Error modulation parameter selection method for dual-axis rotational inertial navigation based on improved annealing algorithm

Abstract

The present invention relates to a method for selecting error modulation parameters for a dual-axis rotating inertial navigation system based on an improved annealing algorithm, belonging to the field of inertial navigation technology. The method comprises the following steps: S1, constructing an error propagation equation for the dual-axis rotating inertial navigation system that takes into account the error modulation effect; S2, setting the indexing order, rotation speed, and rotation-stop time of the dual-axis rotating inertial navigation system; S3, performing error modulation on an actual prototype using the indexing order, rotation speed, and rotation-stop time to obtain a navigation result; comparing the navigation result of the actual prototype with a navigation information reference to obtain a navigation error output; S4, utilizing an LSTM algorithm to obtain inertial device error parameters in the error propagation equation; substituting the inertial device error parameters, navigation result, navigation error output, indexing order, rotation speed, and rotation-stop time into the error propagation equation to obtain a digital prototype; and S5, utilizing an improved simulated annealing algorithm to obtain optimal dual-axis rotating inertial navigation error modulation parameters. The present invention is time-saving and cost-effective.

Description

Technical Field

[0001] The invention belongs to the technical field of inertial navigation, and in particular relates to a method for selecting error modulation parameters of a dual-axis rotating inertial navigation system based on an improved annealing algorithm. Background Art

[0002] Rotating inertial navigation utilizes a rotational modulation strategy to suppress the errors of inertial devices within a cycle through rotation, thereby reducing the impact of errors on the navigation accuracy of the system. Currently, the mainstream rotational modulation technologies include single-axis rotational modulation technology and dual-axis rotational modulation technology. Single-axis rotating inertial navigation systems can only suppress partial errors in two directions, while the error in the other direction still propagates according to the original law. Dual-axis rotating inertial navigation systems can effectively suppress errors in all directions and are widely used in long-duration navigation scenarios. During the rotational modulation process of a dual-axis inertial navigation system, the rotation speed and the rotation-stop time are the most important parameters affecting the error modulation results.

[0003] At present, in the research of dual-axis rotating inertial navigation error modulation, the actual dual-axis rotating inertial navigation prototype is usually used for error modulation research, which has the problems of long time consumption and high cost. Summary of the Invention

[0004] In view of the deficiencies in the prior art, the object of the present invention is to provide a method for selecting error modulation parameters of a dual-axis rotational inertial navigation system based on an improved annealing algorithm, so as to solve or improve the defects in the prior art.

[0005] To achieve the above object, the present invention adopts the following technical solution: a method for selecting error modulation parameters of a dual-axis rotating inertial navigation system based on an improved annealing algorithm, comprising the following steps:

[0006] S1. Construct the error propagation equation of the dual-axis rotating inertial navigation system considering the error modulation effect;

[0007] S2. Set the rotation order, rotation speed and rotation and stop time of the dual-axis rotation inertial navigation system;

[0008] S3. Placing an actual prototype of the dual-axis rotary inertial navigation system on a table, performing error modulation on the prototype according to the rotation order, rotation speed, and rotation-stop time set in step S2, and obtaining a navigation result of the actual prototype; comparing the navigation result of the actual prototype with the navigation information reference to obtain a navigation error output of the actual prototype;

[0009] S4. Based on the error propagation equation constructed in step S1, the LSTM algorithm is used to obtain the inertial device error parameters in the error propagation equation. The obtained inertial device error parameters, the navigation result and navigation error output obtained in step S3, and the indexing order, rotation speed, and rotation-stop time set in step S2 are substituted into the error propagation equation constructed in step S1 to obtain a digital prototype of the dual-axis rotational inertial navigation system.

[0010] S5. Based on the digital prototype obtained in step S4, an improved simulated annealing algorithm is used to obtain optimal dual-axis rotational inertial guidance error modulation parameters.

[0011] Preferably, in step S1, the specific method of constructing the error propagation equation of the dual-axis rotating inertial navigation system considering the error modulation effect includes:

[0012] S11, constructing attitude error equation;

[0013] S12, constructing the velocity error equation;

[0014] S13. Construct a position error equation.

[0015] Preferably, in step S11, the specific method of constructing the posture error equation is:

[0016] The posture error equation is constructed as follows:

[0017]

[0018] Where, is φ n The derivative with respect to time, φ n =[φ E ,φ N ,φ U ] T ,φ E 、φ N 、φ U They are pitch attitude error, roll attitude error, and heading attitude error respectively; is the rotation angular rate error of the navigation system relative to the inertial system, is the angular velocity of the Earth's rotation relative to the inertial system, is the angular rate of rotation of the navigation system relative to the Earth, is the transformation matrix from the turntable coordinate system to the navigation coordinate system, Indicates the gyro measurement error under the navigation system;

[0019] in,

[0020] Where, is the angular velocity of the Earth relative to the inertial system, ω ie It represents the projection of the Earth's rotational angular velocity in the navigation system, L represents the local latitude, V N and V E Respectively represent the northward speed and eastward speed of the carrier in the geographic coordinate system, R m and R n They represent the radius of curvature of the Earth's meridian plane and the radius of curvature of the meridinomial plane respectively;

[0021] in,

[0022] Where, is the rotation angular rate error of the navigation system relative to the inertial system, is the angular rate error of the Earth's rotation relative to the inertial system, is the angular rate of rotation of the navigation system relative to the Earth;

[0023] in,

[0024] Where, is the rotation angular rate error of the Earth relative to the inertial system, ω ie represents the projection of the Earth's rotational angular velocity in the navigation system, L represents the local latitude, and δL represents the local latitude error; is the angular rate of rotation of the navigation system relative to the Earth, V N and V E Respectively represent the northward velocity and eastward velocity of the carrier in the geographic coordinate system, δV N and δV E They represent the north velocity error and east velocity error of the carrier in the geographic coordinate system, R m and R n They represent the radius of curvature of the Earth's meridian plane and the radius of curvature of the meridinomial plane respectively;

[0025] in,

[0026] Where, is the transformation matrix from the turntable coordinate system to the navigation coordinate system, is the transformation matrix from the turntable coordinate system to the carrier system, is the conversion matrix from the carrier system to the navigation system;

[0027] in,

[0028] Where, is the transformation matrix from the turntable coordinate system to the carrier system, ω is the rotation speed, t is the inertial navigation running time, t s is the transfer stop time;

[0029] in,

[0030] Where, is the conversion matrix from the carrier system to the navigation system, θ is the pitch angle, γ is the roll angle, and ψ is the heading angle;

[0031] in,

[0032] Where Sg is the gyro's scale error matrix, δG is the gyro's installation error matrix, is the actual angular rate input of the gyroscope, ε is the zero bias of the gyroscope, is the random drift of the gyroscope;

[0033] in,

[0034] Where S g is the gyro's scale error matrix, is the symmetry scaling error of the X-gyro, is the asymmetric scaling error of the X-gyro, is the symmetry scaling error of the Y gyro, is the asymmetric scaling error of the Y gyro, is the symmetry scaling error of the Z gyro, is the asymmetric scaling error of the Z gyro, is the actual angular rate input of the X gyro, is the actual angular rate input of the Y gyroscope, is the actual angular rate input of the Z gyroscope; sign(·) is the sign function, expressed as

[0035] in,

[0036] Where δG is the gyro installation error matrix, is the installation error of the Y gyro and the Z gyro, is the installation error of the Z gyro and the Y gyro, is the installation error between the Z gyro and the X gyro;

[0037] in,

[0038] Where, is the actual angular rate input of the gyroscope, is the actual angular rate input of the X gyro, is the actual angular rate input of the Y gyroscope, The actual angular rate input of the Z gyro;

[0039] Where, ε=[ε x ,ε y ,ε z ] T ;

[0040] Where ε is the gyro bias, ε x is the zero bias of the X gyro, ε y is the zero bias of the Y gyro, ε z is the zero bias of the Z gyro;

[0041] in,

[0042] Where, is the random drift of the gyroscope, ω dx is the random drift of the X gyro, ω dy is the random drift of the Y gyro, ω dz is the random drift of the Z gyro.

[0043] Preferably, in step S12, the specific method of constructing the speed error equation is:

[0044] The velocity error equation is constructed as follows:

[0045]

[0046] Where, δv n The derivative with respect to time, δv n is the velocity error, v n is the speed, f n is the specific force measured by the accelerometer; φ n =[φ E ,φ N ,φ U ] T ,φ E ,φ N ,φ U They are pitch attitude error, roll attitude error, and heading attitude error respectively; is the transformation matrix from the turntable coordinate system to the navigation coordinate system, is the accelerometer measurement error, is the angular velocity of the Earth's rotation relative to the inertial system, is the angular rate of rotation of the navigation system relative to the Earth, is the angular rate error of the Earth's rotation relative to the inertial system, is the angular rate of rotation of the navigation system relative to the earth, δg is the gravitational acceleration vector error;

[0047] in,

[0048] Where, is the accelerometer measurement error, S a is the scale factor error matrix of the accelerometer, δA is the installation error matrix of the accelerometer, is the actual acceleration input of the accelerometer, is the zero bias of the accelerometer, is the random drift of the accelerometer;

[0049] in,

[0050] Where S a is the scale factor error matrix of the accelerometer, is the symmetry scale error of the X accelerometer, is the asymmetric scaling error of the X accelerometer, is the symmetry scaling error of the Y accelerometer, is the asymmetric scaling error of the Y accelerometer, is the symmetry scaling error of the Z accelerometer, is the asymmetric scaling error of the Z accelerometer, is the actual acceleration input of the X accelerometer, is the actual acceleration input of the Y accelerometer, is the actual acceleration input of the Z accelerometer; sign(·) is the sign function, expressed as

[0051] in,

[0052] Where δA is the installation error matrix of the accelerometer, η xz is the installation error of the X accelerometer and the Z accelerometer, η xy is the installation error of the X accelerometer and the Y accelerometer, η yz is the installation error between the Y accelerometer and the Z accelerometer, η yx is the installation error between the Y accelerometer and the X accelerometer, η zy is the installation error between the Z accelerometer and the Y accelerometer, η zx is the installation error of the Z accelerometer and the X accelerometer;

[0053] in,

[0054] Where, is the zero bias of the accelerometer, is the zero bias of the X accelerometer, is the zero bias of the Y accelerometer, is the zero bias of the Z accelerometer;

[0055] in,

[0056] Where, is the random drift of the accelerometer, f dx is the random drift of the X accelerometer, f dy is the random drift of the Y accelerometer, f dz is the random drift of the Z accelerometer.

[0057] Preferably, in step S13, the specific method of constructing the position error equation is:

[0058] The position error equation is constructed as follows:

[0059]

[0060] Where, is the derivative of δL with respect to time, is the derivative of δλ with respect to time, is the derivative of δh with respect to time, L is latitude, λ is longitude, h is height, R is the average radius of the earth, v N is the north velocity, v E is the eastward velocity, δv N is the north velocity error, δv E is the eastward velocity error, δv U is the celestial velocity error, δψ is the heading error, δL is the latitude error, δλ is the longitude error, and δh is the height error.

[0061] Preferably, in step S2, the specific method of setting the indexing order of the dual-axis rotary inertial navigation is:

[0062] Set multiple sequences, each sequence rotates 180° forward or reverse around the celestial direction or east direction in the coordinate system at a rotation speed of ω. The directions or rotations of two adjacent sequences are different, with t s The stop time is still;

[0063] The entire sequence is considered a rotation cycle, and the rotation cycle is repeated.

[0064] Preferably, in step S2, the indexing order of the dual-axis rotary inertial navigation is set as:

[0065] Order 1: Rotate 180° around the sky in the positive direction with ω as the rotation speed, and t s The stop time is still;

[0066] Order 2: Rotate 180° in the east direction with ω as the rotation speed, and t s The stop time is still;

[0067] Order 3, with the rotation speed ω, reverse 180° around the celestial direction, with t s The stop time is still;

[0068] Order 4: Rotate 180° around the east direction with ω as the rotation speed, and t s The stop time is still;

[0069] Order 5, rotate 180° in the east direction with ω as the rotation speed, and t s The stop time is still;

[0070] Order 6: Rotate 180° around the celestial direction at a speed of ω, and then s The stop time is still;

[0071] Order 7, rotate 180° in the east direction with ω as the rotation speed, and t s The stop time is still;

[0072] Order 8, rotate 180° around the sky in the positive direction with ω as the rotation speed, and t s The stop time is still;

[0073] Order 9, with the rotation speed ω, reverse 180° around the celestial direction, with t s The stop time is still;

[0074] Order 10, with the rotation speed ω, reverse 180° around the east direction, with t s The stop time is still;

[0075] Order 11, rotate 180° around the celestial direction at a speed of ω, and t s The stop time is still;

[0076] Order 12, rotate 180° in the east direction with ω as the rotation speed, and t s The stop time is still;

[0077] Order 13, rotate 180° in the east direction with ω as the rotation speed, and t s The stop time is still;

[0078] Order 14, rotate 180° around the celestial direction at a speed of ω, and t s The stop time is still;

[0079] Order 15, with the rotation speed ω, reverse 180° around the east direction, with t s The stop time is still;

[0080] Order 16, with the rotation speed ω, reverse 180° around the celestial direction, with t s The stop time is still;

[0081] The sequence 1 to sequence 16 constitutes a rotation cycle, and the rotation cycle is repeated.

[0082] Preferably, in step S2, the rotation speed of the dual-axis rotating inertial navigation system is set to 5° / s.

[0083] Preferably, in step S2, the rotation and stop time of the dual-axis rotating inertial navigation system is set to 2s.

[0084] Preferably, in step S3, the navigation information benchmark includes a benchmark for attitude navigation information, a benchmark for speed navigation information and a benchmark for position navigation information, the benchmark for attitude navigation information is the installation reference plane of the actual prototype, the benchmark for speed navigation information is 0, and the benchmark for position navigation information is the local geographic coordinates.

[0085] Preferably, in step S4, the inertial device error parameters include the gyro scale error matrix S g , gyro installation error matrix δG, gyro zero bias ε, gyro random drift Accelerometer scale factor error matrix S a , accelerometer installation error matrix δA, accelerometer zero bias Random drift of the accelerometer

[0086] Preferably, in step S5, the specific method of obtaining the optimal dual-axis rotational inertial guidance error modulation parameters by using an improved simulated annealing algorithm based on the digital prototype obtained in step S4 is:

[0087] Set the cost function as the navigation error of the digital prototype, set the solution parameters as the rotation speed and the rotation-stop time, set the upper and lower limits of the solution parameters, and use the improved simulated annealing algorithm to obtain the optimal solution parameters, that is, the optimal rotation speed and rotation-stop time.

[0088] Preferably, the lower limit of the rotation speed is 1° / s, and the upper limit is 20° / s.

[0089] Preferably, the lower limit of the transfer-stop time is 1 s, and the upper limit is 10 s.

[0090] Compared with the prior art, the present invention has the following beneficial effects: a dual-axis rotational inertial navigation error modulation parameter selection method based on a digital prototype and an improved annealing algorithm of the present invention first constructs an error propagation equation of the dual-axis rotational inertial navigation considering the error modulation effect, then sets the indexing order, rotation speed and rotation-stop time of the dual-axis rotational inertial navigation, and then obtains navigation results and navigation error output through an actual prototype of the dual-axis rotational inertial navigation. Then, an LSTM algorithm is used to obtain the inertial device error parameters in the error propagation equation, thereby obtaining a digital prototype of the dual-axis rotational inertial navigation, and finally, based on the digital prototype and the improved annealing algorithm, the optimal dual-axis rotational inertial navigation error modulation parameters are obtained. The method has the advantages of simple operation, short time consumption, low cost, high navigation accuracy and good practicality, and solves the problem that in the current dual-axis rotational inertial navigation error modulation research, the actual prototype of the dual-axis rotational inertial navigation is usually used for error modulation research, which is time-consuming and costly. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, for ordinary technicians in this field, other drawings can be obtained based on the drawings in the following description without any creative work.

[0092] Figure 1 The figure is a flow chart of a method for selecting error modulation parameters of a dual-axis rotational inertial navigation system based on an improved annealing algorithm according to an embodiment of the present invention. DETAILED DESCRIPTION

[0093] In order to make the purpose, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with the drawings in the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. In order to make the above-mentioned features and advantages of the present invention more obvious and easy to understand, the following embodiments are specifically cited and described in detail with reference to the drawings.

[0094] like Figure 1 As shown, an embodiment of the present invention provides a method for selecting error modulation parameters of a dual-axis rotating inertial navigation system based on an improved annealing algorithm, comprising the following steps:

[0095] S1. Construct the error propagation equation of the dual-axis rotating inertial navigation system considering the error modulation effect;

[0096] S2. Set the rotation order, rotation speed and rotation and stop time of the dual-axis rotation inertial navigation system;

[0097] S3. Placing an actual prototype of the dual-axis rotary inertial navigation system on a table, performing error modulation on the prototype according to the rotation order, rotation speed, and rotation-stop time set in step S2, and obtaining a navigation result of the actual prototype; comparing the navigation result of the actual prototype with the navigation information reference to obtain a navigation error output of the actual prototype;

[0098] S4. Based on the error propagation equation constructed in step S1, the LSTM algorithm is used to obtain the inertial device error parameters in the error propagation equation. The obtained inertial device error parameters, the navigation result and navigation error output obtained in step S3, and the indexing order, rotation speed, and rotation-stop time set in step S2 are substituted into the error propagation equation constructed in step S1 to obtain a digital prototype of the dual-axis rotational inertial navigation system.

[0099] S5. Based on the digital prototype obtained in step S4, an improved simulated annealing algorithm is used to obtain optimal dual-axis rotational inertial guidance error modulation parameters.

[0100] In this embodiment, in step S1, the specific method of constructing the error propagation equation of the dual-axis rotating inertial navigation system considering the error modulation effect includes:

[0101] S11, constructing attitude error equation;

[0102] S12, constructing the velocity error equation;

[0103] S13. Construct a position error equation.

[0104] In this embodiment, in step S11, the specific method of constructing the posture error equation is:

[0105] The posture error equation is constructed as follows:

[0106]

[0107] Where, is φ n The derivative with respect to time, φ n =[φ E ,φ N ,φ U ] T ,φ E 、φ N 、φ U They are pitch attitude error, roll attitude error, and heading attitude error respectively; is the rotation angular rate error of the navigation system relative to the inertial system, is the angular velocity of the Earth's rotation relative to the inertial system, is the angular rate of rotation of the navigation system relative to the Earth, is the transformation matrix from the turntable coordinate system to the navigation coordinate system, Indicates the gyro measurement error under the navigation system;

[0108] in,

[0109] Where, is the angular velocity of the Earth relative to the inertial system, ω ie It represents the projection of the Earth's rotational angular velocity in the navigation system, L represents the local latitude, V N and V E Respectively represent the northward speed and eastward speed of the carrier in the geographic coordinate system, R m and R n They represent the radius of curvature of the Earth's meridian plane and the radius of curvature of the meridinomial plane respectively;

[0110] in,

[0111] Where, is the rotation angular rate error of the navigation system relative to the inertial system, is the angular rate error of the Earth's rotation relative to the inertial system, is the angular rate of rotation of the navigation system relative to the Earth;

[0112] in,

[0113] Where, is the rotation angular rate error of the Earth relative to the inertial system, ω ie represents the projection of the Earth's rotational angular velocity in the navigation system, L represents the local latitude, and δL represents the local latitude error; is the angular rate of rotation of the navigation system relative to the Earth, V N and V E Respectively represent the northward velocity and eastward velocity of the carrier in the geographic coordinate system, δV N and δV E They represent the north velocity error and east velocity error of the carrier in the geographic coordinate system, R m and R n They represent the radius of curvature of the Earth's meridian plane and the radius of curvature of the meridinomial plane respectively;

[0114] in,

[0115] Where, is the transformation matrix from the turntable coordinate system to the navigation coordinate system, is the transformation matrix from the turntable coordinate system to the carrier system, is the conversion matrix from the carrier system to the navigation system;

[0116] in,

[0117] Where, is the transformation matrix from the turntable coordinate system to the carrier system, ω is the rotation speed, t is the inertial navigation running time, t s is the transfer stop time;

[0118] in,

[0119] Where, is the conversion matrix from the carrier system to the navigation system, θ is the pitch angle, γ is the roll angle, and ψ is the heading angle;

[0120] in,

[0121] Where S g is the gyro's scale error matrix, δG is the gyro's installation error matrix, is the actual angular rate input of the gyroscope, ε is the zero bias of the gyroscope, is the random drift of the gyroscope;

[0122] in,

[0123] Where S g is the gyro's scale error matrix, is the symmetry scaling error of the X-gyro, is the asymmetric scaling error of the X-gyro, is the symmetry scaling error of the Y gyro, is the asymmetric scaling error of the Y gyro, is the symmetry scaling error of the Z gyro, is the asymmetric scaling error of the Z gyro, is the actual angular rate input of the X gyro, is the actual angular rate input of the Y gyroscope, is the actual angular rate input of the Z gyroscope; sign(·) is the sign function, expressed as

[0124] in,

[0125] Where δG is the gyro installation error matrix, is the installation error of the Y gyro and the Z gyro, is the installation error of the Z gyro and the Y gyro, is the installation error between the Z gyro and the X gyro;

[0126] in,

[0127] Where, is the actual angular rate input of the gyroscope, is the actual angular rate input of the X gyro, is the actual angular rate input of the Y gyroscope, The actual angular rate input of the Z gyro;

[0128] Where, ε=[ε x ,ε y ,ε z ] T ;

[0129] Where ε is the gyro bias, ε x is the zero bias of the X gyro, ε y is the zero bias of the Y gyro, ε z is the zero bias of the Z gyro;

[0130] in,

[0131] Where, is the random drift of the gyroscope, ωdx is the random drift of the X gyro, ω dy is the random drift of the Y gyro, ω dz is the random drift of the Z gyro.

[0132] In this embodiment, in step S12, the specific method of constructing the speed error equation is:

[0133] The velocity error equation is constructed as follows:

[0134]

[0135] Where, δv n The derivative with respect to time, δv n is the velocity error, v n is the speed, f n is the specific force measured by the accelerometer; φ n =[φ E ,φ N ,φ U ] T ,φ E ,φ N ,φ U They are pitch attitude error, roll attitude error, and heading attitude error respectively; is the transformation matrix from the turntable coordinate system to the navigation coordinate system, is the accelerometer measurement error, is the angular velocity of the Earth's rotation relative to the inertial system, is the angular rate of rotation of the navigation system relative to the Earth, is the angular rate error of the Earth's rotation relative to the inertial system, is the angular rate of rotation of the navigation system relative to the earth, δg is the gravitational acceleration vector error;

[0136] in,

[0137] Where, is the accelerometer measurement error, S a is the scale factor error matrix of the accelerometer, δA is the installation error matrix of the accelerometer, is the actual acceleration input of the accelerometer, is the zero bias of the accelerometer, is the random drift of the accelerometer;

[0138] in,

[0139] Where S a is the scale factor error matrix of the accelerometer, is the symmetry scale error of the X accelerometer, is the asymmetric scaling error of the X accelerometer, is the symmetry scaling error of the Y accelerometer, is the asymmetric scaling error of the Y accelerometer, is the symmetry scaling error of the Z accelerometer, is the asymmetric scaling error of the Z accelerometer, is the actual acceleration input of the X accelerometer, is the actual acceleration input of the Y accelerometer, is the actual acceleration input of the Z accelerometer; sign(·) is the sign function, expressed as

[0140] in,

[0141] Where δA is the installation error matrix of the accelerometer, η xz is the installation error of the X accelerometer and the Z accelerometer, η xy is the installation error of the X accelerometer and the Y accelerometer, η yz is the installation error between the Y accelerometer and the Z accelerometer, η yx is the installation error between the Y accelerometer and the X accelerometer, η zy is the installation error between the Z accelerometer and the Y accelerometer, η zx is the installation error of the Z accelerometer and the X accelerometer;

[0142] in,

[0143] Where, is the zero bias of the accelerometer, is the zero bias of the X accelerometer, is the zero bias of the Y accelerometer, is the zero bias of the Z accelerometer;

[0144] in,

[0145] Where, is the random drift of the accelerometer, f dx is the random drift of the X accelerometer, f dy is the random drift of the Y accelerometer, f dz is the random drift of the Z accelerometer.

[0146] In this embodiment, in step S13, the specific method of constructing the position error equation is:

[0147] The position error equation is constructed as follows:

[0148]

[0149] Where, is the derivative of δL with respect to time, is the derivative of δλ with respect to time, is the derivative of δh with respect to time, L is latitude, λ is longitude, h is height, R is the average radius of the earth, v N is the north velocity, v E is the eastward velocity, δv N is the north velocity error, δv E is the eastward velocity error, δv U is the celestial velocity error, δψ is the heading error, δL is the latitude error, δλ is the longitude error, and δh is the height error.

[0150] In this embodiment, in step S2, the specific method of setting the indexing order of the dual-axis rotating inertial navigation is:

[0151] Set multiple sequences, each sequence rotates 180° forward or reverse around the celestial direction or east direction in the coordinate system at a rotation speed of ω. The directions or rotations of two adjacent sequences are different, with t s The stop time is still;

[0152] The entire sequence is considered a rotation cycle, and the rotation cycle is repeated.

[0153] In this embodiment, in step S2, the indexing order of the dual-axis rotating inertial navigation is preferably, but not limited to, set to:

[0154] Order 1: Rotate 180° around the sky in the positive direction with ω as the rotation speed, and t s The stop time is still;

[0155] Order 2: Rotate 180° in the east direction with ω as the rotation speed, and t s The stop time is still;

[0156] Order 3, with the rotation speed ω, reverse 180° around the celestial direction, with t s The stop time is still;

[0157] Order 4: Rotate 180° around the east direction with ω as the rotation speed, and t s The stop time is still;

[0158] Order 5, rotate 180° in the east direction with ω as the rotation speed, and t s The stop time is still;

[0159] Order 6: Rotate 180° around the celestial direction at a speed of ω, and then s The stop time is still;

[0160] Order 7, rotate 180° in the east direction with ω as the rotation speed, and t s The stop time is still;

[0161] Order 8, rotate 180° around the sky in the positive direction with ω as the rotation speed, and t s The stop time is still;

[0162] Order 9, with the rotation speed ω, reverse 180° around the celestial direction, with t s The stop time is still;

[0163] Order 10, with the rotation speed ω, reverse 180° around the east direction, with t s The stop time is still;

[0164] Order 11, rotate 180° around the celestial direction at a speed of ω, and t s The stop time is still;

[0165] Order 12, rotate 180° in the east direction with ω as the rotation speed, and t s The stop time is still;

[0166] Order 13, rotate 180° in the east direction with ω as the rotation speed, and t s The stop time is still;

[0167] Order 14, rotate 180° around the celestial direction at a speed of ω, and t s The stop time is still;

[0168] Order 15, with the rotation speed ω, reverse 180° around the east direction, with t s The stop time is still;

[0169] Order 16, with the rotation speed ω, reverse 180° around the celestial direction, with t s The stop time is still;

[0170] The sequence 1 to sequence 16 constitutes a rotation cycle, and the rotation cycle is repeated.

[0171] In this embodiment, in step S2, the rotation speed of the dual-axis rotating inertial navigation system is preferably but not limited to being set to 5° / s, and the rotation and stop time of the dual-axis rotating inertial navigation system is preferably but not limited to being set to 2s.

[0172] In this embodiment, in step S3, the navigation information reference includes a reference for attitude navigation information, a reference for speed navigation information, and a reference for position navigation information. The reference for attitude navigation information is the installation reference plane of the actual prototype. Since the actual prototype of the dual-axis rotating inertial navigation system is stationary, the reference for speed navigation information is 0. The reference for position navigation information is the local geographic coordinates.

[0173] In this embodiment, in step S4, the inertial device error parameters include the gyro scale error matrix S g , gyro installation error matrix δG, gyro zero bias ε, gyro random drift Accelerometer scale factor error matrix S a , accelerometer installation error matrix δA, accelerometer zero bias Random drift of the accelerometer

[0174] In this embodiment, in step S4, the LSTM algorithm is a long short-term memory network neural network algorithm, which belongs to the existing technology and will not be described in detail here.

[0175] In this embodiment, in step S5, the specific method of obtaining the optimal dual-axis rotational inertial guidance error modulation parameters using the improved simulated annealing algorithm based on the digital prototype obtained in step S4 is as follows:

[0176] Set the cost function as the navigation error of the digital prototype, set the solution parameters as the rotation speed and the rotation-stop time, set the upper and lower limits of the solution parameters, and use the improved simulated annealing algorithm to obtain the optimal solution parameters, that is, the optimal rotation speed and rotation-stop time.

[0177] In this embodiment, the lower limit of the rotation speed is preferably but not limited to 1° / s, and the upper limit is preferably but not limited to 20° / s; the lower limit of the rotation-stop time is preferably but not limited to 1s, and the upper limit is preferably but not limited to 10s.

[0178] In this embodiment, in step S5, the improved simulated annealing algorithm belongs to the prior art and will not be described in detail here.

[0179] The method of the present invention first constructs an error propagation equation of a dual-axis rotational inertial navigation system considering the error modulation effect, then sets the indexing order, rotation speed and rotation-stop time of the dual-axis rotational inertial navigation system, then obtains navigation results and navigation error output through an actual prototype of the dual-axis rotational inertial navigation system, then uses an LSTM algorithm to obtain the inertial device error parameters in the error propagation equation, thereby obtaining a digital prototype of the dual-axis rotational inertial navigation system, and finally obtains the optimal dual-axis rotational inertial navigation error modulation parameters based on the digital prototype and an improved annealing algorithm. The method has the advantages of simple operation, short time consumption, low cost, high navigation accuracy and good practicality, and solves the problems of long time consumption and high cost in current dual-axis rotational inertial navigation error modulation research, which usually uses an actual prototype of the dual-axis rotational inertial navigation system for error modulation research.

[0180] Parts of the present invention that are not disclosed in detail belong to the common knowledge in the art.

[0181] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for selecting error modulation parameters of a dual-axis rotating inertial navigation system based on an improved annealing algorithm, characterized in that: The steps include: S1. Construct the error propagation equation of the dual-axis rotating inertial navigation system considering the error modulation effect; S2. Set the rotation order, rotation speed and rotation and stop time of the dual-axis rotation inertial navigation system; S3. Placing an actual prototype of the dual-axis rotary inertial navigation system on a table, performing error modulation on the prototype according to the rotation order, rotation speed, and rotation-stop time set in step S2, and obtaining a navigation result of the actual prototype; comparing the navigation result of the actual prototype with the navigation information reference to obtain a navigation error output of the actual prototype; S4. Based on the error propagation equation constructed in step S1, the LSTM algorithm is used to obtain the inertial device error parameters in the error propagation equation. The obtained inertial device error parameters, the navigation result and navigation error output obtained in step S3, and the indexing order, rotation speed, and rotation-stop time set in step S2 are substituted into the error propagation equation constructed in step S1 to obtain a digital prototype of the dual-axis rotational inertial navigation system. S5. Based on the digital prototype obtained in step S4, an improved simulated annealing algorithm is used to obtain optimal dual-axis rotational inertial guidance error modulation parameters.

2. The method for selecting error modulation parameters of a dual-axis rotating inertial navigation system based on an improved annealing algorithm according to claim 1, wherein: In step S1, the specific method of constructing the error propagation equation of the dual-axis rotating inertial navigation system considering the error modulation effect includes: S11, constructing attitude error equation; S12, constructing the velocity error equation; S13. Construct a position error equation.

3. The method for selecting error modulation parameters of a dual-axis rotating inertial navigation system based on an improved annealing algorithm according to claim 2, wherein: In step S11, the specific method of constructing the posture error equation is: The posture error equation is constructed as follows: Where, is φ n The derivative with respect to time, φ n =[φ E ,φ N ,φ U ] T ,φ E 、φ N 、φ U They are pitch attitude error, roll attitude error, and heading attitude error respectively; is the rotation angular rate error of the navigation system relative to the inertial system, is the angular velocity of the Earth's rotation relative to the inertial system, is the angular rate of rotation of the navigation system relative to the Earth, is the transformation matrix from the turntable coordinate system to the navigation coordinate system, Indicates the gyro measurement error under the navigation system; in, Where, is the angular velocity of the Earth relative to the inertial system, ω ie It represents the projection of the Earth's rotational angular velocity in the navigation system, L represents the local latitude, V N and V E Respectively represent the northward speed and eastward speed of the carrier in the geographic coordinate system, R m and R n They represent the radius of curvature of the Earth's meridian plane and the radius of curvature of the meridinomial plane respectively; in, Where, is the rotation angular rate error of the navigation system relative to the inertial system, is the angular rate error of the Earth's rotation relative to the inertial system, is the angular rate of rotation of the navigation system relative to the Earth; in, Where, is the rotation angular rate error of the Earth relative to the inertial system, ω ie represents the projection of the Earth's rotational angular velocity in the navigation system, L represents the local latitude, and δL represents the local latitude error; is the angular rate of rotation of the navigation system relative to the Earth, V N and V E Respectively represent the northward velocity and eastward velocity of the carrier in the geographic coordinate system, δV N and δV E They represent the north velocity error and east velocity error of the carrier in the geographic coordinate system, R m and R n They represent the radius of curvature of the Earth's meridian plane and the radius of curvature of the meridinomial plane respectively; in, Where, is the transformation matrix from the turntable coordinate system to the navigation coordinate system, is the transformation matrix from the turntable coordinate system to the carrier system, is the conversion matrix from the carrier system to the navigation system; in, Where, is the transformation matrix from the turntable coordinate system to the carrier system, ω is the rotation speed, t is the inertial navigation running time, t s is the transfer stop time; in, Where, is the conversion matrix from the carrier system to the navigation system, θ is the pitch angle, γ is the roll angle, and ψ is the heading angle; in, Where S g is the gyro's scale error matrix, δG is the gyro's installation error matrix, is the actual angular rate input of the gyroscope, ε is the zero bias of the gyroscope, is the random drift of the gyroscope; in, Where S g is the gyro's scale error matrix, is the symmetry scaling error of the X-gyro, is the asymmetric scaling error of the X-gyro, is the symmetry scaling error of the Y gyro, is the asymmetric scaling error of the Y gyro, is the symmetry scaling error of the Z gyro, is the asymmetric scaling error of the Z gyro, is the actual angular rate input of the X gyro, is the actual angular rate input of the Y gyroscope, is the actual angular rate input of the Z gyroscope; sign(·) is the sign function, expressed as in, Where δG is the gyro installation error matrix, is the installation error of the Y gyro and the Z gyro, is the installation error of the Z gyro and the Y gyro, is the installation error between the Z gyro and the X gyro; in, Where, is the actual angular rate input of the gyroscope, is the actual angular rate input of the X gyro, is the actual angular rate input of the Y gyroscope, The actual angular rate input of the Z gyro; Where, ε = [ε x ,he y ,he z ] T ; Where ε is the gyro bias, ε x is the zero bias of the X gyro, ε y is the zero bias of the Y gyro, ε z is the zero bias of the Z gyro; where, Where, is the random drift of the gyroscope, ω dx is the random drift of the X gyro, ω dy is the random drift of the Y gyro, ω dz is the random drift of the Z gyro.

4. The method for selecting error modulation parameters of a dual-axis rotating inertial navigation system based on an improved annealing algorithm according to claim 2, wherein: In step S12, the specific method of constructing the speed error equation is: The velocity error equation is constructed as follows: Where, δv n The derivative with respect to time, δv n is the velocity error, v n is the speed, f n is the specific force measured by the accelerometer; φ n =[φ E ,φ N ,φ U ] T ,φ E ,φ N ,φ U They are pitch attitude error, roll attitude error, and heading attitude error respectively; is the transformation matrix from the turntable coordinate system to the navigation coordinate system, is the accelerometer measurement error, is the angular velocity of the Earth's rotation relative to the inertial system, is the angular rate of rotation of the navigation system relative to the Earth, is the angular rate error of the Earth's rotation relative to the inertial system, is the angular rate of rotation of the navigation system relative to the earth, δg is the gravitational acceleration vector error; in, Where, is the accelerometer measurement error, S a is the scale factor error matrix of the accelerometer, δA is the installation error matrix of the accelerometer, is the actual acceleration input of the accelerometer, is the zero bias of the accelerometer, is the random drift of the accelerometer; in, Where S a is the scale factor error matrix of the accelerometer, is the symmetry scaling error of the X accelerometer, is the asymmetric scaling error of the X accelerometer, is the symmetry scaling error of the Y accelerometer, is the asymmetric scaling error of the Y accelerometer, is the symmetry scaling error of the Z accelerometer, is the asymmetric scaling error of the Z accelerometer, is the actual acceleration input of the X accelerometer, is the actual acceleration input of the Y accelerometer, is the actual acceleration input of the Z accelerometer; sign(·) is the sign function, expressed as in, Where δA is the installation error matrix of the accelerometer, η xz is the installation error of the X accelerometer and the Z accelerometer, η xy is the installation error of the X accelerometer and the Y accelerometer, η yz is the installation error between the Y accelerometer and the Z accelerometer, η yx is the installation error between the Y accelerometer and the X accelerometer, η zy is the installation error between the Z accelerometer and the Y accelerometer, η zx is the installation error of the Z accelerometer and the X accelerometer; in, Where, is the zero bias of the accelerometer, is the zero bias of the X accelerometer, is the zero bias of the Y accelerometer, is the zero bias of the Z accelerometer; in, Where, is the random drift of the accelerometer, f dx is the random drift of the X accelerometer, f dy is the random drift of the Y accelerometer, f dz is the random drift of the Z accelerometer.

5. The method for selecting error modulation parameters of a dual-axis rotating inertial navigation system based on an improved annealing algorithm according to claim 2, wherein: In step S13, the specific method of constructing the position error equation is: The position error equation is constructed as follows: Where, is the derivative of δL with respect to time, is the derivative of δλ with respect to time, is the derivative of δh with respect to time, L is latitude, λ is longitude, h is height, R is the average radius of the earth, v N is the north velocity, v E is the eastward velocity, δv N is the north velocity error, δv E is the eastward velocity error, δv U is the celestial velocity error, δψ is the heading error, δL is the latitude error, δλ is the longitude error, and δh is the height error.

6. The method for selecting error modulation parameters of a dual-axis rotating inertial navigation system based on an improved annealing algorithm according to claim 1, wherein: In step S2, the specific method of setting the indexing order of the dual-axis rotating inertial navigation is: Set multiple sequences, each sequence rotates 180° forward or reverse around the celestial direction or east direction in the coordinate system at a rotation speed of ω. The directions or rotations of two adjacent sequences are different, with t s The stop time is still; The entire sequence is considered a rotation cycle, and the rotation cycle is repeated.

7. The method for selecting error modulation parameters of a dual-axis rotating inertial navigation system based on an improved annealing algorithm according to claim 1, wherein: In step S2, the rotation speed of the dual-axis rotating inertial navigation system is set to 5° / s, and the rotation and stop time of the dual-axis rotating inertial navigation system is set to 2s.

8. The method for selecting error modulation parameters of a dual-axis rotating inertial navigation system based on an improved annealing algorithm according to claim 1, wherein: In step S3, the navigation information reference includes a reference for attitude navigation information, a reference for speed navigation information, and a reference for position navigation information. The reference for attitude navigation information is the installation reference plane of the actual prototype, the reference for speed navigation information is 0, and the reference for position navigation information is the local geographic coordinates.

9. The method for selecting error modulation parameters of a dual-axis rotating inertial navigation system based on an improved annealing algorithm according to claim 1, wherein: In step S4, the inertial device error parameters include the gyro scale error matrix S g , gyro installation error matrix δG, gyro zero bias ε, gyro random drift Accelerometer scale factor error matrix S a , accelerometer installation error matrix δA, accelerometer zero bias Random drift of the accelerometer 10. The method for selecting error modulation parameters of a dual-axis rotating inertial navigation system based on an improved annealing algorithm according to claim 1, wherein: In step S5, the specific method of obtaining the optimal dual-axis rotation inertial guidance error modulation parameters by using the improved simulated annealing algorithm based on the digital prototype obtained in step S4 is as follows: The cost function is set as the navigation error of the digital prototype, the solution parameters are set as the rotation speed and the rotation-stop time, the upper and lower limits of the solution parameters are set, and the improved simulated annealing algorithm is used to obtain the optimal solution parameters, that is, the optimal rotation speed and rotation-stop time.

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