and coupling characteristics.

[0003] Currently, noise suppression methods for SERF atomic gyroscopes mainly include traditional filtering methods and conventional adaptive Kalman filtering methods. Traditional filtering methods, such as Butterworth low-pass filtering, moving average filtering, and wavelet transform, have problems such as fixed cutoff frequencies, poor performance in processing non-stationary signals, and the need for pre-selection of basis functions, making them unsuitable for the characteristics of multi-source time-varying noise. Although conventional adaptive Kalman filtering methods can adjust the noise covariance matrix online, they only make empirical corrections based on the statistical properties of innovation and do not accurately model the intrinsic characteristics and coupling relationships of multi-source noise. This results in a lack of physical basis for adjusting the noise covariance matrix, limiting the filtering accuracy and stability.

[0004] Furthermore, existing technologies for noise processing of SERF atomic gyroscopes often employ independent modeling of individual noise components, neglecting the coupling effects between these components. This fails to accurately describe the overall evolution of multi-source noise, resulting in insufficient adaptability of filtering methods to actual operating conditions. Simultaneously, traditional optimization algorithms suffer from slow convergence speeds and a tendency to get trapped in local optima during noise modeling, making it difficult to quickly and accurately uncover the characteristic patterns of multi-source noise.

[0005] To address the aforementioned technical shortcomings, this invention proposes an adaptive filtering method for SERF atomic gyroscopes. It improves the genetic algorithm to identify system noise parameters and combines robust weights with time-varying parameter estimation in an adaptive Kalman filter to dynamically and accurately adjust the covariance matrix. This constructs an integrated adaptive noise reduction framework encompassing modeling, preprocessing, and filtering. By accurately mining noise features and tracking time-varying characteristics in real time, it achieves precise suppression of multi-source time-varying noise throughout the entire process, ultimately significantly improving the accuracy and long-term stability of the SERF atomic gyroscope's output signal. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art and provide a multi-noise modeling and adaptive filtering method for SERF inertial measurement devices, which combines offline modeling with online adaptive filtering. This method solves the problems of multi-source noise coupling, time-varying statistical characteristics, low modeling accuracy, and poor adaptability of traditional filtering methods in SERF inertial measurement devices.

[0007] The technical solution of the present invention is as follows:

[0008] An adaptive filtering method for SERF atomic gyroscopes includes the following steps:

[0009] Step 1: Collect gyroscope output data from the system under static conditions for 2 consecutive hours. Using an improved genetic algorithm combined with Allan variance analysis, identify the system parameters using the improved genetic algorithm. Obtain the quantization noise term Q, angle random walk term N, bias instability term B, angular rate random walk term K, rate ramp term R, and the amplitude and time constant of the Markov process in the signal. , The amplitude and frequency of the sinusoidal noise are , The parameter estimates for these seven types of noise;

[0010] Step 2: Perform wavelet transform preprocessing on the preprocessed gyroscope signal to separate high-frequency noise components and obtain the wavelet-filtered signal.

[0011] Step 3: Based on the identified prior parameters, establish a 5-dimensional time-varying state space model of the system and determine the state transition matrix and observation matrix;

[0012] Step 4: Integrate the noise feature parameters output by the multi-noise joint model into the Sage-Husa adaptive Kalman filter (AKF) framework, combine the wavelet-filtered signal, and estimate and dynamically adjust the process noise covariance matrix and measurement noise covariance matrix online through weighted recursion using the forgetting factor. At the same time, integrate the IGG III robust weight function to suppress outlier interference.

[0013] Step 5: Through AKF filtering prediction and update iteration, the output signal of the SERF inertial measurement device is filtered to obtain the optimal estimated signal.

[0014] Compared with the prior art, the present invention has the following beneficial effects:

[0015] 1. An improved genetic algorithm is used for joint modeling of multiple noises. By using an adaptive crossover mutation operator and an elite retention strategy, the problem of slow convergence and easy getting trapped in local optima of traditional algorithms is solved. At the same time, the coupling relationship of each noise component is considered to construct a high-precision joint model of multiple noises, providing a physical basis for noise covariance adjustment.

[0016] 2. Optimize the discrete wavelet transform preprocessing process, selectively choose the db4 wavelet basis and optimize the number of decomposition layers, and achieve accurate suppression of high-frequency noise and Markov noise through soft thresholding, prioritizing the filtering out of high-frequency noise.

[0017] 3. An adaptive framework of "modeling-preprocessing-filtering" is constructed, which combines a multi-noise joint model with Sage-Husa AKF that incorporates forgetting factors and IGG III robust weights. Prior modeling and online dynamic correction of the noise covariance matrix are achieved through weighted recursion of forgetting factors, taking into account both the convergence speed and steady-state stability of noise estimation. At the same time, IGG III robust weights are used to suppress outlier interference, which significantly enhances the adaptability to multi-source time-varying noise. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the overall process of the multi-noise modeling adaptive filtering method for SERF atomic gyroscopes of the present invention. It shows the entire process from data acquisition and preprocessing, through parameter identification of improved genetic algorithm, discrete wavelet transform preprocessing, construction of time-varying state space model, dynamic adjustment of noise covariance matrix, and finally obtaining the optimal estimated signal through adaptive Kalman filtering iteration. It intuitively presents the logical connection and execution order of each step, reflecting the integrated adaptive framework design of "modeling-preprocessing-filtering" of the present invention.

[0019] Figure 2 shows a comparison of the angular velocity signal processing results using the adaptive filtering method of this invention. With time (in seconds) on the horizontal axis and voltage (in V) on the vertical axis, the time-domain waveforms of the original gyroscope signal (dashed line, labeled "original signal") and the adaptively filtered signal (solid line, labeled "compensated signal") are plotted. After adaptive filtering by this invention, noise is significantly suppressed, and the signal fluctuation range is limited to... Within the V range, the waveform is smooth and retains an effective trend, which intuitively verifies the superior performance of this method in noise suppression of SERF atomic gyroscopes. Detailed Implementation

[0020] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0021] Example:

[0022] The following is in conjunction with the attached diagram ( Figures 1-2 The present invention will be described in detail below with reference to specific embodiments, but the scope of protection of the present invention is not limited to the following embodiments.

[0023] This invention discloses an adaptive filtering method for SERF atomic gyroscopes, which is divided into two stages: offline parameter identification and online real-time compensation. The overall process is as follows: Figure 1 As shown, it specifically includes the following five core steps:

[0024] Step 1: Data Collection

[0025] During the offline phase, the raw angular velocity output signal of the SERF atomic gyroscope was collected continuously for 2 hours under static conditions. This signal was then segmented into fixed-length data segments, and the collected signal can be represented as:

[0026]

[0027] in, This is the original output signal of the gyroscope; This is the actual angular velocity; the input is 0 when stationary. To quantize noise; Random walk for angles; This is due to bias instability; For rate random walk; For rate ramp; It is Markov noise; It is sinusoidal noise.

[0028] Step 2: Improve the system parameter identification of the genetic algorithm

[0029] To address the quantization noise, angle random walk noise, bias instability noise, angular rate random walk noise, rate ramp noise, Markov noise, and sinusoidal noise of the SERF atomic gyroscope, an improved genetic algorithm is used to identify the parameters of various noise types in the system, providing prior information for subsequent adaptive Kalman filtering. The specific implementation process is as follows:

[0030] 1. Determine the optimization variables and encoding method: Use the characteristic parameters of each noise component as the optimization variables, specifically including the quantized noise amplitude Q and the angular random walk noise figure. Bias instability noise figure B, angular velocity random walk noise figure K, velocity ramp noise figure R, Markov noise amplitude and related time sinusoidal noise amplitude A and frequency The real number encoding method is adopted, with each individual being a feature parameter vector, and the population size is set to 100.

[0031] 2. Constructing the objective function: The object of fitting is the total Allan variance of the system, which can be expressed as the superposition of various noise components. The corresponding Allan standard deviation is expressed as:

[0032]

[0033] In the formula, Indicates the system output signal at time intervals Allan standard deviation below Indicates the first The Allan standard deviation components of the noise type over the same time interval. These correspond to quantization noise, angle random walk, zero-bias instability, rate random walk, rate ramp, sinusoidal noise, and Markov noise, respectively. Each component function is determined by the statistical characteristics of the corresponding noise and can be expressed in parameterized form:

[0034]

[0035] In the formula, This represents the Allan standard deviation function form corresponding to the i-th type of noise. These are the characteristic parameters of this type of noise, including physical quantities such as noise figure, time constant, or amplitude. From this, the overall model expression for the system's Allan standard deviation can be obtained as follows:

[0036]

[0037] In the formula, This represents the Allan standard deviation obtained from the model's predictions. It is a vector consisting of all parameters to be identified.

[0038] Considering that Allan variance curves typically span multiple orders of magnitude, and the impact of data at different time scales on the fitting results varies significantly, directly calculating the error in the original domain can easily lead to inaccurate optimization results. Therefore, an objective function is constructed in the logarithmic domain, with the following expression:

[0039]

[0040] in, This represents the Allan standard deviation obtained by fitting the measured data.

[0041] 3. Adaptively improve the crossover and mutation operators of the traditional genetic algorithm, and introduce an elite retention strategy, specifically:

[0042] (1) Adaptive crossover operator: The crossover probability is dynamically adjusted according to the population fitness to avoid premature convergence. The formula is:

[0043]

[0044] in, , , The average fitness of the population. For the maximum fitness of the population, For individual fitness.

[0045] (2) Adaptive mutation operator: The mutation probability is dynamically adjusted according to the individual's fitness. The mutation probability is reduced for excellent individuals and increased for poor individuals. The formula is as follows:

[0046]

[0047] in, , , For individual fitness.

[0048] (3) Elite retention strategy: Select the top 10% of individuals in each generation of the population and retain them directly to the next generation to avoid the loss of excellent genes and improve the convergence speed and modeling accuracy of the algorithm.

[0049] 4. Iterative Convergence and Model Output

[0050] The algorithm is set to a maximum of 200 iterations, with a convergence threshold of the objective function value being less than 0.001. When the algorithm meets the convergence condition or reaches the maximum number of iterations, it stops iterating and outputs the feature models of each noise component and the coupling relationship models between them, collectively forming a multi-noise joint model. This model can output the feature parameters of each noise component in real time.

[0051] Step 3: Discrete wavelet transform preprocessing

[0052] In the online real-time compensation phase, this step uses a sliding window to process the real-time data after 2 hours, with 1 second as the basic processing unit. Discrete wavelet transform is used to preprocess the gyroscope signal obtained in step 1, specifically including:

[0053] 1. Wavelet basis selection: The db4 orthogonal wavelet basis function is selected. This wavelet basis has tight support and good time-frequency local characteristics. It can retain the instantaneous characteristics of the useful signal while separating high-frequency noise, and is suitable for the non-stationary characteristics of SERF gyroscope signals.

[0054] 2. Multi-scale decomposition: The standardized signal is decomposed into a 4-level binary wavelet decomposition to obtain a low-frequency approximation coefficient. (corresponding to the main components of the useful signal) and 4 high-frequency detail coefficients (Noise components corresponding to different frequency bands).

[0055] 3. Thresholding: Soft thresholding is applied to the four high-frequency detail coefficients. The threshold λ is calculated based on the noise statistical characteristics, using the following formula:

[0056]

[0057] in, is the wavelet threshold used to suppress noise components in high-frequency detail coefficients, and L is the number of sample points in the current processed signal segment, i.e., the length of the gyroscope signal sequence participating in wavelet decomposition.

[0058] Step 4: Construct the state-space model of the SERF atomic gyroscope

[0059] 1. State Vector Definition: The Allan variance model of the SERF atomic gyroscope contains 7 typical noise types. Considering the modeling efficiency and the observability of the actual system, this model selects 4 types of noise for explicit modeling: bias instability, angle random walk, rate random walk and Markov noise. The other 3 types of noise are suppressed through the preprocessing in step 3.

[0060] Therefore, the state vector of the SERF atomic gyroscope is defined as:

[0061]

[0062] in, The signal is after wavelet transform preprocessing. This is a bias-unstable term. For random walks of angles, For rate random walk, This is Markov process noise. Since all random errors start from 0 at the initial moment of gyroscope startup, all other terms are initialized to 0.

[0063] 2. State Transition Equations and Process Modeling: For various noise discretization models, the system's state transition equations can be written as:

[0064]

[0065] Wherein, the state transition matrix The specific form is as follows:

[0066]

[0067] in, The system sampling interval, The time constant for the Markov noise identified in step 2. The process noise vector in the state transition equation. It follows a zero-mean Gaussian distribution, and its covariance matrix is... Based on the noise parameters N and B identified in step 2, , :

[0068]

[0069] in, The process noise variance of the random walk at the sampling interval angle of the system is: The process noise variance of the rate random walk is The process noise variance of bias instability is... The process noise variance of Markov noise is .

[0070] 3. Observation model modeling: The observed quantities are the measured outputs of the gyroscope. It consists of the linear superposition of the true angular velocity and each error component:

[0071]

[0072] Among them, the observation matrix For constant row vectors:

[0073]

[0074] Noise measurement It follows a zero-mean Gaussian distribution, and its covariance R is used to equivalently characterize broadband random disturbances such as quantization noise and thermal noise from the detection circuit. Based on the identification results, the quantization noise figure... The order of magnitude is The corresponding initial value of the equivalent measurement noise covariance can be set to .

[0075] Step 4: Adaptive Kalman Filter

[0076] 1. Robust handling of new information

[0077] The information is a core indicator in Kalman filtering for judging the filtering effect and adjusting the filtering parameters. It is defined as the difference between the measured value and the predicted observation value at time k, and its calculation formula is as follows:

[0078]

[0079] in, Let be the predicted state value at time k, derived from the state estimate at the previous time through the state transition equation. The variance of the innovation is used to characterize the dispersion of the innovation, and its calculation formula is:

[0080]

[0081] in, Let be the state prediction covariance matrix at time k, used to describe the degree of uncertainty of the state prediction value.

[0082] To effectively suppress the interference of outliers on the filtering process, an IGG III three-segment weighting function is introduced to adaptively weight the innovation. Through dynamic adjustment of the weight coefficients, the impact of outliers on state updates and noise covariance estimation is reduced. The specific calculation rules are as follows:

[0083]

[0084] in, This is the normalized amplitude of the innovation, used to determine whether the innovation is an outlier. The variance of the new information; , These are the first and second thresholds of the IGG III weighting function, respectively. Corresponding to the boundary between normal interest rate and transition zone interest rate, The boundary between the new information and the wild value in the corresponding transition zone; It is a very small positive number (usually 1e-4) used to avoid the filtering divergence problem caused by a weight of 0, and to ensure the stability of the filtering process.

[0085] 2. Sage-Husa time-varying noise adaptive update

[0086] To achieve accurate tracking of time-varying noise, a Sage-Husa forgetting factor recursive strategy is adopted, with the recursive coefficient of the noise covariance at the k-th iteration being... The calculation formula is as follows:

[0087]

[0088] Where b is the forgetting factor (the range of values ​​is...) b is used to control the update sensitivity of the noise covariance. The closer b is to 1, the smoother the update speed of the noise covariance and the higher the dependence on historical data. The closer b is to 0, the faster the update speed of the noise covariance and the more sensitive the response to current information. It should be reasonably selected according to the noise change characteristics of the SERF gyroscope.

[0089] Measurement noise covariance The adaptive update formula is:

[0090]

[0091] To avoid abrupt changes in the measurement noise covariance, exponential smoothing is introduced into the updated measurement noise covariance. The formula for calculating the smoothed measurement noise covariance is as follows:

[0092]

[0093] in, It is the exponential smoothing coefficient (with a value range of 0 to 1). The larger the value, the closer the measurement noise covariance follows the real-time estimate; This is used to measure the lower limit of the noise covariance, to avoid filter divergence caused by excessively small noise covariance, and to ensure the numerical stability of the filtering process.

[0094] Process noise covariance The adaptive update formula is:

[0095]

[0096] in, is the Kalman gain at time k, used to adjust the fusion weights of the state prediction and the innovation; These are robust weights for the IGG III weight function, used to reduce the impact of outliers on process noise covariance estimation; The lower bound constraint must be satisfied. ,in This is the lower bound matrix of the process noise covariance, used to avoid the problem of decreased filtering accuracy caused by excessively small process noise covariance.

[0097] 3. State Update Formula

[0098] Robust weights obtained based on the IGG III weight function Adjust the effective measurement noise covariance By effectively measuring the adjustment of noise covariance, indirect suppression of outliers is achieved, followed by calculation of the Kalman gain. The calculation formula is as follows:

[0099]

[0100] Based on the Kalman gain and innovation, the state vector is updated to obtain the state estimate at time k. The state update formula is:

[0101]

[0102] Simultaneously, the state covariance matrix is ​​updated for state prediction at the next time step. The state covariance update formula is:

[0103]

[0104] in, Given a 5×5 identity matrix, to ensure the numerical stability of the state covariance matrix and avoid it becoming too small or singular, it is necessary to... A lower limit constraint is imposed to ensure that the value is not less than a preset lower limit, thereby guaranteeing the stable operation of the filtering process.

[0105] By employing adaptive Kalman filtering for prediction and iterative updates, the optimal estimate of the SERF atomic gyroscope output signal is achieved, with iterative output... middle As the filtered optimal angular velocity estimation signal.

[0106] The adaptive filtering method proposed in this invention for SERF atomic gyroscopes achieves high-precision joint modeling of multi-source noise (magnetic, optical, and thermal) through an improved genetic algorithm, accurately uncovering the characteristic patterns and coupling relationships of each noise component. Optimized discrete wavelet transform preprocessing enables precise noise separation, providing high-quality input for subsequent filtering. By integrating the multi-noise joint model into the adaptive Kalman filter framework, a time-varying state-space model is constructed, enabling prior modeling and online correction of the covariance matrices of process noise and measurement noise. This solves the problem of poor adaptability of traditional filtering methods to multi-source time-varying noise.

[0107] This method effectively suppresses multi-source time-varying noise of SERF atomic gyroscopes, significantly reduces zero-bias drift and random noise in the output signal, and improves measurement accuracy and long-term stability. It is suitable for real-time signal processing of various high-precision SERF atomic gyroscopes and has important engineering application value in fields such as deep-sea exploration, deep space exploration, and high-precision inertial navigation.

[0108] Contents not described in detail in this specification are prior art known to those skilled in the art. It is hereby indicated that the above description is intended to help those skilled in the art understand this invention, but does not limit the scope of protection of this invention. Any equivalent substitutions, modifications, improvements, and / or simplifications of the above descriptions that do not depart from the essential content of this invention fall within the scope of protection of this invention.

Claims

1. A multi-noise modeling adaptive filtering method for SERF atomic gyroscopes, characterized in that, The method combines parameter identification of multi-source noise with online adaptive filtering to achieve high-precision suppression and real-time dynamic compensation of time-varying noise, including the following steps: Step 1: Collect gyroscope output data from the system under static conditions for 2 consecutive hours. Using an improved genetic algorithm combined with Allan variance analysis, the amplitude and time constant of the quantization noise term Q, angle random walk term N, bias instability term B, angular rate random walk term K, rate ramp term R, and Markov process in the signal are respectively... , The amplitude and frequency of the sinusoidal noise are , These seven types of noise are parameter identified to obtain the corresponding noise parameter set, which is then stored as prior information for the subsequent online compensation model. Step 2: For the real-time acquisition data after 2 hours, adopt the method of a sliding window per second, with 1 second as the basic processing unit. For the signals within each time window, perform high-frequency noise preprocessing using discrete wavelet transform with the db4 orthogonal wavelet basis. By applying soft threshold denoising and reconstruction to the high-frequency detail components, effectively suppress quantization noise and high-frequency sine interference, and obtain the smoothed signal after wavelet filtering; Step 3: Based on the prior parameters obtained in Step 1, establish a time-varying state-space model of the SERF atomic gyroscope, and determine the state transition matrix and observation matrix; integrate noise characteristic parameters into the adaptive Kalman filter framework, combine with the wavelet-filtered signal, and estimate and dynamically adjust the process noise covariance matrix online through weighted recursion using the forgetting factor. and measurement noise covariance matrix The innovation is weighted by integrating the robust weight function of IGG III (Institute of Geodesy & Geophysics III); the output signal of the SERF atomic gyroscope is filtered by the prediction and update iteration of adaptive Kalman filtering to obtain the compensated angular velocity signal.

2. The method according to claim 1, characterized in that, The time-varying state-space model in step 3 includes state equations and observation equations, and the state vector is... ,in, The signal is after wavelet transform preprocessing. This is a bias-unstable term. For random walks of angles, For rate random walk, This is Markov process noise. Since all random errors start from 0 at the initial moment of gyroscope startup, all other terms are initialized to 0. The initial value is a 5×5 diagonal matrix, depending on the noise parameters N and B identified in step 1. , : in, Let be the system sampling interval, and let be the process noise variance of the random walk at angles. The process noise variance of the rate random walk is The process noise variance of bias instability is... The process noise variance of Markov noise is ; Measurement noise It follows a zero-mean Gaussian distribution, and its covariance matrix is... The random disturbances caused by equivalent quantization noise are compared with the quantization noise figure obtained from parameter identification in step 1. Regarding this, the initial value of the corresponding equivalent measurement noise covariance can be set as follows: .

3. The method according to claim 1, characterized in that, The specific operation of fusing the IGG III robust weight function in step 3 is as follows: calculate the standardized residuals, divide the intervals according to the residuals, and assign corresponding robust weights. The equivalent innovation is obtained by weighting the filtered innovation with weights. The equivalent innovation is then incorporated into the Kalman filter iteration to reduce the impact of abnormal observations on the signal compensation results and improve the compensation accuracy. Weight The specific calculation rules are as follows: in, This is the normalized amplitude of the innovation, used to determine whether the innovation is an outlier. The variance of the new information; , These are the first and second thresholds of the IGG III weighting function, respectively. Corresponding to the boundary between normal interest rate and transition zone interest rate, The boundary between the new information and the wild value in the corresponding transition zone; It is a very small positive number (usually taken as 1e). -4 This is used to avoid the filtering divergence problem caused by a weight of 0, and to ensure the stability of the filtering process.

4. The method according to claim 1, characterized in that, In step 3, the prediction and update iterations of the adaptive Kalman filter, and the recursive coefficients of the noise covariance at the k-th iteration. The calculation formula is: Among them, b is the forgetting factor (the value range is 0 < b < 1), which is used to control the update sensitivity of the noise covariance. The closer b is to 1, the smoother the update speed of the noise covariance, and the higher the dependence on historical data; the closer b is to 0, the faster the update speed of the noise covariance, and the more sensitive the response to the current innovation. It needs to be reasonably selected according to the noise change characteristics of the SERF gyroscope; Measurement noise covariance The adaptive update formula is: in, Let F be the posterior estimation error covariance matrix at time k-1, obtained by combining the state transition matrix F with the process noise covariance matrix. The one-step prediction covariance matrix is ​​obtained by recursion. , The state transition matrix is ​​determined by the parameters obtained from the identification. Let the observation matrix be denoted as . ; To avoid stepwise changes in the measurement noise covariance, exponential smoothing processing is introduced to the update result of the measurement noise covariance. The calculation formula for the smoothed measurement noise covariance is: in, It is the exponential smoothing coefficient (with a value range of 0 to 1). The larger the value, the closer the measurement noise covariance follows the real-time estimate; This is used to measure the lower limit of the noise covariance, to avoid filter divergence caused by excessively small noise covariance, and to ensure the numerical stability of the filtering process. Process noise covariance The adaptive update formula is: in, is the Kalman gain at time k, used to adjust the fusion weights of the state prediction and the innovation; These are robust weights for the IGGIII weight function, used to reduce the impact of outliers on process noise covariance estimation; The lower bound constraint must be satisfied. ,in This is the lower bound matrix of the process noise covariance, used to avoid the problem of decreased filtering accuracy caused by excessively small process noise covariance.

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