A method and terminal for systematic modulation of inertial navigation system errors

Abstract

The application discloses a method and a terminal for systematically modulating inertial navigation system errors, constructs a parameter calibration model, constructs a decoupling method between calibration parameters, designs a calibration path through a Kalman filter according to the decoupling method, and based on a system-level calibration method of double-axis rotation, starts from the principle of calibration, establishes an error model to be calibrated by comprehensively considering various errors of a gyroscope, and constructs a decoupling method between calibration parameters, so that each error can be balanced one by one after being split in the calibration process.

Description

[0001] This case is a divisional application of the patent application filed on December 31, 2020, with application number 202011625747.8 and title "An Automatic Calibration Method and Terminal for an Inertial Navigation System". Technical Field

[0002] This invention relates to the field of inertial navigation, and more particularly to a method and terminal for systematically modulating inertial navigation system errors. Background Technology

[0003] System-level calibration methods are primarily based on the principle of navigation calculation errors: after the inertial navigation system enters navigation mode, its parameter errors (including inertial device parameter errors, initial alignment attitude errors, initial position errors, etc.) are transmitted to the navigation results (position, velocity, attitude, etc.) through navigation calculation, manifesting as navigation errors. If all or part of the navigation error information can be obtained, it may be possible to estimate the parameters of the inertial navigation system and eliminate navigation errors.

[0004] Common calibration methods utilize turntables for rate testing and multi-position static testing. Rate testing primarily involves rotating the turntable to apply a rate excitation of the same magnitude but opposite direction to the gyroscope, calibrating the gyroscope's scale factor and installation error angle. The accuracy of the calibration results depends on the turntable's axis orthogonality and rotational accuracy. Multi-position static testing calibrates the gyroscope's zero bias and the accelerometer's zero bias, scale factor, and installation error angle. The accuracy of the calibration results also depends on the turntable's axis orthogonality and angular position error. However, this calibration method has several drawbacks: firstly, the inertial navigation equipment must be removed from the vehicle, which is time-consuming and labor-intensive; secondly, a high-precision turntable is required, with the turntable's axis orthogonality, rotational error, and angular position error needing to reach a certain level of accuracy, resulting in high calibration costs. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a method and terminal for systematically modulating inertial navigation system errors, so as to realize convenient and low-cost inertial navigation system calibration.

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0007] A method for systematically modulating inertial navigation system errors includes the following steps:

[0008] S1. Establish the first error model of the gyroscope and the second error model of the accelerometer;

[0009] S2. Construct a parameter calibration model based on the first error model and the second error model;

[0010] S3. Obtain the filtering result based on the preset Kalman filter model, the first error model, the second error model, and the parameter calibration model;

[0011] S4. Determine the calibration path based on the filtering result, and calibrate the inertial navigation system based on the calibration path.

[0012] To solve the above-mentioned technical problems, another technical solution adopted by the present invention is as follows:

[0013] A terminal for systematically modulating inertial navigation system errors 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 performs the following steps:

[0014] S1. Establish the first error model of the gyroscope and the second error model of the accelerometer;

[0015] S2. Construct a parameter calibration model based on the first error model and the second error model;

[0016] S3. Obtain the filtering result based on the preset Kalman filter model, the first error model, the second error model, and the parameter calibration model;

[0017] S4. Determine the calibration path based on the filtering result, and calibrate the inertial navigation system based on the calibration path.

[0018] The beneficial effects of this invention are as follows: error models for the gyroscope and accelerometer are established separately, a parameter calibration model is constructed based on the error models, and finally the filtering result is obtained based on the preset Kalman filter model, error model and parameter calibration model. When setting the model, various errors are fully considered. The optimal result can be obtained through the Kalman filter model. Based on this, the inertial navigation system is calibrated to achieve systematic modulation of various errors of the inertial navigation system. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the steps of a method for systematically modulating inertial navigation system errors according to an embodiment of the present invention.

[0020] Figure 2 This is a schematic diagram of the structure of a terminal for systematically modulating inertial navigation system errors according to an embodiment of the present invention;

[0021] Figure 3 This is the gyroscope scaling factor error curve according to an embodiment of the present invention;

[0022] Figure 4 This is a curve showing the gyroscope installation error estimation in an embodiment of the present invention.

[0023] Figure 5This is an accelerometer scaling factor error estimation curve according to an embodiment of the present invention;

[0024] Figure 6 This is an accelerometer installation error estimation curve according to an embodiment of the present invention;

[0025] Figure 7 This is an accelerometer installation error estimation curve according to an embodiment of the present invention;

[0026] Figure 8 This is a schematic diagram illustrating the definition of a coordinate system according to an embodiment of the present invention;

[0027] Label Explanation:

[0028] 1. A terminal for systematically modulating inertial navigation system errors; 2. A processor; 3. A memory. Detailed Implementation

[0029] 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.

[0030] Please refer to Figure 1 and Figures 3 to 7 A method for systematically modulating inertial navigation system errors, comprising the following steps:

[0031] S1. Establish the first error model of the gyroscope and the second error model of the accelerometer;

[0032] S2. Construct a parameter calibration model based on the first error model and the second error model;

[0033] S3. Obtain the filtering result based on the preset Kalman filter model, the first error model, the second error model, and the parameter calibration model;

[0034] S4. Determine the calibration path based on the filtering result, and calibrate the inertial navigation system based on the calibration path.

[0035] As can be seen from the above description, the beneficial effects of the present invention are as follows: error models for the gyroscope and accelerometer are established respectively, a parameter calibration model is constructed based on the error models, and finally the filtering result is obtained based on the preset Kalman filter model, error model and parameter calibration model. When setting the model, various errors are fully considered. The optimal result can be obtained through the Kalman filter model. Based on this, the inertial navigation system is calibrated to realize the systematic modulation of various errors of the inertial navigation system.

[0036] Furthermore, S1 specifically refers to;

[0037] Establish the first error model

[0038] in, ε represents the drift error of the gyroscope. b ε represents the model error of the gyroscope. r The noise of the first-order Markov random process of the gyroscope is represented by w, which represents Gaussian white noise.

[0039] Establish the second error model

[0040] in, S represents the zero bias error of the accelerometer; a This indicates the scale factor error of the accelerometer; This represents the installation error coefficient of the accelerometer; Indicates lever arm effect error; This indicates the output white noise of the accelerometer.

[0041] As described above, the gyroscope error model and accelerometer error model are established, including scaling factor error, installation error coefficient, etc. After comprehensively considering various types of errors, the model is established, which makes the subsequent calculation of the impact of system calibration on the error more accurate.

[0042] Further, step S3 includes constructing a first parameter calibration model corresponding to the gyroscope based on the first error model:

[0043] Obtain angular velocity measurement results:

[0044] The first scaling factor-installation relationship matrix of the gyroscope is:

[0045]

[0046] The first zero-bias error of the gyroscope is:

[0047]

[0048] The first noise of the gyroscope is:

[0049]

[0050] in, This represents the first scaling factor of the gyroscope on the j-axis. This represents the first zero bias value of the gyroscope on the j-axis; x b y b , z b Let x and y represent the three coordinate axes of the b-system. g y g , z g These represent the unit vectors of the three sensitive axes of the gyroscope, respectively. This indicates the installation error angle of the gyroscope; Indicates; i and j represent x respectively. b y b , z b One of them, and the values ​​of i and j are not simultaneously equal;

[0051] Wherein, the b-system is the carrier coordinate system, and the K-system is the carrier coordinate system. g And ω0 is the calibration parameter to be estimated.

[0052] As described above, by constructing angular velocity measurement results, the relationship between the calibration parameters to be estimated and the parameters that can be obtained or are known is established, which facilitates the final setting of constraints to obtain the optimal value, so that the optimization of the gyroscope can achieve better results in the final system optimization process.

[0053] Further, step S3 includes constructing a second parameter calibration model for the accelerometer based on the second error model:

[0054] Obtain the specific force measurement model f b =K a N a -f0-δ f ;

[0055] The second scaling factor-installation relationship matrix of the accelerometer is:

[0056]

[0057] The second zero-bias error of the accelerometer is:

[0058]

[0059] The second noise of the accelerometer is:

[0060]

[0061] in, This represents the second scaling factor of the accelerometer on the j-axis. This represents the second zero bias value of the accelerometer on the j-axis, x. b y b , z b Let x and y represent the three coordinate axes of the b-system. a y a z a These represent the unit vectors of the three sensitive axes of the accelerometer. This indicates the installation error angle of the accelerometer. The values ​​of i and j represent one of x, y, and z, and the values ​​of i and j are not necessarily equal.

[0062] Wherein, K a And f0 is the calibration parameter to be estimated.

[0063] As described above, by constructing a force measurement model and establishing the relationship between the calibration parameters to be estimated and the parameters that can be obtained or are known, it is easier to set constraints and obtain the optimal value, so that the error balance of the accelerometer can achieve a better effect during the system calibration process.

[0064] Further, S3 includes:

[0065] Establish a first measurement error model in the m-system corresponding to the first error model.

[0066]

[0067] in, This represents the true value of the gyroscope measurement data. δK represents the measured value of the gyroscope. G ε represents the scaling factor-installation error matrix of the gyroscope in the m-system. m This indicates the zero bias error of the gyroscope in the m-system.

[0068] Further, S3 includes:

[0069] Establish a second measurement error model in the m-system corresponding to the second error model.

[0070] Where, δf m This represents the true value of the accelerometer measurement data. The measured value of the accelerometer, δK A This represents the scaling factor-installation error matrix of the accelerometer in the m-system. This indicates the zero bias error of the accelerometer in the m-system.

[0071] As described above, the error model is easy to calculate in the carrier coordinate system b. Transforming it to the IMU coordinate system m to establish the error model makes it easier to intuitively obtain the impact of various errors on the rotation process.

[0072] Furthermore, the state of the Kalman filter model in S3 is as follows:

[0073]

[0074] Among them, X 30 This represents a 30-dimensional Kalman filter model. δV represents the three-dimensional attitude error of the gyroscope or accelerometer, δP represents the position error of the gyroscope or accelerometer, and X represents the velocity error of the gyroscope or accelerometer. g X represents the calibration parameter error of the gyroscope. a This indicates the calibration parameter error of the accelerometer.

[0075] As described above, designing a 30-dimensional Kalman filter model, which integrates various errors from the gyroscope and accelerometer, improves the filtering effect and makes the final optimal value closer to the actual optimal value.

[0076] Furthermore, the calibration of the inertial navigation system according to the calibration path in step S4 specifically involves:

[0077] The inertial navigation system is calibrated in the UT-type turntable according to the calibration path.

[0078] As can be seen from the above description, calibration using a UT-type dual-axis rotary table can achieve the desired calibration effect while saving costs.

[0079] Furthermore, after S4, it also includes;

[0080] The calibrated inertial navigation system was then simulated and verified.

[0081] As described above, after calibration, simulation verification of the calibrated inertial navigation system can be performed. The final effect of calibration can be verified in a simulation environment. If the conditions are not met, recalibration can be performed, avoiding the need for recalibration after the inertial navigation system is put into use due to insufficient accuracy, thus improving efficiency.

[0082] Please refer to Figure 2 A terminal for systematically modulating inertial navigation system errors 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 performs the following steps:

[0083] S1. Establish the first error model of the gyroscope and the second error model of the accelerometer;

[0084] S2. Construct a parameter calibration model based on the first error model and the second error model;

[0085] S3. Obtain the filtering result based on the preset Kalman filter model, the first error model, the second error model, and the parameter calibration model;

[0086] S4. Determine the calibration path based on the filtering result, and calibrate the inertial navigation system based on the calibration path.

[0087] The beneficial effects of this invention are as follows: error models for the gyroscope and accelerometer are established separately, a parameter calibration model is constructed based on the error models, and finally the filtering result is obtained based on the preset Kalman filter model, error model and parameter calibration model. When setting the model, various errors are fully considered. The optimal result can be obtained through the Kalman filter model. Based on this, the inertial navigation system is calibrated to achieve systematic modulation of various errors of the inertial navigation system.

[0088] This specification defines nine coordinate systems for a dual-axis rotating inertial navigation system. Please refer to [link / reference]. Figure 8 That is, the coordinate system of the gyroscope component (G system), the coordinate system of the accelerometer component (a system), the coordinate system of the IMU (S system), the coordinate system of the actual platform (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:

[0089] 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;

[0090] 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.

[0091] 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.

[0092] 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};

[0093] 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.

[0094] 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;

[0095] 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.

[0096] 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.

[0097] 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;

[0098] The attitude transformation matrix is

[0099] The coordinate transformation matrix between the load system (b-frame) and the base coordinate system (O-frame) is determined by the installation error angle;

[0100] 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;

[0101] 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.

[0102] The coordinate transformation matrix between the modulated average coordinate system S and the navigation coordinate system n;

[0103] Please refer to Figure 1 and Figures 3 to 7Embodiment 1 of the present invention is as follows:

[0104] A method for systematically modulating inertial navigation system errors includes the following steps:

[0105] S1. Establish the first error model of the gyroscope and the second error model of the accelerometer, specifically as follows:

[0106] Establish the first error model

[0107] in, ε represents the drift error of the gyroscope. b ε represents the model error of the gyroscope. r The noise of the first-order Markov random process of the gyroscope is represented by w, which represents Gaussian white noise.

[0108]

[0109] in, S represents the zero bias error of the gyroscope. g This refers to the scaling factor error of the gyroscope. This represents the installation error coefficient of the gyroscope.

[0110]

[0111] Specifically, the measurement values ​​of the three axes of the gyroscope.

[0112] in, This represents the true value measured by the gyroscope in the b-series. This represents the actual value measured by the gyroscope in the b-series.

[0113] Establish the second error model

[0114] in, S represents the zero bias error of the accelerometer; a This indicates the scale factor error of the accelerometer; This represents the installation error coefficient of the accelerometer; Indicates lever arm effect error; This represents the white noise output of the accelerometer;

[0115] Specifically, the accelerometer measurements f b Where represents the true value measured by the accelerometer in the b-system. This represents the actual value measured by the accelerometer in system b;

[0116] S2. Construct a parameter calibration model based on the first error model and the second error model;

[0117] S3. Obtain the filtering result based on the preset Kalman filter model, the first error model, the second error model, and the parameter calibration model, including:

[0118] S31. Construct the first parameter calibration model for the gyroscope based on the first error model:

[0119] Obtain angular velocity measurement results:

[0120] The first scaling factor-installation relationship matrix of the gyroscope is:

[0121]

[0122] The first zero-bias error of the gyroscope is:

[0123]

[0124] The first noise of the gyroscope is:

[0125]

[0126] in, This represents the first scaling factor of the gyroscope on the j-axis. This represents the first zero bias value of the gyroscope on the j-axis; x b y b , z b Let x and y represent the three coordinate axes of the b-system. g y g , z g These represent the unit vectors of the three sensitive axes of the gyroscope, respectively. This indicates the installation error angle of the gyroscope; The measurement noise of the i-axis gyroscope is represented; i and j represent one of x, y, and z, respectively, and the values ​​of i and j are not necessarily equal.

[0127] Wherein, the b-system is the carrier coordinate system, and the K-system is the carrier coordinate system. g And ω0 is the calibration parameter to be estimated;

[0128] S32. Construct the second parameter calibration model for the accelerometer based on the second error model:

[0129] Obtain the specific force measurement model f b =K a N a -f0-δ f ;

[0130] The second scaling factor-installation relationship matrix of the accelerometer is:

[0131]

[0132] The second zero-bias error of the accelerometer is:

[0133]

[0134] The second noise of the accelerometer is:

[0135]

[0136] in, This represents the second scaling factor of the accelerometer on the j-axis. This represents the second zero bias value of the accelerometer on the j-axis, x. b y b , z b Let x and y represent the three coordinate axes of the b-system. a y a z a These represent the unit vectors of the three sensing axes of the accelerometer. This indicates the installation error angle of the accelerometer. The measurement noise of the i-axis accelerometer is represented; i and j represent one of x, y, and z, and the values ​​of i and j are not equal at the same time.

[0137] Wherein, K a And f0 is the calibration parameter to be estimated;

[0138] S33. Establish a first measurement error model in the m-system corresponding to the first error model.

[0139] in, This indicates the measurement error of the gyroscope. δK represents the measured value of the gyroscope. G ε represents the scaling factor-installation error matrix of the gyroscope in the m-system. m This indicates the zero bias error of the gyroscope in the m-system;

[0140] Establish a second measurement error model in the m-system corresponding to the second error model.

[0141] Where, δf m This represents the true value of the accelerometer measurement data. The measured value of the accelerometer, δK A This represents the scaling factor-installation error matrix of the accelerometer in the m-system. This indicates the zero bias error of the accelerometer in the m-system;

[0142] The state of the Kalman filter model is as follows:

[0143]

[0144] Among them, X 30 This represents a 30-dimensional Kalman filter model. δV represents the three-dimensional attitude error of the gyroscope or accelerometer, δP represents the position error of the gyroscope or accelerometer, and X represents the velocity error of the gyroscope or accelerometer. g X represents the calibration parameter error of the gyroscope. a This indicates the calibration parameter error of the accelerometer;

[0145] S31 and S32 can be performed sequentially or simultaneously. The IMU (Inertial Measurement Unit) consists of three dual-frequency mechanically dithered fiber optic gyroscopes and three quartz flexible accelerometers. The calibration parameters only consider the zero-order and first-order parameters of the IMU, including the zero bias, scale factor, and installation error angle of the gyroscopes and accelerometers. Since the fiber optic gyroscopes are not sensitive to acceleration, the acceleration term is ignored in the gyroscope input-output model.

[0146] S4. Determine the calibration path based on the filtering result, and calibrate the inertial navigation system based on the calibration path;

[0147] S5. Simulation verification of the calibrated inertial navigation system: The trajectory generator is designed to generate gyroscope and accelerometer data according to the calibration path. The calibration error is set as follows: the scale factor of the gyroscope and accelerometer is 200ppm, the installation error angle of the gyroscope and accelerometer is 180″, the zero bias error of the gyroscope is 0.1° / h, the zero bias error of the accelerometer is 200ug, and white noise of 0.01° / h and 50ug is superimposed respectively.

[0148] With the simulation conditions unchanged, 30 Monte Carlo simulation experiments were conducted. The calibration error of each simulation was calculated, and the root mean square error of the 30 simulations was statistically analyzed, as shown in Table 2. The scaling factors (S) of the gyroscope and accelerometer were also analyzed. g ,S a Better than 4ppm, installation error (η) g ,β a (Better than 7″, please refer to...) Figures 3 to 7 The calibration accuracy of the scaling factor and installation error is better than 5″.

[0149] Table 2

[0150]

[0151] Embodiment 2 of the present invention is as follows:

[0152] A method for systematically modulating inertial navigation system errors, which differs from Embodiment 1 in that:

[0153] It also includes decoupling of calibration parameters:

[0154] (1) Gyroscope scaling factor error and decoupling method:

[0155] The observability of gyroscope scaling factor error is poor under static conditions because there is no angular velocity input as excitation. Furthermore, the angular rate measurement error generated by the Earth's rotation-induced scaling factor error is constant under static conditions, coupled with the gyroscope's own zero-bias error, making it indistinguishable. Therefore, to excite the gyroscope scaling factor error, it is only necessary to rotate its corresponding sensitive axis, and it is known that the angular rate measurement error is proportional to the rotation angular rate. Thus, rotating the three sensitive axes of the system can both excite and decouple the gyroscope scaling factor error. If asymmetric scaling factor error is ignored and the gyroscope scaling factor is considered constant, then only unidirectional rotation is required.

[0156] (2) Gyroscope installation errors and decoupling methods:

[0157] The observability properties of gyroscope installation error are basically the same as those of gyroscope scaling factor error. Both require rotation of their corresponding sensitive axis for excitation. However, the direction of the resulting angular rate measurement error differs from that of the gyroscope scaling factor error. For example, when the system rotates around the X-axis, the angular rate measurement error caused by the scaling factor error is also along the X-axis. The angular rate measurement errors caused by gyroscope installation errors occur on the Y-axis and Z-axis, respectively. and Using this simple principle, it can be seen that the installation error of the gyroscope can also be excited and decoupled through the three sensitive axes of the rotating system;

[0158] (3) Gyroscope zero bias error and decoupling method:

[0159] The gyroscope's zero-bias error is a constant error along the sensitive axis and does not require excitation. However, it is coupled with many other errors, including the scaling factor error of the Earth-rotation-excited gyroscope and the angular rate measurement error and azimuth misalignment angle caused by installation errors. Sections 1) and 2) have already introduced the coupling principle between the gyroscope scaling factor error, installation error, and zero-bias error, and provided decoupling methods. This section focuses on analyzing the coupling principle between the azimuth misalignment angle and the gyroscope's zero-bias error:

[0160] In a north-pointing inertial navigation system, the equivalent east-facing gyroscope will not be sensitive to the angular velocity caused by the Earth's rotation. However, the azimuth misalignment will cause the equivalent east-facing gyroscope to incorrectly detect the angular rate measurement error caused by the Earth's rotation (commonly referred to as the compass term). This measurement error, when fed back to the northward Schuler loop, can cause a corresponding northward velocity error. Both compass-based and Kalman-filtered precision alignment utilize this principle. However, under the condition of an equivalent eastward gyroscope zero-bias error, the angular rate measurement error is a coupling relationship between the azimuth misalignment angle and the gyroscope zero-bias error. This coupling can be achieved by changing the system's azimuth.

[0161] At this point, the observability of the X-gyroscope and the azimuth misalignment angle reaches its maximum. Simultaneously, the equivalent north-facing gyroscope has no coupling relationship and can achieve unbiased estimation. However, the observability of the equivalent azimuth gyroscope remains poor under the condition of zero velocity as the only observable. This is because the influence of the zero-bias error of the equivalent azimuth gyroscope on the velocity error needs to accumulate over time, first generating the corresponding azimuth misalignment angle, then transferring it to the equivalent east-facing angular rate measurement error through the compass term, and finally generating the north-facing velocity error. This is a third-order function of time, which is why marine single-axis rotating inertial navigation systems typically require more than 8 hours of static testing to achieve drift measurement of the Z-axis gyroscope. Therefore, to achieve decoupling of the gyroscope's zero-bias error, the calibration path needs to simultaneously include the sensitive axes of all three gyroscopes placed in two positions: east and west, or south and north.

[0162] (4) Accelerometer scale factor error and decoupling method:

[0163] Under conditions without linear motion, only the scaling factor error of the accelerometer pointing upwards can be excited by gravitational acceleration. Simultaneously, the acceleration measurement error generated by the gravitational acceleration-induced scaling factor is coupled with the accelerometer's zero-bias error. Therefore, pointing each axis of the system upwards and downwards respectively maximizes the observability of the corresponding accelerometer scaling factor error, while also decoupling the accelerometer scaling factor error and zero-bias error.

[0164] (5) Accelerometer installation errors and decoupling methods:

[0165] The observability properties of accelerometer installation errors are essentially the same as those of accelerometer scale factor errors; only the installation error corresponding to the upward-pointing accelerometer can be excited by gravitational acceleration. Simultaneously, the acceleration measurement error generated by the gravitational acceleration-excited installation error is coupled with the zero-bias error of the horizontal accelerometer. Taking the Z-axis pointing upwards as an example, the measurement errors of the three-axis accelerometers are as follows:

[0166]

[0167] Under conditions where the IMU in the system does not experience roll maneuvers, even if the maneuver conditions include heading rotation and linear motion, this coupling relationship is still difficult to break. Therefore, for land-based or marine strapdown inertial navigation systems, these two installation errors of the accelerometer are often equivalent to the accelerometer zero bias error estimation or compensation.

[0168] During calibration, pointing each axis of the system to the sky and to the ground respectively can maximize the observability of the corresponding accelerometer installation error, and can also decouple the installation error of the accelerometer in the sky from the zero bias error of the horizontal accelerometer.

[0169] (6) Accelerometer zero bias error and decoupling method:

[0170] The accelerometer zero-bias error is a constant error along the sensitive axis and does not require excitation. Other errors coupled with it mainly include the accelerometer scale factor error caused by gravitational acceleration excitation, acceleration measurement error caused by installation errors, and the horizontal misalignment angle. Sections 4) and 5) have already introduced the coupling principle between the accelerometer scale factor error, installation error, and zero-bias error, and provided decoupling methods. This section focuses on analyzing the coupling principle between the horizontal misalignment angle and the accelerometer zero-bias error:

[0171] Under static conditions, gravitational acceleration acts only in the upward direction, while the horizontal misalignment angle will cause the equivalent horizontal accelerometer to err on the side of gravitational acceleration, resulting in an error in the horizontal acceleration measurement. This error is coupled with the accelerometer's zero-bias error as follows: Decoupling can be achieved by changing the orientation of the system;

[0172] At this point, the observability of the zero bias error of the horizontal accelerometer reaches its maximum. Therefore, to decouple the zero bias error of the accelerometer, the calibration path needs to include the sensitive axes of the three accelerometers simultaneously positioned in two locations: east and west, or south and north respectively.

[0173] Embodiment 3 of the present invention is as follows:

[0174] A method for systematically modulating inertial navigation system errors, which differs from Embodiment 1 or Embodiment 2 in that S31 and S32 specifically involve:

[0175] The three coordinate axes of the volume coordinate system (b system) are x b y b z b The unit vectors of the three gyroscope sensitive axes are x g y g z g The gyroscope output pulse per unit time can be written as:

[0176]

[0177] in, To represent the angular velocity vector in the b-frame, It is the gyroscope pulse output per unit time. and These are the scale factor and zero bias of the j-axis gyroscope, respectively.

[0178] It is the gyroscope installation relationship matrix. Refers to j-axis detachment measurement noise;

[0179] Similar to a gyroscope, the unit vectors of the three accelerometer sensing axes are x a y a z a The accelerometer output pulse per unit time can be written as:

[0180]

[0181] in, It is the representation of the force vector in the b-system. It is the accelerometer pulse output per unit time. and These are the scale factor and zero bias of the j-axis accelerometer, respectively;

[0182] It is an accelerometer installation relationship matrix. Refers to the noise measured by the j-axis accelerometer;

[0183] Under ideal conditions, each sensing axis of the accelerometer coincides with each axis of the load system, i.e., the installation relationship matrix is... and The identity matrix is ​​I3; however, there will inevitably be installation errors during system assembly. Assuming the installation error angle is small, the installation relationship matrix approximately satisfies:

[0184]

[0185]

[0186] in The installation error angle, often referred to as that of a gyroscope or accelerometer;

[0187] Based on the input-output relationship, the angular velocity and specific force measurement results can be obtained from the pulse output of the IMU:

[0188]

[0189]

[0190] Among them, K g and K aIt includes the scaling factors and mounting relationships of the gyroscope and accelerometer, which can be specifically written as follows:

[0191]

[0192]

[0193] Assuming the installation error angle is small, then K g and K a It can be approximated as:

[0194]

[0195] Commonly referred to as K g and K a These are the scaling factors and installation relationship matrices for the gyroscope and accelerometer, respectively; ω0 and f0 can be written as...

[0196]

[0197] ω0 and f0 are the zero biases of the gyroscope and accelerometer, respectively. δ ω and δ f The noise component:

[0198]

[0199] The above equation is the calibration parameter model for an orthogonal three-accelerometer, with matrix K. g K a The zero bias vectors ω0 and f0 are the calibration parameters to be estimated.

[0200] Embodiment four of the present invention is as follows:

[0201] A self-calibration method for an inertial navigation system, which differs from the other embodiments in that:

[0202] Specifically, S3 is:

[0203] For Kalman filtering calibration, a calibration path is designed that uses only a dual-axis indexing mechanism to achieve excitation and decoupling of all calibration parameters. The main approach involves analyzing various calibration errors based on the calibration error model below, obtaining the decoupling relationship of the parameters to be calibrated, and filtering each calibration error according to a specific calibration path.

[0204] In the navigation coordinate system (Northeast-Northeast-Heaven coordinate system), the error equation of the inertial navigation system can be written as:

[0205]

[0206] in, For small-angle attitude error angles, The angular velocity of the navigation coordinate system relative to the inertial frame is generated by the Earth's rotation and the motion of the carrier. For navigation calculation The estimation error, f n For comparison under navigation systems, and These represent the Earth's rotational angular rate and the angular rate generated by the carrier's motion around the Earth, respectively; δg is the gravity vector error; V n =[V E V N V U ] T Let R be the velocity relative to the ground, L, λ, and h be the local latitude, longitude, and altitude, respectively. M R N These are the radii of the local Earth's meridian and circumpolar orbit, respectively. and δf b These are the measurement errors of the gyroscope and the accelerometer, respectively.

[0207] In a rotating inertial navigation system, constraining the carrier system (b-frame) to the IMU coordinate system (m-frame) allows us to replace the subscript b with m. Based on the simplified linear calibration model in the m-frame, the measurement errors of the gyroscope and accelerometer can be written as:

[0208]

[0209]

[0210] Where, δK G and δK A These are the scaling factors and installation error matrices for the gyroscope and accelerometer, respectively; ε m and These represent the zero-bias errors of the gyroscope and accelerometer, respectively. Since the m-system is defined based on the gyroscope's sensitive axis, δK... G δK A ε m and It can be written as:

[0211]

[0212]

[0213] in, and These are the scaling factor errors of the three-axis gyroscope; and These are the scale factor errors of the triaxial accelerometer;

[0214] Assuming all calibration parameter errors are constant, then:

[0215]

[0216] Based on the above inertial navigation system error equations and calibration model, the 30-dimensional Kalman filter state is designed as follows:

[0217] in, δV and δP represent the three-dimensional attitude error, velocity error, and position error, respectively, and X g X a The calibration parameter errors for the gyroscope and accelerometer are respectively:

[0218]

[0219]

[0220] The filter state equation can be expressed as:

[0221]

[0222] in,

[0223] F 30 The matrix contains:

[0224]

[0225]

[0226]

[0227]

[0228]

[0229]

[0230]

[0231]

[0232] The filter input is the measurement noise from the gyroscope and accelerometer. The input matrix is:

[0233]

[0234] The filter observation equation is:

[0235]

[0236] in, The velocity solution for the inertial navigation system is given by: v represents the observation noise, and the observation matrix is:

[0237] H 30 =[0 3×3 I3 0 3×24 ]

[0238] The feedback compensation form of the filtered estimation result is as follows:

[0239]

[0240] Embodiment five of the present invention is as follows:

[0241] According to the above-mentioned inertial navigation system self-calibration method, in a UT-type turntable (the outer frame axis is U-shaped, the rotation axis is horizontal, and the inner frame axis is T-shaped and orthogonal to the outer frame axis), the initial attitude is east-oriented X-axis, north-oriented Y-axis, and sky-oriented Z-axis. Using the right-hand rule, +90° represents a 90-degree counter-clockwise rotation, thus obtaining the calibration path:

[0242]

[0243] Please refer to Table 1 for the specific calibration path:

[0244] Table 1

[0245]

[0246] The rotation speed is 5° / s, with a 180s stop at each position, and the entire rotation path can be completed within 1 hour. The first 9 rotations of this path are mainly used to excite the gyroscope scaling factor error and installation error, including two 180° rotations in one direction for each axis. The last 9 rotations are mainly used to excite the accelerometer scaling factor and installation error, including two positions for each axis: pointing upwards and pointing downwards. Since the random noise of the gyroscope is relatively large in actual calibration, the estimation of the gyroscope zero-bias error in the Kalman filter usually takes a long time. Therefore, depending on the actual situation, two or more calibration path rotations can be performed in one calibration to ensure that the estimation curves of the errors of each calibration parameter completely converge.

[0247] Please refer to Figure 2 Embodiment five of the present invention is as follows:

[0248] A terminal 1 for systematically modulating inertial navigation system errors 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, Embodiment 2, Embodiment 3, or Embodiment 4.

[0249] In summary, this invention provides a method and terminal for systematically modulating inertial navigation system errors. Based on a dual-axis rotation system-level calibration method, it starts with the calibration principle, integrates various gyroscope errors to establish an error model to be calibrated, and constructs a decoupling method between calibration parameters. This allows each error to be decomposed and balanced individually during the calibration process. Finally, a calibration path is designed using a Kalman filter to establish the relationship between navigation output errors and inertial instrument error parameters. During the calibration path confirmation process, all calibration parameters, including accelerometer scaling factor error, gyroscope scaling factor error, gyroscope installation error, accelerometer installation error, accelerometer zero bias, and gyroscope zero bias, are considered. After obtaining the final calibration path, verification is performed, and only after successful verification is formal calibration carried out, ensuring the optimality of the final calibration path.

[0250] 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 for systematically modulating inertial navigation system errors, characterized in that, Including the following steps: S1. Construct a parameter calibration model; S2. Construct a decoupling method between calibration parameters; S3. Design a calibration path using a Kalman filter based on the decoupling method described above; S1 includes: S11. Establish the first error model of the gyroscope and the second error model of the accelerometer; S12. Construct a parameter calibration model based on the first error model and the second error model; Specifically, S1 is: Establish the first error model ; in, This indicates the drift error of the gyroscope. This represents the model error of the gyroscope. This represents the first-order Markov random process noise of the gyroscope. w Indicates Gaussian white noise; Establish the second error model ; in, This indicates the zero bias error of the accelerometer; This indicates the scale factor error of the accelerometer; This represents the installation error coefficient of the accelerometer; Indicates lever arm effect error; This indicates the output white noise of the accelerometer.

2. The method for systematically modulating inertial navigation system errors according to claim 1, characterized in that, S2 includes: The three sensitive axes of the rotating gyroscope are decoupled from the gyroscope scaling factor error and the gyroscope installation error.

3. The method for systematically modulating inertial navigation system errors according to claim 1, characterized in that, S2 includes: By placing the sensitive axes of the three gyroscopes in the inertial navigation system at two positions (east and west) or two positions (north and south), the zero bias error of the gyroscopes can be decoupled.

4. The method for systematically modulating inertial navigation system errors according to claim 1, characterized in that, S2 includes: By placing the sensitive axis of the inertial navigation system at two positions, pointing to the sky and pointing to the ground, the accelerometer scaling factor error and installation error are decoupled.

5. The method for systematically modulating inertial navigation system errors according to claim 1, characterized in that, S2 includes: By placing the sensitive axes of the three accelerometers in the inertial navigation system at two positions (east and west) or two positions (north and south), the zero bias error of the accelerometers can be decoupled.

6. The method for systematically modulating inertial navigation system errors according to claim 1, characterized in that, The state of the Kalman filter in S3 is: ； in, X 30 This represents a 30-dimensional Kalman filter. This represents the three-dimensional attitude error of the gyroscope or accelerometer. This indicates the velocity error of the gyroscope or the accelerometer. This indicates the position error of the gyroscope or the accelerometer. This indicates the calibration parameter error of the gyroscope. This indicates the calibration parameter error of the accelerometer.

7. The method for systematically modulating inertial navigation system errors according to claim 1, characterized in that, Following S3, it also includes; Verify the calibration path.

8. A terminal for systematically modulating inertial navigation system errors, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements a method for systematically modulating inertial navigation system errors as described in any one of claims 1-7.

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