Error-balanced modulation method for rotary inertial navigation system and terminal

Abstract

The application provides a kind of error balanced rotary inertial navigation system modulation method and terminal, obtain the first output error of gyro assembly, the second output error of accelerometer and the scale factor error of the gyro assembly;Obtain the carrier attitude of the carrier where the inertial navigation system is located;After isolating the carrier attitude, the first output error, the second output error and the scale factor error are brought into the preset alternative modulation equation, to obtain the first modulation result;If the first modulation result meets the preset threshold value, mark the alternative modulation equation as the final modulation equation and modulate the inertial navigation system according to the final modulation equation.The application obtains the main error value in the inertial navigation system that has greater influence on the final output result, brings it into the alternative modulation equation for calculation, and realizes the isolation of the influence of the carrier attitude, finally realizes the high-precision system modulation of the inertial navigation system.

Description

[0001] This case is a divisional application of the patent application filed on December 31, 2020, with application number 202011625768.X and titled "A Modulation Method and Terminal for an Fiber Optic Gyroscope Rotation Inertial Navigation System". Technical Field

[0002] This invention relates to the field of gyroscope modulation, and more particularly to a modulation method and terminal for an error-balanced rotating inertial navigation system. Background Technology

[0003] In fiber optic gyroscope inertial navigation systems, rotation modulation technology is often used to eliminate device errors. Rotation modulation technology modulates the errors of inertial devices by introducing deterministic mechanical rotation, which is a technical means to eliminate device errors from a system perspective. This technology can reduce the impact of inertial device errors on system performance and relax the requirements for inertial device performance, thereby reducing system costs. Compared with conventional inertial navigation systems, inertial navigation systems using rotation modulation technology are expected to achieve a significant improvement in system accuracy at the same device level, thereby meeting the long-endurance and high-precision navigation requirements of ships. However, rotation modulation needs to be considered from a system perspective, and existing rotation modulation methods often have the problem of incomplete consideration of factors, which affects the final modulation effect. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide an error-balanced modulation method and terminal for a rotating inertial navigation system to achieve high-precision rotation modulation.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0006] A modulation method for an error-balanced rotating inertial navigation system includes the following steps:

[0007] S1. Obtain the first output error of the gyroscope assembly, the second output error of the accelerometer, and the scaling factor error of the gyroscope assembly;

[0008] S2. Obtain the attitude of the carrier in which the inertial navigation system is located;

[0009] S3. After isolating the carrier attitude, the first output error, the second output error and the scaling factor error are substituted into the preset alternative modulation equation to obtain the first modulation result;

[0010] S4. If the first modulation result satisfies a preset threshold, then the candidate modulation equation is marked as the final modulation equation and the inertial navigation system is modulated according to the final modulation equation.

[0011] To solve the above-mentioned technical problems, another technical solution adopted by the present invention is as follows:

[0012] An error-balanced rotating inertial navigation system modulation terminal includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps in the aforementioned error-balanced rotating inertial navigation system modulation method.

[0013] The beneficial effects of this invention are as follows: The output errors of the gyroscope component and the accelerometer are obtained separately, along with the scaling factor error of the gyroscope component. The carrier attitude of the inertial navigation system is also obtained. With the carrier attitude isolated (i.e., demodulated), both the output error and the scaling factor error are substituted into a preset alternative modulation equation for analysis to obtain a first modulation result. If the first modulation result meets a threshold, the corresponding alternative modulation scheme is used as the final modulation scheme for the inertial navigation system. The main error values ​​in the inertial navigation system that significantly affect the final output result are obtained and substituted into the alternative modulation equation for calculation. If the obtained modulation result meets the threshold, it indicates that all types of errors can be balanced, ensuring the output result meets accuracy requirements. Furthermore, different thresholds can be set according to different accuracy requirements to achieve system modulation of the inertial navigation system. The carrier attitude is also considered in the influence on system modulation, further improving the modulation accuracy of the inertial navigation system. This invention is particularly suitable for modulation of inertial navigation systems on mobile carriers such as ships. Attached Figure Description

[0014] Figure 1 This is a flowchart illustrating the steps of a modulation method for an error-balanced rotating inertial navigation system according to an embodiment of the present invention.

[0015] Figure 2 This is a schematic diagram of the structure of a modulation terminal for an error-balanced rotating inertial navigation system according to an embodiment of the present invention;

[0016] Figure 3 This is a diagram showing the relationship between carrier roll and IMU rotation about the horizontal axis in an embodiment of the present invention.

[0017] Figure 4 This is a diagram showing the relationship between carrier roll and IMU rotation around the celestial axis in an embodiment of the present invention.

[0018] Figure 5 This is a diagram showing the relationship between the carrier's pitching and the IMU's rotation about the horizontal axis in an embodiment of the present invention.

[0019] Figure 6 This is a diagram showing the relationship between the carrier's pitch and the IMU's rotation around the celestial axis in an embodiment of the present invention.

[0020] Figure 7 This is a diagram showing the relationship between the yaw motion of the carrier and the rotation of the IMU around the horizontal axis in an embodiment of the present invention.

[0021] Figure 8 This is a diagram showing the relationship between the yaw motion of the carrier and the rotation of the IMU around the yaw axis in an embodiment of the present invention.

[0022] Figure 9 This is a schematic diagram of the rotation modulation sequence according to an embodiment of the present invention;

[0023] Figure 10 This is a schematic diagram of the dual-axis 64-sequence rotation angle changes according to an embodiment of the present invention;

[0024] Figure 11 This is a signal flow diagram during the carrier isolation process according to an embodiment of the present invention;

[0025] Figure 12 This is a flowchart illustrating the carrier isolation process according to an embodiment of the present invention;

[0026] Figure 13 This is a schematic diagram illustrating the coordinate system definition in an embodiment of the present invention; Detailed Implementation

[0027] To explain in detail the technical content, objectives, and effects of the present invention, the following description is provided in conjunction with the embodiments and accompanying drawings.

[0028] Please refer to Figure 1 Embodiment 1 of the present invention is as follows:

[0029] In this specification, nine coordinate systems are defined for a dual-axis rotating inertial navigation system: the gyroscope component coordinate system (G system), the accelerometer component coordinate system (a system), the IMU coordinate system (S system), the actual platform coordinate system (P system), and the modulation averaging coordinate system. The coordinate systems are: carrier coordinate system (b), system base coordinate system (O), Earth coordinate system (e), and navigation coordinate system (n). The definitions of each coordinate system are as follows: Figure 2 As shown, the coordinate system defined in this section will apply throughout the paper. The coordinate system is described in detail below:

[0030] G-frame: The coordinate system of the gyroscope components o-xgygzg, oxg, oyg and ozg are the sensitive axes of the x-gyroscope, y-gyroscope and z-gyroscope, respectively;

[0031] a-frame: The coordinate system of the accelerometer assembly is o-xayaza, where oxa, oya, and oza are the sensitive axes of the x-accelerometer, y-accelerometer, and z-accelerometer, respectively.

[0032] S-frame: The IMU coordinate system o-xsyszs, centered at the IMU structure center. Initially, the ys axis is defined to coincide with the yg axis, the xs axis is perpendicular to the ys axis in the plane, and the zs axis satisfies the right-handed coordinate system with the xs and ys axes. The S-frame is fixed to the platform and rotates with the platform.

[0033] P-frame: The actual platform coordinate system o-xpypzp, defined by the platform's two actual axes. The ozp axis is along the upward rotation axis, with positive pointing upwards; the oyp axis is along the horizontal axis, with positive pointing forwards; the oxp axis is determined by the right-hand rule. The center of the coordinate system is at the intersection of the two axes. This coordinate system can be represented as {y p ×z p ,y p ,z p};

[0034] System: Modulation average coordinate system It is neither the IMU measurement coordinate system nor the actual gyroscope platform coordinate system. This coordinate system is a fixed coordinate system, centered at the center of the IMU accelerometer assembly. Initially... Pointing to the sky, Pointing to the bow, Point to the right. And without loss of generality, [the following will be observed]. Coinciding with the ozp axis, this coordinate system can therefore be represented as {y P ×z P ,z P ×(y P ×z P ),z P Constructing this coordinate system facilitates the study of non-orthogonal angles of axes.

[0035] b-frame: The carrier coordinate system o-xbybzb, oxb, oyb, ozb points to the right, bow, and top of the ship respectively, with the origin at the centroid of the carrier;

[0036] O-series: The system base coordinate system is o-xoyozo, ozo is perpendicular to the mounting base, oyo is parallel to the horizontal axis of the platform, and the oxo axis is determined according to the right-hand rule. Its coordinate system center coincides with the centroid of the base structure.

[0037] The e-frame: Earth coordinate system o-xeyeze, with its origin at the Earth's center of mass, and the coordinates remaining fixed relative to the rotating Earth. oxe lies in the mean astronomical equatorial plane; oye lies in the mean astronomical equatorial plane, 90° east of the x-axis; the oze axis, oxe axis, and oye axis form a right-handed coordinate system.

[0038] n-system: Navigation coordinate system o-xnynzn, selected as the local horizontal north-pointing coordinate system. The origin is at the vehicle's centroid, oxn points to geographic east, oyn points to geographic north, and ozn satisfies the right-hand rule with oxn and oyn;

[0039] The attitude transformation matrix is

[0040] The coordinate transformation matrix between the load system (b-frame) and the base coordinate system (O-frame) is determined by the installation error angle;

[0041] Base coordinate system O system and modulation average coordinate system The coordinate transformation matrix between systems is determined by the frame angles read by the angle reading device;

[0042] From IMU coordinate system S-frame to modulation average coordinate system The coordinate transformation matrix between the systems is determined by the roll misalignment angle, the axis non-orthogonality angle, and the axis yaw angle;

[0043] The coordinate transformation matrix between the modulated average coordinate system S and the navigation coordinate system n;

[0044] A modulation method for an error-balanced rotating inertial navigation system includes the following steps:

[0045] S1. Obtain the first output error of the gyroscope assembly, the second output error of the accelerometer, and the scaling factor error of the gyroscope assembly;

[0046] In one alternative implementation, the number of gyroscope components is three. In a scenario with three gyroscope components, a scaling factor error matrix is ​​constructed based on the different input angular velocities sensed by each gyroscope component. Symmetric scaling factor errors and asymmetric scaling factor errors are considered to finally obtain the angle error, thereby improving the accuracy of the final obtained angle error.

[0047] In this embodiment, S1 specifically refers to:

[0048] Obtain the first output error

[0049] Among them, S g This represents the scaling factor error matrix of the gyroscope component. Let T represent the installation error matrix of the gyroscope assembly, where T represents the transpose of the matrix. ε represents the output value of the gyroscope component. p This represents the zero bias value of the gyroscope component;

[0050] Specifically, the output of the gyroscope component is the number of angular increment pulses, denoted as N. g Ignoring error terms, the gyroscope's output is the actual angular velocity input. Among them, K g Let represent the scaling factor of the gyroscope component, and t represent the sampling interval; considering the error term, the gyroscope's measurement output is... Where I represents a preset constant; then the first output error

[0051] Obtain the second output error

[0052] Where I represents a preset constant, S a The scale factor error matrix represents the accelerometer (also called an accelerometer). This represents the installation error matrix of the accelerometer. This indicates the output value of the accelerometer. This indicates the zero bias value of the accelerometer;

[0053] Specifically, the accelerometer output is the number of specific force increment pulses N. a If the error term is ignored, the output of the accelerometer is the actual specific force. Among them, K a Let represent the accelerometer scaling factor, and t represent the sampling interval; considering the error term, the accelerometer's measurement output is... Where I represents a preset constant; then the second output error is

[0054] in,

[0055]

[0056] Obtain the scaling factor error, and then obtain the angular velocity error based on the scaling factor error:

[0057] The scaling factor of inertial components cannot be calibrated to absolute accuracy, and it may change with time, environment, and other factors. This results in a persistent scaling factor error in practical systems, which cannot be calibrated once and for all. The performance of the scaling factor is generally measured by linearity at different speeds and repeatability of successive starts at the same speed, and can be expressed as K. gc =K g (I+S g ),K ac =K a (I+S a ); where K gc K is the calculated scaling factor for the gyroscope component. ac This is the calculated value of the accelerometer's scale factor. and K a =diag([K ax K ay K az [) represents the actual value of the scaling factor for the gyroscope assembly and the accelerator, S g =diag([S gx S gy S gz [) represents the scaling factor error matrix of the gyroscope component, S a=diag([S ax S ay S az [) represents the accelerometer scale factor error matrix; the measurement errors of the gyroscope assembly and the accelerometer caused by the scale factor error are respectively...

[0058] Due to the influence of factors such as process and IMU's own operating principle in actual application, the scaling factor generally has positive and negative asymmetry. Ignoring this asymmetry or directly taking the scaling factor as the average of the positive and negative scaling factors will cause a certain scaling factor asymmetry error. Therefore, the asymmetry error is considered when determining the error matrix.

[0059] Obtain the gyroscope scaling factor error matrix:

[0060]

[0061] in, This represents the symmetry scaling factor error of the i-th gyroscope component. This represents the asymmetric scaling factor error of the i-th gyroscope component;

[0062]

[0063] Angular velocity error of the gyroscope component due to scaling factor error

[0064] Specifically:

[0065] Wherein, ω1, ω2 and ω3 represent the input angular velocities sensed by each of the gyroscope components;

[0066] The first output error is obtained by periodically collecting data according to the sampling interval, which is consistent with the characteristics of gyroscope in actual use. The sampling interval, i.e. the period, is taken into consideration, so that the data after modulation according to the first output error is closer to the target value that the gyroscope actually wants to measure.

[0067] There is also an error between the measured value and the actual value of the scaling factor, which will cause an error in the calculated angular velocity value required for the final measurement, thus leading to the output error of the gyroscope. The angular velocity error is calculated based on the scaling factor error. The angle error is also substituted into the alternative modulation equation to obtain the variation law of the angular velocity error under different modulation methods. Thus, the variation of the angular velocity error is taken into consideration, so that the final modulation based on the modulation equation can neutralize the error value to the greatest extent.

[0068] S2. Obtain the attitude of the carrier in which the inertial navigation system is located;

[0069] S3. After isolating the carrier attitude, the first output error, the second output error, the angle error, and the constant drift are substituted into the preset alternative modulation equation to obtain the first modulation result. Since the modulation process is system modulation, the constant offset is also substituted into the alternative modulation equation to observe its change with modulation, thus avoiding the error that may be caused by using the traditional method to compensate for the constant offset in system modulation.

[0070] The alternative modulation equations are:

[0071] in, Indicates rotational speed;

[0072] The modulation process of the system is transformed into a rotation matrix, i.e., a candidate modulation equation, and identified. By directly modifying the parameters in the candidate modulation equation, the changes in each parameter under various modulation methods can be calculated. This facilitates the numerical calibration calculation of the changes in various errors that may occur during the modulation process, and provides supporting data for the determination of the final modulation equation.

[0073] S4. If the first modulation result satisfies a preset threshold, then the candidate modulation equation is marked as the final modulation equation and the fiber optic gyroscope is modulated according to the final modulation equation; including: determining whether the cumulative error angle and cumulative error velocity in the first modulation result are symmetrical about 0 within one rotation cycle of the modulation equation; if so, the first modulation result satisfies the preset threshold; based on the characteristic that the system modulation target is not to eliminate errors but to balance errors so that the final output data is closest to the true value, it is set that as long as the cumulative error angle and cumulative error velocity are symmetrical about 0 within one rotation cycle, the candidate modulation equation is determined to satisfy the threshold, that is, although there may be a large error at some time points within one cycle, the error can be balanced within one cycle so that the final output data is not affected by the error value.

[0074] Embodiment 2 of the present invention is as follows:

[0075] An error-balanced modulation method for a rotating inertial navigation system, which differs from Embodiment 1 in that:

[0076] S3 and earlier included:

[0077] (1) Obtain the constant drift of the gyroscope component.

[0078] in, This represents the constant drift value of the gyroscope on the x-axis of the gyroscope assembly. This represents the constant drift value of the gyroscope on the y-axis of the gyroscope component. This represents the constant drift value of the gyroscope on the z-axis of the gyroscope assembly;

[0079] Considering the constant drift on three axes in different directions, different constant drift values ​​are used for calculation based on different axes, which reduces the error of the final value calculated by constant drift values;

[0080] (2) Obtaining installation error

[0081] The installation error angle refers to the angle (typically on the order of arcseconds) between the actual orientation of the gyroscope's sensing axis and the orientation calculated during calibration. After calibration using an inertial measurement unit, the coordinate system ox composed of the three sensing axes of the fiber optic gyroscope is obtained. g y g z g (Non-orthogonal system) to IMU coordinate system ox p y p z p Transformation matrix of (orthogonal system) Calibration It's not absolutely accurate; it's different from the actual ox. g y g z g to ox p y p z p Transformation matrix between The relationship is

[0082]

[0083] Where, μ ij (i = x, y, z; j = x, y, z; i ≠ j) represents the installation error angle of the gyroscope on the i-th coordinate axis;

[0084] (3) Obtain the random drift of the gyroscope component, considering only the white noise output by the gyroscope component, ε w =[ε wx ε wy ε wz ]; where ε wx ε represents the constant drift value of the gyroscope on the x-axis of the gyroscope assembly. wy ε represents the constant drift value of the gyroscope on the y-axis of the gyroscope component. wz This represents the constant drift value of the gyroscope on the z-axis of the gyroscope assembly;

[0085] Considering that the gyroscope components are installed in different directions during the gyroscope installation process, there will be an error between the installation angle and the coordinate system used for the final calculation when using it as a coordinate system. Including the installation error in the calculation range further improves the error balancing effect of the final determined modulation scheme.

[0086] Embodiment 3 of the present invention is as follows:

[0087] An error-balanced modulation method for a rotating inertial navigation system, which differs from Embodiment 1 or Embodiment 2 in that...

[0088] The first output error after modulation according to the alternative modulation equation is:

[0089]

[0090] in,

[0091]

[0092] in, This represents the coordinate transformation matrix from the navigation coordinate system n to the vehicle coordinate system b. This represents the gyro angular velocity in the navigation coordinate system n. This represents the equivalent angular velocity of the accelerometer in the navigation coordinate system n. This represents the angular velocity of the carrier coordinate system b, which is the angular velocity of the moving carrier.

[0093]

[0094] The second output error after modulation according to the alternative modulation equation is:

[0095]

[0096] The constant drift after modulation according to the alternative modulation equation is:

[0097]

[0098] It can be seen that in a continuously rotating scenario, the rotational speed... As a constant value, the constant drift on the plane perpendicular to the rotation axis is fully modulated within one rotation cycle, while the constant drift on the rotation axis itself cannot be modulated. The forward and reverse rotation of the IMU (Inertial Measurement Unit) causes the drive motor of the rotary table to frequently brake and start. In practical use, to achieve frequent braking and starting of the drive motor of the rotary table, the motor must have sufficient locking time to adapt to and recover from the deformation generated during braking. Furthermore, during the locking period, the constant drift is not modulated into a sine wave. In order to cancel out the error generated during the locking period, the sign of the constant drift on the plane perpendicular to the rotation axis must change during the locking time in each rotation cycle throughout the modulation process. This requires that the rotational speed and braking and starting angular acceleration of forward and reverse rotation stop have an odd symmetric relationship with time in each rotation cycle, and also requires that the stopping position of each rotation be symmetrical about the rotation axis. Moreover, for a dual-axis indexing system, when the motor on one axis rotates, the motor on the other axis must be locked for a period of time during the forward and reverse transition.

[0099] According to the modulation equation, the random drift after modulation is:

[0100]

[0101] ε wi It is Gaussian white noise with a mean of 0 and a variance of . It has the following characteristics:

[0102]

[0103]

[0104] As can be seen from the above formula, after rotation modulation, the noise variance of each axis does not change substantially. In fact, the frequency of the angle sine change is much smaller than the frequency of white noise. Rotation does not reduce the error amplitude of the rapidly changing error. Neither axis rotation can modulate the random drift of the gyroscope.

[0105] The gyroscope output error caused by the scaling factor error after modulation according to the alternative modulation equation is:

[0106]

[0107] The cumulative error angle after one rotation cycle is obtained by integrating within one rotation cycle:

[0108]

[0109] Where, ω ieN ω represents the angular rate of Earth's rotation. ieU γ represents the angular velocity of the carrier orbiting the Earth, and γ represents the rotational velocity.

[0110] As can be seen from the above formula, within one rotation cycle, the symmetry error of the two gyroscope scale factors in the direction perpendicular to the rotation axis is... The asymmetric error terms of the two gyroscope scaling factors in the direction perpendicular to the axis of rotation still exist. However, it disappeared; that is, it can be obtained that, under the condition of isolating the carrier motion, the dual-axis rotation can average out the asymmetric error effect of all inertial elements; and since the eastward component of the Earth's rotation speed is zero under static conditions, it will not cause an eastward angle error, that is, the first term in the formula is zero, and the asymmetric scaling factor error of the gyroscope on the plane perpendicular to the rotation axis can be modulated, while the symmetric error cannot be modulated.

[0111] Obtain the third component in the above formula:

[0112]

[0113] Due to ω ieU >>ω, simplifying the expression, we get:

[0114]

[0115] Analyzing the error in the first term of the above formula, if it is always positive (or negative), that is, if it always rotates in one direction during the modulation process, it will cause error accumulation. Therefore, the rotation scheme should adopt the forward and reverse stop method. The error in the second term represents the error caused by the coupling of the symmetry scaling factor error and the Earth's rotation. It is caused by the rotation of the geographic coordinate system relative to the inertial space. Therefore, as long as it rotates around the geographic system, this error will always exist. However, the electrostatic gyroscope inertial navigation system rotates relative to the inertial coordinate system and will not have this error. The third term is the mathematical platform error angle caused by the coupling of the asymmetry scaling factor error and the rotational motion.

[0116] Regarding the installation error, the angular velocity error generated by the installation error after modulation according to the alternative modulation equation is:

[0117] The angle error within one cycle is then:

[0118]

[0119] When the axis coincides with the IMU body, the single-axis system can automatically compensate for μ in 6 installation error angles. xy ,μ yx ,μ zy ,μ zx , and μ xz ,μ yz Unable to compensate;

[0120] In actual systems, the rotation axis of the indexing mechanism does not coincide with the axis of the IMU coordinate system. This becomes more complex. Assuming the deviation angles of the coordinate system defined by the rotation axis of the indexing mechanism from the IMU coordinate system are α, β, and θ, then the actual rotation value during modulation according to the alternative modulation equation is:

[0121]

[0122] Assuming that α, β, and θ are all small angles It can be further simplified to:

[0123]

[0124] The actual angular error caused by installation error is:

[0125]

[0126] As can be seen from the above equation, the installation error cannot be modulated when the rotation axis of the indexing mechanism does not coincide with the axis of the IMU coordinate system. Analysis reveals that in a dual-axis rotation system, the installation error matrix only contains orthogonal installation errors, meaning the six installation error angles satisfy the following relationship:

[0127] μ yz =μ xz ,μ xy =μ zy ,μ zx =μ yz ;

[0128] It was found that the second and third terms in the matrix were zero, and biaxial rotation could modulate all three terms to zero. Therefore, biaxial rotation can modulate all orthogonal mounting errors, but cannot modulate non-orthogonal mounting errors.

[0129] Please refer to Figure 3 Embodiment four of the present invention is as follows:

[0130] An error-balanced modulation method for a rotating inertial navigation system, which differs from the other embodiments in that:

[0131] Two rotation methods are designed: an initial alignment phase rotation method and a navigation phase rotation method; these two rotation methods have different purposes and consider different influencing factors.

[0132] During dual-axis modulation, the two axes operate alternately. The two situations that have a significant impact on the modulation effect are when the carrier has a roll motion and the IMU modulates around the outer ring axis (i.e., the roll axis) at the same time, and when the carrier has a yaw change and the IMU modulates around the inner ring axis (i.e., the azimuth axis) at the same time.

[0133] The design of the rotation method in the initial alignment stage ensures that the alignment accuracy is effectively improved while estimating the error of the inertial elements; the design of the rotation method in the navigation stage ensures that all constant errors of the inertial elements are completely modulated while modulating as many other errors as possible.

[0134] In a fiber optic gyroscope dual-axis rotating inertial navigation system, through reasonable dual-axis rotation, the main error terms of the inertial elements can be modulated into sine and cosine forms, and the cumulative error angle of the mathematical platform caused by the inertial element errors can also be modulated to 0 within one rotation cycle. However, to determine whether the influence of the inertial element errors on navigation has been eliminated by modulation, it is necessary to see whether the cumulative error angle and velocity within one rotation cycle are symmetrical about 0. Based on the analysis results of Examples 1 and 2, the design principle of the optimal modulation method for dual-axis rotation is as follows:

[0135] 1) It rotates alternately around two axes, and the rotation around each axis has both positive and negative aspects and symmetry;

[0136] 2) Within each rotation cycle, the rotational speeds for forward and reverse rotations and the angular accelerations for braking and starting have an odd symmetric relationship with respect to time, and the position where each rotation stops is symmetrical about the axis of rotation;

[0137] 3) The cumulative angular error or speed error caused by the device error within one rotation cycle is 0, and the mean is also 0;

[0138] The magnitude of the stop time not only affects the length of a modulation cycle, but also involves the transmission alignment time;

[0139] If we disregard the fact that a shorter rotation period is better for the criterion, it not only has a good modulation effect on constant errors, but also has a certain degree of averaging effect on system errors caused by drifts with periods greater than several times the rotation period or drifts that grow linearly with time. For example, assuming that the drift changes according to the law ε = ε0 + kt, in the system's static state, the mathematical plateau error angle at time t in the short term is approximately:

[0140] Δθ≈ε0t+kt 2 / 2

[0141] If the IMU continuously rotates at a period T to modulate this drift error, the error angle of the mathematical platform at time t after the entire rotation cycle is approximately:

[0142]

[0143] Comparing the two equations above, the increase in the error angle of the mathematical platform in the rotating state is independent of the constant component of the drift within one rotation cycle. Compared with the static state, both the growth rate and magnitude are greatly reduced. Furthermore, the slower the rate of drift change and the shorter the rotation cycle, the better the modulation and compensation effect on the error angle.

[0144] To determine the optimal rotation method for the navigation phase, it is necessary to obtain the influence of carrier motion on the rotation modulation effect. Specifically, S2 involves obtaining the first influence model of carrier roll angle motion on the rotation modulation effect, the second influence model of carrier pitch angle motion on the rotation modulation effect, and the third influence model of carrier heading angle motion on the rotation modulation effect.

[0145] When the angular velocity of the modulated rotation is close to and in the same direction as the angular velocity of the carrier motion, a DC component of the gyroscope scaling factor will appear in the equivalent gyroscope drift. This component will couple with the angular velocity of the carrier motion, increasing the equivalent gyroscope drift and thus reducing system accuracy. Therefore, the carrier attitude angular velocity is introduced into the control of the rotation mechanism to isolate the carrier motion while performing rotation modulation. The carrier's heading angle motion is not periodic and can continuously yaw in one direction. Therefore, under a specific motion combination, the equivalent gyroscope scaling factor caused by the heading angle will continue to increase. Over time, the system accuracy will decrease rapidly, and this situation should be avoided. During the navigation phase, the carrier attitude angular velocity is introduced into the control of the rotation mechanism to isolate the carrier motion while performing rotation modulation. Based on the characteristics of the sea state, only the heading angle motion is isolated. In addition to determining the speed and cumulative time of the heading change during isolation to decide whether to isolate the heading angle, two other scenarios need to be considered: one is when the isolation axis is aligned with the modulation axis, in which case the modulation angle and modulation angular velocity are calculated to achieve both modulation and isolation; the other is when the isolation axis is not aligned with the modulation axis, in which case the isolation axis activates a stabilization loop to track the carrier's heading.

[0146] The rotation modulation method described below in this embodiment includes the initial alignment stage rotation method and the navigation stage rotation method; (1) IMU rotates around the roll axis

[0147] Assuming the carrier only undergoes sinusoidal angular motion around the oyb axis, without any other motion, adjustments to the mechanical and electrical zero positions, calibration of the IMU roll misalignment angle, and compensation for non-orthogonal axis angles ensure that, initially, the IMU coordinate system S and the carrier coordinate system b coincide. Further assuming the IMU is installed at the centroid of the carrier, with no lever arm errors requiring compensation, and the IMU rotates around the roll axis oyo of the system base coordinate system O (OZ perpendicular to the mounting surface, OY parallel to the platform's horizontal axis, and OX axis determined by the right-hand rule) according to a pre-designed rotation modulation method; defining coordinate system b′ as the carrier's coordinate system after motion, the relationship between the b and b′ systems is as follows: Figure 3 As shown;

[0148] Based on the transformation relationship between the carrier systems b and b′, ​​the transformation matrix between b and b′ can be obtained. for:

[0149]

[0150] In the formula, α = ωyt, where ωy is the angular velocity of the carrier rotating about the oyb axis;

[0151] When the IMU rotates about the oyb axis, the transformation matrix between the b′ system and the S system is:

[0152]

[0153] In the formula, β=λyt, λy is the angular velocity of the carrier rotating around the oyb axis, and its value is determined by the rotation modulation method (the rotation modulation method includes the rotation sequence of the shaft, the rotation angle, the rotation angular velocity and the dwell time);

[0154] When the carrier rotates only about the oyb axis, the angular velocity of the carrier relative to the inertial frame is... In the formula, Let be the angular velocity of the carrier relative to the inertial frame of reference when it is at rest.

[0155] The gyroscope measurements in the IMU are In the formula,

[0156] The measurement error of the gyroscope is then projected from the s-coordinate system to the navigation coordinate system n. The first projection expression is:

[0157]

[0158] in, The first term on the right side of the equation For the angular motion of the carrier Under the influence of scaling factor error and installation error, the equivalent gyroscope in the b-series drifts; the second term on the right side of the equation... Angular velocity of rotation Under the influence of scaling factor and installation error, the equivalent gyroscope in the b-series drifts; the third term on the right side of the equation... The constant drift of the gyroscope is the equivalent gyroscope drift in the b-system; because the random walk is an uncorrelated random process, the variance of the random walk is still itself, so rotation modulation has no modulation effect on the random walk of the gyroscope.

[0159] Since this is a constant, it can be ignored here. To simplify and highlight the influence of gyroscope scaling factor error on attitude angular velocity error under carrier motion, the installation error term of the gyroscope component is ignored;

[0160] Transformation matrix and Substituting into the first projection expression yields the first influence model:

[0161]

[0162]

[0163]

[0164]

[0165] From the above four equations, it can be seen that when the IMU rotates around the roll axis and the carrier experiences roll angular motion, the scaling factor error of the gyroscope on the y-axis of the gyroscope assembly is directly coupled with the rotational angular velocity, causing the gyroscope's measurement error to increase by two constant values ​​ΔK. Gy ω y and ΔK Gy λ y This leads to an increase in the system's angular velocity error, which in turn increases the system's attitude error. According to the first of the four equations, the equivalent gyroscope error is directly proportional to the time, angular amplitude, and angular velocity of the carrier's roll motion.

[0166] (2) IMU rotation around the celestial axis: Except for the IMU rotating around the celestial axis ozo according to the rotation modulation method in (1), the other assumptions are the same. The coordinate system b′ is defined as the coordinate system after the carrier motion. The relationship between the carrier rotation and the IMU rotation is shown in [reference]. Figure 4 As shown;

[0167] When the IMU rotates about the ozo axis, the transformation matrix between the b′ frame and the S frame is:

[0168]

[0169] In the formula, γ=λzt, λz is the angular velocity of the carrier rotating around the ozo axis, and its value is determined by the rotation modulation method (the rotation modulation method includes the rotation sequence of the rotating shaft, the rotation angle, the rotation angular velocity and the dwell time);

[0170] The gyroscope measurements in the IMU are:

[0171] Will and (2) Substituting into the first projection expression yields the first influence model:

[0172]

[0173]

[0174]

[0175]

[0176] As can be seen from the above four equations, when the IMU rotates around the axial axis and the carrier experiences roll motion, the errors of the z-gyroscope and the x and y-gyroscopes are coupled together, exciting the scaling factor errors of the three gyroscopes. The roll motion is also introduced into the error of the equivalent gyroscope due to the scaling factor error of the gyroscope. The magnitude of the influence is not only affected by the scaling factor of the corresponding gyroscope, but also by the time, amplitude, and angular velocity of the roll motion. At the same time, the larger the angular velocity and amplitude of the carrier's roll motion, the larger the error of the equivalent gyroscope, and therefore, the worse the rotation modulation effect.

[0177] (3) IMU rotation around the roll axis: Assume the carrier only performs pitch motion around oxb, with an angular velocity of ωx for reciprocating motion. Define coordinate system b" as the coordinate system after the carrier's motion. The relationship between the b system and the b" system is shown in [reference needed]. Figure 5 As shown;

[0178] Based on the transformation relationship between the carrier systems b and b", the transformation matrix can be obtained. for

[0179]

[0180] In the formula, α = ωxt, where ωx is the angular velocity of the carrier rotating about the oxb axis;

[0181] When the IMU rotates around the real-time oyb axis, the transformation matrix between the b" frame and the S frame is:

[0182]

[0183] In the formula, β=λyt, where λy is the angular velocity of the carrier rotating around the oyb axis; similarly, its value is determined by the rotation modulation method.

[0184] When the carrier rotates only around the real-time oyb axis, there is

[0185] In the formula, Let be the angular velocity of the carrier relative to the inertial frame of reference when it is at rest.

[0186] The measured values ​​of the gyroscope component in the IMU are In the formula,

[0187] according to and The measurement error of the gyroscope is projected from the s-frame to the navigation coordinate system n-frame. The expression for the second projection is as follows:

[0188] in,

[0189] To highlight the impact of gyroscope scaling factor error on attitude angular velocity error under carrier motion, the installation error term of the gyroscope component is ignored. and Substituting into the second projection expression, we obtain the second influence model:

[0190]

[0191]

[0192]

[0193]

[0194] As can be seen from the above four equations, when the IMU rotates around the horizontal axis and the carrier has a pitch angle motion, the errors of the y gyroscope and the x and z gyroscopes are coupled to each other, and the scaling factor error of all gyroscopes is directly coupled to the rotational angular velocity. That is, the pitch angle velocity excites the scaling factor error of the x and z gyroscopes.

[0195] (4) IMU rotation around the celestial axis: Similarly, define coordinate system b" as the coordinate system after the carrier's motion. The IMU rotates around the celestial axis. The relationship between the b system and the b" system, as well as the rotation of each axis, is shown in [reference needed]. Figure 6 As shown;

[0196] When the carrier rotates only around the real-time oxb axis, there is

[0197] In the formula, Let be the angular velocity of the carrier relative to the inertial frame of reference when it is at rest.

[0198] The gyroscope measurements in the IMU are

[0199] In the formula,

[0200] Depend on and The measurement error of the gyroscope can be projected from the S-frame to the navigation coordinate system n. The expression for the third projection is as follows:

[0201]

[0202] In the formula,

[0203] In (3) and (2) Substituting the third projection expression, we obtain the second influence model:

[0204]

[0205]

[0206]

[0207]

[0208] As can be seen from the above four equations, when the IMU rotates around the celestial axis and the carrier has a pitch angle motion, the errors of the x gyroscope and the y and z gyroscopes are coupled to each other, and the scaling factor error of all gyroscopes is directly coupled to the rotational angular velocity. That is, the pitch angle velocity excites the scaling factor error of the y and z gyroscopes.

[0209] (5) IMU modulation around the roll axis: Assume the carrier is making a turning motion with a turning angular velocity of ωz (sign unchanged) and a duration of t. The coordinate system of the carrier after the motion is the b′ system. The relationship between the coordinate systems is shown in […]. Figure 7 As shown;

[0210] Based on the transformation relationships between coordinate systems, the transformation matrix between coordinate system b and coordinate system b′ is... It can be represented as:

[0211]

[0212] In the formula, α = ωzt, where ωz is the angular velocity of the carrier rotating about the ozb axis, and α is the heading angle of the carrier;

[0213] When the IMU rotates about the oyb′ axis, the transformation matrix between the b′ frame and the S frame is:

[0214]

[0215] In the formula, β=λyt, λy is the angular velocity of the carrier rotating around the oyb′ axis, and its value is determined by the rotation modulation method;

[0216] In (5) and (5) Substituting the first projection expression yields the third influence model, which is the equivalent gyroscope drift in the b-frame under the influence of the carrier's heading angle motion and rotational modulation angular velocity:

[0217]

[0218]

[0219]

[0220]

[0221] From the first of the four equations above, it can be seen that the equivalent gyroscope drift in the b-frame excited by the angular motion of the carrier relative to the inertial frame is related to both the modulation angular velocity and the carrier angular velocity. From the second equation, it can be seen that the equivalent drift of the x, y, and z gyroscopes is related to the angular velocity of the carrier's angular motion and the rotational angular velocity of the IMU during modulation. At the same time, the error in attitude angular velocity is directly proportional to the angular velocity of the carrier's heading angular motion. From the third equation, it can be seen that the modulation angular velocity affects the magnitude of the attitude angular error under the influence of the equivalent scaling factor error of the x and y gyroscopes. From the fourth equation, it can be seen that the constant drift of the gyroscope will not affect the attitude angular velocity error when the carrier has heading angular motion and modulation motion. In summary, since there is no DC component, the heading angular motion of the carrier has little impact on the modulation effect under this combined motion.

[0222] (6) IMU modulation around the celestial axis: When the carrier only experiences a change in heading angle, and the IMU rotates around the celestial axis, the change in coordinate system b is as follows: Figure 8 As shown;

[0223] The transformation matrix from the b-system to the S-system is:

[0224]

[0225] In (5) and (6) Substituting the first projection expression yields the third influence model, namely the equivalent gyroscope drift in the b-frame:

[0226]

[0227]

[0228]

[0229]

[0230] From the first of the four equations above, it can be seen that due to yaw motion, the errors of the z-gyroscope and the x and y gyroscopes are coupled together, and the yaw angular velocity excites the scaling factor error of the x and y gyroscopes. The DC component becomes an unmodulated component and becomes the equivalent constant gyroscope drift. From the second equation, it can be seen that due to yaw motion, the scaling factor error of the z-gyroscope is directly coupled with the yaw angular velocity of the carrier, increasing the equivalent gyroscope error in the b-frame, and this error is proportional to the yaw angular velocity. From the third equation, it can be seen that when the carrier has yaw motion and the IMU rotates around the yaw axis, the scaling factor error of the z-gyroscope is directly coupled with the modulation angular velocity, causing the modulation angular velocity of the IMU to increase the equivalent gyroscope error, thus increasing the equivalent gyroscope drift. From the fourth equation, it can be seen that the constant drift of the gyroscope does not affect the attitude angular velocity error when the carrier has yaw motion and modulation motion. Meanwhile, the constant drift of the z-axis gyroscope was not modulated;

[0231] Based on the above (1)-(6), the influence of carrier motion on the modulation effect is obtained, as shown in Table 1. During modulation, the two axes operate alternately. Analysis shows that the two situations that have a greater impact on the modulation effect are when the carrier has roll motion and the IMU modulates around the outer ring axis (i.e., the roll axis) and when the carrier has a heading change and the IMU modulates around the inner ring axis (i.e., the bearing axis). Since the roll motion is a periodic oscillation symmetrical with respect to the keel in the marine environment, the impact is small. The worst situation is when the carrier has heading motion, which requires isolation.

[0232] Isolate the carrier attitude based on the first influence model, the second influence model, and the third influence model;

[0233] In one alternative implementation, during the navigation phase, the carrier's attitude angular velocity is incorporated into the control of the rotation mechanism, achieving isolation of the carrier's motion while performing rotational modulation; the key signal flow diagram is shown below. Figure 11 The key signal in the diagram is This signal will be used in the calculation of the rotation control angle of the indexing mechanism;

[0234] When the isolation axis aligns with the modulation axis, the modulation angle and modulation angular velocity are calculated, simultaneously achieving modulation and isolation. When the isolation axis and modulation axis are not aligned, the isolation axis initiates a stabilization loop to track the carrier's heading. The flowchart is as follows: Figure 12 As shown

[0235] Table 1

[0236]

[0237] Embodiment five of the present invention is as follows:

[0238] Applying the above-mentioned error-balanced rotating inertial navigation system modulation method to a real-world scenario, the modulation path is as follows: 1. Initial alignment stage rotation method: employing dual-axis rotation with 3-position alignment observability.

[0239] Step 1: Power on and perform a self-test, remain still for 15 minutes to complete coarse alignment; Step 2: Rotate 180 degrees around the positive Z-axis, stop for 30 minutes; Step 3: Rotate 90 degrees around the negative X-axis, stop for 15 minutes to complete fine alignment; Step 4: Return along the original path, initial alignment complete, proceed to the navigation stage; 2. Navigation stage rotation method: The navigation stage rotation adopts a 64-sequence dual-axis rotation scheme, the rotation angle changes are shown in [link to relevant documentation] Figure 10 The scheme is odd-symmetric every 16th cycle, even-symmetric every 32nd cycle, and odd-symmetric throughout the entire period. The rotational angular velocity is 10° / s, and the angular acceleration is 5° / s². 2 The rotation stops in 5 seconds;

[0240] Please refer to Figure 2 Embodiment four of the present invention is as follows:

[0241] An error-balanced rotating inertial navigation system modulation terminal 1 includes a processor 2, a memory 3, and a computer program stored in the memory 3 and executable on the processor 2. When the processor 2 executes the computer program, it implements the steps in Embodiment 1.

[0242] In summary, this invention provides an error-balanced modulation method and terminal for a rotating inertial navigation system. It acquires the first output error, scale factor error, installation error, and constant drift of the gyroscope component, and the second output error of the accelerometer. These values ​​are then substituted into preset candidate modulation equations to obtain a first modulation result. Analysis of the first modulation result reveals the influence of different values ​​set during rotational modulation on the modulation balance of each error within a modulation cycle. When the first modulation result meets a threshold—that is, when the cumulative error angle and cumulative error velocity are symmetrical about 0 within a rotation cycle—it indicates that the candidate modulation equation at this time balances the errors within a cycle, minimizing the final output error and maximizing the output value. The candidate modulation equation satisfying this condition is then marked as the final modulation equation, and dual-axis rotational modulation of the inertial navigation system is performed based on this final modulation equation. This enables system modulation of the fiber optic gyroscope-rotating inertial navigation system, comprehensively considering the modulation results of each error instead of considering them separately, thus improving the measurement accuracy of the fiber optic gyroscope-rotating inertial navigation system in subsequent practical applications.

[0243] The above description is merely an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent modifications made based on the content of the present invention specification and drawings, or direct or indirect applications in related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A method of modulating an error-reducing rotating inertial navigation system, characterized by, The method comprises the steps of: S1, acquiring a carrier attitude of a carrier on which an inertial navigation system is located, specifically: acquiring a first influence model of a roll angle motion of the carrier on a rotation modulation effect, a second influence model of a pitch angle motion of the carrier on the rotation modulation effect, and a third influence model of a heading angle motion of the carrier on the rotation modulation effect; S2, isolating the carrier attitude according to the first influence model, the second influence model, and the third influence model; Before the S1, the method comprises the steps of: acquiring a first output error of a gyro assembly, a second output error of an accelerometer, and a scale factor error of the gyro assembly; the number of the gyro assemblies is three; acquiring the scale factor error, and obtaining an angular velocity error according to the scale factor error; acquiring a scale factor error matrix: ； wherein, represents a scale factor error of the symmetry of the i-th gyro of the gyro package, represents a scale factor error of the asymmetry of the i-th gyro of the gyro package; the angular velocity error ; wherein , and represent the input angular velocities experienced by each of the gyro assemblies, respectively. After the S2, the method comprises the step of: S3, bringing the first output error, the second output error, and the angular velocity error into a preset alternative modulation equation to obtain a first modulation result.

2. The method of claim 1, wherein the modulation is performed by a plurality of modulation elements, each modulation element being associated with a respective one of the plurality of error sources. The method further comprises the steps of: estimating errors of inertial elements in an initial alignment stage; modulating out all constant errors of the inertial elements in a navigation stage.

3. A method of modulating an error-reducing rotating inertial navigation system according to claim 2, characterized in that, The S2 specifically comprises the step of: in the navigation stage, introducing a carrier attitude angular velocity into control of a rotation mechanism to realize isolation of carrier motion while performing rotation modulation.

4. The method of claim 1, wherein, The S3 comprises the steps of: when an isolation axis is consistent with a modulation axis, calculating a modulation angle and a modulation angular velocity to realize modulation and isolation simultaneously; when the isolation axis is inconsistent with the modulation axis, starting a stable loop of the isolation axis to realize tracking of a carrier heading.

5. An error-balanced rotary inertial navigation system modulating terminal comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that, The processor realizes the following steps when executing the computer program: S1, acquiring a carrier attitude of a carrier on which an inertial navigation system is located, specifically: acquiring a first influence model of a roll angle motion of the carrier on a rotation modulation effect, a second influence model of a pitch angle motion of the carrier on the rotation modulation effect, and a third influence model of a heading angle motion of the carrier on the rotation modulation effect; S2, isolating the carrier attitude according to the first influence model, the second influence model, and the third influence model; Before the S1, the method comprises the steps of: acquiring a first output error of a gyro assembly, a second output error of an accelerometer, and a scale factor error of the gyro assembly; the number of the gyro assemblies is three; acquiring the scale factor error, and obtaining an angular velocity error according to the scale factor error; acquiring a scale factor error matrix: ； wherein, represents a scale factor error of the symmetry of the i-th gyro assembly gyro, represents a scale factor error of the asymmetry of the i-th gyro assembly. the angular velocity error ; wherein , and represent the input angular velocities experienced by each of the gyro assemblies, respectively. After the S2, the method comprises the step of: S3, bringing the first output error, the second output error, and the angular velocity error into a preset alternative modulation equation to obtain a first modulation result.

6. A rotationally error-balanced inertial navigation system moding terminal according to claim 5, characterized in that The method further comprises the steps of: estimating errors of inertial elements in an initial alignment stage; modulating out all constant errors of the inertial elements in a navigation stage.

7. An error-reducing rotary inertial navigation system modulation terminal according to claim 6, characterized in that The S2 specifically comprises the step of: in the navigation stage, introducing a carrier attitude angular velocity into control of a rotation mechanism to realize isolation of carrier motion while performing rotation modulation.

8. A modulated terminal of an error-reducing rotational inertial navigation system according to claim 5, characterized in that The S3 comprises the steps of: when an isolation axis is consistent with a modulation axis, calculating a modulation angle and a modulation angular velocity to realize modulation and isolation simultaneously; when the isolation axis is inconsistent with the modulation axis, starting a stable loop of the isolation axis to realize tracking of a carrier heading.

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