IMU attitude estimation and error correction method based on state space physical information neural network

Abstract

The invention relates to the technical field of inertial navigation and sensor fusion, in particular to an IMU (inertial measurement unit) attitude estimation and error correction method based on a state space physical information neural network, which comprises the following steps: acquiring original data of an IMU and preprocessing; constructing a state space model, and designing a state transition physical information neural network based on the state space model; training the state transition physical information neural network based on the preprocessed original data, optimizing network parameters through a joint loss function in the training process, and obtaining the trained state transition physical information neural network; and collecting real-time data streams of the IMU, inputting the real-time data streams into the trained state transition physical information neural network, and outputting the corrected pose, position and speed. According to the method, physical constraints and adaptive noise estimation are fused, so that the attitude estimation precision and the error correction capability in a dynamic complex environment are remarkably improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of inertial navigation and sensor fusion, in particular to an IMU attitude estimation and error correction method based on a state space physical information neural network, which is suitable for high-precision navigation and motion tracking in complex dynamic environments. BACKGROUND

[0002] In modern navigation and control systems, IMU is widely used in aerospace, unmanned driving, robots and other fields due to its advantages of not needing external signal support, fast response and being able to provide real-time dynamic attitude information. However, due to the inherent measurement errors of IMU internal sensors such as bias, noise and nonlinearity, these errors will accumulate over time, leading to a decrease in attitude estimation accuracy, and seriously affecting the stability and reliability of the system.

[0003] Traditional methods such as Kalman filtering can fuse multi-sensor data, but they are not suitable for nonlinear systems and high dynamic environments, and they rely on accurate noise models.

[0004] With the rapid development of deep learning technology, physical information neural network as a new model combining physical knowledge and neural network, has shown great potential in dealing with complex physical problems. PINN can efficiently optimize and model errors while ensuring physical consistency by embedding physical constraints and equations into the loss function of neural network. However, existing PINN focuses on static physical equation residual constraints and lacks the ability to model dynamic system state evolution, making it difficult to be directly applied to IMU, a time-varying system.

[0005] Therefore, there is an urgent need for a method that combines dynamic system state space model and PINN to adaptively estimate sensor noise while ensuring physical law consistency, and to achieve high-precision IMU attitude estimation and error correction. SUMMARY

[0006] The purpose of the present application is to provide an IMU attitude estimation and error correction method based on a state space physical information neural network, which can reduce hardware costs, improve the physical consistency of dynamic system modeling, and enhance the robustness of the model to complex environments.

[0007] To achieve the above purpose, the present application provides the following scheme:

[0008] An IMU attitude estimation and error correction method based on a state space physical information neural network, comprising:

[0009] Collecting and preprocessing the original data of the IMU;

[0010] Construct a state-space model and design a state transition physical information neural network based on the state-space model;

[0011] The state transition physical information neural network is trained based on the preprocessed raw data, and the network parameters are optimized through a joint loss function during the training process to obtain the trained state transition physical information neural network.

[0012] The real-time data stream from the IMU is collected and input into the trained state transition physical information neural network, which outputs the corrected pose, position, and velocity.

[0013] Optionally, collecting the raw data from the IMU includes: collecting data from a three-axis accelerometer and a three-axis gyroscope, and simultaneously recording timestamps.

[0014] Optionally, the preprocessing includes: timestamp alignment, sliding window cropping, and normalization.

[0015] Optionally, the state-space model is constructed as follows:

[0016] x t =[q t ,r t ,v t ] T ;

[0017]

[0018] Where, x t q is a state variable. t Let r be the attitude quaternion. t Let v be the position vector. t Let t be the velocity vector and t be the time. The time derivative of the attitude quaternion. To represent quaternion multiplication, The angular velocity is measured by a three-axis gyroscope. The time derivative of the position vector. The time derivative of the velocity vector. is the specific force measured by the triaxial accelerometer, and g is the gravitational acceleration vector.

[0019] Optionally, the state transition physical information neural network includes:

[0020] The backbone network is used to extract the joint temporal and spatial features of the input data and output a multidimensional feature vector.

[0021] The state prediction branch is used to predict the state variables at time t based on the multidimensional feature vector.

[0022] a noise estimation branch configured to dynamically estimate an observation noise covariance and a process noise covariance based on the multi-dimensional feature vector.

[0023] Optionally, the backbone network extracts features of the input data through a multi-layer perceptron with a residual connection and a ReLU activation function; the state prediction branch outputs a state variable prediction value through a first linear layer; and the noise estimation branch outputs a diagonalized observation noise covariance and a process noise covariance through a second linear layer and a Softplus function.

[0024] Optionally, the joint loss function is:

[0025] L total = L obs + λ1L phys + λ2L bc + λ3L reg ;

[0026]

[0027] L reg = λ(tr(Σ) + tr(Q));

[0028] wherein L total is a total loss, L obs is an observation residual loss, L phys is a physical residual loss, L bc is a boundary condition loss, L reg is a regularization loss, λ1, λ2 and λ3 are weights of the physical residual loss, the boundary condition loss and the regularization loss respectively, t is time, is an IMU observation value, i.e., raw data of an accelerometer and a gyroscope, h(·) is an observation function, is a prediction value of a state variable, f(·) is a state transition equation, u t is a control input, i.e., data of a gyroscope and an accelerometer, is a network-predicted initial time quaternion, is a network-predicted terminal time quaternion, and are reference quaternions, λ is a regularization coefficient for balancing the constraint strength of the noise covariance, Σ is an observation noise covariance matrix, and Q is a process noise covariance matrix.

[0029] Optionally, the optimization of the network parameters in the process through the joint loss function comprises: training the state transition physical information neural network through a back propagation algorithm, dynamically adjusting the weights of the network and the parameters of the noise covariance, until the loss function converges, wherein the noise covariance is used to suppress the influence of abnormal values of a three-axis accelerometer on attitude estimation through calculation of a Mahalanobis distance weight.

[0030] Also provided is a computer system comprising: one or more processors, a computer readable storage medium for storing one or more programs which, when executed by the one or more processors, cause the one or more processors to implement the method.

[0031] Also provided is a computer readable storage medium storing computer executable instructions which, when executed, implement the method.

[0032] The present application has the following beneficial effects:

[0033] The IMU attitude estimation and error correction method based on a state space physical information neural network provided by the present application significantly improves the attitude estimation accuracy and error correction capability in a dynamic complex environment by fusing physical constraints and adaptive noise estimation; the present application embeds the IMU kinematic equation into the neural network, forces the network output to comply with the physical law, and avoids the attitude drift problem of traditional data-driven methods; by estimating the observation noise and process noise covariance in real time, combining the Mahalanobis distance weighted suppression of outliers, and jointly optimizing the observation residual, the physical residual and the boundary condition loss, the cooperative optimization of attitude estimation and error correction is realized. The SS-PINN can exhibit strong robustness in complex noise environments such as vibration and electromagnetic interference; further, based on the nonlinear modeling capability of the neural network, it can handle high-order nonlinear relationships without relying on linearization assumptions, providing a high-precision, low-latency dynamic attitude estimation solution for autonomous driving, robot navigation and other fields. BRIEF DESCRIPTION OF DRAWINGS

[0034] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of these drawings.

[0035] Figure 1 A flow chart of the IMU attitude estimation and error correction method based on a state space physical information neural network of an embodiment of the present application;

[0036] Figure 2 A state transition physical information neural network structure diagram of an embodiment of the present application;

[0037] Figure 3 An IMU three-axis attitude estimation and error correction result diagram of an embodiment of the present application. DETAILED DESCRIPTION

[0038] With reference to the accompanying drawings, the technical solutions in the embodiments of the present application will be described clearly and completely. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative effort belong to the scope of the present application.

[0039] In order to make the above objectives, characteristics and advantages of the present application more apparent, the present application will be described in further detail below with reference to the accompanying drawings and specific embodiments.

[0040] The embodiment provides an IMU attitude estimation and error correction method based on a state space physical information neural network, as shown in Figure 1 , which comprises the following steps.

[0041] Raw data of the IMU is collected and preprocessed;

[0042] A state space model is constructed, and a state transition physical information neural network is designed based on the state space model;

[0043] The state transition physical information neural network is trained based on the preprocessed raw data, and the network parameters are optimized through a joint loss function during the training process, so as to obtain the trained state transition physical information neural network;

[0044] Real-time data stream of the IMU is collected and input into the trained state transition physical information neural network, and corrected attitude, position and velocity are output.

[0045] Specifically, the embodiment collects raw data of a three-axis accelerometer and a gyroscope through the IMU in real time, synchronously acquires reference attitude data, and pre-processes the raw data. Then, a state space model is constructed, a state variable is defined, a state transition differential equation set, a position equation and a velocity equation are established based on an IMU kinematics equation, and a physical information neural network is designed. In the network training stage, a joint loss function is used and the Adam optimizer is used for back propagation, and the parameters are updated in batches by using a sliding window strategy; the corrected attitude quaternion is converted into Euler angles through a real-time inference module, for calling by a navigation system. The noise parameter is constrained to be positive definite through a Softplus function throughout the process, and the loss weight is dynamically adjusted, so as to ensure the robustness and precision of the model in a complex dynamic environment. The method comprises the following four parts.

[0046] (1) Real-time collection and preprocessing of IMU data:

[0047] Raw data is collected in real time by using an inertial measurement unit carried on a carrier, including three-axis accelerometer data and three-axis gyroscope data Synchronize the recording timestamp t. Then pre-process the raw data:

[0048] 1) Time stamp alignment: compensate the time delay between sensors by interpolation, ensure the synchronization of accelerometer and gyroscope data.

[0049] 2) Sliding window clipping: clip the previous 1000 consecutive sampling points with the current time as the end point, and complete the window length by linear interpolation when the window length is insufficient.

[0050] 3) Normalization: normalize the accelerometer data according to the gravitational acceleration g = 9.81 m / s 2 , and the gyroscope data according to the maximum range (such as ±2000° / s).

[0051] (2) State space model construction and SS-PINN network design:

[0052] 1) Define state variables:

[0053] x t =[q t ,r t ,v t ] T ;

[0054] where, is the attitude quaternion, representing the rotation state of the carrier at time t; r t is the position vector, representing the three-dimensional coordinates of the carrier in the global coordinate system; v t is the velocity vector, representing the instantaneous velocity of the carrier in the global coordinate system.

[0055] And based on the differential equation, the state transition process is constructed:

[0056]

[0057] where, is the time derivative of the quaternion, represents the quaternion multiplication, is the angular velocity measured by the three-axis gyroscope, is the specific force measured by the three-axis accelerometer, and g is the gravitational acceleration vector.

[0058] 2) Design the state transition physical information neural network (SS-PINN) structure:

[0059] As shown in Figure 2 , the input of SS-PINN is time t and IMU raw data The output includes: a. State prediction value b. Observation noise covariance matrix Σ and process noise covariance matrix Q.

[0060] SS-PINN adopts a multi-branch neural network structure, which consists of a backbone network and two task branches (state prediction branch, noise estimation branch). The core design is as follows:

[0061] 1. The backbone network is used to extract the time-space joint features of the input data, providing shared low-level feature representation for state prediction and noise estimation. The network structure is as follows:

[0062] Input layer: 7-dimensional vector [t, a x , a y , a z , ω x , ω y , ω z ] (timestamp + IMU six-axis data).

[0063] Hidden layer: 3 layers of fully connected (MLP), each layer with 128 dimensions, and the activation function is ReLU, used to extract time-space features. Residual connection is used between layers to alleviate the problem of gradient disappearance.

[0064] Output layer: 128-dimensional feature vector h t .

[0065] 2. The state prediction branch is used to predict the state variables at time t: attitude quaternion q t , position r t , velocity v t . The network structure is as follows:

[0066] Input layer: feature h t output by the backbone network.

[0067] Output layer: linear layer (Linear(128→10)), output 10-dimensional vector quaternion part forced normalization

[0068] 3. The noise estimation branch is used to dynamically estimate the observation noise covariance Σ and the process noise covariance Q, both of which are diagonal matrices. The network structure is as follows:

[0069] Input layer: feature h t output by the backbone network.

[0070] Output layer: linear layer (Linear(128→6)), output 6-dimensional vector Through the Softplus function to generate diagonal observation noise covariance Σ and process noise covariance Q, to ensure positive definiteness.

[0071] (3) Joint loss function optimization and model training:

[0072] 1) Design a loss function that jointly optimizes the following four terms:

[0073] Observation residual loss (data-driven term):

[0074]

[0075] in, These are IMU observations. h(·) is the observation function. quaternion_rotate() is the quaternion rotation function, where Σ is dynamically estimated by the network and substituted into the equation:

[0076]

[0077] Physical residual loss (physical constraint term):

[0078]

[0079] Where f(·) is the state transition equation, and Q is the network estimate used to weight the state transition error, which, when substituted, gives:

[0080]

[0081] Boundary condition loss:

[0082]

[0083] Force the initial and final time quaternions to align with the reference values.

[0084] Regularization loss:

[0085] L reg =λ(tr(Σ)+tr(Q));

[0086] This embodiment specifically refers to: L reg =0.01(tr(Σ)+tr(Q)), to prevent excessive divergence of noise covariance.

[0087] 2) Model training and optimization:

[0088] The specific steps are as follows:

[0089] 1. Forward propagation: Input time series, output state prediction and noise parameters through backbone network and branch network.

[0090] 2. Residual calculation: Use automatic differentiation to verify physical consistency.

[0091] 3. Loss Weighting: Dynamically Adjusted L obs L phys L bc Weights.

[0092] 4. Back propagation: update parameters using Adam optimizer, prioritize optimizing physical residual term.

[0093] Training strategy: Adam optimizer, initial learning rate 1x10 -3 , decay rate 0.95 every 2000 steps.

[0094] Termination condition: loss change less than 1x10 -5 for 100 consecutive training cycles or reach maximum iteration number (5000).

[0095] (4) Real-time inference and error correction:

[0096] 1) Deploy the trained SS-PINN model to the embedded platform, input real-time IMU data stream, output corrected attitude position and velocity

[0097] 2) Dynamic noise suppression:

[0098] According to the real-time estimated observation noise covariance matrix Σ and process noise covariance matrix Q, Mahalanobis distance weighted filtering is performed on the accelerometer outliers (such as vibration interference). Adjust the state prediction confidence to suppress the accumulation of process noise.

[0099] Also includes experimental verification steps:

[0100] a. Verify quaternion unit constraint in static scene

[0101] b. Calculate attitude angle root mean square error (RMSE) in dynamic scene.

[0102] The results before and after IMU three-axis attitude estimation and error correction using the method provided in the embodiment are shown in Figure 3 , where the dashed line is the original error, representing the deviation between the original measurement value of the IMU accelerometer and the true value; the solid line is the PINN residual, reflecting the final deviation between the SS-PINN predicted value and the true value; the dotted line is the SS-PINN corrected value, showing the difference between the SS-PINN predicted value and the original measurement value, and reflecting the correction amplitude of the model to noise. Among them, the SS-PINN corrected value tends to zero (±0.1m / s 2 ) as a whole, and the fluctuation is smooth, proving that SS-PINN significantly improves the accuracy of attitude estimation.

[0103] The embodiment also provides a computer system, comprising: one or more processors, a computer readable storage medium for storing one or more programs, which when executed by the one or more processors, cause the one or more processors to implement the method.

[0104] and a computer readable storage medium storing computer executable instructions, which when executed, implement the method.

[0105] The above described embodiments are merely intended to describe the preferred modes of the present application, and are not intended to limit the scope of the present application. Various modifications and improvements made by those skilled in the art to the technical solutions of the present application without departing from the design spirit of the present application shall fall within the protection scope of the present application defined by the claims.

Claims

1. A method for IMU attitude estimation and error correction based on a state-space physical information neural network, characterized in that, include: Collect raw data from the IMU and preprocess it; Construct a state-space model and design a state transition physical information neural network based on the state-space model; The state transition physical information neural network is trained based on the preprocessed raw data, and the network parameters are optimized through a joint loss function during the training process to obtain the trained state transition physical information neural network. The real-time data stream from the IMU is collected and input into the trained state transition physical information neural network, which outputs the corrected pose, position, and velocity.

2. The IMU attitude estimation and error correction method based on state-space physical information neural network according to claim 1, characterized in that, The raw data collected from the IMU includes: collecting data from the three-axis accelerometer and the three-axis gyroscope, and recording the timestamps simultaneously.

3. The IMU attitude estimation and error correction method based on state-space physical information neural network according to claim 1, characterized in that, The preprocessing includes: timestamp alignment, sliding window cropping, and normalization.

4. The IMU attitude estimation and error correction method based on state-space physical information neural network according to claim 1, characterized in that, The state-space model is constructed as follows: x t =[q t ,r t ,v t ] T ; Where, x t q is a state variable. t Let r be the attitude quaternion. t Let v be the position vector. t Let t be the velocity vector and t be the time. The time derivative of the attitude quaternion. To represent quaternion multiplication, The angular velocity is measured by a three-axis gyroscope. The time derivative of the position vector. The time derivative of the velocity vector. is the specific force measured by the triaxial accelerometer, and g is the gravitational acceleration vector.

5. The IMU attitude estimation and error correction method based on state-space physical information neural network according to claim 1, characterized in that, The state transition physical information neural network includes: The backbone network is used to extract the joint temporal and spatial features of the input data and output a multidimensional feature vector. The state prediction branch is used to predict the state variables at time t based on the multidimensional feature vector. The noise estimation branch is used to dynamically estimate the observation noise covariance and process noise covariance based on the multidimensional feature vector.

6. The IMU attitude estimation and error correction method based on state-space physical information neural network according to claim 5, characterized in that, The backbone network uses a multilayer perceptron with residual connections and a ReLU activation function to extract features from the input data; the state prediction branch outputs predicted values ​​of state variables through a first linear layer; and the noise estimation branch outputs diagonalized observation noise covariance and process noise covariance through a second linear layer and a Softplus function.

7. The IMU attitude estimation and error correction method based on state-space physical information neural network according to claim 1, characterized in that, The joint loss function is: L total =L obs +λ1L phys +λ2L bc +λ3L reg ; 50 reg =λ(tr(Σ)+tr(Q)); Among them, L total For the total loss, L obs To observe residual loss, L phys For physical residual loss, L bc For boundary condition loss, L reg The loss is denoted as regularization loss, where λ1, λ2, and λ3 are the weights of the physical residual loss, boundary condition loss, and regularization loss, respectively, and t is the time interval. The values ​​are IMU observations, i.e., raw data from the accelerometer and gyroscope, and h(·) is the observation function. Let f(·) be the predicted value of the state variable, and u be the state transition equation. t For control input, namely gyroscope and accelerometer data, The initial time step quaternion predicted by the network. Let be the quaternion for the predicted termination time of the network. and λ is the reference quaternion, λ is the regularization coefficient used to balance the constraint strength of the noise covariance, Σ is the observation noise covariance matrix, and Q is the process noise covariance matrix.

8. The IMU attitude estimation and error correction method based on state-space physical information neural network according to claim 1, characterized in that, The optimization of network parameters through the joint loss function during the training process includes: training the state transition physical information neural network through the backpropagation algorithm, dynamically adjusting the parameters of the network weights and noise covariance until the loss function converges, wherein the noise covariance is used to suppress the influence of triaxial accelerometer outliers on attitude estimation by calculating Mahalanobis distance weights.

9. A computer system, comprising: One or more processors, a computer-readable storage medium, for storing one or more programs, characterized in that: when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method according to any one of claims 1 to 8.

10. A computer-readable storage medium storing computer-executable instructions, characterized in that: When executed, the instructions are used to implement the method according to any one of claims 1 to 8.

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