A self-alignment method for an inertial navigation system combining multi-turn rotation and stopping

Abstract

The present invention discloses a self-alignment method for an inertial navigation system that combines multiple rotations and stops. Specifically, the system is placed on a stable platform, recorded as the first position, with the x, y, and z axes basically pointing to the east, north, and sky, and remains stationary at the initial first position for t1 time; the internal motor rotates 180° in the forward direction to the second position, consuming time t2, and then remains stationary for t3 time; the internal motor rotates 180° in the forward direction to the first position again, consuming time t4, and then remains stationary for t5 time; the internal motor rotates 180° in the reverse direction to the second position, consuming time t6, and then remains stationary for t7 time; the internal motor rotates 180° in the reverse direction to the first position, consuming time t8; repeat the above process n times, establish an alignment filter model, select the ratio of rotation and stop time and rotation angular velocity, and improve the azimuth alignment accuracy. The method provided by the present invention can effectively improve the azimuth alignment accuracy.

Description

Technical Field

[0001] The invention belongs to the technical field of inertial navigation, and in particular relates to a self-alignment method of an inertial navigation system combining multi-turn rotation and stopping. Background Art

[0002] As an autonomous navigation system, inertial navigation can covertly and continuously provide three-dimensional positioning and orientation information in all weather conditions, making it a crucial option in the navigation field. Before entering navigation mode, inertial navigation systems require initial alignment to determine the initial attitude. The accuracy of this initial alignment directly determines the navigation accuracy of the system. Rotary navigation systems, which offset the constant errors of inertial measurement units through periodic rotation, have been a revolutionary development in recent years.

[0003] Fiber-optic gyroscopes (FOGs) are widely used in rotational inertial navigation systems due to their small size, cost-effectiveness, and high precision. However, high-precision optical gyros often increase the size and weight of the entire system. Therefore, to save size and weight, nested inertial navigation systems (INS) have been developed. These systems employ two medium-diameter, medium-precision FOGs (FOGs) nested orthogonally within the fiber ring of a large-diameter, high-precision FOG, reducing system size and weight. However, due to the different horizontal accuracies of the two gyros, commonly used rotational alignment schemes simply utilize information from both gyros. Mixing the measurements of medium- and high-precision gyros reduces the system's ultimate alignment accuracy. While dual-position alignment schemes can utilize all high-precision gyro measurements for alignment, they inevitably introduce equivalent eastward drift, impacting heading alignment accuracy. Therefore, it is necessary to investigate alignment schemes for inconsistent horizontal gyro accuracies. While these schemes can modulate both the constant and slow-varying drifts of the horizontal gyros, they can also improve the utilization of precision measurement information, maximize the performance of the high-precision gyros, and enhance alignment accuracy. Summary of the Invention

[0004] The present invention proposes a self-alignment method for an inertial navigation system that combines multiple rotations and stops. The method can solve the problem that the alignment accuracy is affected by the low-precision gyroscope when the accuracies of two horizontal gyroscopes in the inertial navigation system are inconsistent, thereby giving full play to the performance of the high-precision gyroscope and greatly improving the azimuth alignment accuracy.

[0005] The present invention is achieved through the following method scheme:

[0006] The inertial navigation system self-alignment method combining multi-turn rotation and stopping includes the following steps:

[0007] Step 1: The inertial navigation system is placed on a stable platform, which is recorded as the first position. The x, y, and z axes basically point to the east, north, and sky, and remain stationary at the initial first position for t1 time.

[0008] Step 2: The inner motor rotates 180° in the forward direction to the second position, which takes time t2, and then remains stationary for time t3;

[0009] Step 3: The inner motor rotates 180° forward to the first position, which takes time t4, and then remains stationary for time t5;

[0010] Step 4: The inner motor rotates 180° in the opposite direction to the second position, which takes time t6, and then remains stationary for time t7;

[0011] Step 5: The inner motor rotates 180° in the opposite direction to the first position, which takes time t8;

[0012] Step 6. Repeat steps 1 to 5 for n times.

[0013] Step 7: Establish an alignment filter model;

[0014] Step 8. According to the formula of gyroscope random walk and system azimuth alignment accuracy, reasonably select the ratio of rotation and stop time and rotation angular velocity so that the system can fully utilize the measurement information of the high-precision gyroscope and improve the azimuth alignment accuracy.

[0015] Furthermore, the filtering model in step 7 uses data from the entire alignment process, including rotation and stop data. The fine alignment model uses the initial platform deflection angle, equivalent north drift, equivalent celestial drift, and z gyro scale factor error in three directions as state quantities, and the horizontal deflection angle obtained by projecting the accelerometer output of the inertial reference coordinate system on the geographic system and the heading angle change of the inertial reference coordinate system as three-dimensional measurements. The recursive least squares method is used for estimation, and the state vector can be expressed as:

[0016] X=[φ E0 φ N0 φ U0 Δε N Δε U δK gz ] T

[0017] Among them, φ E0 、φ N0 、φ U0 are the initial platform deflection angles in the east, north and celestial directions, Δε N , Δε U are the northward and celestial drifts, δK gz is the z gyro scale factor error.

[0018] The expression for the quantity measurement is:

[0019]

[0020] Where g is the acceleration due to gravity, ψb is the heading angle of the inertial reference coordinate system b, is the velocity increment in the geographic system, Δt is the sampling time interval, ψ b0 is the initial value of the heading angle of the inertial reference coordinate system b at the time of entering fine alignment.

[0021] The measurement matrix expression is:

[0022]

[0023] Among them, ω N 、ω U are the northward and celestial components of the Earth's rotation angular velocity, respectively, and t is the total time of rotation and rest of the system.

[0024] Furthermore, the formula for the alignment accuracy of the gyro random walk and the system orientation in step 7 is expressed as:

[0025]

[0026] Among them, φ z is the azimuth alignment accuracy, RWC x is the random walk coefficient of x gyro, RWC y is the random walk coefficient of the y-gyro, t stay is the total time the system is stationary, ω ie is the angular velocity of the Earth's rotation, L is the local latitude, t rotate is the total time of motor rotation in the system, and t is the total time of static and rotating.

[0027] t stay =n(t1+t3+t5+t7)

[0028] t rotate =n(t2+t4+t6+t8)

[0029] t stay +t rotate =t

[0030] The ratio of rotation and stop time is determined by the azimuth alignment accuracy formula. In order to better modulate the horizontal gyro drift, the time of each stationary segment and the rotation segment is generally made the same, so:

[0031] t stay =4nt s , t rotate =4nt r

[0032] 4nt s +4nt r =t

[0033] Among them, t s, t r are the single stationary time and rotation time during the alignment process, respectively.

[0034] The present invention has the following technical effects:

[0035] The present invention is simple and easy to implement. By performing a rotation and stop alignment method on the system, a filtering model is established. According to the relationship formula between the random walk of the gyroscope and the azimuth alignment accuracy of the system, the ratio of rotation and stop time and the rotation angular velocity are reasonably selected, so that the system can fully utilize the measurement information of the high-precision gyroscope, improve the azimuth alignment accuracy, and has good engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 A schematic diagram of an inertial navigation system self-alignment method combining multi-turn rotation and stopping provided by an example of the present invention. DETAILED DESCRIPTION

[0037] In order to illustrate the present invention more clearly, the present invention is further described below with reference to embodiments and drawings.

[0038] like Figure 1 As shown, the present invention discloses a self-alignment method for an inertial navigation system that combines multiple rotations and stops. The method mainly addresses the problem that when the accuracies of two horizontal gyroscopes of a rotating inertial navigation system are inconsistent, the azimuth alignment accuracy is affected by the low-precision gyroscope. A theoretical formula for the relationship between the azimuth angle alignment error and the random walk coefficient of the horizontal gyroscope when two horizontal gyroscopes of arbitrary precision are used in a rotating inertial navigation system is derived, and an alignment filtering model is established. The inertial navigation system self-alignment method combining multiple rotations and stops is specifically as follows: the system is placed on a stable platform, recorded as the first position, with the x, y, and z axes basically pointing to the east, north, and sky, and remains stationary at the initial first position for t1 time; the internal motor rotates 180° forward to the second position, consuming time t2, and then remains stationary for t3 time; the internal motor rotates 180° forward again to the first position, consuming time t4, and then remains stationary for t5 time; the internal motor rotates 180° in the opposite direction to the second position, consuming time t6, and then remains stationary for t7 time; the internal motor rotates 180° in the opposite direction to the first position, consuming time t8; repeat the above process n times, establish an alignment filter model, and then according to the relationship formula between the gyro random walk and the system azimuth alignment accuracy, reasonably select the ratio of rotation and stop time and the rotation angular velocity to improve the azimuth alignment accuracy. The inertial navigation system self-alignment method combining multiple rotations and stops provided by the present invention has been experimentally proved to effectively improve the azimuth alignment accuracy compared with traditional rotation alignment and multi-position alignment methods.

[0039] Specifically, the coordinate systems required by this embodiment are first defined: i—inertial coordinate system; n—geographical coordinate system; b—inertial reference coordinate system; s—inertial measurement coordinate system.

[0040] Step 1: The inertial navigation system is placed on a stable platform, which is recorded as the first position. The x, y, and z axes basically point to the east, north, and sky, and remain stationary at the initial first position for t1 time.

[0041] Step 2: The inner motor rotates 180° in the forward direction to the second position, which takes time t2, and then remains stationary for time t3.

[0042] Step 3: The inner motor rotates 180° in the forward direction to the first position, which takes time t4, and then remains stationary for time t5.

[0043] Step 4: The inner motor rotates 180° in the opposite direction to the second position, which takes time t6, and then remains stationary for time t7.

[0044] Step 5: The inner motor rotates 180° in the opposite direction to the first position, and the time consumed is t8.

[0045] Step 6. Repeat steps 1 to 5 for n times.

[0046] Step 7: Establish an alignment filter model.

[0047] The filtering model uses data from the entire alignment process, including rotation and stop data. The fine alignment model uses the initial platform deflection angle in three directions, equivalent north drift, equivalent celestial drift, and z gyro scale factor error as state variables. The horizontal deflection angle obtained by projecting the accelerometer output of the inertial reference coordinate system onto the geographic coordinate system and the heading angle change of the inertial reference coordinate system are used as three-dimensional measurements. The recursive least squares method is used for estimation. The state vector can be expressed as:

[0048] X=[φ E0 φ N0 φ U0 Δε N Δε U δK gz ] T

[0049] Among them, φ E0 、φ N0 、φ U0 are the initial platform deflection angles in the east, north and celestial directions, Δε N , Δε U are the northward and celestial drifts, δK gz is the z gyro scale factor error.

[0050] The expression for the quantity measurement is:

[0051]

[0052] Where g is the acceleration due to gravity, ψb is the heading angle of the inertial reference coordinate system b, is the velocity increment in the geographic system, Δt is the sampling time interval, ψ b0 is the initial value of the heading angle of the inertial reference coordinate system b at the time of entering fine alignment.

[0053] The measurement matrix expression is:

[0054]

[0055] Among them, ω N 、ω U are the northward and celestial components of the Earth's rotation angular velocity, respectively, and t is the total time of rotation and rest of the system.

[0056] Step 8: Based on the relationship between the gyro's random walk and the system's azimuth alignment accuracy, reasonably select the ratio of rotation and stop time and the rotation angular velocity so that the system can fully utilize the high-precision gyro's measurement information and improve the azimuth alignment accuracy.

[0057] The completion time of each position stop is:

[0058] Where n is the number of cycles, t is the total alignment time, and L is the local latitude. T0 is the time from time 0, T1 is the time it takes to stop at the first position at the beginning, T2 is the time it takes to move to the second position for the first time, and T8 is the time it takes to complete steps 1 to 5 for the first time. 8n is the time consumed by looping steps 1 to 5 n times. Then, during one alignment process, the equivalent easting angle measurement error caused by the random walk of the horizontal gyro angle is:

[0059]

[0060] Among them, ω r1 is the angular velocity of the inner motor (z axis), ω x (τ) and ω y (τ) are the white noise of the angular rate of the x-gyro and y-gyro respectively. To facilitate the derivation, record:

[0061]

[0062]

[0063]

[0064]

[0065]

[0066]

[0067]

[0068]

[0069] i=1,2,…,n

[0070] Then we have:

[0071]

[0072] Its mean is:

[0073] μ θ (t) = 0

[0074] The standard deviation is:

[0075]

[0076] Where E is the expectation. Since white noise is uncorrelated at different times, we have:

[0077]

[0078]

[0079] E{A ki ×B hj}=0

[0080] in, They represent the white noise variance of x and y gyro angular rates respectively. Therefore, the standard deviation can be simplified as:

[0081]

[0082] remember:

[0083]

[0084]

[0085] t stay +t rotate =t

[0086] Among them, t stay , t rotate They are the total static time and the total rotation time during the alignment process, and the standard deviation can be simplified as:

[0087]

[0088] Therefore, in the inertial navigation system self-alignment method combining multi-turn rotation and stopping, the influence of the random walk of the two horizontal gyroscopes on the alignment accuracy can be expressed as:

[0089]

[0090] Among them, φ z is the azimuth alignment accuracy, RWC x is the random walk coefficient of x gyro, RWC y is the random walk coefficient of the y-gyro, t stay is the total time the system is stationary, ω ie is the angular velocity of the Earth's rotation, L is the local latitude, t rotate is the total time of motor rotation in the system, t is the total time of static and rotating, and n is the number of cycles. That is:

[0091] t stay =n(t1+t3+t5+t7)

[0092] t rotate =n(t2+t4+t6+t8)

[0093] t stay +t rotate =t

[0094] The ratio of rotation and stop time is determined by the azimuth alignment accuracy formula. In order to better modulate the horizontal gyro drift, the time of each stationary segment and the rotation segment is generally made the same. Therefore, we can get:

[0095] t stay =4nt s , t rotate =4nt r

[0096] 4nt s +4nt r =t

[0097] Among them, t s , t r are the single stationary time and rotation time during the alignment process, respectively.

[0098] In order to fully utilize the advantages of rotary modulation technology, it is necessary to ensure that n is a positive integer, t s You can choose 0s, 10s, 30s, and 90s, corresponding to n of 4, 3, 2, and 1, respectively. Substituting the different accuracies of the two horizontal gyros into the formula for gyro random walk and system azimuth alignment accuracy yields the corresponding azimuth alignment accuracy, thereby determining the rotation time and stop time.

[0099] Since the variance of the equivalent east gyro drift determines the variance of the heading angle alignment, that is, the heading angle alignment accuracy, let the rotation angular rate be ω r , during the n-turn process, the equivalent eastward gyro drift can be expressed as:

[0100]

[0101] Therefore, the azimuth alignment accuracy is also related to the inner frame rotation angular velocity. It is difficult to derive the equivalent gyro drift under rotation modulation through mathematical deduction, so it is calculated through simulation. When the simulation time is L, The variance of can be expressed as:

[0102]

[0103] in, is the eastward drift variance, and m is the number of alignments.

[0104] Software simulation is used to generate a zero bias instability error of 0.001° / h. The simulation time can be set to 2 hours. When the alignment time is 8 minutes, the heading alignment error caused by the zero bias instability error at different rotational speeds can be obtained according to the above calculation method, thereby selecting the optimal rotation speed.

[0105] To verify the practicality of the inertial navigation system self-alignment method combining multi-turn rotation and stopping proposed in this invention, an experiment was conducted on a dual-axis nested inertial navigation system. The inertial navigation parameters are shown in the following table. The alignment scheme is a coarse alignment of 2 minutes and a fine alignment of 8 minutes.

[0106] Table 1 Parameters of dual-axis nested inertial navigation system

[0107]

[0108] The precision alignment speed is set to 18° / s, t s When set to 90s, the static time is 6 minutes and the rotation time is 2 minutes. The standard deviation of the azimuth alignment accuracy of the 10 experimental results is taken as the result and compared with the traditional rotation alignment, as shown in the table below.

[0109] Table 2 Azimuth alignment accuracy standard deviation

[0110]

[0111] From the above experiments, it can be seen that when the horizontal gyro precision is different, compared with the traditional continuous rotation alignment method, the alignment method combining multiple rotations and stops proposed in the present invention improves the precision by 17%.

[0112] Although the above describes the specific embodiments of the present invention, it should be clear that the present invention is not limited to the scope of the specific embodiments. As long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concepts of the present invention are protected.

Claims

1. A self-alignment method for an inertial navigation system combining multi-turn rotation and stopping, characterized in that: The following steps are involved: Step 1: The inertial navigation system is placed on a stable platform, which is recorded as the first position. The x, y, and z axes point to the east, north, and sky, and remain stationary at the initial first position for t1 time. Step 2: The inner motor rotates 180° in the forward direction to the second position, which takes time t2, and then remains stationary for time t3; Step 3: The inner motor rotates 180° forward to the first position, which takes time t4, and then remains stationary for time t5; Step 4: The inner motor rotates 180° in the opposite direction to the second position, which takes time t6, and then remains stationary for time t7; Step 5: The inner motor rotates 180° in the opposite direction to the first position, which takes time t8; Step 6. Repeat steps 1 to 5 for n times. Step 7: Establish an alignment filter model; Step 8: Based on the formula for the gyro random walk and the system azimuth alignment accuracy, select the ratio of rotation and stop time and the rotation angular velocity so that the system can fully utilize the measurement information of the high-precision gyro and improve the azimuth alignment accuracy; The formula for the alignment accuracy of the gyro random walk and the system orientation is expressed as: in, is the azimuth alignment accuracy, is the random walk coefficient of x gyro, is the random walk coefficient of the y-gyro, is the total time the system is stationary, is the Earth's rotation angular velocity, is the local latitude, is the total rotation time of the motor in the system, is the total time of rest and rotation; that is: In order to modulate the horizontal gyro drift, the time of each stationary segment and the rotating segment is made the same, that is: in, are the single stationary time and rotation time during the alignment process, respectively.

2. The inertial navigation system self-alignment method combining multi-turn rotation and stopping according to claim 1, characterized in that: The filtering model uses data from the entire alignment process, including rotation and stop data. The fine alignment model uses the initial platform deflection angle in three directions, equivalent north drift, equivalent celestial drift, and z gyro scale factor error as state quantities. The horizontal deflection angle obtained by projecting the accelerometer output of the inertial reference coordinate system onto the geographic system and the heading angle change of the inertial reference coordinate system are measured as three-dimensional quantities and estimated using the recursive least squares method. The state vector is expressed as: in, 、 、 are the initial platform deflection angles in the east, north and sky directions, respectively. 、 are the northward and celestial drifts, is the z gyro scale factor error; The expression for the quantity measurement is: in, is the acceleration due to gravity, 、 is the velocity increment in the geographic system, is the sampling time interval, is the heading angle of the inertial reference coordinate system b, is the initial value of the heading angle of the inertial reference coordinate system b at the time of entering fine alignment; The measurement matrix expression is: in, 、 are the north and celestial components of the Earth's rotation angular velocity, is the total time the system rotates and remains stationary.

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