A method for calibrating an inertial navigation system

Abstract

The application relates to the technical field of inertial navigation, and provides an inertial navigation system internal parameter calibration method, which comprises the following steps: acquiring sensor measurement data of an inertial navigation system at a plurality of preset positions, the sensors comprising gyroscopes and accelerometers; eliminating zero offset interference through differential operation on the basis of the sensor measurement data to acquire an initial attitude; controlling an excitation device to provide a known angular velocity excitation to the inertial navigation system; taking the norm of the angular velocity vector provided by the excitation device as a reference to construct a calibration loss function; and solving the internal parameters of the inertial navigation system on the basis of the calibration loss function and the initial attitude. The norm of the angular velocity vector of external excitation is used as a strong reference, the dependence on precise alignment of the coordinate system is avoided, the zero offset interference is effectively eliminated through differential operation, and high-robustness and high-precision internal parameter calibration is realized.

Description

Technical Field

[0001] This invention relates to the field of inertial navigation technology, and more specifically to a method for calibrating the intrinsic parameters of an inertial navigation system. Background Technology

[0002] Currently, microelectromechanical systems (MEMS) strapdown inertial navigation systems (SINS) are widely used due to their small size and low cost. However, MEMS inertial sensors are limited by manufacturing processes and suffer from inherent bottlenecks such as low mechanical precision, high output noise, and weak effective signals, leading to significant systematic errors (i.e., "intrinsic parameters," including scale factor error, cross-axis coupling error, and constant zero bias). In high-dynamic environments such as high-speed aircraft, these errors accumulate rapidly, resulting in severe navigation drift. Existing calibration methods typically rely on weak reference signals such as the Earth's rotation rate, resulting in low signal-to-noise ratios and extremely high requirements for the alignment accuracy between the inertial navigation system and the turntable. Even a small installation deviation can drastically reduce calibration accuracy, making it difficult to meet the high-precision calibration requirements of MEMS devices in weak signal and high-noise environments. Therefore, there is an urgent need for an intrinsic parameter calibration method that can overcome the influence of weak signals, is insensitive to installation errors, and achieves high-precision calibration. Summary of the Invention

[0003] To address the problems of weak calibration reference signals and low calibration accuracy due to sensitivity to installation alignment precision in existing technologies, this application proposes an inertial navigation system intrinsic parameter calibration method. This method utilizes the norm of the angular velocity vector of external excitation as a strong reference and combines differential operations to eliminate zero-bias interference, thereby achieving high-precision intrinsic parameter calibration that is insensitive to installation errors.

[0004] To achieve the above objectives, the present invention adopts the following technical solution: A method for calibrating the intrinsic parameters of an inertial navigation system includes: acquiring sensor measurement data of the inertial navigation system at multiple preset positions, wherein the sensors include gyroscopes and accelerometers; based on the sensor measurement data, eliminating zero-bias interference through differential operations to obtain an initial attitude; controlling an excitation device to provide a known angular velocity excitation to the inertial navigation system; constructing a calibration loss function based on the norm of the angular velocity vector provided by the excitation device; and solving for the intrinsic parameters of the inertial navigation system based on the calibration loss function and the initial attitude.

[0005] The above scheme constructs a loss function based on the norm of the angular velocity vector of the external excitation, replacing the traditional weak reference signal. This fundamentally avoids the dependence on precise alignment of the coordinate system. At the same time, it effectively eliminates zero-bias interference through differential operations, achieving highly robust and high-precision intrinsic parameter calibration.

[0006] Optionally, the excitation device includes a turntable, and the control excitation device provides a known angular velocity excitation to the inertial navigation system, including controlling the turntable to drive the inertial navigation system to rotate about at least one axis at a constant angular velocity.

[0007] Optionally, the step of constructing a calibration loss function based on the norm of the angular velocity vector provided by the excitation device includes: constructing an error model that includes scale factor error, cross-axis coupling error, and constant zero bias; and constructing the calibration loss function, wherein the calibration loss function is used to minimize the sum of squares of the difference between the measured angular velocity norm corrected by the error model and the reference angular velocity norm provided by the turntable.

[0008] Optionally, the plurality of preset positions includes four positions. The step of eliminating zero-bias interference and obtaining the initial attitude based on the sensor measurement data through differential operation includes: controlling the inertial navigation system to sequentially reach the first position, the second position, the third position, and the fourth position; wherein the first position and the second position are flipped by 180°, the third position and the fourth position are flipped by 180°, and the first position and the third position are rotated by 90°; performing differential operation based on the sensor measurement data of the first position and the second position to obtain a first set of attitude angles; performing differential operation based on the sensor measurement data of the third position and the fourth position to obtain a second set of attitude angles; and taking the average of the first set of attitude angles and the second set of attitude angles to obtain the initial attitude.

[0009] The above scheme effectively eliminates the interference of constant zero bias and common-mode noise by using a specific combination of four flip positions and differential operations of symmetrical positions, thereby achieving high-precision initial attitude determination without the need for precise alignment.

[0010] Optionally, the sensor measurement data includes accelerometer measurements and gyroscope measurements; the step of performing differential calculations based on the sensor measurement data of the first position and the second position to obtain a first set of attitude angles includes: solving for the pitch angle and roll angle using the gravity vector projection relationship based on the difference between the accelerometer measurements of the first position and the second position; and solving for the azimuth angle using the Earth's rotation rate projection relationship based on the difference between the gyroscope measurements of the first position and the second position.

[0011] Optionally, solving for the intrinsic parameters of the inertial navigation system includes: using a nonlinear optimization algorithm to iteratively solve the calibration loss function to obtain the optimal intrinsic parameters.

[0012] Optionally, the nonlinear optimization algorithm includes the Levenberg-Marquardt algorithm; the step of iteratively solving the calibration loss function using the nonlinear optimization algorithm includes: calculating the iteration step size, which is determined based on the Jacobian matrix, damping factor, and residual vector; and updating the intrinsic parameter vector until the convergence condition is met.

[0013] Optionally, before solving the intrinsic parameters of the inertial navigation system, the method further includes: estimating the initial zero bias values ​​of the gyroscope and the accelerometer based on static measurement data; estimating the initial scale factor value of the gyroscope based on rotational measurement data around the axis; and using the initial zero bias value and the initial scale factor value as the starting point for the solution.

[0014] The above scheme provides a high-quality iterative starting point for the nonlinear optimization algorithm by pre-estimating the initial values ​​of the zero bias and scale factor, which significantly improves the convergence speed of the algorithm and the accuracy of the calibration results.

[0015] Furthermore, the present invention also provides an inertial navigation system intrinsic parameter calibration device, comprising: a data acquisition module for acquiring sensor measurement data of the inertial navigation system at multiple preset positions, wherein the sensors include gyroscopes and accelerometers; an initial alignment module for obtaining an initial attitude by eliminating zero-bias interference through differential operations based on the sensor measurement data; an excitation control module for controlling an excitation device to provide a known angular velocity excitation to the inertial navigation system; a function construction module for constructing a calibration loss function based on the norm of the angular velocity vector provided by the excitation device; and a parameter solving module for solving the intrinsic parameters of the inertial navigation system based on the calibration loss function and the initial attitude.

[0016] Optionally, the device includes a precision turntable, a data acquisition unit, and a processing unit; the precision turntable is used to support the inertial navigation system and provide known angular velocity excitation; the data acquisition unit is used to acquire sensor measurement data of the inertial navigation system; and the processing unit is used to execute the method described in the above scheme.

[0017] Beneficial effects: Compared with the prior art, the technical solution provided by this invention has the following significant progress and beneficial effects: 1) Created a strong reference calibration environment: By adopting the precision turntable angular velocity norm as the calibration reference, the traditional Earth rotation angular rate norm with extremely low signal-to-noise ratio is replaced, providing a stable and robust physical reference for the intrinsic parameter calibration of the gyroscope, fundamentally solving its core pain point of "weak signal and difficult calibration".

[0018] 2) Breakthrough in the technical bottleneck of precision alignment: The rotation norm normalization calibration framework proposed in this invention is theoretically insensitive to alignment errors between the inertial frame and the turntable coordinate system. This significantly reduces the stringent requirements for installation accuracy, simplifies the calibration process, reduces the error chain introduced by assembly and adjustment, and greatly improves the engineering practicality and repeatability of the method.

[0019] 3) Achieved integrated and accurate estimation of high-dimensional parameters: By constructing a systematic error model and loss function containing all intrinsic parameters, and combining four-bit flip-difference initial alignment with a nonlinear algorithm with optimized initial values, the simultaneous and high-precision optimization solution of all systematic error parameters, including scale factor, cross-axis coupling error and constant zero bias, was achieved, ensuring the integrity and accuracy of the calibration. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating a method for calibrating intrinsic parameters of an inertial navigation system according to an embodiment of the present invention; Figure 2 This is a schematic diagram illustrating the coordinate system definition and transformation relationships involved in the embodiments of the present invention; Figure 3 This is a flowchart and positional diagram of the four-bit flipping differential initial alignment method according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the twelve-position rotational excitation path according to an embodiment of the present invention; Figure 5 This is a schematic diagram illustrating the location for obtaining the initial value for error optimization according to an embodiment of the present invention; Figure 6 This is a scatter plot of the gyroscope scale factor calibration results according to an embodiment of the present invention. Figure 7 This is a scatter plot of the gyroscope constant zero bias calibration results according to an embodiment of the present invention; Figure 8 This is a bar graph showing the error of the gyroscope scale factor calibration results according to an embodiment of the present invention; Figure 9 This is a bar graph showing the error of the gyroscope constant zero bias calibration results according to an embodiment of the present invention; Figure 10 This is a schematic diagram of the hardware structure of the calibration experimental platform according to an embodiment of the present invention; Figure 11 This is a comparison curve of attitude error at the 0° position in the embodiment of the present invention; Figure 12 This is a comparison curve of attitude error at the 120° position according to an embodiment of the present invention; Figure 13 This is a comparison curve of attitude error at the 240° position in the embodiment of the present invention.

[0021] Among them, 1-precision turntable, 2-inertial navigation system. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments 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.

[0023] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.

[0024] Example 1: This embodiment provides a method for calibrating the intrinsic parameters of an inertial navigation system, the flowchart of which is shown below. Figure 1 This method aims to solve the problems of weak calibration reference signals and low calibration accuracy caused by sensitivity to installation alignment accuracy in existing technologies. The following section combines... Figure 2 and Figure 3 This embodiment will be described in detail.

[0025] Step S100: Acquire sensor measurement data of the inertial navigation system at multiple preset positions, wherein the sensors include gyroscopes and accelerometers.

[0026] Specifically, such as Figure 2 As shown, the coordinate systems involved in this embodiment include inertial coordinate system i, Earth coordinate system e, navigation coordinate system m, and vehicle coordinate system b. Before calibration, the inertial navigation system to be calibrated needs to be installed on an excitation device (such as a precision turntable). The multiple preset positions refer to a set of specific spatial attitude positions designed to achieve initial alignment. The gyroscope and accelerometer in the inertial navigation system are used to sense the angular velocity and specific force information of the vehicle, respectively. Due to the limitations of the manufacturing process, the raw output data of MEMS inertial sensors often contains significant systematic errors (i.e., intrinsic parameters), such as scale factor error, cross-axis coupling error, and constant zero bias, and the output noise is high. Therefore, this step collects static measurement data at multiple preset positions to provide a data basis for subsequent elimination of zero bias interference and calculation of the initial attitude.

[0027] Step S200: Based on the sensor measurement data, zero-bias interference is eliminated through differential operation to obtain the initial attitude.

[0028] Zero bias is a constant error in the output of an inertial sensor, which can cause significant attitude drift when integrated over time. This embodiment uses differential computation as the core method to eliminate this interference. Figure 3 As shown, by controlling the inertial navigation system to flip between specific paired positions (such as position 1 and position 2), the projection directions of the gravity vector and the Earth's rotation angular rate vector in the carrier coordinate system undergo specific changes, while the zero-bias term remains relatively stable for a short period. At this time, performing differential operations on the sensor measurement data at the paired positions eliminates the zero-bias term in the mathematical model, thereby extracting the pure gravity or Earth rotation signal components. Using these pure signal components, combined with... Figure 2 The coordinate system transformation relationship shown can be used to accurately solve for the initial attitude angles (including pitch, roll, and azimuth) of the carrier coordinate system relative to the navigation coordinate system. The key technical advantage of this step is that it does not rely on high-precision external alignment equipment. It can achieve high-precision initial alignment through differential processing at the algorithm level, which greatly reduces the dependence of the calibration process on installation accuracy and simplifies the operation process.

[0029] Step S300: The control excitation device provides a known angular velocity excitation to the inertial navigation system.

[0030] After acquiring the initial attitude, a strong external reference signal is needed to calibrate the intrinsic parameters. In this step, an excitation device (e.g., a precision turntable) is used to generate precise rotational motion according to preset commands. The excitation device drives the inertial navigation system to rotate around one or more of its axes at a constant angular velocity. The angular velocity vector of this rotational motion is known and has high accuracy, making it a reference signal for subsequent calibration calculations. Compared to traditional methods that use the Earth's rotational angular rate with extremely low signal-to-noise ratio as a reference, this embodiment creates a strong reference calibration environment by actively applying a known angular velocity excitation through the excitation device, fundamentally solving the pain point of "weak signal and difficult calibration" for MEMS gyroscopes.

[0031] Step S400: Construct a calibration loss function based on the norm of the angular velocity vector provided by the excitation device.

[0032] Constructing a calibration loss function is one of the core innovations of this embodiment. Angular velocity vector is a physical quantity with both direction and magnitude, and its direction information is easily affected by installation errors between the inertial navigation system (INS) and the excitation device. If the angular velocity vector is directly used as a reference, extremely precise coordinate system alignment is required, which is often difficult to achieve in engineering practice. However, the norm of the angular velocity vector (i.e., the magnitude of the angular velocity, a scalar) is a physical quantity independent of coordinate system rotation. Regardless of how the INS is installed relative to the excitation device, as long as the excitation device provides a constant magnitude of angular velocity, the norm of the angular velocity vector measured by the INS should theoretically be equal to the reference angular velocity norm provided by the excitation device. Based on this principle, this embodiment constructs a calibration loss function that aims to minimize the difference between the measured angular velocity norm after error model correction and the reference angular velocity norm. In this way, the calibration process is naturally insensitive to installation errors, thus overcoming the technical bottleneck of precise alignment.

[0033] Step S500: Based on the calibration loss function and the initial attitude, solve for the intrinsic parameters of the inertial navigation system.

[0034] As mentioned earlier, intrinsic parameters include scale factor errors, cross-axis coupling errors, and constant zero bias of the gyroscope and accelerometer. After constructing the calibration loss function and obtaining an accurate initial attitude, the problem is transformed into a nonlinear optimization problem. This step uses numerical optimization algorithms (such as least squares or iterative algorithms) to solve the loss function, finding a set of optimal intrinsic parameter estimates that minimize the loss function. The initial attitude serves to unify the measurement data from different times and attitudes into the same reference coordinate system for calculation, ensuring the correctness of the optimization process. Finally, through the above steps, this embodiment achieves high-precision, high-robust integrated calibration of the intrinsic parameters of the inertial navigation system without the need for precise alignment.

[0035] Example 2: Based on Example 1, this embodiment provides a detailed explanation of the specific method for the excitation device to provide known angular velocity excitation and the process for constructing the calibration loss function.

[0036] The excitation device provided in this embodiment includes a turntable. The control excitation device provides a known angular velocity excitation to the inertial navigation system, including controlling the turntable to drive the inertial navigation system to rotate around at least one axis at a constant angular velocity.

[0037] Specifically, such as Figure 4 As shown, this embodiment designs an excitation path including twelve positions and forward and reverse rotation directions. The turntable, as the excitation device, has the core function of providing a high-precision reference angular velocity. During calibration, the turntable is controlled to move sequentially to... Figure 4At each of the positions shown, the turntable is controlled to move, causing the inertial navigation system to rotate around the X-axis, Y-axis, or Z-axis of the carrier coordinate system at a set constant angular velocity.

[0038] Regarding the construction of the calibration loss function, the construction of the calibration loss function based on the norm of the angular velocity vector provided by the excitation device includes: constructing an error model that includes scale factor error, cross-axis coupling error, and constant zero bias; and constructing the calibration loss function, which is used to minimize the sum of squares of the difference between the measured angular velocity norm corrected by the error model and the reference angular velocity norm provided by the turntable.

[0039] Specifically, this is the core innovation of this embodiment in achieving "insensitivity to installation errors." First, an error model for the inertial navigation system is established. For the gyroscope, the relationship between its measured output value and the actual angular velocity can be modeled as follows:

[0040] in, This is the true angular velocity vector in the carrier coordinate system. These are the raw measurements from the gyroscope. The scaling factor error matrix, The cross-axis coupling error matrix is... This is a constant zero-bias vector. The error model for the accelerometer has a similar form. This error model covers all the major intrinsic parameters affecting the accuracy of the inertial navigation system.

[0041] Next, the calibration loss function is constructed. This embodiment abandons the traditional approach that relies on vector direction alignment, and instead utilizes the scalar properties of the norm of the angular velocity vector. The norm of the angular velocity vector, i.e., the magnitude of the angular velocity, is a physical quantity independent of coordinate system rotation. Regardless of the installation deviation angle of the inertial navigation system relative to the turntable coordinate system, as long as the turntable provides a constant angular velocity... Angular velocity vector measured by the inertial navigation system The norm should theoretically be strictly equal to Based on this principle, a calibration loss function of the following form is constructed:

[0042] in, The total number of sampling points. It represents the 2-norm of a vector (i.e., the Euclidean norm). For the turntable at the The reference angular velocity vector provided by each sampling point.

[0043] The physical meaning of this loss function lies in finding an optimal set of intrinsic parameters. This minimizes the sum of squares of the differences between the measured angular velocity norm corrected by this intrinsic parameter and the reference angular velocity norm provided by the turntable. Since the norm is a scalar and does not contain directional information, the installation error angle (usually an unknown rotation matrix) between the turntable coordinate system and the carrier coordinate system is naturally eliminated in the norm calculation. This means that the calibration method described in this embodiment is theoretically completely unaffected by installation errors and can achieve high-precision calibration without precise optical alignment, fundamentally solving the technical bottleneck of traditional calibration methods being extremely sensitive to installation alignment accuracy.

[0044] Furthermore, based on Embodiment 1, this embodiment provides a detailed explanation of the specific implementation process of step S200, "based on the sensor measurement data, eliminating zero-bias interference through differential operation to obtain the initial attitude." The core of this embodiment lies in using a specific combination of four flip positions and differential operation of symmetrical positions to eliminate constant zero bias, thereby achieving high-precision initial attitude determination without the need for precise alignment.

[0045] The plurality of preset positions includes four positions. The process of eliminating zero-bias interference and obtaining the initial attitude based on the sensor measurement data through differential calculation includes: controlling the inertial navigation system to sequentially reach a first position (position 1), a second position (position 2), a third position (position 1'), and a fourth position (position 2'); wherein the first position and the second position are flipped 180° apart, the third position and the fourth position are flipped 180° apart, and the first position and the third position are rotated 90° apart; differential calculation is performed based on the sensor measurement data of the first position and the second position to obtain a first set of attitude angles (roll angles). Pitch angle Azimuth Based on the sensor measurement data at the third and fourth positions, a differential calculation is performed to obtain the second set of attitude angles (roll angles). Pitch angle Azimuth The initial attitude is obtained by averaging the first set of attitude angles and the second set of attitude angles.

[0046] like Figure 3As shown, this embodiment designs a static alignment frame with four specific flip positions. The core design idea of ​​this frame is to utilize the symmetry of the 180° flip between paired positions. When the inertial navigation system flips 180° between position 1 and position 2 (or position 1′ and position 2′), the projection directions of the gravity vector and the Earth's rotation angular rate vector in the carrier coordinate system will change specifically, while the constant zero bias of the sensor remains relatively stable for a short period of time. At this time, by performing differential operations on the sensor measurement data of the paired positions, the zero bias term can be eliminated in the mathematical model, thereby extracting the pure gravity or Earth rotation signal components.

[0047] The sensor measurement data includes accelerometer measurements and gyroscope measurements; the differential calculation based on the sensor measurement data of the first position and the second position to obtain the first set of attitude angles includes: solving the pitch angle and roll angle using the gravity vector projection relationship based on the difference between the accelerometer measurements of the first position and the second position; and solving the azimuth angle using the Earth's rotation rate projection relationship based on the difference between the gyroscope measurements of the first position and the second position.

[0048] Specifically, taking a 180° rotation around the Y-axis of the carrier as an example, the accelerometer readings at the first and second positions satisfy the following relationship: At the first position, the projection component of the gravity vector onto the carrier's X-axis is: At the second position (after flipping 180°), the projection component becomes: Adding the two equations above eliminates the term containing zero bias, and by combining this with the relationships of other axes, the pitch angle can finally be derived. and roll angle The expression: For azimuth angle The solution is obtained by calculating the difference between gyroscope measurements. Again, taking a 180° rotation around the Y-axis of the carrier as an example, the component relationship of the Earth's rotation angular rate along the X-axis of the carrier is as follows:

[0049] First position: Second position: Subtracting the two equations above eliminates the terms containing the Earth's rotation northward component and the zero-bias term, thus deriving the azimuth angle. The expression: in: Through the aforementioned differential operations, the zero-bias term, as a constant error, is effectively eliminated. This is particularly important for MEMS inertial sensors, as MEMS devices typically exhibit significant zero-bias instability, and directly using the original measurements for attitude calculation can lead to severe error accumulation. The four-bit flip-differential method described in this embodiment eliminates zero-bias interference from a fundamental mathematical perspective, thereby achieving high-precision initial attitude determination even in the high-noise environment of MEMS.

[0050] Finally, the average of the first set of attitude angles (position 1 and position 2) and the second set of attitude angles (position 1′ and position 2′) is taken to obtain the final initial attitude: This averaging process further reduces the impact of random noise and improves the repeatability accuracy of the initial alignment. It should be understood that although this embodiment is illustrated by rotating 180° around the Y-axis, in other embodiments, a scheme of rotating around the X-axis or Z-axis can also be used, as long as the paired positions are rotated 180° and the two sets of positions are rotated 90° apart, they are all within the protection scope of this invention.

[0051] Example 3: This embodiment, based on Embodiment 1, provides a detailed explanation of the specific numerical calculation process for "solving the intrinsic parameters of the inertial navigation system" in step S500. After constructing the calibration loss function and obtaining the initial attitude, solving the intrinsic parameters is essentially a multidimensional nonlinear optimization problem. To ensure the convergence speed and accuracy of the solution process, this embodiment employs a nonlinear optimization strategy with initial value estimation.

[0052] Before solving the intrinsic parameters of the inertial navigation system, an initial value acquisition step is included: estimating the initial zero bias of the gyroscope and the accelerometer based on static measurement data; estimating the initial scale factor of the gyroscope based on rotational measurement data around the axis; and using the initial zero bias and the initial scale factor as the starting point for the solution.

[0053] Specifically, the convergence of nonlinear optimization algorithms (such as the least squares method) largely depends on the quality of the initial parameter values. If the initial values ​​deviate too much, the iterative process may get trapped in local optima, or even cause the algorithm to diverge. This embodiment combines... Figure 5A fast initial value estimation method is proposed for the four positions shown. First, the initial zero-bias values ​​of the gyroscope and accelerometer are estimated using static measurement data collected at the four flip positions. Under static conditions, ideally, the gyroscope only senses the Earth's rotation angular rate (a weak signal), and the accelerometer only senses gravitational acceleration. By averaging or differentiating the static data from multiple positions, the constant zero-bias component can be separated relatively accurately. Second, the initial value of the gyroscope's scaling factor is estimated using angular velocity measurement data when the turntable rotates around each axis. When the turntable rotates at a known constant angular velocity, the ratio between the gyroscope output value and the true angular velocity reflects the scaling factor. A rough estimate of the scaling factor can be obtained through simple ratio calculation. As for the initial value of the cross-axis coupling error matrix, since its value is usually small, it can be set as the identity matrix. Using the estimated initial zero-bias values, initial scaling factor values, and identity matrix as the starting point for nonlinear optimization iterations can significantly shorten the search path and improve calibration efficiency.

[0054] The process of solving the intrinsic parameters of the inertial navigation system includes: using a nonlinear optimization algorithm to iteratively solve the calibration loss function to obtain the optimal intrinsic parameters.

[0055] Specifically, in this embodiment, the Levenberg-Marquardt (LM) algorithm is preferably used to iteratively solve the aforementioned calibration loss function. The LM algorithm is a hybrid optimization algorithm that combines the Gauss-Newton method and the gradient descent method. It has the advantages of fast convergence speed and strong robustness, and is particularly suitable for nonlinear least squares problems with complex residual function forms, such as those in this embodiment.

[0056] The nonlinear optimization algorithm includes the Levenberg-Marquardt algorithm; the iterative solution of the calibration loss function using the nonlinear optimization algorithm includes: calculating the iteration step size, which is determined based on the Jacobian matrix, damping factor and residual vector; updating the intrinsic parameter vector until the convergence condition is met.

[0057] Iteration step size The following equation is obtained by solving: in, It is a Jacobian matrix. It is the damping factor. It is an identity matrix.

[0058] During the iteration process, convergence criteria must be set to terminate the loop. Common convergence criteria include: the change in the residual function is less than a preset threshold (e.g., ...). The iteration terminates when any of the above conditions are met: the intrinsic parameter vector is updated if the update amount is less than a preset threshold, or the maximum number of iterations (e.g., 500) is reached. This represents the optimal intrinsic parameters obtained through the solution. By combining the initial value acquisition with iterative optimization described above, this embodiment achieves high-precision and high-efficiency solution of the intrinsic parameters, further enhancing the engineering practicality of the calibration method.

[0059] Example 4: To verify the effectiveness and superiority of the inertial navigation system intrinsic parameter calibration method provided by this invention, this embodiment combines... Figures 6 to 13 The method was verified in detail through Monte Carlo simulation experiments and physical navigation experiments. It should be noted that the experimental data and results described in this embodiment are for illustrative purposes only and do not constitute a limitation on the scope of protection of this invention.

[0060] First, set up a calibration experimental platform. For example... Figure 10 As shown, the experimental platform mainly includes a precision turntable (1), an inertial navigation system (2), a data acquisition unit, and a processing unit. In this embodiment, the inertial navigation system (2) is the STIM318 MEMS inertial navigation system from Sensonor Corporation. This device is characterized by its small size and light weight, representing typical MEMS inertial sensor characteristics. The precision turntable (1) is used to support the inertial navigation system (2) and provide high-precision angular velocity excitation. The data acquisition unit is used to synchronously acquire the raw sensor output data of the inertial navigation system (2) and the reference data of the turntable. The processing unit executes the calibration method steps as described in Examples 1 to 4. It is particularly important to emphasize that during the experiment, the inertial navigation system (2) is only fixed to the turntable surface through a simple mechanical connection, without any optical precision alignment operation, and there is an unknown installation error angle between the turntable coordinate system and the inertial navigation coordinate system. This experimental setup aims to verify the calibration performance of the method of the present invention under non-precision alignment conditions.

[0061] Secondly, Monte Carlo simulation verification was performed. To evaluate the statistical performance of the calibration method, Monte Carlo simulation experiments were conducted. Combined with... Figure 6 and Figure 7 The scatter plot of the calibration results shown compares the calibration results of the method of this invention (indicated by the red pentagram in the figure), the traditional multi-position method (indicated by the green square in the figure), and the traditional norm method (indicated by the blue rhombus in the figure). From Figure 6 As can be seen, in the gyroscope scale factor calibration results, the data points of the method of this invention are closely clustered near the true value (black dashed line), while the data points of the traditional method are more dispersed, and some data points deviate far from the true value. Figure 7 The demonstrated gyroscope constant zero-bias calibration results also show that the method of this invention has smaller dispersion. Further combined with... Figure 8 and Figure 9The error bar plots quantitatively demonstrate that the calibration errors (mean error and root mean square error) of the method described in this invention on the three-axis scale factor and constant zero bias of the gyroscope are significantly smaller than those of the traditional method. Statistical data shows that, compared to the traditional method, the intrinsic parameter calibration accuracy of the method described in this invention is improved by nearly 20%, and the repeatability accuracy is improved by nearly 50%. This strongly proves that the present invention, by constructing a rotation norm normalized loss function, effectively overcomes the influence of installation errors on the calibration results, significantly improving the accuracy and consistency of the calibration.

[0062] Finally, a navigation accuracy verification experiment was conducted. The intrinsic parameters obtained from the different calibration methods were substituted into the same strapdown inertial navigation (SINS) calculation algorithm to perform pure inertial navigation calculations. Figure 11 , Figure 12 and Figure 13 The figure shows the attitude error comparison curves at three different positions: Yaw0°, Yaw 120°, and Yaw 240°. In the figure, the blue curve represents the traditional multi-position method, the green curve represents the traditional norm method, and the red curve represents the method of this invention. It is clear from the figure that during the 300-second navigation time, the attitude error of the method of this invention (red curve) remained within a small range, oscillating slightly around the zero axis, with amplitudes mainly between -0.05° and 0.06°. In contrast, the attitude error curves of the traditional multi-position method (blue curve) and the traditional norm method (green curve) showed significant divergence or large fluctuations over time, with the maximum deviation even exceeding 0.15°. This experimental result intuitively demonstrates that the attitude guidance accuracy of the inertial navigation system calibrated by the method of this invention is improved by nearly 50%. This is attributed to the fact that the present invention eliminates zero-bias interference through four-position tilt differential initial alignment and achieves high-precision intrinsic parameter calibration that is insensitive to installation errors based on the angular velocity norm, thereby effectively suppressing error accumulation during navigation.

[0063] In summary, the experimental data fully demonstrate that even under experimental conditions without precise alignment, the inertial navigation system intrinsic parameter calibration method provided by this invention can still obtain high-precision and highly repeatable calibration results, significantly improving the navigation accuracy of the inertial navigation system and verifying the superiority and robustness of the method in engineering practice.

[0064] Example 5: This embodiment provides an inertial navigation system intrinsic parameter calibration device. This device, through the division of functional modules, implements the inertial navigation system intrinsic parameter calibration methods described in Embodiments 1 to 4. The device mainly includes a data acquisition module, an initial alignment module, an excitation control module, a function construction module, and a parameter solving module.

[0065] The data acquisition module is used to acquire sensor measurement data of the inertial navigation system at multiple preset positions, and the sensors include gyroscopes and accelerometers.

[0066] Specifically, the data acquisition module is the input terminal of the device, responsible for communicating with the hardware interface of the inertial navigation system and acquiring the raw output signals of the gyroscope and accelerometer in real time. In hardware implementation, this module can be represented as a data acquisition card, an FPGA data acquisition circuit, or a GPIO interface driver for an embedded processor. The data acquisition module is not only responsible for reading data but also for performing necessary preprocessing on the raw data, such as analog-to-digital conversion, time synchronization, and unit conversion, converting the raw voltage signals into physically meaningful angular velocity and specific force data, and storing them in the storage unit for subsequent modules to access.

[0067] The initial alignment module is used to eliminate zero-bias interference and obtain the initial attitude based on the sensor measurement data through differential operation.

[0068] Specifically, the initial alignment module is connected to the data acquisition module and reads the stored static measurement data. This module has a pre-built four-bit tilting differential algorithm logic as described in Example 3. It can identify the preset position number of the inertial navigation system and automatically call the corresponding measurement data set. By executing the differential operation program, this module can separate the gravity vector and the Earth's rotation angular rate components from the high-noise MEMS sensor data, and then calculate the initial attitude angle of the carrier coordinate system relative to the navigation coordinate system. The core value of this module lies in replacing the reliance on precision optical alignment equipment in traditional methods through differential processing at the algorithm level, significantly reducing the requirements for hardware installation accuracy.

[0069] The excitation control module is used to control the excitation device to provide a known angular velocity excitation to the inertial navigation system.

[0070] The excitation control module serves as the interface between the device and external excitation equipment (such as a precision rotary table). This module generates corresponding control commands based on a preset calibration path plan (such as the twelve-position rotary excitation path described in Example 2). These control commands are sent to the controller of the excitation device via a communication bus (such as RS-422, CAN, or Ethernet), driving the rotary table to move precisely according to the set angular velocity, acceleration, and trajectory. Simultaneously, the excitation control module is also responsible for synchronously recording the reference angular velocity information output by the excitation device, ensuring strict alignment of the excitation signal and the sensor measurement signal on the time axis, providing accurate reference data for subsequent construction of the calibration loss function.

[0071] The function construction module is used to construct a calibration loss function based on the norm of the angular velocity vector provided by the excitation device. The function construction module is one of the core computing units of the device. It receives measurement data from the data acquisition module and reference angular velocity data from the excitation control module. This module internally stores the error model parameters of the inertial navigation system and can calculate the corrected measurement angular velocity vector based on the current intrinsic parameter estimates. More importantly, this module executes the core logic of "rotation norm normalization," that is, calculating the norm of the measurement angular velocity vector and comparing it with the norm of the reference angular velocity vector to construct the calibration loss function as described in Example 2. By utilizing the scalar properties of the norm, the loss function constructed by this module is naturally immune to directional errors caused by coordinate system rotation, thereby achieving decoupling from installation errors in the calibration environment.

[0072] The parameter solving module is used to solve for the intrinsic parameters of the inertial navigation system based on the calibration loss function and the initial attitude. The parameter solving module is the core of the device's optimization calculation. It calls the initial attitude output by the initial alignment module to unify the measurement data at different times and attitudes into the same reference coordinate system. Subsequently, the module runs a nonlinear optimization algorithm (such as the Levenberg-Marquardt algorithm described in Example 4) to iteratively solve the loss function generated by the function construction module. During the iteration process, the module calculates the Jacobian matrix, residual vector, and iteration step size in real time, continuously updating the intrinsic parameter vector until the convergence condition is met. Finally, the module outputs the optimized intrinsic parameter calibration results, including parameters such as the scale factor of the gyroscope and accelerometer, cross-axis coupling error, and constant zero bias, and feeds the results back to the user or stores them in the system memory.

[0073] Through the coordinated operation of the five functional modules described above, the inertial navigation system intrinsic parameter calibration device of this embodiment transforms the complex calibration algorithm process into modular hardware or software functions, realizing fully automated processing from data acquisition, preprocessing, initial alignment, excitation application, function construction to parameter optimization solution, effectively supporting the implementation of the technical effects of the aforementioned method embodiments. It should be understood that the above module division is only a logical functional division; in actual implementation, the functions of multiple modules can be integrated into the same physical processor or split into multiple independent hardware units, both of which fall within the protection scope of this invention.

[0074] Example 6: This embodiment provides an inertial navigation system intrinsic parameter calibration device, which implements the inertial navigation system intrinsic parameter calibration method described in embodiments 1 to 4 through specific hardware entities. Combined with... Figure 10 As shown, the device mainly includes a precision turntable (1), an inertial navigation system (2), a data acquisition unit, and a processing unit.

[0075] The precision turntable (1) is used to support the inertial navigation system (2) and provide known angular velocity excitation.

[0076] Specifically, the precision turntable (1) is the physical reference source of the entire calibration system. In this embodiment, the precision turntable (1) is preferably a high-precision three-axis turntable, each axis of which has an independent drive motor and a high-precision encoder, capable of generating precise angular velocity and angular position movements according to preset instructions. The main function of the precision turntable (1) is to provide the "known angular velocity excitation" described in Embodiment 1. In terms of physical connection, the inertial navigation system (2) is rigidly fixed to the center of the table surface of the precision turntable (1) by a special mounting fixture. It should be emphasized that the installation process in this embodiment only needs to ensure that the inertial navigation system (2) is relatively fixed to the table surface of the turntable, without the need for cumbersome optical alignment operations. This directly reflects the characteristic of the present invention being insensitive to installation errors and reduces the complexity of hardware operation. The precision turntable (1) receives motion commands from the processing unit or external control terminal through the servo control system, driving the inertial navigation system (2) to execute the four-position flipping action as described in Embodiment 3 or the twelve-position rotation excitation path as described in Embodiment 2.

[0077] The inertial navigation system (2), as the object to be calibrated, is used to sense the angular and linear motion of the carrier and output raw sensor measurement data. The inertial navigation system (2) integrates inertial sensors such as gyroscopes and accelerometers. In this embodiment, the inertial navigation system (2) can be the STIM318 MEMS inertial navigation system from Sensonor Corporation. This device represents typical MEMS sensor characteristics, featuring small size, low cost, but high noise. The inertial navigation system (2) is connected to the data acquisition unit via a cable and outputs digital or analog signals containing gyroscope and accelerometer measurements in real time. These raw data contain the intrinsic parameter error information to be calibrated, which is the data basis for subsequent algorithm processing.

[0078] The data acquisition unit is used to acquire sensor measurement data from the inertial navigation system (2). The data acquisition unit acts as a data bridge. It is responsible for synchronously acquiring sensor data output from the inertial navigation system (2) and reference data (such as real-time angle and angular velocity of the turntable) output from the precision turntable (1) controller. The data acquisition unit can be a standalone data acquisition card (DAQ) or a data acquisition module integrated on the processing unit's motherboard. Its key indicators include sampling frequency and synchronization accuracy. It is necessary to ensure strict alignment of sensor data and turntable reference data on the time axis to avoid introducing additional timing errors. After preprocessing (such as filtering and unit conversion), the acquired data is transmitted to the processing unit for storage and computation via a high-speed data bus (such as PCIe, USB 3.0, or Ethernet).

[0079] The processing unit is used to execute the method as described in any one of claims 1 to 8. The processing unit is the core of the calculation and control of the entire calibration device. In terms of hardware, the processing unit can be an industrial control computer, an embedded processor, or a high-performance workstation. The processing unit stores a computer program, which, when executed, implements the steps described in embodiments 1 to 5. Specifically, it includes: controlling the precision turntable (1) to execute a preset motion trajectory; acquiring sensor measurement data through the data acquisition unit; executing a four-bit flipping differential algorithm to calculate the initial attitude; constructing a rotation norm normalized loss function; and running the Levenberg-Marquardt nonlinear optimization algorithm to solve for intrinsic parameters. The processing unit outputs the final calibration intrinsic parameter results (such as scale factor, zero bias, cross-axis coupling error) to a display or storage device for subsequent navigation calculation. It should be understood that the processing unit and the data acquisition unit can be two separate devices or integrated in the same computer, as long as they can achieve data acquisition and processing functions.

[0080] By organically combining the aforementioned precision turntable (1), inertial navigation system (2), data acquisition unit, and processing unit, this embodiment constructs a complete hardware calibration platform. This platform not only provides high-precision physical excitation, but more importantly, in conjunction with the calibration algorithm described in the previous embodiment, it can achieve high-precision intrinsic parameter calibration under hardware conditions that do not require precise alignment, significantly improving calibration efficiency and engineering practicality.

[0081] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for calibrating intrinsic parameters of an inertial navigation system, characterized in that, include: Acquire sensor measurement data of the inertial navigation system at multiple preset positions, wherein the sensors include gyroscopes and accelerometers; Based on the sensor measurement data, zero-bias interference is eliminated through differential operation to obtain the initial attitude; The control excitation device provides a known angular velocity excitation to the inertial navigation system; A calibration loss function is constructed based on the norm of the angular velocity vector provided by the excitation device; Based on the calibration loss function and the initial attitude, the intrinsic parameters of the inertial navigation system are solved.

2. The method according to claim 1, characterized in that, The excitation device includes a turntable, and the control excitation device provides a known angular velocity excitation to the inertial navigation system, including: The turntable is controlled to drive the inertial navigation system to rotate around at least one axis at a constant angular velocity.

3. The method according to claim 2, characterized in that, The step of constructing a calibration loss function based on the norm of the angular velocity vector provided by the excitation device includes: Construct an error model that includes scaling factor error, cross-axis coupling error, and constant zero bias; The calibration loss function is constructed to minimize the sum of squares of the difference between the measured angular velocity norm corrected by the error model and the reference angular velocity norm provided by the turntable.

4. The method according to claim 1, characterized in that, The plurality of preset positions includes four positions. The process of eliminating zero-bias interference and obtaining the initial attitude based on the sensor measurement data includes: The inertial navigation system is controlled to sequentially reach the first position, the second position, the third position, and the fourth position; Wherein, the first position and the second position are flipped by 180°, the third position and the fourth position are flipped by 180°, and the first position and the third position are rotated by 90°; A differential calculation is performed based on the sensor measurement data at the first and second positions to obtain the first set of attitude angles; A second set of attitude angles is obtained by performing differential calculations based on the sensor measurement data at the third and fourth positions. The initial attitude is obtained by averaging the first set of attitude angles and the second set of attitude angles.

5. The method according to claim 4, characterized in that, The sensor measurement data includes accelerometer measurements and gyroscope measurements; The differential calculation based on the sensor measurement data at the first and second positions yields a first set of attitude angles, including: Based on the difference between the accelerometer measurements at the first and second positions, the pitch and roll angles are solved using the gravity vector projection relationship; The azimuth angle is calculated based on the difference between the gyroscope measurements at the first and second positions using the Earth's rotation angular rate projection relationship.

6. The method according to claim 1, characterized in that, The process of solving for the intrinsic parameters of the inertial navigation system includes: The calibration loss function is iteratively solved using a nonlinear optimization algorithm to obtain the optimal intrinsic parameters.

7. The method according to claim 6, characterized in that, The nonlinear optimization algorithm includes the Levenberg-Marquardt algorithm; The step of iteratively solving the calibration loss function using a nonlinear optimization algorithm includes: Calculate the iteration step size, which is determined based on the Jacobian matrix, damping factor, and residual vector; Update the intrinsic parameter vector until the convergence condition is met.

8. The method according to claim 1, characterized in that, Before solving the intrinsic parameters of the inertial navigation system, the method further includes: The initial zero bias values ​​of the gyroscope and the accelerometer are estimated based on static measurement data; The initial value of the scale factor of the gyroscope is estimated based on the rotation measurement data around the axis; The initial zero bias value and the initial scale factor value are used as the starting point for the solution.

9. A device for calibrating intrinsic parameters of an inertial navigation system, characterized in that, include: The data acquisition module is used to acquire sensor measurement data of the inertial navigation system at multiple preset positions, including gyroscopes and accelerometers; The initial alignment module is used to eliminate zero-bias interference and obtain the initial attitude based on the sensor measurement data through differential operation; An excitation control module is used to control the excitation device to provide a known angular velocity excitation to the inertial navigation system. The function construction module is used to construct a calibration loss function based on the norm of the angular velocity vector provided by the excitation device. The parameter solving module is used to solve the intrinsic parameters of the inertial navigation system based on the calibration loss function and the initial attitude.

10. The apparatus according to claim 9, characterized in that, The device includes a precision turntable, a data acquisition unit, and a processing unit; The precision turntable is used to support the inertial navigation system and provide known angular velocity excitation; The data acquisition unit is used to acquire sensor measurement data of the inertial navigation system; The processing unit is configured to perform the method as described in any one of claims 1 to 8.

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