CN116124180B - Gyro inertial navigation self-adaptive alignment method based on multistage temperature prediction - Google Patents

Gyro inertial navigation self-adaptive alignment method based on multistage temperature prediction Download PDF

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CN116124180B
CN116124180B CN202310349355.0A CN202310349355A CN116124180B CN 116124180 B CN116124180 B CN 116124180B CN 202310349355 A CN202310349355 A CN 202310349355A CN 116124180 B CN116124180 B CN 116124180B
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inertial navigation
temperature
change rate
layer
temperature change
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CN116124180A (en
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李德春
张永宾
马林
刘伯晗
胡小毛
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707th Research Institute of CSIC
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
    • G01C25/005—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass initial alignment, calibration or starting-up of inertial devices
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Abstract

The invention relates to the technical field of gyroscopes, in particular to a gyro inertial navigation self-adaptive alignment method based on multistage temperature prediction, which comprises the following steps of: acquiring temperatures of a plurality of closed spaces at sampling moments of gyro inertial navigation, performing temperature fitting to obtain a non-uniform rational B-spline curve fitting equation, solving to obtain a non-uniform rational B-spline curve, and solving to obtain a contribution coefficient
Figure ZY_1
Based on the contribution coefficient
Figure ZY_2
Obtaining a predicted value of the closed space where the gyro inertial navigation is located when other closed space influences are considered
Figure ZY_3
Will be
Figure ZY_4
Solving the inertial navigation rotation angular velocity of the gyroscope according to the substituted angular velocity adjustment empirical formula
Figure ZY_5
Enabling the gyro inertial navigation to solve the gyro inertial navigation rotation angular velocity
Figure ZY_6
The value rotation is adaptively aligned. The method provided by the invention can prevent adverse effects such as overshoot, impact and unstable angular velocity of the motor, and prevent larger angular velocity errors in the alignment process, and reduce the alignment time.

Description

Gyro inertial navigation self-adaptive alignment method based on multistage temperature prediction
Technical Field
The invention relates to the technical field of gyroscopes, in particular to a gyro inertial navigation self-adaptive alignment method based on multistage temperature prediction.
Background
The rotary optical fiber inertial navigation system needs to perform initial alignment before performing navigation work, and mainly obtains or eliminates the azimuth error angle of the inertial platform. The basic idea for finding the azimuth error angle is to measure the component of the earth's rotational angular velocity on the gyro's sensitive axis. Because of the coupling relation between the self error (gyro drift) and the azimuth error angle, the azimuth error angle can be separated only after the gyro drift is eliminated. Since the fiber optic gyroscope mounted on the inertial platform body is very sensitive to the spatial temperature field in which it is located, the change in temperature is liable to cause the change in scale factor and zero offset (enemy billows, xu Mengtong, liu Wei, ma Haibin. The fiber optic gyroscope temperature compensation method based on ACO-BP neural network is studied [ J/OL ], electro-optic and control, 2022.), the inertial navigation system usually adopts a multistage temperature control method, which requires a long time to reach thermal equilibrium. In the process that the temperature is stable and reaches the thermal balance, the gyro drift is unstable, namely the drift is not constant, and in a rotary platform type inertial navigation system, the influence of the constant gyro drift is hardly accurately measured and compensated by adopting a method of periodically rotating a physical platform. In addition, because the temperature imbalance causes unstable drift, the method of rotating the platform by adopting a fixed period in the case cannot completely cancel the influence of the drift positively and negatively, so that an ideal inertial navigation alignment effect is difficult to obtain.
In order to avoid the problem of poor alignment effect caused by unbalanced temperature, one method is to heat quickly, but the problem of high power consumption of equipment is caused, and the other method is to perform initial alignment after heat balance, so that the problem of long alignment time is caused. The prior rotational inertial navigation alignment method is like that of patents (Wang Wei, lu Yao, guo Zhenwei, etc.), based on a multi-axis alternating rotation method of a three-axis hybrid optical fiber inertial navigation system, CN 115164939A, tang Jianghe, liu Feng, hu Pinghua, etc., a rapid self-calibration and self-alignment method of a dual-axis optical fiber inertial navigation system, CN 106705992A) and papers (Lejin, a method research [ J ] suitable for dual-axis rotational laser gyro inertial navigation alignment, optical and optical technologies, 2011, 09 (04), wu Xiuzhen, zhou Shaolei, li Ruitao, precise alignment analysis of dual-axis rotational inertial navigation systems under different indexing schemes [ J ]. Modern defense technology, 2013, 41 (3): 5) are researched, etc., but the alignment sequence is based on constant temperature conditions or the influence of temperature change on the calibration process is not considered, larger angular velocity errors can be generated in the alignment process, and the alignment effect is not ideal.
Disclosure of Invention
The invention aims to solve the technical problem of providing a multi-stage temperature prediction-based adaptive alignment method for gyro inertial navigation, which predicts the temperature change in closed spaces of different rotary shaft systems and the heat conduction process of adjacent closed spaces by using a non-uniform and rational B-spline curve, avoids the hysteresis effect existing in the temperature measurement during the continuous temperature rising and falling process of a system, avoids the temperature balance waiting time, and in the alignment process, each rotary shaft predicts according to the temperature change rate, adaptively adjusts the rotation angular velocity in the alignment process, and improves the alignment precision of the rotary fiber optic gyro inertial navigation on the premise of ensuring the relative stability of temperature conditions and reducing the alignment time.
The invention is realized by the following technical scheme:
a gyro inertial navigation self-adaptive alignment method based on multi-stage temperature prediction comprises the following steps:
s1: acquiring sampling moments of multiple enclosed spaces of gyro inertial navigation
Figure SMS_1
、/>
Figure SMS_4
、/>
Figure SMS_8
...、/>
Figure SMS_2
The temperatures of (2) are respectively->
Figure SMS_5
、
Figure SMS_7
、/>
Figure SMS_10
…、/>
Figure SMS_3
Wherein->
Figure SMS_6
For the sequence number of the sampling instant>
Figure SMS_9
Layer number of the closed space;
s2: the temperature at each sampling moment according to the step S1 is based on a non-uniform rational B-spline curve and the actual temperature change rate of each layer of closed space
Figure SMS_11
Performing temperature fitting to obtain a non-uniform rational B spline curve equation;
s3: all control points of the non-uniform rational B-spline curve equation are calculated, so that a non-uniform rational B-spline curve fitted by the temperatures of the closed spaces of all layers is obtained:
s4: obtaining a predicted value of a temperature change rate of each layer of closed space without considering the influence of other closed spaces based on non-uniform rational B-spline curve fitted to the temperature of each layer of closed space
Figure SMS_12
And will->
Figure SMS_13
Substituting the inner layer enclosed space wrapped by the outer layer enclosed space +.>
Figure SMS_14
The relation between the temperature change rate of the outer enclosed space and the temperature change rate of the outer enclosed spaceIn the formula (1), the temperature change rate of each layer of closed space is fitted, and the condition that each layer of closed space is in the way of inner layer of closed space is solved>
Figure SMS_15
Contribution coefficient of temperature change Rate->
Figure SMS_16
；
Figure SMS_17
（1）
Wherein:
Figure SMS_18
is->
Figure SMS_19
Inner layer closed space at each sampling moment>
Figure SMS_20
Is a temperature change rate of the actual temperature of the substrate;
s5: repeating the steps S1-S3, updating the non-uniform rational B-spline curve fitted by the temperatures of the closed spaces of all layers, and obtaining the predicted value of the closed spaces of all layers without considering the influence of other closed spaces based on the updated non-uniform rational B-spline curve fitted by the temperatures of the closed spaces of all layers
Figure SMS_21
And is solved with step S4 +.>
Figure SMS_22
Substituting the two values into the closed space (2) together to obtain a predicted value +.>
Figure SMS_23
；
Figure SMS_24
（2）
Wherein:
Figure SMS_25
for update->
Figure SMS_26
Inner layer closed space at each sampling moment>
Figure SMS_27
Is a temperature change rate of the actual temperature of the substrate;
s6: will be
Figure SMS_28
Solving a gyroscopic inertial navigation rotation angular velocity +.>
Figure SMS_29
Enabling gyro inertial navigation to solve gyro inertial navigation rotation angular velocity +.>
Figure SMS_30
Performing self-adaptive alignment by value rotation;
Figure SMS_31
（3）
wherein:
Figure SMS_32
for each modulation order corresponding angle in the alignment process, +.>
Figure SMS_33
For modulating the angular velocity at constant temperature +.>
Figure SMS_34
Is the difference of temperature->
Figure SMS_35
The amount of change in the scale factor.
Further, in the step S2, the expression of the non-uniform rational B-spline curve is represented by formula (4), the actual temperature change rate equation of the closed space of each layer is represented by formula (5), and the fitted non-uniform rational B-spline curve equation is represented by formula (6);
Figure SMS_36
（4）
Figure SMS_37
（5）
Figure SMS_38
（6）
wherein:
Figure SMS_55
is the highest power of the relevant symbol, +.>
Figure SMS_59
For sampling time, +.>
Figure SMS_63
Is->
Figure SMS_41
Time->
Figure SMS_45
Temperature of the layer enclosure->
Figure SMS_50
For the control point of the curve equation +.>
Figure SMS_51
Weights corresponding to control points of the curve equation, +.>
Figure SMS_56
Is a basis function of a curve equation>
Figure SMS_62
Is->
Figure SMS_65
Layer enclosure no->
Figure SMS_68
Actual temperature change rate corresponding to each sampling instant, < >>
Figure SMS_58
Is that
Figure SMS_61
Time->
Figure SMS_66
Derivative of the temperature of the layer enclosure,/->
Figure SMS_69
Is the derivative of the basis function of the curve equation, +.>
Figure SMS_57
Is that
Figure SMS_60
Corresponding basis function of the curve equation>
Figure SMS_64
Is->
Figure SMS_67
Derivative of>
Figure SMS_39
Is->
Figure SMS_44
Corresponding basis function of the curve equation>
Figure SMS_48
Is->
Figure SMS_54
Derivative of>
Figure SMS_40
Is->
Figure SMS_43
Corresponding curve control point, < >>
Figure SMS_47
Is->
Figure SMS_52
Corresponding curve control point, < >>
Figure SMS_42
For control point->
Figure SMS_46
Weight of->
Figure SMS_49
For control point->
Figure SMS_53
Is a weight of (2).
Further, when all control points of the non-uniform rational B-spline curve equation are calculated, the equation (6) is transformed into a matrix form to obtain the equation (7), and then all control points of the non-uniform rational B-spline curve equation are calculated by solving the equation (7):
Figure SMS_70
（7）。
the number of layers of the closed space is four, and the gyroscope is installed in the innermost closed space in an inertial navigation mode.
Advantageous effects of the invention
According to the multi-stage temperature prediction-based gyro inertial navigation self-adaptive alignment method, temperature changes in closed spaces of different rotary shaft systems and heat conduction processes of adjacent closed spaces of gyro inertial navigation are predicted by means of non-uniform rational B-spline curves, hysteresis effects and temperature balance waiting time existing in temperature measurement are avoided in a continuous temperature rising and falling process of a system, rotation angular speeds of rotary shafts in an alignment process are predicted according to the temperature change rates in the alignment process, the rotation angular speeds in the alignment process are adjusted in a self-adaptive mode, adverse effects such as overshoot, impact and unstable angular speeds of motors are prevented, larger angular speed errors are prevented from being caused in the alignment process, and the alignment accuracy of gyro inertial navigation is improved.
Drawings
FIG. 1 is a schematic diagram of the basic spatial configuration of a gyroscopic inertial navigation unit.
FIG. 2 is a schematic diagram of a gyroscopic inertial navigation installation.
FIG. 3 is a schematic diagram of a typical closed space temperature fit non-uniform rational B-spline curve.
In the figure: 1. and (3) gyroscopes, 2. Accelerometers, and 3. Gyroscopes are used for inertial navigation.
Detailed Description
A gyro inertial navigation self-adaptive alignment method based on multi-stage temperature prediction comprises the following steps:
s1: acquiring sampling moments of multiple enclosed spaces of gyro inertial navigation
Figure SMS_72
、/>
Figure SMS_75
、/>
Figure SMS_78
...、/>
Figure SMS_73
The temperatures of (2) are respectively->
Figure SMS_76
、
Figure SMS_79
、/>
Figure SMS_80
…、/>
Figure SMS_71
Wherein->
Figure SMS_74
For the sequence number of the sampling instant>
Figure SMS_77
Layer number of the closed space;
s2: according to the temperature at each sampling moment in the step S1, performing temperature fitting based on the non-uniform rational B-spline curve expression (4) and the temperature change rate equation (5) of each layer of closed space to obtain a non-uniform rational B-spline curve fitting equation (6):
Figure SMS_81
（4）
Figure SMS_82
（5）
Figure SMS_83
（6）
wherein:
Figure SMS_100
is the highest power of the relevant symbol, +.>
Figure SMS_104
For sampling time, +.>
Figure SMS_109
Is->
Figure SMS_85
Time->
Figure SMS_88
Temperature of the layer enclosure->
Figure SMS_92
For the control point of the curve equation +.>
Figure SMS_96
Weights corresponding to control points of the curve equation, +.>
Figure SMS_87
Is a basis function of a curve equation>
Figure SMS_91
Is->
Figure SMS_93
Layer enclosure no->
Figure SMS_98
Actual temperature change rate corresponding to each sampling instant, < >>
Figure SMS_101
Is that
Figure SMS_107
Time->
Figure SMS_111
Derivative of the temperature of the layer enclosure,/->
Figure SMS_113
The derivative of the basis function of the curve equation; />
Figure SMS_103
Is that
Figure SMS_106
Corresponding basis function of the curve equation>
Figure SMS_110
Is->
Figure SMS_114
Derivative of>
Figure SMS_84
Is->
Figure SMS_90
Corresponding basis function of the curve equation>
Figure SMS_94
Is->
Figure SMS_99
Derivative of>
Figure SMS_86
Is->
Figure SMS_89
Corresponding curve control point, < >>
Figure SMS_95
Is->
Figure SMS_97
Corresponding curve control point, < >>
Figure SMS_102
For control point->
Figure SMS_105
Weight of->
Figure SMS_108
For control point->
Figure SMS_112
Is a weight of (2).
Because the non-uniform rational B-spline curve has the characteristics of local adjustability, convex hull property, invariance of geometric and perspective projection transformation and the like, the method is suitable for fitting and predicting various freely-changing physical models. The patent uses a quadratic inhomogeneous rational B-spline curve for temperature fitting, so
Figure SMS_115
The value is equal to 2, the weight corresponding to the curve equation control point can be made +.>
Figure SMS_116
Equal to 1; />
Figure SMS_117
Front ∈under the layer enclosure>
Figure SMS_118
The temperature at the individual sampling instants is known, the temperature difference can be used to determine the +.>
Figure SMS_119
Temperature change rate corresponding to each sampling instant +.>
Figure SMS_120
. Then, according to the sampling temperature and the corresponding temperature change rate information, a secondary non-uniform rational B-spline curve can be constructed to pass through the known points, and the limiting condition of the given derivative of the head point and the tail point is met, so that a non-uniform rational B-spline curve fitting equation can be obtained;
s3: converting the formula (6) into a matrix form to obtain an equation (7), solving the equation (7) to obtain all control points of a non-uniform rational B-spline curve equation, thereby obtaining a non-uniform rational B-spline curve fitted by the temperatures of the closed spaces of each layer, continuously updating the values of temperature sampling points according to the measured values of the actual temperatures at the subsequent moments, and further updating the non-uniform rational B-spline curve, wherein a typical non-uniform rational B-spline curve diagram fitted by the temperatures of the closed spaces is shown in FIG. 3;
Figure SMS_121
（7）
s4: obtaining a predicted value of a temperature change rate of each layer of closed space without considering the influence of other closed spaces based on non-uniform rational B-spline curve fitted to the temperature of each layer of closed space
Figure SMS_122
And will->
Figure SMS_123
Substituting the inner layer enclosed space wrapped by the outer layer enclosed space +.>
Figure SMS_124
In the relation (1) between the temperature change rate of the outer closed space and the temperature change rate of each layer of closed space, fitting the temperature change rate of each layer of closed space, and solving the +.>
Figure SMS_125
Contribution coefficient of temperature change Rate->
Figure SMS_126
；
Figure SMS_127
（1）
Wherein:
Figure SMS_128
for +.>
Figure SMS_129
Inner layer closed space at each sampling moment>
Figure SMS_130
Is a temperature change rate of the actual temperature of the substrate;
s5: repeating the steps S1-S3, updating the non-uniform rational B-spline curve fitted by the temperatures of the closed spaces of all layers, and obtaining the predicted value of the closed spaces of all layers without considering the influence of other closed spaces based on the updated non-uniform rational B-spline curve fitted by the temperatures of the closed spaces of all layers
Figure SMS_131
And is solved with step S4 +.>
Figure SMS_132
Substituting the two values into the closed space (2) together to obtain a predicted value +.>
Figure SMS_133
；
Figure SMS_134
（2）
Wherein:
Figure SMS_135
update +.>
Figure SMS_136
Inner layer closed space at each sampling moment>
Figure SMS_137
Is a temperature change rate of the actual temperature of the substrate;
s6: will be
Figure SMS_138
Solving a gyroscopic inertial navigation rotation angular velocity +.>
Figure SMS_139
Enabling gyro inertial navigation to solve gyro inertial navigation rotation angular velocity +.>
Figure SMS_140
Performing self-adaptive alignment by value rotation;
Figure SMS_141
（3）
wherein:
Figure SMS_142
for each modulation order corresponding angle in the alignment process, +.>
Figure SMS_143
For modulating the angular velocity at constant temperature, generally +.>
Figure SMS_144
，/>
Figure SMS_145
Is the difference of temperature->
Figure SMS_146
The amount of change in the scale factor.
The general gyro inertial navigation is three-axis rotating optical fiber gyro inertial navigation, the basic space constitution schematic diagram of a gyro inertial navigation unit is shown in fig. 1, the gyro inertial navigation unit consists of three gyroscopes 1 and three accelerometers 2, the gyro inertial navigation 3 is installed at the innermost layer of a multi-layer closed space, four layers of the closed space are taken as an example, the gyro inertial navigation installation schematic diagram is shown in fig. 2, when the gyro inertial navigation is rotated and modulated, the inertial navigation unit rotates around a z axis as an example, and the rotation angular velocity error caused by a calibration factor is (8):
Figure SMS_147
（8）
wherein the method comprises the steps of
Figure SMS_165
Priming of the vector for Scale factor error +.>
Figure SMS_167
Relative to inertial system->
Figure SMS_170
Is in the navigation coordinate system +.>
Figure SMS_149
Lower projection->
Figure SMS_152
For angular velocity errors in the navigation coordinate system +.>
Figure SMS_158
Is->
Figure SMS_162
Directional component (I)>
Figure SMS_150
For angular velocity errors in the navigation coordinate system +.>
Figure SMS_154
Is->
Figure SMS_156
Directional component (I)>
Figure SMS_160
For angular velocity errors in the navigation coordinate system +.>
Figure SMS_151
Is->
Figure SMS_155
Directional component (I)>
Figure SMS_159
Is->
Figure SMS_163
Directional gyro scale factor error,/>
Figure SMS_164
Is->
Figure SMS_168
Directional gyro scale factor error,/>
Figure SMS_171
Is->
Figure SMS_172
The scale factor error of the directional gyroscope,
Figure SMS_148
for the earth coordinate system->
Figure SMS_153
Relative to inertial coordinate system->
Figure SMS_157
A component of the rotational angular velocity in the north direction; />
Figure SMS_161
For the earth coordinate system->
Figure SMS_166
Relative to inertial coordinate system->
Figure SMS_169
A component of the rotational angular velocity in the direction of the sky;
integrating the formula (8) to obtain
Figure SMS_173
、/>
Figure SMS_174
Gyro scale factor errorThe relation of (2) is represented by the following formula (9):
Figure SMS_175
（9）
as can be seen from equation (9), the rotational angular velocity is the same as the gyro scale factor error
Figure SMS_176
The larger the error accumulated in the rotation direction during modulation, the smaller.
But in the actual alignment process, the rotational angular velocity
Figure SMS_177
Too large, an adverse effect such as overshoot, impact, unstable angular velocity, etc. of the motor may be caused, thereby affecting the effect of rotational modulation. Furthermore, it can be seen from equation (9) that after one rotation period 2 pi, the scale factor error of two gyroscopes in the direction perpendicular to the z-axis of the rotation axis is +.>
Figure SMS_178
Still present, and due to the presence of the rotational angular velocity of the earth, the larger the gyro scale factor error, the earth angular velocity error produced by the scale factor
Figure SMS_179
Northbound fixed error term during modulation>
Figure SMS_180
The larger. Since the fiber optic gyroscope is sensitive to temperature change, the gyroscope scale factor error is easy to increase, so that when the temperature change rate is large, the gyroscope scale factor error is increased, and at the moment, if a large rotation angular velocity is adopted, a larger angular velocity error is caused, so that the modulated angle error is increased.
Therefore, the current environment temperature, the temperature change rate and the temperature fitting curve are combined to accurately predict the temperature and the temperature change rate in a short period in the future, the hysteresis effect of using temperature measurement in the continuous temperature rising and falling process of the system is avoided, the temperature balance waiting time is avoided, then the weight coefficient method thought is adopted, the angular velocity adjusting empirical formula (3) is designed, the temperature and the temperature change rate in the short period in the future are applied to the angular velocity adjusting empirical formula to guide the angular velocity of rotation of each axis in the alignment process, the basic thought is that when the temperature change rate is smaller, the scale factor error of the gyroscope is more stable, the faster rotation angle speed can be adopted, and when the temperature change rate is larger, the scale factor error of the gyroscope is unstable, and the slower rotation angle speed is adopted to reduce the influence brought by the scale factor error. In the alignment process, each rotating shaft predicts according to the temperature change rate, and the rotating angular speed in the alignment process is adaptively adjusted, so that adverse effects such as overshoot, impact and unstable angular speed of a motor can be prevented from being caused, larger angular speed errors can be prevented from being caused in the alignment process, and the alignment precision of gyro inertial navigation is improved.
The number of layers of the closed space is four, and the gyroscope is installed in the innermost closed space in an inertial navigation mode.
With reference to FIG. 2, the enclosed spaces of each layer are A, B, C, D from outside to inside, and the gyroscope inertial navigation is installed in the enclosed space of the D layer, and the relation of the temperature change rate of the adjacent enclosed spaces can be obtained according to the formula (1) and is the formula (10)
Figure SMS_181
（10）
The relationship between the rate of change of the temperature of the enclosed space D and the rate of change of the temperature of the enclosed space A, B, C, which can be obtained according to the formula (10), is represented by the formula (11):
Figure SMS_182
（11）
expanding the formula (11) to obtain the formula (12)
Figure SMS_183
（12）
Wherein:
Figure SMS_186
for the temperature change rate of the closed space D determined according to formula (5), the ratio of +.>
Figure SMS_188
Predicted values for the enclosure D based on non-uniform rational B-spline curve without consideration of other enclosure effects, < >>
Figure SMS_191
For the temperature change rate of the closed space C determined according to formula (5), the ratio of +.>
Figure SMS_185
Predicted values obtained for the closed space C based on non-uniform rational B-spline curve without consideration of other closed space effects, +.>
Figure SMS_189
For the temperature change rate of the closed space B determined according to formula (5), the ratio of +.>
Figure SMS_192
For the prediction value of the closed space B based on the non-uniform rational B-spline curve without considering the influence of other closed spaces,
Figure SMS_193
for the temperature change rate of the closed space A determined according to formula (5), the +.>
Figure SMS_184
For the contribution coefficient of A space to B space temperature change rate,>
Figure SMS_187
for the contribution coefficient of B space to C space temperature change rate,>
Figure SMS_190
the contribution coefficient of the C space to the D space temperature change rate is used as the contribution coefficient;
according to the formula (12), the closed space where the gyro inertial navigation is located can be obtained according to the steps S5-S6 to consider the influence of other closed spacesPredicted value at time
Figure SMS_194
Will->
Figure SMS_195
Substitution (3) solving gyro inertial navigation rotation angular velocity +.>
Figure SMS_196
Enabling gyro inertial navigation to solve gyro inertial navigation rotation angular velocity +.>
Figure SMS_197
The value rotation is adaptively aligned. The method can prevent the adverse effects of overshoot, impact, unstable angular speed and the like of the motor caused by overlarge rotation angle speed in the alignment process, prevent larger angular speed error in the alignment process, and improve the alignment precision of gyro inertial navigation.
In summary, according to the gyro inertial navigation self-adaptive alignment method based on multi-stage temperature prediction, in the alignment process, each rotating shaft predicts according to the temperature change rate, the rotating angular speed in the alignment process is adaptively adjusted, the hysteresis effect and the temperature balance waiting time existing in the temperature measurement process of the system are avoided, adverse effects such as overshoot, impact and unstable angular speed of a motor are prevented, larger angular speed error is prevented in the alignment process, and the alignment precision of gyro inertial navigation is improved.
The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (4)

1. A gyro inertial navigation self-adaptive alignment method based on multi-stage temperature prediction is characterized in that: the method comprises the following steps:
s1: acquiring sampling moments of multiple enclosed spaces of gyro inertial navigation
Figure QLYQS_2
、/>
Figure QLYQS_4
、/>
Figure QLYQS_7
...、/>
Figure QLYQS_3
The temperatures of (2) are respectively->
Figure QLYQS_6
、/>
Figure QLYQS_8
、
Figure QLYQS_10
…、/>
Figure QLYQS_1
Wherein->
Figure QLYQS_5
For the sequence number of the sampling instant>
Figure QLYQS_9
Layer number of the closed space;
s2: the temperature at each sampling moment according to the step S1 is based on a non-uniform rational B-spline curve and the actual temperature change rate of each layer of closed space
Figure QLYQS_11
Performing temperature fitting to obtain a non-uniform rational B spline curve equation;
s3: all control points of the non-uniform rational B-spline curve equation are calculated, so that a non-uniform rational B-spline curve fitted by the temperatures of the closed spaces of all layers is obtained:
s4: non-uniformity based on temperature fitting of closed spaces of each layerObtaining predicted values of temperature change rates of closed spaces of each layer by using rational B-spline curves without considering influences of other closed spaces
Figure QLYQS_12
And will->
Figure QLYQS_13
Substituting the inner layer enclosed space wrapped by the outer layer enclosed space +.>
Figure QLYQS_14
In the relation (1) between the temperature change rate of the outer closed space and the temperature change rate of each layer of closed space, fitting the temperature change rate of each layer of closed space, and solving the +.>
Figure QLYQS_15
Contribution coefficient of temperature change rate
Figure QLYQS_16
；
Figure QLYQS_17
（1）
Wherein:
Figure QLYQS_18
is->
Figure QLYQS_19
Inner layer closed space at each sampling moment>
Figure QLYQS_20
Is a temperature change rate of the actual temperature of the substrate;
s5: repeating the steps S1-S3, updating the non-uniform rational B-spline curve fitted by the temperatures of the closed spaces of all layers, and obtaining the predicted value of the closed spaces of all layers without considering the influence of other closed spaces based on the updated non-uniform rational B-spline curve fitted by the temperatures of the closed spaces of all layers
Figure QLYQS_21
And is solved with step S4 +.>
Figure QLYQS_22
Substituting the two values into the closed space (2) together to obtain a predicted value +.>
Figure QLYQS_23
；
Figure QLYQS_24
（2）
Wherein:
Figure QLYQS_25
for update->
Figure QLYQS_26
Inner layer closed space at each sampling moment>
Figure QLYQS_27
Is a temperature change rate of the actual temperature of the substrate;
s6: will be
Figure QLYQS_28
Solving a gyroscopic inertial navigation rotation angular velocity +.>
Figure QLYQS_29
Enabling gyro inertial navigation to solve gyro inertial navigation rotation angular velocity +.>
Figure QLYQS_30
Performing self-adaptive alignment by value rotation;
Figure QLYQS_31
（3）
wherein:
Figure QLYQS_32
for each modulation order corresponding angle in the alignment process, +.>
Figure QLYQS_33
For modulating the angular velocity at constant temperature +.>
Figure QLYQS_34
Is the difference of temperature->
Figure QLYQS_35
The amount of change in the scale factor.
2. The gyro inertial navigation self-adaptive alignment method based on multi-stage temperature prediction according to claim 1, wherein the method comprises the following steps: in the step S2, the expression of the non-uniform rational B spline curve is shown as a formula (4), the actual temperature change rate equation of the closed space of each layer is shown as a formula (5), and the fitted non-uniform rational B spline curve equation is shown as a formula (6);
Figure QLYQS_36
（4）
Figure QLYQS_37
（5）
Figure QLYQS_38
（6）
wherein:
Figure QLYQS_55
is the highest power of the relevant symbol, +.>
Figure QLYQS_62
For sampling time, +.>
Figure QLYQS_66
Is->
Figure QLYQS_40
Time->
Figure QLYQS_44
Temperature of the layer enclosure->
Figure QLYQS_50
For the control point of the curve equation +.>
Figure QLYQS_52
Weights corresponding to control points of the curve equation, +.>
Figure QLYQS_57
Is a basis function of a curve equation>
Figure QLYQS_61
Is->
Figure QLYQS_65
Layer enclosure no->
Figure QLYQS_68
Actual temperature change rate corresponding to each sampling instant, < >>
Figure QLYQS_58
Is->
Figure QLYQS_60
Time->
Figure QLYQS_64
Derivative of the temperature of the layer enclosure,/->
Figure QLYQS_69
Is the derivative of the basis function of the curve equation, +.>
Figure QLYQS_42
Is->
Figure QLYQS_46
Corresponding basis function of the curve equation>
Figure QLYQS_49
Is->
Figure QLYQS_54
Derivative of>
Figure QLYQS_39
Is->
Figure QLYQS_45
Corresponding basis function of the curve equation>
Figure QLYQS_48
Is->
Figure QLYQS_53
Derivative of>
Figure QLYQS_41
Is->
Figure QLYQS_43
Corresponding curve control point, < >>
Figure QLYQS_47
Is->
Figure QLYQS_51
Corresponding curve control point, < >>
Figure QLYQS_56
For control point->
Figure QLYQS_59
Weight of->
Figure QLYQS_63
For control point->
Figure QLYQS_67
Is a weight of (2).
3. The gyro inertial navigation self-adaptive alignment method based on multi-stage temperature prediction according to claim 2, wherein the method comprises the following steps: when all control points of the non-uniform rational B-spline curve equation are calculated, converting the formula (6) into a matrix form to obtain the formula (7), and solving the formula (7) to calculate all control points of the non-uniform rational B-spline curve equation;
Figure QLYQS_70
（7）。
4. the gyro inertial navigation self-adaptive alignment method based on multi-stage temperature prediction according to claim 1, wherein the method comprises the following steps: the number of layers of the enclosed space is four, and the gyroscope is installed in the innermost enclosed space in an inertial navigation manner.
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