A compound interference filter method for dynamics aided gyro error separation estimation

Abstract

The application belongs to the field of navigation sensor error estimation, and particularly relates to a compound interference filtering method for gyro error separation estimation assisted by dynamics. Firstly, micro electro mechanical system (MEMS) gyro error data are collected offline and preprocessed; wavelet transform is used to decompose the sequence data, autoregressive moving average (ARMA) models of stationary sub-sequences and long short-term memory (LSTM) network models of non-stationary sub-sequences are respectively established, and a mixed model of the gyro error is obtained by combining the two. Then, system equations are established based on a rotor unmanned aerial vehicle (UAV) dynamics model and the error mixed model. The gyro error is estimated in real time and the error model is updated by using the real-time measurement value of the gyro and the control value of the rotor UAV through the compound interference filtering method, and finally the gyro measurement is compensated. The application realizes online estimation of the gyro error in a motion state without increasing hardware, and improves navigation accuracy.

Description

Technical Field

[0001] This invention belongs to the field of navigation sensor error estimation and relates to a composite disturbance filtering method for dynamic-assisted gyroscope error separation estimation. This method establishes a MEMS (Micro-Electro-Mechanical Systems) gyroscope error hybrid model through wavelet transform, combines it with the carrier dynamic model to provide motion information, and incorporates the system equations into the framework of the CDF (composite disturbance filtering) filtering algorithm to achieve online estimation of gyroscope error in motion. Background Technology

[0002] Currently, MEMS gyroscopes, with their significant advantages of low cost, small size, and low power consumption, are widely used in inertial technology fields such as navigation and attitude determination. However, due to the large measurement errors inherent in MEMS gyroscopes, their long-term orientation accuracy remains unsatisfactory, hindering their further application. Errors in MEMS gyroscopes can be broadly categorized into deterministic errors and random errors. Deterministic errors include scaling factor errors, constant bias errors, installation angle errors, and lever errors, which typically exhibit fixed patterns and repeatability, and can be compensated for through experimental calibration. Random errors, caused by complex random interference such as environmental noise, mechanical vibration, and electronic noise, are random in nature and can be reduced through signal processing techniques, error modeling, and multi-sensor fusion, but are difficult to completely eliminate. Therefore, random errors are the main factor limiting the accuracy of MEMS gyroscopes.

[0003] Existing methods mainly fall into two categories: one is based on statistical models, such as ARMA (autoregressive moving average), first-order Gauss-Markov models, and random walk models. These methods can capture linear relationships in error sequences, but typically require the sequences to be stationary and struggle to handle non-stationary and nonlinear characteristics. The other category is based on neural networks and artificial intelligence methods, which can capture nonlinearity and long-term dependencies, but often require large amounts of training data, risk overfitting, and suffer from insufficient generalization and interpretability.

[0004] Existing research has proposed various combined methods. For example, Chinese patent CN107330149B utilizes ARMA modeling combined with BP neural network to learn residuals to compensate for weak time-varying and weak nonlinear errors. However, the stationarity assumption of ARMA modeling does not match reality, affecting model accuracy. The paper "Recurrent-neural-network-based unscented Kalman filter for estimating and compensating the random drift of MEMSgyroscopes in real time" uses RNN network to establish a generalized nonlinear autoregressive moving average (NARMA) model, breaking the traditional ARMA model's assumption that the error is a linear combination of its previous value and previous driving noise. However, RNN requires a large amount of data for training, and if the training data is insufficient, it may face the problem of insufficient generalization ability, and its accuracy in short-term sequence prediction is not as good as the ARMA model.

[0005] The above studies all focus on real-time estimation of gyroscope errors when the gyroscope is stationary. Estimation and compensation for errors in motion are often relatively simple. Without adding hardware, a vehicle dynamics model is used to provide motion information. The paper "A Model Aided Inertial Navigation System for Automatic Landing of Unmanned Aerial Vehicles" studies the use of model-aided navigation in UAV landing, treating gyroscope errors as constant random values, which deviates significantly from reality. The paper "Accelerometer Fault-Tolerant Model-Aided State Estimation for High-Altitude Long-Endurance UAV" proposes a dynamic model-aided navigation filter to address accelerometer failures. However, the gyroscope error estimation part considers the error as a simple first-order Gaussian Markov model, resulting in a coarse characterization of the error. Therefore, a composite interference filtering method for separating and estimating dynamic-aided gyroscope errors is urgently needed to achieve effective modeling and online estimation of gyroscope errors in motion. Summary of the Invention

[0006] The technical problem to be solved by this invention is: to address the adverse effects of MEMS gyroscope errors on measurement accuracy in motion, a composite interference filtering method for separating and estimating gyroscope errors with dynamics is proposed. A hybrid model of ARMA and LSTM is established through wavelet transform, and a carrier dynamics model is established to provide motion information. The system equations are incorporated into the framework of the CDF filtering algorithm to achieve online separation and estimation of gyroscope errors in motion.

[0007] The technical solution adopted by this invention to solve the above-mentioned technical problems is as follows: a composite interference filtering method for error separation estimation of a dynamic-assisted gyroscope, the implementation steps of which are as follows:

[0008] Step 1: Data Acquisition and Preprocessing: Offline acquisition of MEMS gyroscope error data and normalization processing.

[0009] Step 2, Error Sequence Decomposition: Using wavelet transform to decompose the error sequence of the MEMS gyroscope. Decompose the sequence into... There are one stationary subsequence and one non-stationary subsequence, among which It is a positive integer greater than or equal to 1. The specific implementation is as follows:

[0010] The normalized MEMS gyroscope error sequence is denoted as... , Indicates after normalization The observed values ​​of the time error; selecting the Daubechies wavelet basis function, and using discrete wavelet transform to decompose the error sequence. Among them, the th... The formula for subwavelet decomposition is:

[0011] ,

[0012] in, Indicates the first The trend sequence is obtained after wavelet decomposition. The sequence length; For the first Trend sequence after decomposition The sequence length; For the first The detailed sequence after the decomposition; Indicates a low-pass filter; Indicates a high-pass filter; when hour, This is the original error sequence.

[0013] For each subsequence, the signal is reconstructed so that the length of the subsequence is the same as that of the original sequence. The reconstruction formula is as follows:

[0014] ,

[0015] The KPSS (Kwiatkowski–Phillips–Schmidt–Shin) stationarity test was performed on each of the decomposed subsequences to obtain the following results. a stationary subsequence and nonstationary subsequences The sum of the two is the total number of subsequences. Several non-stationary subsequences are merged into one non-stationary subsequence by addition. .

[0016] Step 3: Offline Mixed Model Establishment: For each stationary subsequence, establish an ARMA time series model. For non-stationary subsequences, an LSTM network model is established. The combined error mixture model is obtained as follows: The specific implementation is as follows:

[0017] Firstly, regarding a stationary subsequence The ARMA models are established separately, and the specific establishment process is as follows:

[0018] Using the Akaike Information Criterion (AIC) The model's order is determined visually by plotting a heatmap corresponding to the AIC value, which visually identifies the order at which the AIC value is minimized. and The AIC criterion is expressed as:

[0019] ,

[0020] in This is the maximum likelihood estimate of the model residual variance; The number of observations;

[0021] After determining the model order, the maximum likelihood estimation method is used to fit the model parameters, thereby obtaining the model order. ARMA model of stationary subsequences:

[0022] ,

[0023] in , These are the autoregressive order and the moving average order of the ARMA model, respectively. These are observations of a stationary subsequence; It is a historical random interference sequence; and These are the model coefficients; For ARMA model residuals.

[0024] For non-stationary subsequences The LSTM model is built using the following steps:

[0025] The non-stationary subsequence data is divided into several samples, with a window size of [missing value]. The rolling window, with its size referring to the input time period, is used. Each time window constitutes a sample as input to the LSTM, and the sequence value at the next time step after the window is the target value. The LSTM parameters, including the weight matrix and offset, can be obtained after training with the training set. Therefore, single-step prediction of the non-stationary subsequence of gyroscope error can be defined as using the previous... The non-stationary subsequence value at time 1 is used to predict the non-stationary subsequence value at the current time, as follows:

[0026] ,

[0027] in Represents the LSTM model. This represents the prediction error of the network model; by training the LSTM network, the dynamic characteristics of non-stationary subsequences are learned, thereby accurately predicting the value of the non-stationary subsequence at the next time step and continuously updating the internal state of the network.

[0028] In summary, by combining the stationary subsequence ARMA model and the non-stationary subsequence LSTM network model, a hybrid model of MEMS gyroscope error is obtained:

[0029] ,

[0030] in represent Error value at any given time; Representing the ARMA model estimation of stationary subsequences; LSTM model estimation representing non-stationary subsequences; This represents the model error of the mixture model, including the error of each ARMA model. and LSTM model .

[0031] Step 4: System Equation Establishment: Based on the dynamic model of the rotary-wing UAV, the state equations are obtained by simultaneously solving the error hybrid model. The mapping relationship between gyroscope measurements and motion state / error is analyzed to establish the measurement equations. The specific implementation is as follows:

[0032] Take the local horizontal coordinate system as the inertial coordinate system The body coordinate system is denoted as Based on the Newton-Euler equations, a torque analysis is performed on the quadcopter UAV:

[0033] ,

[0034] in This refers to the torque generated by the quadcopter about the fuselage axis. For the inertia tensor of the unmanned aerial vehicle, Let be the rotational angular velocity. Here we neglect the gyroscope torque generated by the propeller rotation. .

[0035] Expanding the above equation, we can obtain the rotational dynamics equation for the quadcopter UAV as follows:

[0036] ,

[0037] remember The time control quantity is Discretizing the continuity equation yields:

[0038] ,

[0039] in Sampling time, It is a constant value. This refers to the error introduced when discretizing the dynamic model.

[0040] Considering that excessively high model order would lead to a dramatic increase in filtering computation, based on the state variables in the error model defined by the network model, the system state is defined as follows: ,in This represents the non-stationary subsequence of MEMS gyroscope errors. By simultaneously applying the rotational dynamics equations and the network model, the system's state equations are obtained:

[0041] ,

[0042] in, Represents a nonlinear transfer function; , for 3D identity matrix; express A zero-dimensional matrix, where Represent any positive integer; Indicates process noise. The covariance is denoted as ;

[0043] Consider a gyroscope mounted on the z-axis, and the gyroscope measurement values. The relationship with the state variables is as follows:

[0044] ,

[0045] in, For measurement matrix; This represents the total stationary error term predicted by the ARMA model. Since the ARMA model is not updated during the online update phase, it can be considered as a known constant. This represents the mixed modeling error. Subtracting LSTM prediction residuals The latter part, in this article, Modeled as a zero-mean Gaussian random variable, its covariance is .

[0046] In summary, the system equations are:

[0047] ,

[0048] Step 5: Online Error Estimation Method Based on Composite Interference Filter (CDF): Building upon the system equations in Step 4, a CDF method is designed to achieve real-time estimation of gyroscope errors and real-time updating of the error model. The specific implementation is as follows:

[0049] To estimate MEMS gyroscope errors in real time, a CDF filtering algorithm is designed based on the system equations. The algorithm consists of two parts: a filtering module and a model update module.

[0050] (1) Filtering module

[0051] a) Time update phase

[0052] right Optimal state estimate at time step Sampling is performed on the posterior probability distribution:

[0053] ,

[0054] In the formula For the first One volume point; and They represent The posterior state estimate and error covariance matrix at time t; This represents the square root of the matrix obtained by Cholesky decomposition. List;

[0055] Next, the sample points are transformed using a nonlinear function, and the predicted mean and covariance are calculated. Each volume point achieves state transition through a nonlinear transfer function:

[0056] ,

[0057] Each volume point needs to be propagated through the same nonlinear mapping. However, with the introduction of LSTM, its internal state and time memory units change with time steps and input. Therefore, the LSTM network is... Hidden state of time and memory cell state copy This corresponds to each volume point. Furthermore, the weights and biases of the LSTM network are... The time is fixed, thus ensuring that during the nonlinear transmission process, It remains unchanged.

[0058] Final weighted calculation Prior probability distribution of the state variable at time step:

[0059] ,

[0060] b) Measurement update phase

[0061] ,

[0062] therefore, optimal state estimate at time step and its error covariance for:

[0063] ,

[0064] in .

[0065] After completing the measurement update phase, from Extract the optimal error estimate This information is then used as input for subsequent LSTM updates. To simultaneously capture both short-term fluctuations and long-term trends in the error dynamics, we design a two-layer update strategy to update the LSTM network.

[0066] (2) Model update module

[0067] To strike a balance between short-term responsiveness and long-term adaptability, we designed a two-layer update strategy for the LSTM network: internal state update—enabling the network to respond quickly to recent changes; and model parameter update—gradually adapting to long-term drift through periodic fine-tuning. This design improves the robustness and consistency of the hybrid model.

[0068] a) Internal state update

[0069] Will Internal state at time 1 and The value is replicated to all volume points and kept constant during propagation. After the measurement update is complete, the optimal state estimate is... The input is fed into the LSTM unit to refresh its internal state.

[0070] ,

[0071] in This is the weight matrix. For bias terms, This represents the sigmoid activation function. This represents the activation function.

[0072] b) Model parameter update

[0073] The model parameters (i.e., weights and biases) are updated intermittently using a strategy inspired by incremental learning. Unlike methods that fully retrain the entire LSTM model at fixed intervals, we employ a sliding buffer to store the latest filter state estimates. Once a sufficient number of new estimates have accumulated in the buffer, a computationally inexpensive fine-tuning process is initiated, updating the model using mini-batch samples constructed from the buffer data. This process fine-tunes the previously learned parameters, allowing the model to gradually adapt to long-term changes in error dynamics at extremely low computational cost.

[0074] Specifically, Indicates in The time-constructed buffer contains Mini-batch of sequences. LSTM parameters. (Including all weights and biases) is updated by minimizing the mean squared error over mini-batches:

[0075] ,

[0076] in, For learning rate, This represents the current LSTM model. This update method allows the network to track changes in error patterns without requiring a complete retraining. With these updated parameters, the LSTM model can better capture error characteristics under real-time conditions.

[0077] It should be noted that these parameter updates are decoupled from the prediction phase in the filtering module and will not interfere with the propagation of volume points, because the updated parameters are only applied after the measurement update is completed. Relying on real-time weight updates and internal state evolution, the latest error information can be effectively incorporated into the LSTM network, thereby ensuring the consistency of the mixed error model and the accuracy of the state estimation results.

[0078] Compared with existing technologies, the present invention has the following advantages:

[0079] (1) Existing dynamic model-assisted gyroscope error modeling and real-time estimation methods often simply consider the error model as a random constant or a first-order Markov model. However, in reality, the gyroscope error sequence is affected by the error and exhibits randomness and non-stationarity. To address this issue, this invention proposes the concept of a hybrid model. Wavelet transform is used to extract the stationary component in the non-stationary error sequence to achieve error separation. ARMA model and LSTM model are established for stationary and non-stationary subsequences respectively, thereby obtaining a hybrid model of MEMS gyroscope error. This model can make full use of the useful information in the sequence, laying the foundation for real-time and accurate error estimation.

[0080] (2) This invention combines the hybrid model of gyroscope error with the carrier dynamics model and further incorporates it into the framework of the real-time filtering algorithm CDF. For the LSTM module, a two-layer update strategy is designed: on the one hand, the internal state (hidden state and memory unit state) of the LSTM is accurately refreshed based on the measurement update results to ensure that the network can quickly respond to short-term changes in error dynamics; on the other hand, the latest estimation results stored in the sliding buffer are used to periodically fine-tune the parameters (weights and biases) of the LSTM in small batches, enabling the model to gradually adapt to long-term drift trends. Through this two-layer update mechanism, real-time estimation and compensation of errors can be achieved, significantly improving the consistency of the hybrid model and the accuracy and robustness of the filtering results. Attached Figure Description

[0081] Figure 1 This is a flowchart of a composite interference filtering method for error separation and estimation of a dynamic-assisted gyroscope according to the present invention;

[0082] Figure 2 This is a schematic diagram of an online error estimation method based on composite interference filtering.

[0083] Figure 3 For different model error estimates; Detailed Implementation

[0084] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the protection scope of the present invention.

[0085] The method of this invention is specifically implemented as follows:

[0086] Step 1: Data Acquisition and Preprocessing: Offline acquisition of MEMS gyroscope error data and normalization processing.

[0087] Step 2, Error Sequence Decomposition: Using wavelet transform to decompose the error sequence of the MEMS gyroscope. Decompose the sequence into... There are one stationary subsequence and one non-stationary subsequence, among which It is a positive integer greater than or equal to 1. The specific implementation is as follows:

[0088] The normalized MEMS gyroscope error sequence is denoted as... , Indicates after normalization The observed values ​​of the time error; selecting the Daubechies wavelet basis function, and using discrete wavelet transform to decompose the error sequence. Among them, the th... The formula for subwavelet decomposition is:

[0089] ,

[0090] in, Indicates the first The trend sequence is obtained after wavelet decomposition. The sequence length; For the first Trend sequence after decomposition The sequence length; For the first The detailed sequence after the decomposition; Indicates a low-pass filter; Indicates a high-pass filter; when hour, This is the original error sequence.

[0091] For each subsequence, the signal is reconstructed so that the length of the subsequence is the same as that of the original sequence. The reconstruction formula is as follows:

[0092] ,

[0093] The KPSS stationarity test was performed on each of the decomposed subsequences to obtain the following results. a stationary subsequence and nonstationary subsequences The sum of the two is the total number of subsequences. Several non-stationary subsequences are merged into one non-stationary subsequence by addition. .

[0094] Step 3: Offline Mixed Model Establishment: For each stationary subsequence, establish an ARMA time series model. For non-stationary subsequences, an LSTM network model is established. The combined error mixture model is obtained as follows: The specific implementation is as follows:

[0095] Firstly, regarding a stationary subsequence The ARMA models are established separately, and the specific establishment process is as follows:

[0096] Using the Akaike Information Content Criterion (AIC) The model's order is determined visually by plotting a heatmap corresponding to the AIC value, which visually identifies the order at which the AIC value is minimized. and The AIC criterion is expressed as:

[0097] ,

[0098] in This is the maximum likelihood estimate of the model residual variance; The number of observations;

[0099] After determining the model order, the maximum likelihood estimation method is used to fit the model parameters, thereby obtaining the model order. ARMA model of stationary subsequences:

[0100] ,

[0101] in , These are the autoregressive order and the moving average order of the ARMA model, respectively. These are observations of a stationary subsequence; It is a historical random interference sequence; and These are the model coefficients; For ARMA model residuals.

[0102] For non-stationary subsequences The LSTM model is built using the following steps:

[0103] The non-stationary subsequence data is divided into several samples, with a window size of [missing value]. The rolling window, with its size referring to the input time period, is used. Each time window constitutes a sample as input to the LSTM, and the sequence value at the next time step after the window is the target value. The LSTM parameters, including the weight matrix and offset, can be obtained after training with the training set. Therefore, single-step prediction of the non-stationary subsequence of gyroscope error can be defined as using the previous... The non-stationary subsequence value at time 1 is used to predict the non-stationary subsequence value at the current time, as follows:

[0104] ,

[0105] in Represents the LSTM model. This represents the prediction error of the network model; by training the LSTM network, the dynamic characteristics of non-stationary subsequences are learned, thereby accurately predicting the value of the non-stationary subsequence at the next time step and continuously updating the internal state of the network.

[0106] In summary, by combining the stationary subsequence ARMA model and the non-stationary subsequence LSTM network model, a hybrid model of MEMS gyroscope error is obtained:

[0107] ,

[0108] in represent Error value at any given time; Representing the ARMA model estimation of stationary subsequences; LSTM model estimation representing non-stationary subsequences; This represents the model error of the mixture model, including the error of each ARMA model. and LSTM model .

[0109] Step 4: System Equation Establishment: Based on the dynamic model of the rotary-wing UAV, the state equations are obtained by simultaneously solving the error hybrid model. The mapping relationship between gyroscope measurements and motion state / error is analyzed to establish the measurement equations. The specific implementation is as follows:

[0110] Take the local horizontal coordinate system as the inertial coordinate system The body coordinate system is denoted as Based on the Newton-Euler equations, a torque analysis is performed on the quadcopter UAV:

[0111] ,

[0112] in This refers to the torque generated by the quadcopter about the fuselage axis. For the inertia tensor of the unmanned aerial vehicle, Let be the rotational angular velocity. Here we neglect the gyroscope torque generated by the propeller rotation. .

[0113] Expanding the above equation, we can obtain the rotational dynamics equation for the quadcopter UAV as follows:

[0114] ,

[0115] remember The time control quantity is Discretizing the continuity equation yields:

[0116] ,

[0117] in Sampling time, It is a constant value. This refers to the error introduced when discretizing the dynamic model.

[0118] Considering that excessively high model order would lead to a dramatic increase in filtering computation, based on the state variables in the error model defined by the network model, the system state is defined as follows: ,in This represents the non-stationary subsequence of MEMS gyroscope errors. By simultaneously applying the rotational dynamics equations and the network model, the system's state equations are obtained:

[0119] ,

[0120] in, Represents a nonlinear transfer function; , for 3D identity matrix; express A zero-dimensional matrix, where Represent any positive integer; Indicates process noise. The covariance is denoted as ;

[0121] Consider a gyroscope mounted on the z-axis, and the gyroscope measurement values. The relationship with the state variables is as follows:

[0122] ,

[0123] in, For measurement matrix; This represents the total stationary error term predicted by the ARMA model. Since the ARMA model is not updated during the online update phase, it can be considered as a known constant. This represents the mixed modeling error. Subtracting LSTM prediction residuals The latter part, in this article, Modeled as a zero-mean Gaussian random variable, its covariance is .

[0124] In summary, the system equations are:

[0125] ,

[0126] Step 5: Online Error Estimation Method Based on Composite Interference Filter (CDF): Building upon the system equations in Step 4, a CDF method is designed to achieve real-time estimation of gyroscope errors and real-time updating of the error model. The specific implementation is as follows:

[0127] To estimate MEMS gyroscope errors in real time, a CDF filtering algorithm is designed based on the system equations. The algorithm consists of two parts: a filtering module and a model update module.

[0128] (1) Filtering module

[0129] a) Time update phase

[0130] right Optimal state estimate at time step Sampling is performed on the posterior probability distribution:

[0131] ,

[0132] In the formula For the first One volume point; and They represent The posterior state estimate and error covariance matrix at time t; This represents the square root of the matrix obtained by Cholesky decomposition. List;

[0133] Next, the sample points are transformed using a nonlinear function, and the predicted mean and covariance are calculated. Each volume point achieves state transition through a nonlinear transfer function:

[0134] ,

[0135] Each volume point needs to be propagated through the same nonlinear mapping. However, with the introduction of LSTM, its internal state and time memory units change with time steps and input. Therefore, the LSTM network is... Hidden state of time and memory cell state copy This corresponds to each volume point. Furthermore, the weights and biases of the LSTM network are... The time is fixed, thus ensuring that during the nonlinear transmission process, It remains unchanged.

[0136] Final weighted calculation Prior probability distribution of the state variable at time step:

[0137] ,

[0138] b) Measurement update phase

[0139] ,

[0140] therefore, optimal state estimate at time step and its error covariance for:

[0141] ,

[0142] in .

[0143] After completing the measurement update phase, from Extract the optimal error estimate This information is then used as input for subsequent LSTM updates. To simultaneously capture both short-term fluctuations and long-term trends in the error dynamics, we design a two-layer update strategy to update the LSTM network.

[0144] (2) Model update module

[0145] To strike a balance between short-term responsiveness and long-term adaptability, we designed a two-layer update strategy for the LSTM network: internal state update—enabling the network to respond quickly to recent changes; and model parameter update—gradually adapting to long-term drift through periodic fine-tuning. This design improves the robustness and consistency of the hybrid model.

[0146] a) Internal state update

[0147] Will Internal state at time 1 and The value is replicated to all volume points and kept constant during propagation. After the measurement update is complete, the optimal state estimate is... The input is fed into the LSTM unit to refresh its internal state.

[0148] ,

[0149] in This is the weight matrix. For bias terms, This represents the sigmoid activation function. This represents the activation function.

[0150] b) Model parameter update

[0151] The model parameters (i.e., weights and biases) are updated intermittently using a strategy inspired by incremental learning. Unlike methods that fully retrain the entire LSTM model at fixed intervals, we employ a sliding buffer to store the latest filter state estimates. Once a sufficient number of new estimates have accumulated in the buffer, a computationally inexpensive fine-tuning process is initiated, updating the model using mini-batch samples constructed from the buffer data. This process fine-tunes the previously learned parameters, allowing the model to gradually adapt to long-term changes in error dynamics at extremely low computational cost.

[0152] Specifically, Indicates in The time-constructed buffer contains Mini-batch of sequences. LSTM parameters. (Including all weights and biases) is updated by minimizing the mean squared error over mini-batches:

[0153] ,

[0154] in, For learning rate, This represents the current LSTM model. This update method allows the network to track changes in error patterns without requiring a complete retraining. With these updated parameters, the LSTM model can better capture error characteristics under real-time conditions.

[0155] It should be noted that these parameter updates are decoupled from the prediction phase in the filtering module and will not interfere with the propagation of volume points, because the updated parameters are only applied after the measurement update is completed. Relying on real-time weight updates and internal state evolution, the latest error information can be effectively incorporated into the LSTM network, thereby ensuring the consistency of the mixed error model and the accuracy of the state estimation results.

[0156] Example:

[0157] To verify the effectiveness of the proposed method, semi-physical simulation results are presented below. The comparison methods are the ARMA model and the LSTM model combined with capacitive Kalman filtering (CKF) for dynamic-assisted gyroscope error estimation.

[0158] Design a quadcopter drone to perform a figure-eight maneuver and generate true values ​​for IMU measurement and control quantities. Acquire actual MEMS gyroscope errors and inject them into the z-axis gyroscope measurement values, while simultaneously injecting noise into the control quantities. The experimental equipment for gyroscope error acquisition includes a power supply, a MEMS inertial measurement unit ADIS16465, and a host computer. The ADIS16465 contains a three-axis digital gyroscope with zero-bias stability. Angle random walk is The IMU was placed statically on the test bench and preheated to a stable temperature before error data was collected.

[0159] Since gyroscope error data is a discrete signal, it meets the conditions for discrete wavelet transform. This invention uses the Daubechies wavelet 4 as the mother wavelet, striking a trade-off between wavelength and smoothness. To fully extract stationary information from non-stationary sequences, a four-level wavelet decomposition is performed. Four groups of stationary subsequences and one group of non-stationary subsequences are obtained through KPSS stationarity detection. Based on the AIC criterion, the ARMA model orders for the four groups of stationary subsequences are determined to be [7,6], [10,8], [10,9], and [10,10]. The LSTM model consists of a single-layer structure containing 64 hidden units, followed by a dropout layer (scale = 0.2) and a fully connected output layer. The network is trained using the Adam optimizer for 200 iterations with an initial learning rate of... The input sequence is constructed using a sliding window with a window size of 4. During parameter updates, the LSTM parameters are updated every 100 time steps, with the updated samples taken from the latest filtered state stored in the sliding buffer. Each update iteration consists of 10 loops, with a learning rate of... This allows the model to gradually adapt to the dynamic evolution of the error, while reducing the risk of overfitting. Error estimation results under different methods are shown below. Figure 2 As shown.

[0160] To quantitatively compare different error estimation methods, we selected three statistics for comparison regarding the estimation error compensation residuals, including the coefficient of determination (COP). (Measures the model's fit to the data; the closer to 1, the better the model fit), Mean Absolute Error (MAE) ) and mean square error ( Specifically defined as:

[0161] ,

[0162] in This represents the error estimate; This is the true value of the error; This represents the amount of data in the test set. The statistical information on the prediction errors of the three methods is shown in Table 1.

[0163] Table 1. Statistical information on residuals from error estimation using different methods

[0164]

[0165] like Figure 2As shown in Table 1, the proposed hybrid model + CDF method can estimate the error more accurately with the assistance of a dynamic model. , and As the main performance indicators, the performance of various error estimation and compensation methods was evaluated. The results show that the proposed method outperforms other methods in all three indicators.

[0166] Although the illustrative specific embodiments of the present invention have been described above to enable those skilled in the art to understand the invention, it should be understood that the invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes will be obvious as long as they are within the spirit and scope of the invention as defined and determined by the appended claims, and all inventions utilizing the concept of the present invention are protected.

Claims

1. A composite interference filtering method for error separation and estimation of a dynamic-assisted gyroscope, characterized in that, Includes the following steps: Step 1: Data Acquisition and Preprocessing: Offline acquisition of error data from MEMS gyroscopes and normalization processing. Step 2, Error Sequence Decomposition: Using wavelet transform to decompose the error sequence of the MEMS gyroscope. Decompose the sequence into... There are one stationary subsequence and one non-stationary subsequence, among which It is a positive integer greater than or equal to 1; Step 3: Offline Mixed Model Establishment: For each stationary subsequence, establish an ARMA time series model. For non-stationary subsequences, an LSTM network model is established. The combined error mixture model is obtained as follows: ; Step 4: Establishing System Equations: Based on the dynamic model of the rotary-wing UAV, the state equations are obtained by combining them with the error hybrid model; the mapping relationship between gyroscope measurements and motion state and error is analyzed to establish measurement equations; Step 5: Online error estimation method based on composite interference filter CDF: Based on the system equations in Step 4, CDF is designed to realize real-time estimation of gyroscope error and real-time updating of error model; The fifth step is as follows: To estimate MEMS gyroscope errors in real time, a CDF filtering algorithm is designed for the system equations. The algorithm consists of two parts: a filtering module and a model update module. (1) Filtering module a) Time update phase right Optimal state estimate at time step Sampling is performed on the posterior probability distribution: ， In the formula For the first One volume point; and They represent The posterior state estimate and error covariance matrix at time t; This represents the square root of the matrix obtained by Cholesky decomposition. List; Next, the sample points are transformed using a nonlinear function, and the predicted mean and covariance are calculated; Each volume point achieves state transition through a nonlinear transfer function: ， Each volume point needs to be propagated through the same nonlinear mapping; however, with the introduction of LSTM, its internal state and time memory units change with time steps and input; therefore, the LSTM network is... Hidden state of time and memory cell state copy This corresponds to each volume point; furthermore, the weights and bias parameters of the LSTM network are... The time is fixed, thus ensuring that during the nonlinear transmission process, Remain unchanged; Final weighted calculation Prior probability distribution of the state variable at time step: ， b) Measurement update phase ， therefore, optimal state estimate at time step and its error covariance for: ； in ; After completing the measurement update phase, from Extract the optimal error estimate We use this as input for subsequent LSTM updates; in order to capture both short-term fluctuations and long-term trends in the error dynamics, we design a two-layer update strategy to update the LSTM network. (2) Model update module To achieve a balance between short-term responsiveness and long-term adaptability, we designed a two-layer update strategy for LSTM networks: internal state update—enabling the network to respond quickly to recent changes; and model parameter update—gradually adapting to long-term drift through periodic fine-tuning. This design improves the robustness and consistency of the hybrid model. a) Internal state update Will Internal state at time 1 and The data is copied to all volume points and kept fixed during propagation; after the measurement update is complete, the optimal state estimate is... The input is fed into the LSTM unit to refresh its internal state. ， in This is the weight matrix. For bias terms, This represents the sigmoid activation function. Indicates the activation function; b) Model parameter update The model parameters are updated intermittently using a strategy inspired by incremental learning; unlike methods that fully retrain the entire LSTM model at fixed intervals, we use a sliding buffer to store the latest filter state estimates. Once a sufficient number of new estimates have accumulated in the buffer, a computationally inexpensive fine-tuning process will be initiated, updating the model using a small batch of samples constructed from the buffer data. This process fine-tunes the previously learned parameters, enabling the model to gradually adapt to long-term changes in error dynamics at extremely low computational cost. Specifically, Indicates in The time-constructed buffer contains Mini-batch of sequences; LSTM parameters Update by minimizing the mean squared error over mini-batch: ， in, For learning rate, This represents the current LSTM model; this update method enables the network to track changes in error patterns without requiring complete retraining; with these updated parameters, the LSTM model can better capture error characteristics under real-time conditions; It should be noted that these parameter updates are decoupled from the prediction stage in the filtering module and will not interfere with the propagation of volume points, because the updated parameters are only applied after the measurement update is completed; relying on real-time weight updates and internal state evolution, the latest error information can be effectively incorporated into the LSTM network, thereby ensuring the consistency of the mixed error model and the accuracy of the state estimation results.

2. The composite interference filtering method for error separation and estimation of a dynamic-assisted gyroscope according to claim 1, characterized in that, In the second step, wavelet transform is introduced to extract the stationary components from the non-stationary sequence. The specific steps are as follows: The normalized MEMS gyroscope error sequence is denoted as... , Indicates after normalization The observed value of the time error; The Daubechies wavelet basis functions are selected, and the error sequence is decomposed using discrete wavelet transform; where, the th The formula for subwavelet decomposition is: ， in, Indicates the first The trend sequence is obtained after wavelet decomposition. The sequence length; For the first Trend sequence after decomposition The sequence length; For the first The detailed sequence after the decomposition; Indicates a low-pass filter; Indicates a high-pass filter; when hour, This is the original error sequence; For each subsequence, the signal is reconstructed so that the length of the subsequence is the same as that of the original sequence. The reconstruction formula is as follows: ， The KPSS stationarity test was performed on each of the decomposed subsequences to obtain the following results. a stationary subsequence and nonstationary subsequences The sum of the two is the total number of subsequences; Several non-stationary subsequences are merged into one non-stationary subsequence by addition. .

3. The composite interference filtering method for error separation and estimation of a dynamic-assisted gyroscope according to claim 1, characterized in that, The third step is as follows: Firstly, regarding a stationary subsequence The ARMA models are established separately, and the specific establishment process is as follows: Using the Akaike Information Content Criterion (AIC) The model's order is determined visually by plotting a heatmap corresponding to the AIC value, which visually identifies the order at which the AIC value is minimized. and The AIC criterion is expressed as: ， in This is the maximum likelihood estimate of the model residual variance; The number of observations; After determining the model order, the maximum likelihood estimation method is used to fit the model parameters, thereby obtaining the model order. ARMA model of stationary subsequences: ， in , These are the autoregressive order and the moving average order of the ARMA model, respectively. These are observations of a stationary subsequence; It is a historical random interference sequence; and These are the model coefficients; For ARMA model residuals; For non-stationary subsequences The LSTM model is built using the following steps: The non-stationary subsequence data is divided into several samples, with a window size of [missing value]. The rolling window, with its size referring to the input time period, is used. Each time window constitutes a sample as input to the LSTM, and the sequence value at the next time step after the window is the target value. The LSTM parameters, including the weight matrix and offset, can be obtained after training with the training set. Therefore, single-step prediction of the non-stationary subsequence of gyroscope error can be defined as using the previous... The non-stationary subsequence value at time 1 is used to predict the non-stationary subsequence value at the current time, as follows: ， in Represents the LSTM model. This represents the prediction error of the network model; by training the LSTM network, the dynamic characteristics of non-stationary subsequences are learned, thereby accurately predicting the value of the non-stationary subsequence at the next time step and continuously updating the internal state of the network. In summary, by combining the stationary subsequence ARMA model and the non-stationary subsequence LSTM network model, a hybrid model of MEMS gyroscope error is obtained: ， in represent Error value at any given time; Representing the ARMA model estimation of stationary subsequences; LSTM model estimation representing non-stationary subsequences; This represents the model error of the mixture model, including the error of each ARMA model. and LSTM model .

4. The composite interference filtering method for error separation and estimation of a dynamic-assisted gyroscope according to claim 1, characterized in that, The fourth step is as follows: Take the local horizontal coordinate system as the inertial coordinate system The body coordinate system is denoted as Based on the Newton-Euler equations, a torque analysis is performed on the quadcopter UAV: ， in This refers to the torque generated by the quadcopter about the fuselage axis. For the inertia tensor of the unmanned aerial vehicle, Here we are referring to the rotational angular velocity; we are neglecting the gyroscope torque generated by the propeller rotation. ; Expanding the above equation, we can obtain the rotational dynamics equation for the quadcopter UAV as follows: ， remember Time control quantity is Discretizing the continuity equation yields: ， in Sampling time, It is a constant value. The error introduced when discretizing the dynamic model; Considering that excessively high model order would lead to a dramatic increase in filtering computation, based on the state variables in the error model defined by the network model, the system state is defined as follows: ,in The non-stationary subsequence of MEMS gyroscope error is given; by simultaneously solving the rotational dynamics equations and the network model, the system's state equation is obtained: ， in, Represents a nonlinear transfer function; , for 3D identity matrix; express A zero-dimensional matrix, where Represent any positive integer; Indicates process noise. The covariance is denoted as ; Consider a gyroscope mounted on the z-axis, and the gyroscope measurement values. The relationship with the state variables is as follows: ， in, For measurement matrix; This represents the total stationary error term predicted by the ARMA model. Since the ARMA model is not updated during the online update phase, it can be considered as a known constant. Indicates hybrid modeling error Subtracting LSTM prediction residuals The latter part, in this article, Modeled as a zero-mean Gaussian random variable, its covariance is ; In summary, the system equations are: 。

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