Calibration and Alignment Method for Rotating Inertial Navigation Systems Under Shaking Base

Abstract

A calibration and alignment method suitable for rotating inertial navigation systems (RINS) on swaying bases was first designed using a new 20-position rotation method combining rotation and stationary positioning. Then, an IMU error model and a 39-dimensional RINS navigation error model were established. Next, a coarse alignment was performed using an optimization-based method to obtain the initial attitude of the carrier. Then, an iterative Kalman filter method based on zero-velocity observation was used for simultaneous calibration and alignment. After each calibration, all error parameters were recorded and compensated, and the current state variables and their corresponding covariance matrices were used as the initial values ​​for the next iteration until the covariance matrix converged to a threshold or the required number of iterations was reached. This method not only compensated for various errors in a short time but also obtained a high-precision initial attitude, ensuring the long-term navigation and positioning accuracy of the RINS.

Description

Technical Field

[0001] This invention is applicable to underwater vehicles rapidly entering the field of high-precision autonomous navigation in emergency situations, specifically a calibration and alignment method for a rotating inertial navigation system on a swaying base. Background Technology

[0002] Underwater vehicles play a crucial role in deep-sea topography and geomorphological exploration, as well as large-scale marine environmental surveys. To ensure their successful completion of these tasks, their navigation systems must possess long-term autonomous navigation and positioning capabilities. Before entering autonomous navigation, the inertial navigation system needs calibration and initial alignment to improve its positioning accuracy. To enable rapid navigation entry, all error parameters must be calibrated and high-precision initial alignment achieved within a short timeframe.

[0003] Currently, the most commonly used autonomous navigation equipment for underwater vehicles is the Strapdown Inertial Navigation System (SINS). While SINS offers advantages such as strong autonomy, good stealth, and rapid update frequency, it requires periodic calibration and error compensation on a laboratory turntable to improve its navigation and positioning accuracy. To reduce INS' dependence on high-precision turntables, Rotational Inertial Navigation Systems (RINS) have gained increasing attention. RINS, relying on its own rotation mechanism, can perform periodic autonomous alignment and calibration to maintain long-term navigation accuracy. Autonomous alignment technology requires RINS to perform initial alignment without relying on external equipment to obtain an initial attitude for calculations during the autonomous navigation phase. The accuracy of the initial alignment directly affects the autonomous navigation and positioning accuracy of the RINS. Initial alignment technology consists of two parts: coarse alignment and fine alignment. Currently, coarse alignment is commonly performed on a static base. In reality, vehicles are subject to swaying motion due to water flow; therefore, an optimized coarse alignment (OBA) method has been proposed to address the coarse alignment problem on a moving base. Currently used dual-position-based precision alignment methods primarily consider the effects of gyro bias and accelerometer bias errors in the RINS (Resistant Navigation System). Theoretically, considering other RINS errors, such as scaling factor errors, installation errors, and lever arm errors, would improve the precision alignment accuracy. Simultaneously, to improve the long-term navigation and positioning accuracy of the vehicle, system-level error calibration techniques are required. System-level autonomous calibration mainly involves designing a reasonable rotation and using Kalman filtering techniques for parameter identification. To calibrate as many RINS error parameters as possible, the system state variables increase, leading to a higher matrix dimension and slower filter convergence. Most current calibration methods require 0.5 hours, and some even reach 1 hour. Therefore, calibrating and compensating as many error parameters as possible within a short time, while simultaneously performing initial alignment, is crucial for high-precision autonomous navigation of the vehicle.

[0004] To calibrate more errors and perform alignment simultaneously in a short time, this invention designs a new and easily implemented 20-position rotation scheme using a combination of rotation and stop. This scheme excites the RINS's gyro bias, gyro scaling factor error, gyro installation error, accelerometer bias, accelerometer scaling factor error, accelerometer installation error, accelerometer quadratic term error, and inner lever arm error parameters. Then, by improving a 39-dimensional Kalman filter, real-time error compensation and initial alignment are achieved, enabling the vehicle to complete preparation and enter the autonomous navigation phase within 15 minutes.

[0005] The differences between this application and the prior art are as follows:

[0006] Technical comparison with patent CN104880182A "A method for separating the combined error coefficients of a laser gyroscope based on dual-axis rotation"

[0007] Patent CN104880182A describes a 16-position rotation design for a dual-axis rotating laser gyroscope, with a calibration time of over 4000 seconds. Our design for a three-axis rotating inertial navigation system, however, describes a 20-position rotation, taking 810 seconds, or 13.5 minutes.

[0008] Patent CN112561998B uses a Kalman filter method to calibrate the zero term, linearity deviation, and installation error. Our method, however, employs a backward-iterative Kalman filter to calibrate and compensate for gyroscope zero bias, accelerometer zero bias, gyroscope installation error, accelerometer installation error, gyroscope scaling factor error, accelerometer installation error, accelerometer quadratic term error, and inner rod error. Simultaneously, we completed coarse and fine alignment. The entire calibration, compensation, and initial alignment process took less than 15 minutes.

[0009] Technical Comparison with Patent CN108507592A "A Method for Calibrating Non-Orthogonal Angles of Rotation Axes in a Dual-Axis Rotational Inertial Navigation System"

[0010] Patent CN108507592 uses a two-position method to calibrate the non-orthogonal angles in a dual-axis rotating inertial navigation system. Our approach, however, involves first designing a 20-position rotation, then performing optimized coarse alignment on a wobbling base, followed by simultaneous calibration and fine alignment using a backward-iterative Kalman filter. Furthermore, in addition to calibrating the non-orthogonal angle error (installation error), we also calibrated the zero-bias error, scale factor error, accelerometer quadratic term error, and inner arm error.

[0011] Technical Comparison with Patent CN103245360A "Self-Alignment Method for Shipborne Aircraft Rotary Strapdown Inertial Navigation System under Shaking Base"

[0012] Patent CN103245360A uses the gravitational acceleration in the inertial frame as a reference vector to calculate the coarse initial attitude. Then, to isolate the influence of swaying on the initial alignment, a fading adaptive Kalman filter is used for fine alignment. In contrast, we use an optimization-based method for coarse alignment. This optimization method constructs multiple sets of observation equations during the alignment process and makes full use of the observation vectors constructed throughout the alignment process, thus improving the initial alignment speed of the swaying carrier.

[0013] Patent CN103245360A only solved the self-alignment problem of a rotating strapdown inertial navigation system under a wobbling base. Our solution, however, addresses the problem of simultaneously performing self-calibration and self-alignment within a short time under a wobbling base.

[0014] Technical comparison with patent CN113639766B, "System-level calibration method for dual-axis rotating inertial navigation system containing non-orthogonal angles".

[0015] Patent CN113639766B constructed a 34-dimensional error model of the non-orthogonal angles between the axes of a dual-axis rotating inertial navigation system, and then used a Kalman filter algorithm to calibrate the various parameters of the system. In contrast, we constructed a 39-dimensional error model of a three-axis rotating inertial navigation system, and then used a backward-iterative Kalman filter algorithm to calibrate and compensate the various parameters of the system, while also performing initial alignment.

[0016] Patent CN113639766B, based on system observability analysis, designed a self-calibrating rotation scheme. This scheme only uses angular velocity rotation to calibrate non-orthogonal angle error, zero bias error, and scale factor error. Our combined rotation-stop design, a 20-position rotation scheme, can not only calibrate the aforementioned errors, but also calibrate the accelerometer quadratic term error and inner lever arm error within 13.5 minutes. Summary of the Invention

[0017] To address the issues of long self-calibration time and low initial alignment accuracy of RINS, this invention proposes a calibration and alignment method suitable for rotating inertial navigation systems on wobbly bases. This method not only quickly calibrates and compensates for all errors of the RINS, but also performs high-precision initial alignment, thereby improving the rapid navigation capability and long-term navigation and positioning accuracy of the RINS.

[0018] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0019] A calibration and alignment method applicable to rotating inertial navigation systems under wobbly bases includes the following steps:

[0020] Step 1: A new 20-position transpose was designed:

[0021] RINS includes a three-axis gyroscope and a three-axis accelerometer. In order to fully excite the gyroscope zero bias, gyroscope scaling factor error, gyroscope installation error, accelerometer zero bias, accelerometer scaling factor error, accelerometer installation error, accelerometer quadratic term error and inner rod arm error, a static-rotational combination method is used for the rotation design.

[0022] Step 2: Establish the IMU error model and the 39-dimensional RINS navigation error model:

[0023] Models for 3 gyroscope zero bias errors, 3 accelerometer zero bias errors, 3 gyroscope scaling factor errors, 6 gyroscope installation errors, 3 accelerometer scaling factor errors, 3 accelerometer installation errors, 3 accelerometer quadratic term errors, and 9 inner lever arm errors were established respectively. Based on the above errors, attitude errors, and velocity errors, a 39-dimensional state variable was constructed.

[0024] Step 3: Obtain the initial pose based on optimized coarse alignment:

[0025] First, the real-time attitude matrix of the carrier is decomposed into two time-varying matrices and one constant matrix. Then, the non-collinear observation vectors of the gyroscope and accelerometer at multiple moments are obtained by using the rotation method. Finally, the initial attitude of the carrier is determined by an optimization algorithm.

[0026] Step 4: Iterative Kalman Filtering Method Based on Zero-Voltage Observations

[0027] The observation equations for a Kalman filter are constructed using velocity errors. During RINS rotation, the accumulated error is calculated using attitude and velocity error models. When the RINS is stationary, the difference between the accumulated velocity error and the matrix is ​​used as the observation for Kalman filter measurement updates. After calibration, all error parameters and state variables X are recorded. k The covariance matrix P k ;

[0028] Step 5: Algorithm termination check:

[0029] After one calibration, record all errors and the state variable X at that time. k The covariance matrix P k Then determine P k Has convergence reached the threshold? If not, proceed to the next iteration, compensate for all errors in the original RINS data, and use the X value from the previous iteration. k and P k As the initial value for this iteration, if P k Converging to the threshold, the system outputs all the error parameters obtained from the calibration and the initial attitude, thus completing error calibration compensation and fine alignment simultaneously within 13.5 minutes.

[0030] As a further improvement of this invention, step 3 performs simultaneous calibration and fine alignment using a backward-iterative Kalman filter method based on zero-velocity observation. During RINS rotation, the accumulated error is calculated using the attitude error model and velocity error model. When the RINS is stationary for a period of time, its accumulated velocity error is used as the observation measurement for Kalman filtering and updating. The observation equation is:

[0031] Z = [δv] E δv N δvU ] T

[0032] The measurement matrix is ​​H = [0 3×3 Ι 3×3 0 36×36 After calibration, record all error parameters and state variables X. k The covariance matrix P k .

[0033] As a further improvement of the present invention, in step 5, after performing a calibration, all errors and the state quantity X at this time are recorded. k The covariance matrix P k Then determine if P k If convergence reaches the threshold, and if not, proceed to the next iteration. Before each iteration, compensate for all errors in the original RINS data using the following compensation model:

[0034]

[0035]

[0036] and the X from the previous iteration k and P k Use this as the initial value for this iteration. If P k Converging to the threshold, the system outputs all the error parameters obtained from the calibration and the initial attitude, thus completing error calibration compensation and fine alignment simultaneously within 13.5 minutes.

[0037] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0038] This invention provides a method for rapid and simultaneous autonomous calibration and alignment of a Rotating Inertial Navigation System (RINS) on a wobbling base. First, a new 20-position rotation mechanism is designed using a combination of rotation and stop. Then, an IMU error model is established, and a 39-dimensional RINS navigation error model is constructed. The state variables include attitude error, velocity error, gyroscope bias, gyroscope scaling factor error, gyroscope installation error, accelerometer bias, accelerometer scaling factor error, accelerometer installation error, accelerometer quadratic term error, and inner arm error. Next, coarse alignment is performed using an optimization-based method to obtain the initial attitude of the carrier. Then, an iterative Kalman filter method based on zero-velocity observation is used for simultaneous calibration and alignment. After each calibration, all error parameters are recorded and compensated, and the current state variables and their corresponding covariance matrix are used as the initial values ​​for the next iteration until the covariance matrix converges to a threshold or the required number of iterations is reached. This not only compensates for various errors in a short time but also obtains a high-precision initial attitude, ensuring the long-term navigation and positioning accuracy of the RINS. Attached Figure Description

[0039] Figure 1 The flowchart shows the proposed algorithm for simultaneous calibration and alignment in a short time.

[0040] Figure 2 The graph shows the calibration results of the accelerometer zero bias error.

[0041] Figure 3 The graph shows the calibration results of the gyroscope's proportional factor error. Detailed Implementation

[0042] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0043] like Figure 1 As shown, this invention proposes a calibration and alignment method for a rotating inertial navigation system under a wobbling base, comprising the following steps:

[0044] 1) A new 20-position indexer was designed.

[0045] Because RINS has its own rotation mechanism, its inner frame corresponds to the x-axis, the middle frame to the y-axis, and the outer frame to the z-axis. The rotation design is shown in Table 1: 120 seconds of rest, 180 degrees clockwise rotation of the middle frame, 20 seconds of rest, 180 degrees clockwise rotation of the middle frame, 20 seconds of rest, 180 degrees counterclockwise rotation of the middle frame, 20 seconds of rest, 180 degrees counterclockwise rotation of the middle frame, 20 seconds of rest. The outer frame rotates 90 degrees, rests for 20 seconds, the inner frame rotates 180 degrees clockwise, rests for 20 seconds, the inner frame rotates 180 degrees clockwise, rests for 20 seconds, the inner frame counterclockwise rotation of the inner frame, 20 seconds of rest, the inner frame counterclockwise rotation of the inner frame, 20 seconds of rest, the inner frame counterclockwise rotation of the inner frame, 20 seconds of rest. The middle frame rotates 90 degrees, rests for 20 seconds, the outer frame rotates 180 degrees clockwise, rests for 20 seconds, the outer frame rotates 180 degrees clockwise, rests for 20 seconds, the outer frame counterclockwise rotation of the outer frame, 20 seconds of rest, the outer frame counterclockwise rotation of the outer frame, 20 seconds of rest. The inner frame rotates 90 degrees clockwise and remains still for 20 seconds. The middle frame rotates 90 degrees counterclockwise and remains still for 20 seconds. The outer frame rotates 180 degrees clockwise and remains still for 20 seconds. The outer frame rotates 180 degrees clockwise and remains still for 20 seconds. The outer frame rotates 180 degrees counterclockwise and remains still for 20 seconds. The outer frame rotates 180 degrees counterclockwise and remains still for 20 seconds. The entire process takes 13.5 minutes.

[0046] Table 1. Design of Calibration Interpolation Sequence

[0047]

[0048] 2) Establish the IMU error model and the 42-dimensional RINS navigation error model: The gyroscope measurement model is as follows:

[0049]

[0050] K gxx ,K gyy ,K gzzThis indicates the gyroscope's scaling factor error, expressed in ppm. K gxy ,K gxz ,K gyx ,K gyz ,K gzx ,K gzy The installation error is expressed in arcseconds. This indicates zero bias of the gyroscope, expressed in ° / h. Using the gyroscope coordinates as the reference coordinate system, the accelerometer's measurement model is as follows:

[0051]

[0052] K axx ,K ayy ,K azz This indicates the accelerometer proportional factor error, expressed in ppm. K ayx ,K azx ,K azy This indicates the installation error of the accelerometer, expressed in arcseconds. This represents the accelerometer's zero bias, expressed in μg. The model for the accelerometer's quadratic error is:

[0053]

[0054] K a2x ,K a2y ,K a2z Denotes the error coefficient of the quadratic term, where Calculate using the following formula:

[0055]

[0056] r x ,r y ,r z Indicates the parameters of the inner arm. This represents the acceleration at the origin. This represents the installation error angle between the acceleration-sensitive axis and the frame coordinate system. The 42-dimensional system state variables are:

[0057]

[0058] Where φ E φ N φ U δv E δv N δv U These are attitude error and velocity error, respectively.

[0059] The attitude error model is as follows:

[0060]

[0061] The velocity error model is as follows:

[0062]

[0063] 2) Initial Attitude Acquisition Based on Optimized Coarse Alignment: To adapt to different alignment requirements, the optimization-based method can be applied to both static and moving bases. First, the attitude-determined vector observation model is represented in quaternion form:

[0064]

[0065] In the formula, This represents quaternion multiplication, (·). * This represents the conjugate operation on a quaternion. It involves multiplying both sides of the above expression by the quaternion on the right. get:

[0066]

[0067] Since both the reference vector and the observation vector are three-dimensional vectors, for ease of calculation, two matrix forms are constructed based on the above formula as follows:

[0068]

[0069] The right side of equation (1.2) passes through the matrix [α] k ⊙] is converted to:

[0070]

[0071] The left side of equation (1.2) is passed through a matrix Convert to:

[0072]

[0073] Substituting equations (1.4) and (1.5) into (1.2), the measurement model can be reformulated as follows:

[0074]

[0075] Using the least squares constraint method, the following cost function is obtained through equation (1.6):

[0076]

[0077] make Satisfy the minimum cost function Quaternions That is, the smallest eigenvalue λ of the K matrix. min The corresponding feature vector.

[0078] Discretizing the K matrix expression in equation (1.7) and expressing iteratively as follows:

[0079]

[0080] The attitude calculation method based on OBA uses all sampled observation vector information when calculating the K matrix, which has a higher utilization rate of observation information compared to other methods.

[0081] 3) Backward-Iterative Kalman Filtering Method Based on Zero-Voltage Observations:

[0082] After obtaining the initial attitude in the previous step, the accumulated error is calculated by solving the attitude error model and velocity error model during the RINS rotation. When the RINS is stationary, its accumulated velocity error is used as an observation for Kalman filtering measurement update. The observation equation is:

[0083] Z = [δv] E δv N δv U ] T

[0084] The measurement matrix is ​​H = [0 3×3 Ι 3×3 0 36×36 I is the identity matrix. After calibration, record all error parameters and state variables X. k The covariance matrix P k .

[0085] 4) Algorithm termination judgment:

[0086] First, after performing a calibration, record all errors and the state variable X at that time. k The covariance matrix P k Then determine if P k The method for determining convergence to the threshold is as follows:

[0087] P k <ε||k>N p

[0088] Where ε is the threshold for determining the algorithm's termination condition, which should be set considering factors such as the actual initial alignment environment and inertial navigation type; k is the number of iterations, N p This represents the maximum number of iterations.

[0089] If the target is not reached, proceed to the next iteration. Before the next iteration, compensate for all errors in the original RINS data. The compensation model is as follows:

[0090]

[0091] and the X from the previous iterationk and P k Use this as the initial value for this iteration. If P k Converging to the threshold, the system outputs all the error parameters obtained from the calibration and the initial attitude, thus completing error calibration compensation and fine alignment simultaneously within 13.5 minutes.

[0092] The embodiments of the present invention are described in detail below. These embodiments are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0093] To verify the effectiveness of this invention, the algorithm was simulated using the MATLAB platform. The simulation parameter settings for the rotating inertial navigation system are shown in Table 1.

[0094] Table 1 Simulation condition parameter settings

[0095]

[0096] The calibration results are as follows Figure 2-3 As shown, the calibration and alignment results were obtained using a newly designed transposer and a three-step backward-iterative Kalman filter method. The figure shows that the accelerometer zero-bias error and gyroscope scaling factor error converged within 13.5 minutes, thus verifying the effectiveness of the proposed method.

[0097] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any modifications or equivalent changes made based on the technical essence of the present invention shall still fall within the scope of protection claimed by the present invention.

Claims

1. A calibration and alignment method for a rotating inertial navigation system under a wobbling base, characterized in that: Includes the following steps: Step 1: A new 20-position transpose was designed: RINS includes a three-axis gyroscope and a three-axis accelerometer. In order to fully excite the gyroscope zero bias, gyroscope scaling factor error, gyroscope installation error, accelerometer zero bias, accelerometer scaling factor error, accelerometer installation error, accelerometer quadratic term error and inner rod arm error, a static-rotational combination method is used for the rotation design. Step 2: Establish the IMU error model and the 39-dimensional RINS navigation error model: Models for 3 gyroscope zero bias errors, 3 accelerometer zero bias errors, 3 gyroscope scaling factor errors, 6 gyroscope installation errors, 3 accelerometer scaling factor errors, 3 accelerometer installation errors, 3 accelerometer quadratic term errors, and 9 inner lever arm errors were established respectively. Based on the above errors, attitude errors, and velocity errors, a 39-dimensional state variable was constructed. Step 3: Obtain the initial pose based on optimized coarse alignment: First, the real-time attitude matrix of the carrier is decomposed into two time-varying matrices and one constant matrix. The observation vectors of the gyroscope and accelerometer at multiple time points and which are not collinear are obtained by using the rotation. Then, the initial attitude of the carrier is determined by an optimization algorithm. Step 4: Iterative Kalman Filtering Method Based on Zero-Voltage Observations The observation equations for a Kalman filter are constructed using velocity errors. During RINS rotation, the accumulated error is calculated using attitude and velocity error models. When the RINS is stationary, the difference between the accumulated velocity error and the matrix is ​​used as the observation for Kalman filter measurement updates. After calibration, all error parameters and state variables X are recorded. k The covariance matrix P k ; Step 5: Algorithm termination check: After one calibration, record all errors and the state variable X at that time. k The covariance matrix P k Then determine P k Has convergence reached the threshold? If not, proceed to the next iteration, compensate for all errors in the original RINS data, and use the X value from the previous iteration. k and P k As the initial value for this iteration, if P k Converging to the threshold, the system outputs all the error parameters obtained from the calibration and the initial attitude, thus completing error calibration compensation and fine alignment simultaneously within 13.5 minutes.

2. The calibration and alignment method for a rotating inertial navigation system under a wobbling base according to claim 1, characterized in that: Step 3: Simultaneous calibration and fine alignment are performed using the backward-iterative Kalman filter method based on zero-velocity observation. During RINS rotation, the accumulated error is calculated using the attitude error model and velocity error model. When the RINS is stationary, its accumulated velocity error is used as the observation measurement for Kalman filtering and updating. The observation equation is: Z=[δv E δv N δv U ] T The measurement matrix is ​​H = [0 3×3 Ι 3×3 0 36×36 After calibration, record all error parameters and state variables X. k The covariance matrix P k .

3. The calibration and alignment method for a rotating inertial navigation system under a wobbling base according to claim 1, characterized in that: In step 5, after performing a calibration, record all errors and the state variable X at this point. k The covariance matrix P k， Then determine if P. k If convergence reaches the threshold, and if not, proceed to the next iteration. Before each iteration, compensate for all errors in the original RINS data using the following compensation model: and the X from the previous iteration k and P k As the initial value for this iteration, if P k Converging to the threshold, the system outputs all the error parameters obtained from the calibration and the initial attitude, thus completing error calibration compensation and fine alignment simultaneously within 13.5 minutes.

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