An inertial pre-integration adjustment method for autonomous navigation

Abstract

This invention discloses an inertial pre-integration adjustment method for autonomous navigation, belonging to the field of autonomous navigation. The method includes the following steps: receiving output data from an inertial sensor and calculating the measurement time change based on the inertial sensor output data; determining the pre-integration adjustment status based on the measurement time change; constructing a corresponding fast inertial pre-integration adjustment module based on the pre-integration adjustment status; the fast inertial pre-integration adjustment module rapidly adjusting the inertial pre-integration information using a Jacobian matrix to obtain the adjusted inertial pre-integration information; and constructing the Jacobian matrix corresponding to the adjusted inertial pre-integration information to update the inertial pre-integration factor. This invention significantly reduces the consumption of computational resources and improves the system's real-time performance and response speed.

Description

Technical Field

[0001] This invention belongs to the field of autonomous navigation technology, and particularly relates to an inertial pre-integration adjustment method for autonomous navigation. Background Technology

[0002] Navigation and positioning technology serves as a core enabling element for fields such as autonomous driving, drone inspection, and industrial robot control. Facing typical application demands such as dynamic obstacle avoidance in complex urban scenarios, continuous positioning in underground spaces without satellite signals, and precise capture of human motion postures, navigation systems not only need to overcome the performance limitations of single sensors but also require multi-source information fusion mechanisms to achieve synergistic optimization of robustness, real-time performance, and accuracy.

[0003] Inertial navigation systems calculate the position changes of a vehicle by integrating information from the output of inertial sensors (such as accelerometers and gyroscopes) and achieve continuous positioning through recursion. However, since the output contains errors that increase rapidly during integration, it is necessary to suppress these errors to meet navigation requirements. Multi-source fusion architectures, represented by factor graph optimization, have gradually become an important technical path to improve the error suppression capability of navigation systems because they can fully utilize sensor observation information from historical moments for global state estimation. Compared to the recursive processing mode of traditional Kalman filtering, which only considers the optimal value of the previous moment, factor graphs construct a nonlinear optimization problem to simultaneously optimize information from multiple historical moments, thereby obtaining more stable pose estimation results in complex interference environments. However, the output of high-frequency inertial devices participates in factor graph optimization through integration, requiring re-integration of the inertial data from historical moments when estimating errors, resulting in a large computational load and severely limiting the real-time computing capability of the system.

[0004] Existing inertial pre-integration methods can achieve error re-estimation without re-integration by solving the Jacobian matrix of the inertial integral and the error, demonstrating good computational efficiency. However, their mathematical models are usually based on the assumption of a fixed time window. When the measurement interval changes due to environmental disturbances, communication delays, or dynamic scheduling, traditional methods require repeated integration of historical pre-integration data to re-establish the constraint relationship. This repeated calculation not only consumes computational resources but also causes a rapid increase in computational load during high-frequency triggering, severely restricting the system's real-time response capability under complex conditions such as clock asynchrony. Therefore, it is necessary to propose a fast inertial pre-integration adjustment method to achieve rapid adjustment of pre-integration parameters under dynamic measurement intervals, reducing computational complexity while maintaining error suppression effects, and overcoming the key technical bottleneck in improving the robustness and universality of inertial-based fusion navigation systems. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention proposes an inertial pre-integration adjustment method for autonomous navigation, thereby resolving the issues present in the prior art.

[0006] To achieve the above objectives, the present invention provides an inertial pre-integration adjustment method for autonomous navigation, comprising:

[0007] Receive data output from the inertial sensor and calculate the change in measurement time based on the data output from the inertial sensor;

[0008] Based on the changes in the measurement time, determine the pre-integral adjustment;

[0009] Based on the aforementioned pre-integral adjustment, a corresponding inertial pre-integral fast adjustment module is constructed;

[0010] The inertial pre-integration fast adjustment module uses the Jacobian matrix to quickly adjust the inertial pre-integration information to obtain the adjusted inertial pre-integration information.

[0011] Construct the Jacobian matrix corresponding to the adjusted inertial pre-integration information to update the inertial pre-integration factor.

[0012] Optionally, the pre-integration adjustment includes: reducing inertial data at the head, increasing inertial data at the head, reducing inertial data at the tail, and increasing inertial data at the tail.

[0013] Optionally, the inertial pre-integration fast adjustment module under reduced inertial data includes: attitude pre-integration fast adjustment module, velocity pre-integration fast adjustment module, position pre-integration fast adjustment module and covariance pre-integration fast adjustment module;

[0014] The expression for the attitude pre-integration fast adjustment module is as follows:

[0015]

[0016] In the formula, R i+n,j This represents the rotation matrix representing the change from time j to time i+n. This represents the output of the gyroscope at time k between two zero velocity points. This indicates the zero bias of the gyroscope at time k. Exp represents the random noise of the gyroscope at time k; Exp represents the mapping from the equivalent rotation vector to the rotation matrix; Δt represents the output interval of the inertial sensor.

[0017] The expression for the speed pre-integral rapid adjustment module is:

[0018]

[0019] In the formula, Δv i+n,jLet be the change in velocity of the machine's coordinate system from time i+n to time j relative to time i+n. The output of the accelerometer at time k between the two zero velocity points. The zero bias of the accelerometer at time k, The random noise of the accelerometer at time k;

[0020] The expression for the position pre-integration fast adjustment module is:

[0021]

[0022] In the formula, Δp i+n,j This represents the change in the body's position relative to the coordinate system at time i+n from time i+n to time j.

[0023] The expression for the covariance pre-integration fast adjustment module is:

[0024]

[0025] In the formula, Σ i+n,j Let i+n be the covariance from time i to time j. This represents the transformation matrix used to remove the covariance at time i. Σ represents the transformation matrix for removing system noise at time i. η This is the system noise matrix.

[0026] Optionally, the process of constructing the Jacobian matrix corresponding to the adjusted inertial pre-integral information includes:

[0027] Based on the Jacobian matrix of zero bias relative to state variables of MEMS-IMU, a Jacobian matrix of residuals relative to state variables is constructed. The Jacobian matrix of residuals relative to state variables includes attitude residual Jacobian matrix, velocity residual Jacobian matrix, position residual Jacobian matrix and zero bias residual Jacobian matrix.

[0028] Optionally, the attitude residual Jacobian matrix is:

[0029]

[0030] In the formula, e R R is the residual of the rotation matrix. i Let v be the rotation matrix at time i. i Let p be the velocity at time i. i Let i be the position at time i. The gyroscope is at zero bias at time i. J is zero bias acceleration at time i. r (·) represents the attitude right Jacobian update matrix. The inverse of the attitude right Jacobian update matrix is ​​given by... Let be the Jacobian matrix of attitude change relative to gyroscope zero bias during inertial pre-integration.

[0031] Optionally, the velocity residual Jacobian matrix is:

[0032]

[0033] In the formula, It is the Jacobian matrix of the MEMS-IMU gyroscope with respect to the state, e v Represents the velocity residual. This represents the velocity information in the world coordinate system at time i. These are the Jacobian matrices of the velocity change relative to the gyroscope zero bias and the accelerometer zero bias during inertial pre-integration, respectively.

[0034] Optionally, the position residual Jacobian matrix is:

[0035]

[0036] In the formula, e p Indicates the positional residual. This represents the rotation matrix from the machine coordinate system to the world coordinate system at time i. Let Δt represent the position in the world coordinate system at time j. ij This represents the time elapsed from time i to time j. Let j represent the rotation matrix from the machine coordinate system to the world coordinate system at time j. These are the Jacobian matrices of the position relative to the gyroscope zero bias and the accelerometer zero bias during inertial pre-integration, respectively.

[0037] Optionally, the zero-bias residual Jacobian matrix is:

[0038]

[0039] In the formula, e b This indicates zero-biased residuals.

[0040] Optionally, updating the inertial pre-integration factor includes updating the residual value based on the change in the zero bias and the Jacobian matrix of the MEMS-IMU zero bias relative to the state quantity.

[0041] Compared with the prior art, the present invention has the following advantages and technical effects:

[0042] The inertial pre-integration adjustment method for autonomous navigation of the present invention has significant technical advantages. By receiving output data from inertial sensors and calculating measurement time changes, the pre-integration adjustment status can be accurately determined, thereby constructing a highly efficient inertial pre-integration fast adjustment module. This module utilizes the Jacobian matrix to achieve rapid adjustment, effectively improving the update efficiency of inertial pre-integration information. Simultaneously, by constructing the Jacobian matrix corresponding to the adjusted inertial pre-integration information, the update process of the inertial pre-integration factor is further optimized, enhancing the stability and reliability of the system. This method significantly reduces the consumption of computational resources, improves the real-time performance and response speed of the system, and is particularly suitable for inertial navigation systems with high requirements for accuracy and efficiency, providing strong support for high-precision positioning and navigation in complex environments. Attached Figure Description

[0043] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0044] Figure 1 This is a graph showing the integral adjustment time under a single measurement change according to an embodiment of the present invention.

[0045] Figure 2 This is a graph showing the integral adjustment time consumption under multiple measurement changes in an embodiment of the present invention;

[0046] Figure 3 This is a flowchart of a method according to an embodiment of the present invention. Detailed Implementation

[0047] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0048] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0049] Example 1

[0050] In robot state estimation, inertial pre-integration enables rapid fusion of inertial data with sensor measurement data from different sampling periods. For example... Figure 3 As shown, this embodiment provides an efficient adjustment method for the situation where the inertial pre-integration head data decreases due to changes in measurement time. The present invention constructs a fast calculation method for the state changes and corresponding Jacobian matrices under the conditions of increased or decreased pre-integration head and tail data, and obtains the adjusted inertial pre-integration information.

[0051] This invention constructs an inertial pre-integration Jacobian matrix, including Jacobian matrices for adjusting attitude, velocity, and position, as well as a covariance-adjusted Jacobian matrix. By rapidly extracting or adding inertial data to existing inertial pre-integrations using the Jacobian matrix, the real-time performance of inertial-based integrated navigation under varying measurement delays can be significantly improved.

[0052] This example provides an efficient adjustment method for situations where changes in measurement time lead to a reduction in inertial pre-integration header data, specifically including the following steps:

[0053] Step 1. In the already constructed inertial pre-integration, when the previous measurement time changes from time i to time i... c At time n, calculate the number of inertial measurements n that the head reduces;

[0054]

[0055] Where Δt is the output interval of the inertial sensor.

[0056] Step 2. The change in inertial pre-integration when the head reduces n inertial measurement data is as follows;

[0057] Since inertial integration involves multiple coordinate systems, the coordinate systems used must first be defined. The outputs of the gyroscope and accelerometer are based on the IMU coordinate system, denoted as the b-frame. The three axes of the IMU coordinate system point to the right, forward, and upward, respectively, and the IMU coordinate system at time t is denoted as b. t The navigation results of the carrier are represented in the world coordinate system, denoted as the w-system. The origin of the world coordinate system coincides with the IMU coordinate system at the initial moment, and its three axes point to east, north, and sky, respectively.

[0058] Because the interval between zero velocity points is short, the error characteristics of the inertial sensor change only slightly within a short period. Therefore, the two consecutive sampling time points t i With t j The zero bias of the MEMS-IMU between the two zero velocity points can be considered a constant. The outputs of the gyroscope and accelerometer at time k between the two zero velocity points... and as follows:

[0059]

[0060] in, and Let represent the actual angular velocity in the machine system and the actual acceleration in the world coordinate system at time k, respectively. This represents the rotation from the world coordinate system to the body coordinate system at time k. and This indicates the zero bias of the gyroscope and accelerometer at time k. and This represents the random noise of the gyroscope and accelerometer at time k.

[0061] Pre-integration fast adjustment includes four scenarios: reducing inertial data at the head, increasing key data at the head, reducing inertial data at the tail, and increasing inertial data at the tail. The specific scenarios are as follows:

[0062] In traditional inertial pre-integration, it is necessary to re-integrate based on the reduced inertial data. The reduction in the pre-integration head is shown in the following equation:

[0063]

[0064] Where Exp represents the mapping from the equivalent rotation vector to the rotation matrix. For ease of understanding, state variables without superscripts represent the body coordinate system at the time preceding the subscript, j represents the time corresponding to the next measurement, and ΔR i+n,j Let R be the rotation matrix from time i+n to time j relative to the body coordinate system at time i+n, where R is the rotation matrix from time i+n to time j in this invention. ·，* The parameter format represents the rotation matrix of the change from time * to time ·, ΔR ·，* The parameter in the format represents the rotation matrix from time * to time * relative to the body coordinate system at time *, Δv i+n,j Let be the change in velocity of the body coordinate system from time i+n to time j relative to time i+n, where Δv ·，* The parameter in the format represents the change in velocity relative to the body coordinate system from time * to time *, Δp i+n,j Let be the change in position of the body in the coordinate system from time i+n to time j relative to time i+n, where Δp ·，* The parameter in the format represents the change in position of the machine relative to the coordinate system at time * from time *. i+n,j Let A be the covariance from time i+n to time j, which can be considered as a confidence reference. j-1 It is the state transition matrix, B j-1 This is the noise transition matrix, as follows:

[0065]

[0066] The pre-integral head is increased as follows:

[0067]

[0068] The case where the pre-integral tail increases is as follows:

[0069]

[0070] The case where the tail of the pre-integral decreases is as follows:

[0071]

[0072] Step 3. Construct an inertial pre-integration fast adjustment module when the head reduces n inertial measurement data, including an attitude pre-integration fast adjustment module, a velocity pre-integration fast adjustment module, a position pre-integration fast adjustment module, and a covariance pre-integration fast adjustment module;

[0073] The pre-integral head reduction rapid attitude adjustment module is as follows:

[0074]

[0075] In the formula, R i+n,j This represents the rotation matrix representing the change from time j to time i+n. This represents the output of the gyroscope at time k between two zero velocity points. This indicates the zero bias of the gyroscope at time k. Δt represents the random noise of the gyroscope at time k; Exp represents the mapping from the equivalent rotation vector to the rotation matrix; and Δt represents the output interval of the inertial sensor.

[0076] The rapid speed adjustment module for reducing the pre-integral head is as follows:

[0077]

[0078] In the formula, Δv i+n,j Let be the change in velocity of the machine's coordinate system from time i+n to time j relative to time i+n. The output of the accelerometer at time k between the two zero velocity points. The zero bias of the accelerometer at time k, Let be the random noise of the accelerometer at time k.

[0079] The module for rapid position adjustment when the pre-integral head decreases is as follows:

[0080]

[0081] In the formula, Δp i+n,j Let be the change in position of the machine body in the coordinate system from time i+n to time j relative to time i+n.

[0082] The covariance fast adjustment module for reducing the pre-integral head is as follows:

[0083]

[0084] In the formula, Σ i+n,j Let i+n be the covariance from time i to time j. This represents the transformation matrix used to remove the covariance at time i. Σ represents the transformation matrix for removing system noise at time i. η This is the system noise matrix.

[0085] in, This represents the transformation matrix for removing the covariance at time i, with the aim of transforming the coordinate system within the covariance. The transformation matrix for removing system noise at time i is as follows:

[0086]

[0087] Since the zero-bias estimates of the main events before and after may change, the header data adjustment needs to be based on the zero-bias that constitute this pre-integration. Represents zero bias The state at that time, Let represent the pose right Jacobian update matrix at time k.

[0088] The adjusted Jacobian matrix is ​​then calculated to reconstruct the inertial pre-integration module.

[0089] Step 4. Construct the Jacobian matrix corresponding to the inertial pre-integration residual when the head reduces n inertial measurement data, including the Jacobian matrix of attitude, velocity, position and zero bias residual;

[0090] For MEMS-IMU-based inertial pre-integration, assuming zero bias remains constant between two main events, the residual E imuij It can be represented as:

[0091]

[0092] in, This means that when the zero bias equals The change in state over time. δb a and δb g These are the differences between the zero bias in the current iteration and the initial value of the optimization process. It is the Jacobian matrix of the MEMS-IMU zero bias relative to the state, which can be used to efficiently adjust the pre-integral changes caused by the zero bias, as shown in Equation (14).

[0093]

[0094] Based on the Jacobian matrix of the state variables relative to the MEMS-IMU error, the Jacobian matrix of the residuals relative to the state variables can be constructed, specifically listed according to attitude, velocity, position, and error. Attitude is shown in equation (15):

[0095]

[0096] In the formula, e R R is the residual of the rotation matrix. i Let v be the rotation matrix at time i. i Let p be the velocity at time i. i Let i be the position at time i. The gyroscope is at zero bias at time i. J is zero bias acceleration at time i. r (·) represents the attitude right Jacobian update matrix. The inverse of the attitude right Jacobian update matrix is ​​given by... Let be the Jacobian matrix of attitude change relative to gyroscope zero bias during inertial pre-integration.

[0097] The speed is as shown in equation (16):

[0098]

[0099] In the formula, It is the Jacobian matrix of the MEMS-IMU gyroscope with respect to the state, e v Represents the velocity residual. This represents the velocity information in the world coordinate system at time i. These are the Jacobian matrices of the velocity change relative to the gyroscope zero bias and the accelerometer zero bias during inertial pre-integration, respectively.

[0100] Position as shown in equation (17):

[0101]

[0102] In the formula, e p Indicates the positional residual. This represents the rotation matrix from the machine coordinate system to the world coordinate system at time i. Let Δt represent the position in the world coordinate system at time j. ij This represents the time elapsed from time i to time j. Let j represent the rotation matrix from the machine coordinate system to the world coordinate system at time j. These are the Jacobian matrices of the position relative to the gyroscope zero bias and the accelerometer zero bias during inertial pre-integration, respectively.

[0103] Zero bias as in equation (18):

[0104]

[0105] In the formula, e b This indicates zero-biased residuals.

[0106] After reducing the original pre-integral head by n inertial data points, the residual is as shown in equation (19):

[0107]

[0108] From the Jacobian matrix of the residuals relative to the state, it can be seen that, except for the Jacobian matrix of the MEMS-IMU zero bias relative to the state which needs to be obtained recursively, the other elements can be adjusted through a linear computation graph, resulting in low complexity. This section constructs an efficient method for adjusting the Jacobian matrix of the MEMS-IMU zero bias relative to the state to further reduce the computational load, as shown in (20):

[0109]

[0110]

[0111] By substituting the adjusted matrix into the original Jacobian matrix, the Jacobian matrix after reducing the original pre-integral header by n inertial data points can be quickly calculated.

[0112] By using the above adjustment method, the state variables, residuals, and Jacobian matrix can be updated after reducing the original pre-integration header by n inertial data, thus updating the inertial pre-integration factor.

[0113] The final experimental results are as follows Figure 1 , Figure 2 As shown.

[0114] A single measurement experiment compared the time required for re-integration when the last zero-velocity measurement occurred 0.05 seconds later, i.e., after 10 inertial measurements had changed. The time required to adjust for a single inertial measurement change is shown in the figure. Both pre-integration and EKF require approximately 2.30 ms. The proposed method requires only 0.36 ms to 1.88 ms for IMU measurement changes from 1 to 9.

[0115] Multiple measurement experiments compared the time required for re-integration when measurement changes occurred every ten steps, with the number of changes ranging from 1 to 9. This situation is more common in practice because the factor graph optimization fusion uses a sliding window optimization technique. As shown in the figure, traditional EKF-based filtering methods incur significant time consumption, ranging from 2.25ms to 69.72ms, pre-integration methods consume 2.27ms to 15.50ms, while the method proposed in this invention consumes only 0.75ms to 6.74ms.

[0116] By comparing the adjustment time under two different measurement change conditions, it can be seen that the algorithm proposed in this invention reduces the computational load by 70% compared to traditional algorithms. Factor graph optimization fusion requires dozens of iterations, each with the possibility of measurement changes. In high-performance embedded systems such as Raspberry Pi, each iteration can save 2-10ms, and a single optimization can reduce the time by up to hundreds of milliseconds. In more common embedded systems such as STM32, this could reduce computation time by several seconds, which is crucial for real-time operation.

[0117] In addition, more accurate measurement construction will enable more precise zero-bias estimation, further improving the accuracy of positioning estimation. Through the efficient pre-integration adjustment method proposed in this invention, a factor graph optimization fusion framework for measurement closed-loop optimization can be constructed, achieving higher-precision state estimation.

[0118] This invention discloses an inertial pre-integration adjustment method for autonomous navigation. It constructs an inertial pre-integration Jacobian matrix, including Jacobian matrices for attitude, velocity, and position adjustments, as well as a covariance adjustment Jacobian matrix. By rapidly extracting or adding inertial data to existing inertial pre-integration data using the Jacobian matrix, the real-time performance of inertial-based navigation under varying measurement delays is improved. Furthermore, a factor graph optimization fusion framework for measurement closed-loop optimization can be constructed to achieve higher-precision state estimation.

[0119] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. An inertial pre-integration adjustment method for autonomous navigation, characterized in that, Includes the following steps: Receive data output from the inertial sensor and calculate the change in measurement time based on the data output from the inertial sensor; Based on the changes in the measurement time, determine the pre-integral adjustment; Based on the aforementioned pre-integral adjustment, a corresponding inertial pre-integral fast adjustment module is constructed; The inertial pre-integration fast adjustment module uses the Jacobian matrix to quickly adjust the inertial pre-integration information to obtain the adjusted inertial pre-integration information. Construct the Jacobian matrix corresponding to the adjusted inertial pre-integration information to update the inertial pre-integration factor; The pre-integration adjustment includes: reducing inertial data at the head, increasing inertial data at the head, reducing inertial data at the tail, and increasing inertial data at the tail. The inertial pre-integration fast adjustment module under head reduction inertial data includes: attitude fast adjustment module under pre-integration head reduction, velocity fast adjustment module under pre-integration head reduction, position fast adjustment module under pre-integration head reduction, and covariance fast adjustment module under pre-integration head reduction. The expression for the attitude fast adjustment module under the condition of pre-integration head reduction is as follows: ； In the formula, Indicates from j Time's up i+n Rotation matrix of time-varying quantities Indicates the distance between two zero velocity points The output of the gyroscope at any given time. Indicates time The zero bias of the gyroscope at that location, Indicates time Random noise from the gyroscope at that location; This represents the mapping from the equivalent rotation vector to the rotation matrix. The output interval of the inertial sensor is represented by ΔRi+n,j, which is the rotation matrix from time i+n to time j relative to the body coordinate system at time i+n. The expression for the velocity rapid adjustment module when the pre-integral head is reduced is: In the formula, From i+n Time's up j Time relative to i+n The change in velocity of the body coordinate system at any given time. Between two zero velocity points The output of the accelerometer at all times, For time The zero bias of the accelerometer at that location, For time Random noise from the accelerometer at that location; The expression for the fast position adjustment module when the pre-integral head is reduced is: In the formula, From i+n Time's up j Time relative to i+n The change in position of the body coordinate system at any given moment; The expression for the covariance fast adjustment module under the condition of reduced pre-integral head is: ； In the formula, From i+ 1 hour has arrived j Covariance at time, Indicates removal The transformation matrix of the time-varying covariance. Indicates removal The transformation matrix of the system noise at any given time. This is the system noise matrix.

2. The method for inertial pre-integration adjustment for autonomous navigation of claim 1, wherein, The process of constructing the Jacobian matrix corresponding to the adjusted inertial pre-integral information includes: Based on the Jacobian matrix of zero bias relative to state variables of MEMS-IMU, a Jacobian matrix of residuals relative to state variables is constructed. The Jacobian matrix of residuals relative to state variables includes attitude residual Jacobian matrix, velocity residual Jacobian matrix, position residual Jacobian matrix and zero bias residual Jacobian matrix.

3. The method for inertial pre-integration adjustment for autonomous navigation of claim 2, wherein, The attitude residual Jacobian matrix is: ； In the formula, For the rotation matrix residual, for i Rotation matrix at any time, for i Speed ​​at any moment for i Time and location for i The gyroscope is at zero bias at all times. for i Acceleration is always zero bias. For the attitude right Jacobian update matrix, The inverse of the attitude right Jacobian update matrix is ​​given by... Let be the Jacobian matrix of attitude change relative to gyroscope zero bias during inertial pre-integration. This represents the difference between the zero bias and the initial value of the optimization process in the current iteration of the gyroscope.

4. The method for inertial pre-integration adjustment for autonomous navigation of claim 3, wherein, The velocity residual Jacobian matrix is: ； In the formula, It is the Jacobian matrix of the zero bias of the MEMS-IMU gyroscope relative to the state. Represents the velocity residual. express i Velocity information in the world coordinate system at any given time. , These are the Jacobian matrices of the velocity change relative to the gyroscope zero bias and the accelerometer zero bias during inertial pre-integration, respectively. Let represent the rotation matrix from the slave coordinate system to the world coordinate system at time i, and T represent the matrix transpose.

5. The inertial pre-integration adjustment method for autonomous navigation according to claim 4, characterized in that, The position residual Jacobian matrix is: ； In the formula, Indicates the positional residual. express i The rotation matrix from the machine coordinate system to the world coordinate system at all times. express j The position of a point in the world coordinate system at any given time. express i arrive j Time that has passed express j The rotation matrix from the machine coordinate system to the world coordinate system at all times. , These are the Jacobian matrices of the position relative to the gyroscope zero bias and the accelerometer zero bias during inertial pre-integration, respectively.

6. The method for inertial pre-integration adjustment for autonomous navigation of claim 5, wherein, The zero-bias residual Jacobian matrix is: ； In the formula, represents zero bias residuals.

7. The method for inertial pre-integration adjustment for autonomous navigation of claim 1, wherein, The update of the inertial pre-integration factor includes updating the residual value based on the change of the zero bias and the Jacobian matrix of the MEMS-IMU zero bias relative to the state quantity.

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