An IMU installation angle estimation method and system based on an exponential decay function

Abstract

This invention provides a method and system for estimating the IMU mounting angle based on an exponential decay function. The method includes: establishing a gyroscope zero-bias estimation model for the vehicle and an accelerometer-gravity projection correlation model in a stationary state; calculating the effective acceleration using an exponential decay function to suppress acceleration amplitudes during cornering, performing trajectory recursion only during straight-line acceleration to obtain the horizontal displacement; calculating the heading mounting angle at each epoch using the displacement vector direction, filtering candidate heading mounting angles using consecutive adjacent angle differences, and verifying the candidate heading mounting angle results through inertial navigation recursion. This invention calculates the roll and pitch mounting angles when stationary and the heading mounting angle through acceleration during motion, achieving integrated estimation of the three mounting angles. It is suitable for initial calibration scenarios of vehicle-mounted inertial navigation, requires no external references such as GNSS or odometers, and acceleration is not limited to the stationary-to-start phase, significantly simplifying the implementation conditions for mounting angle calibration.

Description

Technical Field

[0001] This invention relates to the field of integrated navigation technology, and in particular to an IMU installation angle estimation method and system based on an exponential decay function. Background Technology

[0002] In vehicle-mounted integrated navigation systems, the inertial measurement unit (INS) serves as the core sensing device, typically forming a GNSS-INS fusion architecture in conjunction with the Global Navigation Satellite System (GNSS). This architecture, by collaboratively processing the angular velocity information output from the gyroscope and the specific force information output from the accelerometer, can calculate the vehicle's attitude, position, velocity, and other state parameters in real time, providing crucial support for applications such as intelligent driving and special vehicle control.

[0003] GNSS provides stable absolute position and velocity information, effectively suppressing the drift error accumulated by the IMU over time. The IMU, in the event of satellite signal obstruction, maintains system output through its short-term, high-precision autonomous calculation capabilities. Deep fusion of these two systems hinges on strict spatial alignment of the data, requiring accurate knowledge of the IMU's installation relative to the vehicle coordinate system. Deviations in the installation angle will distort the motion information sensed by the IMU when projected onto the vehicle system: heading errors will cause misalignment between the IMU's output forward information and the vehicle's actual driving direction, disrupting the consistency between GNSS observations and IMU recursion in the fusion system; while deviations in roll and pitch will cause incorrect distribution of gravity components across axes, leading to attitude calculations deviating from the true value and indirectly affecting position estimation accuracy, ultimately reducing the reliability of the entire navigation system. Therefore, precise calibration of the IMU's installation angle after installation is a necessary prerequisite for stable and reliable fusion calculations.

[0004] Currently, the mainstream research approaches for estimating the installation angle of vehicle-mounted IMUs can be summarized into the following two categories: Firstly, there is the data fusion method based on external reference information. This type of approach typically uses GNSS as the basic reference and introduces auxiliary equipment such as wheel speed sensors and visual cameras. By constructing estimation models such as Kalman filtering, the raw IMU output is fused with observations from external equipment (such as GNSS position and wheel speed pulses) to achieve online identification of the deviations in the three installation angles of roll, pitch, and yaw. The advantage of this method is that it uses the absolute characteristics of the external reference to constrain the relative measurement error of the IMU, thereby improving the estimation accuracy.

[0005] Secondly, there is the static-acceleration start-up method that utilizes only the IMU's own measurements. This method requires no external equipment. The basic idea is as follows: First, based on the IMU output during the vehicle's stationary phase, the roll and pitch installation angles are calculated using the relationship between accelerometer measurements and the gravity vector. Then, relying on the vehicle's acceleration process from standstill to start (i.e., linear acceleration under zero initial velocity), a trajectory is formed by double integration of the horizontal acceleration, and the heading installation angle is determined based on the angle between the trajectory direction and the IMU's forward axis. The successful implementation of this method depends on the vehicle strictly satisfying the "stationary start-up + linear acceleration" assumption to ensure that the recursive trajectory direction is unique and solvable.

[0006] However, both of these technologies face several limitations in practical applications, making it difficult to fully meet the engineering requirements of complex in-vehicle environments: (1) Although fusion methods relying on external sensors can achieve high accuracy with the help of GNSS, the introduction of additional equipment such as wheel speedometers or cameras means an increase in hardware costs and system complexity. Additional investment is required in aspects such as installation and calibration, and parameter matching. At the same time, the effectiveness of such methods is highly dependent on the quality of GNSS observations. Once the vehicle enters areas with suppressed signals, such as tunnels, underground parking lots, or urban canyons, the failure of the external reference will directly lead to the inability to estimate the installation angle, resulting in a significant application blind spot.

[0007] (2) While the pure IMU method based on static-start acceleration avoids the dependence on additional sensors, it imposes stringent constraints on the vehicle's motion pattern. It requires the vehicle to start from a stationary state and complete a significant forward linear acceleration. However, in actual driving, due to traffic conditions (such as slow starts in congested areas or creeping on slopes), the acceleration signal is often weak or submerged by noise, resulting in a significant decrease in the accuracy of heading angle estimation. At the same time, if the vehicle needs to be recalibrated during operation (for example, due to temperature changes causing a shift in the installation relationship), this method must force a stop and re-execute the start-up process. The rigid operation process greatly limits its dynamic adaptation capability during normal driving.

[0008] In summary, existing IMU installation angle estimation methods generally suffer from the following shortcomings: strong dependence on additional hardware, sensitivity to GNSS signal quality, overly strict constraints on motion conditions, and poor adaptability to dynamic scenarios. They are unable to meet the requirements of low cost, high robustness, and adaptation to complex working conditions, thus restricting their widespread application in vehicle environments. Summary of the Invention

[0009] This invention provides an IMU installation angle estimation method and system based on an exponential decay function, addressing the shortcomings of existing technologies such as high hardware costs, poor scene adaptability, reliance on specific startup conditions, and failure to exclude interference from turning when acceleration is high. The method utilizes an exponential decay function to constrain the acceleration amplitude during turns; that is, it reduces the used acceleration amplitude during turns, with a larger reduction for larger turns, thus decreasing the proportion of data used during turns. During inertial navigation recursion, the data used is primarily from straight-line travel, resulting in high accuracy in installation angle calculation. In a first aspect, the present invention provides an IMU installation angle estimation method based on an exponential decay function, comprising: Establish a zero-bias estimation model for the vehicle's gyroscope and a correlation model between the accelerometer and gravity projection in a stationary state, respectively. The effective acceleration is calculated using an exponential decay function to suppress the acceleration amplitude during cornering. Trajectory recursion is performed only during the straight acceleration period to obtain the horizontal displacement. The heading installation angle is calculated at each epoch by the displacement vector direction. Candidate heading installation angles are selected by the difference between consecutive adjacent angles, and the results of the candidate heading installation angles are verified by inertial navigation recursion.

[0010] According to the present invention, an IMU mounting angle estimation method based on an exponential decay function is provided, which establishes a gyroscope zero-bias estimation model for a vehicle and an accelerometer-gravity projection correlation model under stationary conditions, including: A gyroscope measurement model is constructed, and the average value of the gyroscope output is calculated when the vehicle is stationary. The zero bias of each axis of the gyroscope is obtained, and the measurement data is compensated and discretized. Based on the correlation model of accelerometer and gravity projection under static conditions, the projection of gravity in the IMU frame is derived. By solving the constraint equations, the roll and pitch installation angles are calculated.

[0011] According to the present invention, an IMU installation angle estimation method based on an exponential decay function is provided. This method calculates the effective acceleration using the exponential decay function to suppress acceleration amplitudes during cornering, and performs trajectory recursion only during the straight-line acceleration period to obtain the horizontal displacement. The method includes: Calculate the angular velocity magnitude, design an exponential decay weighting function, and perform effective acceleration calculation and screening; Construct a recursive model of horizontal acceleration and trajectory, perform coordinate system transformation, recursively calculate velocity and displacement integrals, and output the trajectory direction.

[0012] According to the present invention, an IMU installation angle estimation method based on an exponential decay function is provided, which calculates the angular velocity magnitude, designs an exponential decay weight function, and performs effective acceleration calculation and screening, including: For the first 3D angular velocity of the gyroscope after zero bias compensation at the epoch Its vector is defined as:

[0013] The three terms on the right side of the equation are respectively X, Y, Z The angular velocity of the three-axis gyroscope is used to quantify the overall rotational intensity of the vehicle by calculating the magnitude of this vector. The formula for the magnitude is:

[0014] The larger the modulus, the more violent the vehicle rotation, and the less suitable the corresponding acceleration data is for estimating the heading angle. Define weight function Dynamic decay is achieved by taking the magnitude of angular velocity as input, and the function is as follows:

[0015] in The attenuation coefficient is the core characteristic of the function: when hour, Acceleration data is fully retained; when hour, Acceleration data was significantly suppressed; when exist At time, The angular velocity decreases smoothly from 1 to 0.05 as the angular velocity increases, thus achieving adaptive processing of transitional scenes. For the first IMU horizontal acceleration after epoch-rate zero bias and gravity compensation Multiply by weight Effective acceleration is obtained: Only when the forward component of the effective acceleration The absolute value exceeds the threshold If the epoch is deemed valid, it is included in the subsequent heading and installation angle estimation process; otherwise, it is considered invalid and is directly discarded.

[0016] According to the present invention, an IMU installation angle estimation method based on an exponential decay function is provided, which constructs a horizontal acceleration and trajectory recursive model, performs coordinate system transformation, recursively calculates velocity and displacement integrals, and outputs the trajectory direction, including: The horizontal acceleration transformation between the IMU coordinate system and the vehicle coordinate system is described by a planar rotation matrix. The input is the effective acceleration that has suppressed cornering interference. The transformation formula is:

[0017] in, The effective forward acceleration in the vehicle coordinate system. For the heading installation angle, , The effective acceleration in the IMU coordinate system; Using the effective acceleration as input, the horizontal displacement trajectory in the IMU coordinate system is obtained through quadratic integration. The initial integration condition is set as the starting epoch of the acceleration segment. Both the velocity and displacement are 0; No. Epoch velocity calculation:

[0018] in Initial velocity , This is the starting epoch of the valid data segment; No. Epoch Displacement Calculation:

[0019] Initial displacement ; Finally, the number was obtained Horizontal displacement vector of an epoch Its direction is relative to the IMU coordinate system. The included angle of the axis is the heading installation angle. The basis for instantaneous estimation.

[0020] The present invention provides an IMU installation angle estimation method based on an exponential decay function, which calculates the heading installation angle at each epoch by means of the displacement vector direction, filters candidate heading installation angles using the difference between consecutive adjacent angles, and verifies the candidate heading installation angle results through inertial navigation recursion, including: A preliminary solution for the heading angle is performed, and a first-stage consistency verification is conducted to screen stable results, thereby obtaining candidate heading installation angles. The second phase of time stability verification was conducted to screen the final results and obtain the final heading installation angle.

[0021] According to the IMU installation angle estimation method based on the exponential decay function provided by the present invention, a preliminary solution for the heading angle is performed, and a first-stage consistency verification is conducted to screen stable results to obtain candidate heading installation angles, including: The heading installation angle for each epoch is obtained from the displacement vector direction, and the angle coverage range is determined using the four-quadrant arctangent function. :

[0022] For the first Horizontal displacement vector of an epoch; During the effective acceleration phase, the difference in heading angle between adjacent epochs is calculated sequentially. ; If it is determined that the difference between adjacent heading angles of consecutive first epochs in the sequence is less than the first preset threshold, then the average value of the heading angles of the second epoch in the sequence is extracted to obtain the candidate heading installation angle.

[0023] According to the IMU installation angle estimation method based on the exponential decay function provided by the present invention, a second-stage time stability verification is performed to screen the final results and obtain the final heading installation angle, including: The new starting point of the sequence is the end of the first phase epoch. Reset initial speed Initial displacement ( This is to eliminate the cumulative effect of previous integration errors; use Using IMU data, when the acceleration is large, the horizontal displacement of subsequent epochs is calculated using the same integration method. And solve for the corresponding heading angle estimate. ; If the deviation between the estimated heading angle and the candidate heading installation angle for a consecutive second number of epochs is less than a second preset threshold, and the second preset threshold is greater than the first preset threshold, then the candidate heading installation angle is determined as the final heading installation angle.

[0024] Secondly, the present invention also provides an IMU installation angle estimation system based on an exponential decay function, comprising: A module is established to create a gyroscope zero-bias estimation model for the vehicle and an accelerometer-gravity projection correlation model in a stationary state, respectively. The calculation module is used to calculate the effective acceleration using the exponential decay function to suppress the acceleration amplitude when there is a turn, and only performs trajectory recursion during the straight acceleration period to obtain the horizontal displacement. The estimation module is used to calculate the heading installation angle at each epoch by using the displacement vector direction, filter candidate heading installation angles by the difference between consecutive adjacent angles, and verify the candidate heading installation angle results by inertial navigation recursion.

[0025] Thirdly, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the IMU installation angle estimation method based on the exponential decay function as described above.

[0026] Fourthly, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the IMU installation angle estimation method based on the exponential decay function as described above.

[0027] The IMU installation angle estimation method and system based on the exponential decay function provided by this invention achieves integrated estimation of three installation angles by calculating the roll and pitch installation angles when stationary and the heading installation angle by calculating the acceleration during movement. It is suitable for the initial calibration scenario of vehicle inertial navigation, does not require external references such as GNSS or odometers, and the acceleration is not limited to the stage from stationary to startup, which significantly simplifies the implementation conditions of installation angle calibration. Attached Figure Description

[0028] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0029] Figure 1 This is a flowchart illustrating the IMU installation angle estimation method based on the exponential decay function provided by this invention. Figure 2 This is a schematic diagram of the installation angle of the GNSS / INS integrated navigation vehicle IMU provided by the present invention; Figure 3 This is a schematic diagram of the exponential decay function with different attenuation coefficients provided by the present invention; Figure 4 This is a schematic diagram showing the relationship between continuous integral of acceleration and heading angle provided by the present invention; Figure 5 This is a schematic diagram of the structure of the IMU installation angle estimation system based on the exponential decay function provided by the present invention; Figure 6 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0031] To address the limitations of existing technologies, this invention provides a method for estimating the unassisted mounting angle of an onboard IMU based on the acceleration amplitude constrained by an exponential decay function during cornering. Figure 1 As shown, it includes: Step 100: Establish the gyroscope zero-bias estimation model and the accelerometer-gravity projection correlation model in a stationary state for the vehicle, respectively; Step 200: Calculate the effective acceleration using the exponential decay function to suppress the acceleration amplitude during turning, and perform trajectory recursion only during the straight acceleration period to obtain the horizontal displacement. Step 300: Calculate the heading installation angle at each epoch using the displacement vector direction, filter candidate heading installation angles using the difference between consecutive adjacent angles, and verify the candidate heading installation angle results through inertial navigation recursion.

[0032] Specifically, this embodiment of the invention first establishes a gyroscope zero-bias estimation model. During the vehicle's stationary phase, the mean value of the gyroscope output is calculated to obtain the zero bias of each gyroscope axis, and the measurement data is compensated. Then, a correlation model between the accelerometer and the gravity projection in a stationary state is established. The projection of gravity in the IMU frame is derived, and the constraint equations are solved to obtain the roll and pitch installation angles. The effective acceleration is calculated using an exponential decay function, thereby suppressing the acceleration amplitude during cornering, which is equivalent to recursively calculating the trajectory only during the straight-line acceleration period to obtain the horizontal displacement vector. Finally, the heading installation angle is solved. The heading installation angle is calculated at each epoch using the displacement vector direction, and candidate heading installation angles are selected using the difference between consecutive adjacent angles. The angle results are verified by inertial navigation recursion.

[0033] This invention innovatively employs an exponential decay function to suppress acceleration during turns when calculating the heading installation angle using vehicle acceleration, thereby avoiding interference from acceleration during turns and increasing the accuracy of the installation angle calculation.

[0034] Based on the above embodiments, step 100 includes: First, a gyroscope zero-bias estimation model is established. The mean value of the gyroscope output is calculated when the vehicle is stationary to obtain the zero bias of each axis of the gyroscope and compensate for the measurement data.

[0035] The zero bias of a MEMS gyroscope is one of the main error sources affecting the accuracy of inertial navigation. It is defined as the output offset (constant error) of the gyroscope when there is no rotational input. In the initial installation angle estimation of a vehicle, accurate estimation of the gyroscope's zero bias can effectively eliminate rotational errors in the static stage, laying the foundation for subsequent dynamic recursion. This section derives the zero bias estimation formula based on the gyroscope output when the vehicle is stationary.

[0036] (1) Gyroscope measurement model When the vehicle is stationary, the IMU has no rotational motion, and the ideal output of the gyroscope should be 0. However, due to manufacturing process errors and environmental interference in MEMS devices, the actual output includes zero bias and random noise. Its measurement model can be expressed as: (1) in: for The IMU gyroscope at the moment The raw output of the axis ( (corresponding to forward, right, and down directions respectively). For the gyroscope Zero offset of the shaft (constant error, does not change with time); The measurement noise of the gyroscope (random error, with a mean of 0 and a variance of 0) (Gaussian distribution).

[0037] The core assumption of this model is that the output of the gyroscope in a static state consists only of zero bias and noise, with no rotational angular velocity input. Therefore, noise can be suppressed and zero bias extracted by time averaging.

[0038] (2) Derivation of the zero bias estimation formula The core idea of ​​zero-bias estimation is: during the static observation period Inside (from) arrive The gyroscope output is integrated over time and averaged. Since the noise mean is 0, the cumulative effect of the noise is suppressed after integration, thus obtaining a zero-biased unbiased estimate.

[0039] For both sides of the measurement model Integral over the interval: (2) Analyze the two terms on the right side of the equation: 1. First item: Since it is a constant, the integral result is: ; 2. Second item: The mean is 0, when the observation duration is Over a sufficiently long time (usually 10 seconds), the integral result The impact of noise is negligible.

[0040] Substituting the above result into the integral, and dividing both sides by... The gyroscope's first... Estimation formula for zero axis offset: (3) in, Indicates the gyroscope's first The estimated value of the axis zero bias.

[0041] (3) Zero bias compensation and discretization implementation By compensating the original gyroscope output with the zero-bias estimate, the effective angular velocity output after removing the zero bias can be obtained. The compensation formula is as follows: (4) When the vehicle is stationary, the compensated output It should be approximately 0, containing only random noise, to verify the effectiveness of the zero-biased estimation.

[0042] In practical engineering applications, IMU data is acquired through discrete sampling, requiring the continuous integral formula to be discretized. Let the sampling frequency during the stationary phase be... (Sampling interval) ), then in Collected within the time period There are 10 data points. At this point, the discretization formula for the zero-biased estimate is: (5) in, Indicates the first The gyroscope at the sampling point The original output value of the axis. This discretization formula is easy to implement in embedded systems and is a commonly used zero-bias estimation method in engineering.

[0043] Then, a correlation model between the accelerometer and the gravity projection under static conditions is established. The projection of gravity in the IMU frame is derived, and the constraint equations are solved to obtain the roll and pitch installation angles.

[0044] like Figure 2 In the schematic diagram of the GNSS / INS integrated navigation vehicle-mounted IMU installation angle shown, the vehicle coordinate system is called the v system, and the carrier (IMU) coordinate system is called the b system. The XYZ axes of the v system point to the lower right front of the vehicle body, while the XYZ axes of the b system do not coincide with the lower right front of the vehicle body, but form an angle. Therefore, it is necessary to construct a rotation matrix from the vehicle system to the IMU system.

[0045] When the vehicle is stationary, the IMU has no translational acceleration, and the accelerometer output only reflects the projection of gravity in the IMU coordinate system (ignoring the influence of zero bias). This section derives the mathematical relationship between the accelerometer measurement and the gravity vector when the vehicle is stationary, based on the relationship between coordinate system rotation and gravity projection, providing a theoretical basis for the subsequent calculation of roll and pitch angles.

[0046] (1) Accelerometer measurement model (stationary state) When the vehicle is stationary, the translational acceleration of the IMU is 0, and the accelerometer output consists only of gravity projection and random noise. Its measurement model is as follows: (6) in: For a moment IMU accelerometer The raw output of the axis; For gravity in the IMU coordinate system The projected components of the axis (constant values, not changing with time). The measurement noise of the accelerometer (random error, with a mean of 0 and a variance of 0) (Gaussian distribution).

[0047] The core assumption of this model is that the output of the accelerometer in a stationary state is only related to the gravity projection and has no translational acceleration input. Therefore, noise can be suppressed by time averaging and the gravity projection component can be extracted.

[0048] (2) Accelerometer output noise reduction To suppress the impact of measurement noise on the extraction of gravity projection components, it is necessary to adjust the static duration. The accelerometer output within the model is time-averaged. The measurement model is then compared on both sides. Integrate over the interval and take the average: (7) Analyze the two terms on the right side of the equation: 1. First item: Since it is a constant, the integral result is: ; 2. Second item: The mean is 0, when For a sufficiently long time, The noise impact is negligible.

[0049] Therefore, the accelerometer output after noise reduction Approximately equal to gravity in the IMU coordinate system The projection components of the axis, namely: (8) in, These are the time averages of the forward, rightward, and downward outputs of the accelerometer, respectively. The denoised values ​​are used in the subsequent formula derivations.

[0050] (3) Coordinate system projection of the gravity vector According to the direction cosine matrix, the gravity vector in the vehicle coordinate system ( (system) and IMU coordinate system ( The projection relationships between systems follow standard vector transformation rules.

[0051] First, when the vehicle is stationary on a horizontal surface, gravity acts only along the vehicle's coordinate system. The force acts along the axis (downward). Therefore, the vector expression for gravity in the vehicle coordinate system is: (9) in, This is the magnitude of gravitational acceleration. This vector is only... The axle has a component, which is consistent with the force state of a vehicle on a horizontal ground (gravity and ground support force are balanced, and there is no horizontal component).

[0052] Next, we derive the projection of gravity onto the IMU coordinate system. The IMU accelerometer measures specific force, which is the non-gravitational external force per unit mass. In the IMU coordinate system, the specific force equation is: Absolute acceleration when the vehicle is stationary. The equation then simplifies to: (10) in, This is the accelerometer output in the IMU coordinate system after noise reduction and zero-bias calibration. It is the projection of the gravity vector into the IMU coordinate system. For example... Figure 3 In the schematic diagram showing the correlation between accelerometer measurements and gravity projection, the specific force output by the accelerometer is in the opposite direction to gravity. The specific force projection is obtained in the b-frame. , , That is the measurement from the accelerometer.

[0053] Based on the above formula, the component expressions of the gravity vector in the IMU coordinate system can be directly obtained: (11) Finally, based on the vector transformation relationship of the direction cosine matrix, the vector of gravity in the IMU coordinate system is... It can also be determined by its vector in the vehicle coordinate system. By rotation matrix (From the vehicle system to the IMU system) we get: (12) The above derivation establishes the measurement output of the IMU accelerometer and the mounting angle between the IMU and the vehicle (included in...). The direct mathematical connection between the two (in Chinese) laid the foundation for subsequent calculations of roll and pitch angles using static data.

[0054] (4) Expansion of the gravitational projection components The installation deviation of the IMU relative to the vehicle is described by three attitude angles, and the rotation sequence follows the commonly used engineering sequence of "yaw-pitch-roll". Agreement (conforming to the laws governing changes in vehicle motion posture): Heading installation angle : Relative Tie The rotation angle of the axis (downward); Pitch installation angle : Relative Tie Rotation angle of the axis (to the right); Roll installation angle : Relative Tie Rotation angle of the axis (forward).

[0055] Tie Vector transformation of the system is achieved through the composite direction cosine matrix. This matrix is ​​based on " The complete expression for the rotation order derivation is: (13) Will and Substituting into the vector transformation formula, we get: (14) The gravity projection components of each axis of the IMU coordinate system are obtained by unfolding. Because... Only The axis has a non-zero component (the third element is...). (The first two elements are 0), therefore matrix multiplication only requires calculating The third column and The product of, i.e.: (15) After processing, the relationship between the accelerometer output and the installation angle can be obtained: (16) The physical meaning of this expansion is: the accelerometer output (the projection of the supporting force opposite to gravity) is determined by the roll angle. Pitch angle With gravitational acceleration The decision was made jointly, and the specific analysis is as follows: 1. Forward ( (axis) output Only related to pitch angle Related, When the vehicle looks up ( When the vehicle tilts its head down, the forward accelerometer output is positive; when the vehicle tilts its head down (…), the forward accelerometer output is positive. When ), the forward accelerometer output is negative.

[0056] 2. To the right ( (axis) output : with roll angle and pitch angle All are related. When the vehicle tilts to the right ( When the vehicle tilts to the left, the right-hand accelerometer output is negative; when the vehicle tilts to the left... When ), the right-hand accelerometer output is positive.

[0057] 3. downward ( (axis) output : with roll angle and pitch angle All are related. ,because and The absolute values ​​of all of them are less than 1, therefore The absolute value is always less than And it decreases as the installation angle increases.

[0058] This expansion is the core equation for subsequent solutions to roll and pitch angles. By correlating accelerometer measurements with the installation angle, it enables a quantitative conversion from sensor data to attitude angles.

[0059] (5) Discretization implementation Similar to gyroscope bias estimation, accelerometer output denoising also requires a discretization formula. Assume data is collected during the stationary phase. If there are 10 data points, the discretization formula for the accelerometer output after denoising is: (17) in, Indicates the first The accelerometer at the sampling point is... The original output value of the axis. This formula is easy to implement in embedded systems. It can directly use the sampled data during the stationary phase to calculate the denoised accelerometer output, providing input for subsequent attitude angle calculations (note that this value is opposite to the direction of gravity projection).

[0060] (6) Solve for roll and pitch installation angles Pitch angle The solution can be achieved by summing the squares of the last two equations in equation (14): (18) Take the absolute value after taking the square root: (19) Divide the first equation of combination (16) with equation (19), and use... Within the range From the properties of, we can obtain: (20) This formula can be solved directly using the arctangent function, without requiring small angle assumptions, and is applicable to any installation orientation.

[0061] Roll angle The solution can be obtained by dividing the last two equations of equation (16): (twenty one) because The four-quadrant arctangent function needs to be used to ensure quadrant correctness: (twenty two) in The quadrant is automatically determined based on the input sign, and the output range exactly covers all possible values ​​of the roll angle.

[0062] Based on the above embodiments, step 200 includes: The effective acceleration is calculated using an exponential decay function, thereby suppressing the acceleration amplitude during cornering. This is equivalent to recursively calculating the trajectory only during the straight-line acceleration period to obtain the horizontal displacement vector.

[0063] (1) Calculation and selection criteria for effective acceleration To overcome the limitations of directly determining linear acceleration, a dynamic weight decay mechanism is used to calculate the "effective acceleration," automatically suppressing interference data in turning scenarios and retaining only effective information suitable for estimating the heading angle. The specific implementation is as follows: 1. Calculation of angular velocity magnitude For the first 3D angular velocity of the gyroscope after zero bias compensation at the epoch Its vector is defined as: (twenty three) The three terms on the right side of the equation are respectively X, Y, Z The angular velocity of the 3-axis gyroscope. By calculating the magnitude of this vector, the overall rotational intensity of the vehicle (including steering, attitude sway, etc.) is quantified. The formula for the magnitude is: (twenty four) The larger the modulus, the more violent the vehicle rotation, and the less suitable the corresponding acceleration data is for estimating the heading angle.

[0064] 2. Design of Exponentially Decreasing Weight Function Define weight function Dynamic decay is achieved by taking the magnitude of angular velocity as input, and the function is as follows: (25) in The attenuation coefficient (which can take values) The core characteristics of the function are: when (In pure linear motion, without turning / swinging) Acceleration data is fully retained; when (about When making an obvious turn, Acceleration data was significantly suppressed; when exist During periods of slight fluctuation, The angular velocity decreases smoothly from 1 to 0.05 as the angular velocity increases, thus achieving adaptive processing of transitional scenes.

[0065] like Figure 3 In the schematic diagram of the exponential decay function with different attenuation coefficients, as the angular velocity magnitude gradually increases from 0, the function value rapidly decreases from 1. (Attenuation coefficient) The larger the value, the faster the decay rate.

[0066] 3. Effective acceleration calculation and screening For the first IMU horizontal acceleration after epoch-rate zero bias and gravity compensation Multiply by weight Effective acceleration is obtained: (26) Only when the forward component of the effective acceleration ( The absolute value exceeds the threshold. (0.2 is acceptable) If the epoch is considered "valid data" and included in the subsequent heading angle estimation process, then the epoch is considered invalid data (such as turning or constant speed scenarios) and is directly discarded.

[0067] (2) Horizontal acceleration and trajectory recursive model When a vehicle is moving in a straight line, the actual horizontal acceleration is strictly along the vehicle coordinate system. The lateral acceleration is 0 on the forward axis. Combined with the yaw angle... The coordinate system transformation relationship is used, with effective acceleration as input, to complete the trajectory recursion. The specific derivation is as follows: 1. Coordinate system transformation relationships The horizontal acceleration transformation between the IMU coordinate system and the vehicle coordinate system is described by a planar rotation matrix. In this case, the input is the effective acceleration (with cornering interference suppressed), and the transformation formula is: (27) in: This is the effective forward acceleration in the vehicle coordinate system (lateral component is 0); Forward installation angle (parameter to be estimated); left side , The effective acceleration in the IMU coordinate system (with turning interference removed by weight attenuation, conforming to the "linear motion" assumption).

[0068] 2. Recursive derivation of velocity and displacement integrals Using the effective acceleration as input, the horizontal displacement trajectory in the IMU coordinate system is obtained through quadratic integration. The initial integration condition is set as the starting epoch of the acceleration segment. Both velocity and displacement are 0 (the direction of displacement is determined only by the direction of acceleration and is independent of the initial velocity): No. Epoch velocity calculation ( ): (28) Initial velocity: ( (The starting epoch of the valid data segment). No. Epoch Displacement Calculation ( ): (29) Initial displacement: .

[0069] 3. Trajectory direction output Finally, the number was obtained Horizontal displacement vector of an epoch Its direction is relative to the IMU coordinate system. The included angle of the axis is the heading installation angle. Based on the instantaneous estimation, a stable installation angle result can be obtained by subsequent convergence verification.

[0070] Based on the above embodiments, step 300 includes: The heading installation angle is calculated by using the displacement vector direction at each epoch. Candidate heading installation angles are then selected by using the difference between consecutive adjacent angles. The angle results are verified by recursion using inertial navigation.

[0071] like Figure 4 In the diagram showing the relationship between continuous integral of acceleration and heading angle, the heading angle... Defined as IMU coordinate system ( (system) relative to the vehicle coordinate system ( (system) around The rotation angle of the axis (downward) reflects the forward axis (of the IMU) rotation angle. ) and the vehicle's actual front axle ( Deviation in the horizontal plane. (And roll angle) Pitch angle Unlike in a static state, the gravitational vector acts only in the vertical direction, without an independent horizontal vector to assist it, and therefore cannot be directly solved using accelerometer data. This method utilizes the horizontal acceleration and angular velocity generated by the vehicle's short-term motion (such as straight-line travel), combined with the displacement recursion principle in inertial navigation, to achieve estimation. In the straight-line travel region, when the acceleration exceeds a threshold, the velocity is obtained by integrating the acceleration, and the horizontal displacement vector is obtained by integrating again, thus calculating the heading angle. This method relies solely on the IMU's own measurement data, requiring no additional sensors, and is suitable for engineering application scenarios.

[0072] (1) Preliminary solution and first-stage verification of the heading installation angle The heading angle at each epoch can be directly calculated from the direction of the displacement vector, and the four-quadrant arctangent function is used to ensure coverage of the angle range. : (30) This formula is derived through displacement. Axial components and The ratio of the axis components determines the angle, which physically represents the relationship between the trajectory direction and the IMU. The included angle of the axis, i.e., the instantaneous estimate of the heading installation angle.

[0073] Since IMU measurement noise may cause instantaneous fluctuations in the estimates, stable results need to be screened through a first-stage consistency verification: during the effective acceleration phase, the difference in heading angle between adjacent epochs is calculated sequentially. ( (This refers to the current epoch number). If there are 10 consecutive epochs... The difference between adjacent values ​​is less than the threshold. (Possible value: 0.2) ),Right now: (31) This indicates that the estimated heading angles over these 10 epochs are stable (without significant jumps). At this point, the mean heading angle of the last 5 epochs in the sequence is calculated: (32) Will Marked as “candidate heading installation angle” (taking the last 5 epochs can further reduce the impact of the earlier integration error).

[0074] (2) Second-stage verification and result confirmation To further ensure the reliability of the candidate values, their temporal stability needs to be verified through a second-stage validation process. 1. Reset initial scoring conditions: End epoch at the end of Phase 1. For a new beginning (referred to as ), reset initial velocity Initial displacement ( This eliminates the cumulative effects of previous integration errors; 2. Subsequent trajectory recursion: using Using IMU data, when the acceleration is large, the horizontal displacement of subsequent epochs is calculated using the same integration method. And solve for the corresponding heading angle estimate. ; 3. Consistency check: If 5 consecutive epochs... The estimated value With candidate values The deviations are all less than the threshold. (Possible value: 0.4) Slightly larger (with compatibility with integral cumulative error), that is: (33) Then confirm the candidate value For the final heading installation angle .

[0075] The IMU installation angle estimation system based on the exponential decay function provided by the present invention will be described below. The IMU installation angle estimation system based on the exponential decay function described below can be referred to in correspondence with the IMU installation angle estimation method based on the exponential decay function described above.

[0076] Figure 5 This is a schematic diagram of the IMU installation angle estimation system based on the exponential decay function provided by the present invention, as shown below. Figure 5 As shown, it includes: a setup module 51, a calculation module 52, and an estimation module 53, wherein: The establishment module 51 is used to establish the gyroscope zero-bias estimation model and the accelerometer-gravity projection correlation model in a stationary state, respectively; the calculation module 52 is used to calculate the effective acceleration using the exponential decay function to suppress the acceleration amplitude during turning, and only perform trajectory recursion during the straight acceleration period to obtain the horizontal displacement; the estimation module 53 is used to calculate the heading angle at each epoch by the displacement vector direction, use the difference between consecutive adjacent angles to screen candidate heading angles, and verify the candidate heading angle results through inertial navigation recursion.

[0077] Figure 6 An example is a schematic diagram of the physical structure of an electronic device, such as... Figure 6As shown, the electronic device may include: a processor 610, a communication interface 620, a memory 630, and a communication bus 640. The processor 610, communication interface 620, and memory 630 communicate with each other via the communication bus 640. The processor 610 can call logic instructions in the memory 630 to execute an IMU installation angle estimation method based on an exponential decay function. This method includes: establishing a gyroscope zero-bias estimation model for the vehicle and an accelerometer-gravity projection correlation model in a stationary state; calculating the effective acceleration using an exponential decay function to suppress acceleration amplitudes during cornering, performing trajectory recursion only during straight-line acceleration periods to obtain the horizontal displacement; calculating the heading installation angle at each epoch using the displacement vector direction, filtering candidate heading installation angles using consecutive adjacent angle differences, and verifying the candidate heading installation angle results via inertial navigation recursion.

[0078] Furthermore, the logical instructions in the aforementioned memory 630 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0079] On the other hand, the present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon. When executed by a processor, the computer program implements the IMU installation angle estimation method based on the exponential decay function provided by the above methods. The method includes: establishing a gyroscope zero-bias estimation model for the vehicle and an accelerometer-gravity projection correlation model in a stationary state; calculating the effective acceleration using the exponential decay function to suppress the acceleration amplitude during turning, performing trajectory recursion only during the straight-line acceleration period to obtain the horizontal displacement; calculating the heading installation angle at each epoch using the displacement vector direction, filtering candidate heading installation angles using the difference between consecutive adjacent angles, and verifying the candidate heading installation angle results through inertial navigation recursion.

[0080] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0081] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0082] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the solutions of the embodiments of the present invention.

Claims

1. A method for estimating the installation angle of an IMU based on an exponential decay function, characterized in that, include: Establish a zero-bias estimation model for the vehicle's gyroscope and a correlation model between the accelerometer and gravity projection in a stationary state, respectively. The effective acceleration is calculated using an exponential decay function to suppress the acceleration amplitude during cornering. Trajectory recursion is performed only during the straight acceleration period to obtain the horizontal displacement. The heading installation angle is calculated at each epoch by the displacement vector direction. Candidate heading installation angles are selected by the difference between consecutive adjacent angles, and the results of the candidate heading installation angles are verified by inertial navigation recursion.

2. The IMU installation angle estimation method based on the exponential decay function according to claim 1, characterized in that, A zero-bias estimation model for the vehicle's gyroscope and a correlation model between the accelerometer and gravity projection in a stationary state are established, including: A gyroscope measurement model is constructed, and the average value of the gyroscope output is calculated when the vehicle is stationary. The zero bias of each axis of the gyroscope is obtained, and the measurement data is compensated and discretized. Based on the correlation model of accelerometer and gravity projection under static conditions, the projection of gravity in the IMU frame is derived. By solving the constraint equations, the roll and pitch installation angles are calculated.

3. The IMU installation angle estimation method based on the exponential decay function according to claim 1, characterized in that, The effective acceleration is calculated using an exponential decay function to suppress acceleration amplitudes during cornering. Trajectory recursion is performed only during the linear acceleration period to obtain the horizontal displacement, including: Calculate the angular velocity magnitude, design an exponential decay weighting function, and perform effective acceleration calculation and screening; Construct a recursive model of horizontal acceleration and trajectory, perform coordinate system transformation, recursively calculate velocity and displacement integrals, and output the trajectory direction.

4. The IMU installation angle estimation method based on the exponential decay function according to claim 3, characterized in that, Calculate the angular velocity magnitude, design an exponentially decaying weighting function, and perform effective acceleration calculation and screening, including: For the first 3D angular velocity of the gyroscope after zero bias compensation at the epoch Its vector is defined as: The three terms on the right side of the equation are respectively X, Y, Z The angular velocity of the three-axis gyroscope is used to quantify the overall rotational intensity of the vehicle by calculating the magnitude of this vector. The formula for the magnitude is: The larger the modulus, the more violent the vehicle rotation, and the less suitable the corresponding acceleration data is for estimating the heading angle. Define weight function Dynamic decay is achieved by taking the magnitude of angular velocity as input, and the function is as follows: in The attenuation coefficient is the core characteristic of the function: when hour, Acceleration data is fully retained; when hour, Acceleration data was significantly suppressed; when exist At time, The angular velocity decreases smoothly from 1 to 0.05 as the angular velocity increases, thus achieving adaptive processing of transitional scenes. For the first IMU horizontal acceleration after epoch-rate zero bias and gravity compensation Multiply by weight Effective acceleration is obtained: Only when the forward component of the effective acceleration The absolute value exceeds the threshold If the epoch is deemed valid, it is included in the subsequent heading and installation angle estimation process; otherwise, it is considered invalid and is directly discarded.

5. The IMU installation angle estimation method based on the exponential decay function according to claim 4, characterized in that, Construct a recursive model of horizontal acceleration and trajectory, perform coordinate system transformation, recursively calculate velocity and displacement integrals, and output the trajectory direction, including: The horizontal acceleration transformation between the IMU coordinate system and the vehicle coordinate system is described by a planar rotation matrix. The input is the effective acceleration that has suppressed cornering interference. The transformation formula is: in, The effective forward acceleration in the vehicle coordinate system. For the heading installation angle, , The effective acceleration in the IMU coordinate system; Using the effective acceleration as input, the horizontal displacement trajectory in the IMU coordinate system is obtained through quadratic integration. The initial integration condition is set as the starting epoch of the acceleration segment. Both the velocity and displacement are 0; No. Epoch velocity calculation: in Initial velocity , This is the starting epoch of the valid data segment; No. Epoch Displacement Calculation: Initial displacement ; Finally, the number was obtained Horizontal displacement vector of an epoch Its direction is relative to the IMU coordinate system. The included angle of the axis is the heading installation angle. The basis for instantaneous estimation.

6. The IMU installation angle estimation method based on the exponential decay function according to claim 1, characterized in that, The heading and installation angle are calculated at each epoch using the displacement vector direction. Candidate heading and installation angles are selected using the difference between consecutive adjacent angles. The results of the candidate heading and installation angles are then verified recursively by the inertial navigation system, including: A preliminary solution for the heading angle is performed, and a first-stage consistency verification is conducted to screen stable results, thereby obtaining candidate heading installation angles. The second phase of time stability verification was conducted to screen the final results and obtain the final heading installation angle.

7. The IMU installation angle estimation method based on the exponential decay function according to claim 6, characterized in that, A preliminary solution for the heading angle is performed, and a first-stage consistency verification is conducted to screen stable results, yielding candidate heading installation angles, including: The heading installation angle for each epoch is obtained from the displacement vector direction, and the angle coverage range is determined using the four-quadrant arctangent function. : For the first Horizontal displacement vector of an epoch; During the effective acceleration phase, the difference in heading angle between adjacent epochs is calculated sequentially. ; If it is determined that the difference between adjacent heading angles of consecutive first epochs in the sequence is less than the first preset threshold, then the average value of the heading angles of the second epoch in the sequence is extracted to obtain the candidate heading installation angle.

8. The IMU installation angle estimation method based on the exponential decay function according to claim 7, characterized in that, The second phase of time stability verification was conducted to screen the final results, yielding the final heading installation angle, including: The new starting point of the sequence is the end of the first phase epoch. Reset initial speed Initial displacement ( This is to eliminate the cumulative effect of previous integration errors; use Using IMU data, when the acceleration is large, the horizontal displacement of subsequent epochs is calculated using the same integration method. And solve for the corresponding heading angle estimate. ; If the deviation between the estimated heading angle and the candidate heading installation angle for a consecutive second number of epochs is less than a second preset threshold, and the second preset threshold is greater than the first preset threshold, then the candidate heading installation angle is determined as the final heading installation angle.

9. An IMU installation angle estimation system based on an exponential decay function, characterized in that, include: A module is established to create a gyroscope zero-bias estimation model for the vehicle and an accelerometer-gravity projection correlation model in a stationary state, respectively. The calculation module is used to calculate the effective acceleration using the exponential decay function to suppress the acceleration amplitude when there is a turn, and only performs trajectory recursion during the straight acceleration period to obtain the horizontal displacement. The estimation module is used to calculate the heading installation angle at each epoch by using the displacement vector direction, filter candidate heading installation angles by the difference between consecutive adjacent angles, and verify the candidate heading installation angle results by inertial navigation recursion.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the IMU installation angle estimation method based on the exponential decay function as described in any one of claims 1 to 8.

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