CN112729332A - Alignment method based on rotation modulation - Google Patents

Alignment method based on rotation modulation Download PDF

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CN112729332A
CN112729332A CN202011283857.0A CN202011283857A CN112729332A CN 112729332 A CN112729332 A CN 112729332A CN 202011283857 A CN202011283857 A CN 202011283857A CN 112729332 A CN112729332 A CN 112729332A
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navigation
alignment
imu
rotation
time
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CN112729332B (en
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侯志宁
蒋茂荣
项铮
刘康
沈扬清
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707th Research Institute of CSIC
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    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
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Abstract

The invention relates to a rotary modulation alignment method, which is technically characterized in that: the method comprises the steps of carrying out rotation modulation in a coarse alignment stage, modulating a constant error of an equivalent horizontal accelerometer and a constant error of an equivalent east gyroscope, improving the accuracy of coarse alignment, ensuring the integrity of a rotation modulation period in a fine alignment stage when a reverse navigation is carried out to the coarse alignment stage in the fine alignment stage, improving the accuracy of accuracy, and carrying out smooth filtering on state vector estimation of a misalignment angle obtained by forward navigation alignment and reverse navigation alignment by utilizing information fusion filtering to obtain the optimal estimation of the misalignment angle so as to further improve the accuracy of the inertial navigation system.

Description

Alignment method based on rotation modulation
Technical Field
The invention belongs to the technical field of inertial navigation, and particularly relates to an alignment method based on rotation modulation.
Background
With the increasing requirements of the vehicle-mounted weapon systems on rapidity and maneuverability, the vehicle-mounted positioning and orientation system must have the capability of rapidly entering into a working state. The rapidity and the accuracy of the initial alignment are key indexes for the vehicle-mounted positioning and orientation system to rapidly enter a working state. However, the rapidity and the accuracy of the initial alignment are often contradictory, so how to realize the rapid high-accuracy initial alignment of the vehicle-mounted positioning and orientation system has important significance for improving the rapidity and the maneuverability of the vehicle-mounted weapon system.
The initial alignment of the rotary vehicle-mounted positioning and orientation system is mainly divided into two stages of coarse alignment and fine alignment. In the coarse alignment stage, coarse alignment based on an inertial coordinate system is usually adopted, in order to reduce the influence of linear motion interference, an Inertial Measurement Unit (IMU) is in a static state, and the approximate values of the initial horizontal attitude and the course of the vehicle-mounted positioning and orientation system are determined through the measurement output of an inertial element by taking the gravity acceleration and the earth rotation angular rate as reference quantities; and in the fine alignment stage, assuming that a misalignment angle between the coarse alignment attitude and the real attitude is a small error, estimating the misalignment angle through a misalignment angle error model by using a navigation speed error as an observed quantity, so as to obtain a high-precision initial attitude matrix.
Based on the rough alignment of the inertial coordinate system, the alignment accuracy of the horizontal misalignment angle mainly depends on the equivalent horizontal measurement error of the accelerometer, and the alignment accuracy of the azimuth misalignment angle mainly depends on the equivalent east measurement error of the gyroscope. In the static state of the IMU, equivalent errors of an accelerometer and a gyroscope cannot be eliminated, and the precision of coarse alignment is limited by the constant error of an inertial element.
When reverse navigation is carried out in the fine alignment stage, because the IMU is in a static state during coarse alignment, the fine alignment rotation modulation period is damaged, and the equivalent errors of the accelerometer and the gyroscope cannot be effectively subjected to rotation modulation, so that the fine alignment accuracy is further influenced.
The existing alignment method does not carry out smooth filtering on the state vector estimation of the misalignment angle obtained by forward navigation alignment and reverse navigation alignment to obtain the optimal estimation of the misalignment angle.
In summary, the following problems exist in the prior art: 1. equivalent errors of an accelerometer and a gyroscope in a coarse alignment stage cannot be effectively subjected to rotation modulation; 2. the rotation modulation period in the fine alignment stage is damaged, and the complete rotation modulation period in the fine alignment process cannot be ensured; 3. the forward navigation alignment and the reverse navigation alignment can respectively estimate the same state vector, and the prior alignment method does not combine the complementation and the redundant information of the forward navigation alignment and the reverse navigation alignment in time and space according to a certain optimization criterion, and the full-local optimal estimation of the state is obtained after the fusion.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides an alignment method based on rotation modulation, wherein rotation modulation is carried out in a coarse alignment stage, a constant error of an equivalent horizontal accelerometer and a constant error of an equivalent east gyroscope are modulated, the coarse alignment precision is improved, meanwhile, when a reverse navigation is carried out in a fine alignment stage to a coarse alignment stage, the integrity of a rotation modulation period in the fine alignment stage is ensured, the precision of the precision is improved, and the optimal estimation of a misalignment angle is obtained by carrying out smooth filtering on state vector estimation of the misalignment angle obtained by forward navigation alignment and reverse navigation alignment by utilizing information fusion filtering, so that the precision of an inertial navigation system is further improved.
The invention solves the practical problem by adopting the following technical scheme:
an alignment method based on rotation modulation comprises the following steps:
step 1, after a system is electrified and receives a starting command, carrying out rotation modulation around an azimuth axis based on a rotation modulation strategy;
step 2, in the rotation modulation process of the step 1, the system adopts an indirect coarse alignment scheme based on an inertial system to perform coarse rotation modulation alignment;
step 3, after the coarse alignment of the rotation modulation is finished, the system carries out the accurate alignment of the rotation modulation forward navigation;
step 4, after the rotary modulation forward navigation fine alignment is finished, setting the initial value posture and position of the reverse navigation algorithm as the posture and position of the forward navigation finish time, and changing the model parameters into a small error model parameter system to carry out rotary modulation reverse navigation fine alignment;
step 5, filtering to the initial time t of coarse alignment in the reverse navigation Kalman0Adjusting the error model parameters again, enabling the alignment program to enter rotary modulation precision alignment, sampling a gyroscope in a forward algorithm, adopting symbols of forward calculation for gyroscope constant drift and earth rotation angular rate symbols, setting an initial value attitude and position of a reverse navigation algorithm as the attitude and position of a forward navigation ending moment, negating a speed symbol of the reverse navigation ending moment as the speed of the forward navigation initial moment, starting forward calculation and Kalman filtering on sampling data from a rough alignment starting moment, carrying out rotary modulation precision alignment, estimating a misalignment angle until the reverse navigation starting moment tre(ii) a Performing fixed point smoothing filtering in the reverse navigation process, and performing online smoothing on the filtered state vector by fully utilizing all observation values in the measurement period to realize the optimized estimation of the state variable;
step 6, repeatedly executing the operation times of the step 4 and the step 5, repeatedly utilizing the navigation data and the external reference information in the alignment time, and determining the repeated calculation times according to the calculation capability and the alignment time length of the navigation computer;
step 7, after the rotational modulation forward navigation fine alignment of the step 6 is completed, performing information fusion by using misalignment angle state quantity and state estimation mean square error obtained by forward and reverse navigation calculation, and finally obtaining global optimal estimation of the misalignment angle state, thereby improving the alignment precision of the system;
step 8, after the information fusion after the step 7 is completed, from treThe forward navigation fine alignment is carried out from the moment until the alignment end time teThe misalignment angle and velocity information are partially feedback corrected during alignment.
Further, the specific steps of step 1 include:
(1) alignment start time t0(setting t)00) the IMU is in a static state relative to the carrier, the IMU is in an electric zero position of the indexing mechanism, at the moment, an IMU coordinate system (p system) is coincident with an inertial navigation carrier coordinate system (b system), and tsAt the moment IMU (p series) starts
Figure BDA0002781689880000031
Is rotated by 180 DEG about the azimuth axis relative to the carrier (system b), wherein trThe rotation time of the turntable is long, and the IMU is positioned at an electrical 180-degree position of the indexing mechanism at the moment;
(2) the IMU is then stationary relative to the carrier for a period of time tsIMU (p is) around the azimuth axis
Figure BDA0002781689880000041
Is rotated 180 deg. relative to the carrier (system b), when the IMU is in the electrical zero position of the indexing mechanism, and then the IMU is stationary relative to the inertial frame for a period ts；
(3) Then, IMU (p series) is wound around the azimuth axis
Figure BDA0002781689880000042
Is rotated 180 deg. relative to the carrier (system b), the IMU is now located at the electrical-180 deg. position of the indexing mechanism, the IMU is stationary relative to the inertial frame, the stationary duration is ts；
(4) Then IMU to
Figure BDA0002781689880000043
Is rotated by 180 DEG around the azimuth axis relative to the inertial navigation coordinate system, the IMU is located at the electrical zero position of the indexing mechanism, and then the IMU is stationary relative to the inertial navigation coordinate system for a period of time tsTo this end, the IMU completes a rotational modulation period TrRotation of (2);
wherein:
b, a carrier coordinate system, defining the right front upper part as positive, and assuming that inertial navigation is superposed with the carrier system;
a p system-IMU coordinate system, wherein the p system of the indexing mechanism in the electric zero position is a b system of a right front upper coordinate system of the inertial navigation carrier;
p0system-initial moment IMU inertial system, coinciding with the IMU coordinate system at the initial alignment start moment (p-system), then without rotation with respect to the inertial space;
n is a navigation coordinate system, namely a northeast geographic coordinate system;
n0system-initial moment navigation inertial system, coinciding with the navigation coordinate system (n system) at the initial alignment start instant, then without rotation with respect to the inertial space;
Figure BDA0002781689880000044
the attitude-angle relationship of the IMU coordinate system (system p) of the output of the goniometer with respect to the carrier coordinate system (system b)
Figure BDA0002781689880000051
Moreover, the step 2 inertial system is indirectly roughly aligned
Figure BDA0002781689880000052
The key point of indirect coarse alignment of the inertial system is to find p0Is related to n0Conversion of systems, i.e. constant-value matrices
Figure BDA0002781689880000053
The method comprises the following specific steps:
(1)
Figure BDA0002781689880000054
is solved for
Figure BDA0002781689880000055
Due to the fact that
Figure BDA0002781689880000056
Is constant, i.e. n is relative to n0The rotation is made to be fixed-axis rotation, therefore,
Figure BDA0002781689880000057
wherein L is latitude, omegaieIs the angular velocity of the earth's rotation,
Figure BDA0002781689880000058
is the component of the earth in the geographic system of rotational angular velocity,
Figure BDA0002781689880000059
(2)
Figure BDA00027816898800000510
is solved for
Figure BDA00027816898800000511
Figure BDA00027816898800000512
The initial value of attitude quaternion is the measured value of the gyroscope
Figure BDA00027816898800000513
Real-time attitude matrix obtained by utilizing attitude updating algorithm
Figure BDA00027816898800000514
Here need not be to
Figure BDA00027816898800000515
The size of the coarse alignment algorithm is limited, so that the inertial system indirect coarse alignment algorithm has strong capability of resisting angular motion interference.
Angular rate by gyroscope
Figure BDA00027816898800000516
The integral yields an equivalent rotation vector, i.e.
Figure BDA00027816898800000517
Wherein, for the gyroscope output by the angular increment, phi is the angular increment information output by the gyroscope in real time;
the rotation angle phi is | phi |;
the rotation direction u is equal to phi/phi;
converting the equivalent rotation vector into a quaternion:
Figure BDA0002781689880000061
where m represents the current time and m-1 represents the previous time.
The quaternion of the current moment can be obtained
Figure BDA0002781689880000062
Converting quaternion of current time into quaternion of current time
Figure BDA0002781689880000063
Figure BDA0002781689880000064
(3)
Figure BDA0002781689880000065
Is solved for
Gravity acceleration vector is in n0Is projected as
Figure BDA0002781689880000066
Wherein, gn＝[00-g]TFor the component of the gravity acceleration vector under the navigation system, we can obtain:
Figure BDA0002781689880000067
specific force of accelerometer
Figure BDA0002781689880000068
At p0The projection is as follows:
Figure BDA0002781689880000069
by passing
Figure BDA00027816898800000610
A relationship between gravitational acceleration and accelerometer specific force may be established. General formula
Figure BDA00027816898800000611
Are simultaneously left-multiplied on two sides
Figure BDA00027816898800000612
To obtain
Figure BDA00027816898800000613
Namely, it is
Figure BDA00027816898800000614
Wherein the content of the first and second substances,
Figure BDA00027816898800000615
in order to be equivalent to the accelerometer measurement error,
Figure BDA00027816898800000616
is the specific force output of the accelerometer,
Figure BDA00027816898800000617
is shown in p0Measuring errors and linear acceleration interference by an accelerometer of the system;
therefore, only two matrix equations are established by obtaining the gravity and specific force measurement values at two moments, and the two matrix equations can be solved through a double-vector attitude determination algorithm
Figure BDA0002781689880000071
Because the inertia system indirect coarse alignment algorithm has relatively weak capacity of resisting line shaking interference in a short time, in order to reduce the influence of the line shaking interference, the above formula is integrated and recorded in the initial alignment process
Figure BDA0002781689880000072
Then there is
Figure BDA0002781689880000073
Usually take t2＝2t1，t1Modulating the period T for rotationr，t2＝tcIs the coarse alignment end time;
by adopting a mode of carrying out quadratic integration on the acceleration information in the inertia space, the following results can be obtained:
Figure BDA0002781689880000074
according to a double-vector attitude determination algorithm, the method can obtain
Figure BDA0002781689880000075
(4)
Figure BDA0002781689880000076
Is solved for
P of the indexing mechanism at the electric zero position is a system b of a right front upper coordinate system of the strapdown inertial navigation carrier, and the IMU winds around z in the alignment processpHas a rotation angle of theta (t) of
Figure BDA0002781689880000077
And theta (t) is obtained in real time from an angle measuring device in a control loop of the indexing mechanism.
The specific method of step 3 is: constructing an attitude matrix by using the rough initial attitude obtained by the rough alignment, carrying out forward navigation fine alignment, and estimating by using a Kalman filter through an misalignment angle error model misalignment angle until the reverse navigation initial time treThe reverse navigation starting time t can be determined according to the computing power and the alignment time length of the navigation computerre；
Further, the specific steps of step 4 include:
(1) calculating the starting time t of backward navigation in forward navigationreSampling a gyroscope in a forward algorithm, carrying out gyroscope constant drift and earth rotation angular rate symbol negation, setting an initial value posture and position of a reverse navigation algorithm as a posture and position of a forward navigation ending moment, and negating a speed symbol of the forward navigation ending moment as a speed of the reverse navigation initial moment;
(2) the sampling data is processed reversely, so that reverse navigation calculation and Kalman filtering from the reverse navigation starting moment to the coarse alignment starting moment can be realized, and the misalignment angle is estimated until the coarse alignment starting moment t0。
Moreover, the method for performing the fixed point smoothing filtering process in the reverse navigation process in step 5 includes:
at the initial moment, the state estimate is obtained by a Kalman filter
Figure BDA0002781689880000081
Sum state error mean square error matrix PkThe fixed point smoothing algorithm firstly gives an initial value to the smooth state estimation value and the prediction covariance matrix according to a Kalman filtering result:
Figure BDA0002781689880000082
when the Kalman filtering time k is more than or equal to the smooth time j, calculating a smooth gain matrix by using the following formula
Figure BDA0002781689880000083
Fixed point state smoothing estimate
Figure BDA0002781689880000084
And its covariance
Figure BDA0002781689880000085
Figure BDA0002781689880000086
Where the superscript s denotes fixed-point smoothing filtering.
Moreover, the calculation formula of step 7 is:
Figure BDA0002781689880000091
Figure BDA0002781689880000092
wherein the content of the first and second substances,
Figure BDA0002781689880000093
representing the local estimation, P, of the same state vector X obtained from a plurality of forward and backtracking null correction processesiRepresenting the mean square error of state estimation, N representing the sum of times of forward navigation or backtracking zero-speed correction process, and fusing state information estimated in all the forward zero-speed correction and backtracking zero-speed correction processes to obtain the global optimal estimation of state
Figure BDA0002781689880000094
Global estimation error PgLess than any local error Pi。
Moreover, the partial feedback correction method in step 8 is as follows:
suppose PrealFor estimation of true values of navigation parameters, PcalcuFor calculating values, X, of navigation parameterspBeing Kalman filtersAn estimated value is
Figure BDA0002781689880000095
Wherein, Pc′alcu＝(Pcalcu-α·Xp)，X′p＝(1-α)Xp，α∈[0,1]The method is a partial feedback coefficient, namely, a state estimation value of the Kalman filter is partially fed back to an inertial navigation calculation value, so that the calculation value is closer to a true value, the rest part is continuously kept in the Kalman filter, alpha is 0 and represents no feedback, alpha is 1 and represents full feedback, alpha is more than 0 and less than 1, partial feedback is performed, an error state is changed into a small amount through partial feedback correction, the linearity of an error system is kept, the convergence speed of the Kalman filter is higher, the state estimation is more accurate, and meanwhile, the calculation value in the alignment process is smoother.
Part of the feedback coefficients take the form:
Figure BDA0002781689880000096
wherein, TsThe time interval of the partial feedback correction of the Kalman filter is represented, tau epsilon (0, and + ∞) is a time constant of the partial feedback correction, and is set according to the needs of the system, the larger tau is, the smaller feedback quantity each time is, and the smoother navigation parameters are.
The invention has the advantages and beneficial effects that:
1. in the coarse alignment stage, equivalent errors of the accelerometer and the gyroscope are modulated through regular rotation of positive and negative rotation stop of a complete period, the convergence time of the coarse alignment is shortened, and the coarse alignment precision is improved.
2. According to the invention, through the rotation modulation in the coarse alignment stage, the integrity of the reverse navigation rotation modulation period in the fine alignment stage is ensured, and the fine alignment convergence speed and the alignment precision are further improved;
3. the invention adopts a scheme of determining the attitude of the position vector in the inertial space, avoids the influence of linear interference on the velocity vector caused by rotation modulation and size effect, and improves the precision of coarse precision.
4. The invention fully utilizes all observation values during measurement to carry out online smoothing processing on the filtered state vector through a smoothing technology, thereby realizing the optimized estimation of the state variable and improving the alignment accuracy of the system.
5. The partial feedback correction of the invention changes the error state into a small amount, ensures the linearity of an error system under the condition of larger misalignment angle error, leads the convergence speed of a linear Kalman filter to be faster, leads the state estimation to be more accurate, and leads the calculation value in the navigation alignment process to be smoother.
Drawings
FIG. 1 is a diagram of a rotary modulation strategy according to the present invention;
FIG. 2 is a schematic diagram of the rotational modulation coarse alignment of the present invention;
FIG. 3 is a reverse navigation fine alignment flowchart of the present invention.
Detailed Description
The embodiments of the invention will be described in further detail below with reference to the accompanying drawings:
an alignment method based on rotation modulation comprises rotation modulation coarse alignment, rotation modulation forward navigation fine alignment, rotation modulation reverse navigation fine alignment, partial feedback correction and misalignment angle information fusion.
The method comprises the following specific steps:
step 1, after a system receives a starting command, performing rotation modulation around an azimuth axis based on a rotation modulation strategy shown in figure 1;
the specific steps of the step 1 comprise:
(1) alignment start time t0(setting t)00) the IMU is in a static state relative to the carrier, the IMU is in an electric zero position of the indexing mechanism, at the moment, an IMU coordinate system (p system) is coincident with an inertial navigation carrier coordinate system (b system), and tsAt the moment IMU (p series) starts
Figure BDA0002781689880000111
Is rotated by 180 DEG about the azimuth axis relative to the carrier (system b),trthe rotation time of the turntable is long, and the IMU is positioned at an electrical 180-degree position of the indexing mechanism at the moment;
(2) the IMU is then stationary relative to the carrier for a period of time tsIMU (p is) around the azimuth axis
Figure BDA0002781689880000112
Is rotated 180 deg. relative to the carrier (system b), when the IMU is in the electrical zero position of the indexing mechanism, and then the IMU is stationary relative to the inertial frame for a period ts；
(3) Then, IMU (p series) is wound around the azimuth axis
Figure BDA0002781689880000113
Is rotated 180 deg. relative to the carrier (system b), the IMU is now located at the electrical-180 deg. position of the indexing mechanism, the IMU is stationary relative to the inertial frame, the stationary duration is ts；
(4) Then IMU to
Figure BDA0002781689880000114
Is rotated by 180 DEG around the azimuth axis relative to the inertial navigation coordinate system, the IMU is located at the electrical zero position of the indexing mechanism, and then the IMU is stationary relative to the inertial navigation coordinate system for a period of time tsTo this end, the IMU completes a rotational modulation period TrThe rotation of (2).
In the present embodiment, a coordinate system is defined as:
b, a carrier coordinate system, defining the right front upper part as positive, and assuming that inertial navigation is superposed with the carrier system;
a p system-IMU coordinate system, wherein the p system of the indexing mechanism in the electric zero position is a b system of a right front upper coordinate system of the inertial navigation carrier;
p0system-initial moment IMU inertial system, coinciding with the IMU coordinate system at the initial alignment start moment (p-system), then without rotation with respect to the inertial space;
n is a navigation coordinate system, namely a northeast geographic coordinate system;
n0system-initial time navigation inertial system, aligned with initial timeThe navigation coordinate systems (n systems) at the initial moment are overlapped and then do not rotate relative to the inertial space;
Figure BDA0002781689880000121
the attitude-angle relationship of the IMU coordinate system (system p) of the output of the goniometer with respect to the carrier coordinate system (system b)
Figure BDA0002781689880000122
In the present embodiment, the design rotation modulation strategy is:
an alignment method based on rotation modulation, the rotation modulation strategy of the whole alignment process is shown as figure 1, and the alignment starting time t0(setting t)00) the IMU is in a static state relative to the carrier, the IMU is in an electric zero position of a rotating mechanism, at the moment, an IMU coordinate system (p system) and an inertial navigation carrier coordinate system (b system) are superposed, and tsAt the moment IMU (p series) starts
Figure BDA0002781689880000123
Is rotated by 180 DEG about the azimuth axis relative to the carrier (system b), wherein trFor the duration of the turntable rotation, the IMU is now in the indexing mechanism electrical 180 ° position, and then the IMU is stationary relative to the carrier for a period of time tsIMU (p is) around the azimuth axis
Figure BDA0002781689880000124
Is rotated 180 deg. relative to the carrier (system b), when the IMU is in the null position of the indexing mechanism, and then the IMU is stationary relative to the inertial frame for a period tsThen, IMU (system p) is rotated around the azimuth axis
Figure BDA0002781689880000125
Is rotated 180 deg. relative to the carrier (system b), the IMU is now located at the electrical-180 deg. position of the indexing mechanism, the IMU is stationary relative to the inertial frame, the stationary duration is tsThen IMU to
Figure BDA0002781689880000126
The rotation angular velocity is rotated by 180 degrees around the azimuth axis relative to the inertial navigation coordinate system, the IMU is positioned at the electric zero position of the displacement mechanism, then the IMU is static relative to the inertial navigation coordinate system, and the static duration is tsTo this end, the IMU completes a rotational modulation period TrThe rotation of (2).
In order to completely modulate equivalent errors of a gyroscope and an accelerometer in the coarse alignment stage and improve the coarse alignment precision, the duration of the coarse alignment is integral multiple of the rotation modulation period in the coarse alignment stage, and the coarse alignment time is recommended to be equal to 2TrThat is, the time length of 2 rotational modulation periods, the specific coarse alignment time length is determined according to the system application requirements, and then the rotational modulation period duration is determined by the integral multiple relationship between the coarse alignment time and the coarse alignment rotational modulation period.
The selective modulation transposition sequence of the fine alignment stage is consistent with the transposition sequence of the coarse alignment stage, the rotary modulation period can be designed according to the system alignment time requirement, and the stop time t in the rotary modulation processsAnd a rotation time trThe fine alignment rotational modulation period is determined according to the fine alignment rotational modulation period, i.e. the fine alignment rotational modulation period can be consistent with the coarse alignment rotational modulation period, or can be designed to be inconsistent with the coarse alignment rotational modulation period.
Step 2, in the rotation modulation process of the step 1, the system adopts an indirect coarse alignment scheme based on an inertial system to perform coarse rotation modulation alignment;
the specific steps of the step 2 comprise:
the inertial system indirect coarse alignment is shown in figure 2,
Figure BDA0002781689880000131
the key point of the inertial system indirect coarse alignment is to find p0Is related to n0Conversion of systems, i.e. constant-value matrices
Figure BDA0002781689880000132
(1)
Figure BDA0002781689880000133
Is solved for
Figure BDA0002781689880000134
Due to the fact that
Figure BDA0002781689880000135
Is constant, i.e. n is relative to n0The rotation is made to be fixed-axis rotation, therefore,
Figure BDA0002781689880000136
wherein L is latitude, omegaieIs the angular velocity of the earth's rotation,
Figure BDA0002781689880000137
is the component of the earth in the geographic system of rotational angular velocity,
Figure BDA0002781689880000138
(2)
Figure BDA0002781689880000139
is solved for
Figure BDA00027816898800001310
Figure BDA00027816898800001311
The initial value of attitude quaternion is the measured value of the gyroscope
Figure BDA00027816898800001312
Real-time attitude matrix obtained by utilizing attitude updating algorithm
Figure BDA0002781689880000141
Here need not be to
Figure BDA0002781689880000142
The size of the coarse alignment algorithm is limited, so that the inertial system indirect coarse alignment algorithm has strong capability of resisting angular motion interference.
Angular rate by gyroscope
Figure BDA0002781689880000143
The integral yields an equivalent rotation vector, i.e.
Figure BDA0002781689880000144
Wherein, for the gyroscope output by the angular increment, phi is the angular increment information output by the gyroscope in real time;
the rotation angle phi is | phi |;
the rotation direction u is equal to phi/phi;
converting the equivalent rotation vector into a quaternion:
Figure BDA0002781689880000145
where m represents the current time and m-1 represents the previous time.
The quaternion of the current moment can be obtained
Figure BDA0002781689880000146
Converting quaternion of current time into quaternion of current time
Figure BDA0002781689880000147
Figure BDA0002781689880000148
(3)
Figure BDA0002781689880000149
Is solved for
Gravity acceleration vector is in n0Is projected as
Figure BDA00027816898800001410
Wherein, gn＝[00-g]TFor the component of the gravity acceleration vector under the navigation system, we can obtain:
Figure BDA00027816898800001411
specific force of accelerometer
Figure BDA00027816898800001412
At p0The projection is as follows:
Figure BDA00027816898800001413
by passing
Figure BDA0002781689880000151
A relationship between gravitational acceleration and accelerometer specific force may be established. General formula
Figure BDA0002781689880000152
Are simultaneously left-multiplied on two sides
Figure BDA0002781689880000153
To obtain
Figure BDA0002781689880000154
Namely, it is
Figure BDA0002781689880000155
Wherein the content of the first and second substances,
Figure BDA0002781689880000156
in order to be equivalent to the accelerometer measurement error,
Figure BDA0002781689880000157
is the specific force output of the accelerometer,
Figure BDA0002781689880000158
is shown in p0The accelerometer of the system measures errors and linear acceleration disturbances.
Therefore, only two matrix equations are established by obtaining the gravity and specific force measurement values at two moments, and the two matrix equations can be solved through a double-vector attitude determination algorithm
Figure BDA0002781689880000159
Because the inertia system indirect coarse alignment algorithm has relatively weak capacity of resisting line shaking interference in a short time, in order to reduce the influence of the line shaking interference, the above formula is integrated and recorded in the initial alignment process
Figure BDA00027816898800001510
Then there is
Figure BDA00027816898800001511
Usually take t2＝2t1，t1Modulating the period T for rotationr，t2＝tcIs the coarse alignment end time.
In order to further reduce the influence of line interference on alignment precision caused by rotation and size effects, the invention adopts a mode of carrying out quadratic integration on acceleration information in an inertia space, and the method can obtain the acceleration information
Figure BDA00027816898800001512
According to a double-vector attitude determination algorithm, the method can obtain
Figure BDA0002781689880000161
(4)
Figure BDA0002781689880000162
Is solved for
P of the indexing mechanism at the electric zero position is a system b of a right front upper coordinate system of the strapdown inertial navigation carrier, and the IMU winds around z in the alignment processpHas a rotation angle of theta (t) of
Figure BDA0002781689880000163
And theta (t) is obtained in real time from an angle measuring device in a control loop of the indexing mechanism.
In this embodiment, the rotational modulation coarse alignment adopts an indirect coarse alignment scheme based on an inertial system, and since the indirect coarse alignment does not limit the angular rate of the inertial system and the IMU, the indirect coarse alignment algorithm has a strong capability of resisting angular motion interference, and is more suitable for the application of rotational modulation, and according to the application requirements of the system, the coarse alignment time is designed to be equal to 2N times of the rotational modulation period, so as to ensure that the equivalent errors of the accelerometer and the gyroscope in the coarse alignment stage can obtain complete and effective rotational modulation, i.e., tc＝2NtrWherein, tcFor coarse alignment time, trIs a rotation modulation period;
step 3, after the coarse alignment of the rotation modulation is finished, the system carries out the accurate alignment of the rotation modulation forward navigation;
the specific method of the step 3 comprises the following steps: constructing an attitude matrix by using the rough initial attitude obtained by the rough alignment, carrying out forward navigation fine alignment, and estimating by using a Kalman filter through a misalignment angle of a misalignment angle error model until a reverse navigation starting time treAccording to the computing power of the navigation computerAnd determining the reverse navigation starting time t by the alignment time lengthre；
(1) Updating the forward navigation algorithm after recursive discretization:
posture updating formula:
Figure BDA0002781689880000164
velocity update formula:
Figure BDA0002781689880000171
location update formula:
Figure BDA0002781689880000172
Figure BDA0002781689880000173
Figure BDA0002781689880000174
wherein k represents the kth inertial navigation resolving moment, and k-1 represents the previous moment of the kth moment;
Figure BDA0002781689880000175
Figure BDA0002781689880000176
Figure BDA0002781689880000177
Figure BDA0002781689880000178
Figure BDA0002781689880000179
representing an inertial navigation attitude direction cosine matrix;
vn＝[vE vN vU]Trepresenting the speed under the navigation system;
l represents latitude;
λ represents longitude;
h represents height;
Figure BDA00027816898800001710
representing a gyro angular velocity measurement;
Figure BDA00027816898800001711
accelerometer specific force measurement;
ωierepresenting the earth rotation angular rate;
g and local gravitational acceleration;
RMrepresents the meridian and radius of the local earth;
RNrepresenting the radius of the prime cycle;
Figure RE-GDA0002980151220000181
x is represented by a rotational angular velocity
Figure RE-GDA0002980151220000182
A composed antisymmetric matrix, the operator (· ×) representing the antisymmetric matrix composed of vectors;
Tsrepresenting an inertial navigation sampling period;
(2) designing a Kalman filter for forward navigation fine alignment:
the state variables are as follows:
Figure BDA0002781689880000184
wherein the content of the first and second substances,
φE,φN,φUrespectively a pitch misalignment angle, a roll misalignment angle and a heading misalignment angle;
δvE,δvN,δvUeast-direction speed error, north-direction speed error and vertical-direction speed error are respectively included;
δ L, δ λ, δ h are latitude error, longitude error and altitude error, respectively;
Figure BDA0002781689880000185
x gyro drift, Y gyro drift and Z gyro drift are respectively;
Figure BDA0002781689880000186
respectively X plus zero position, Y plus zero position and Z plus zero position.
(3) According to an error equation of inertial navigation, establishing a state equation of a continuous system as follows:
Figure BDA0002781689880000187
wherein the content of the first and second substances,
Figure BDA0002781689880000188
Figure BDA0002781689880000189
Figure BDA0002781689880000191
Figure BDA0002781689880000192
Figure BDA0002781689880000193
wherein f isE,fN,fURespectively representing the projection of the specific force measured by the triaxial accelerometer under the navigation system "east-north-sky", i.e.
Figure BDA0002781689880000194
Figure BDA0002781689880000195
Figure BDA0002781689880000196
Figure BDA0002781689880000197
Figure BDA0002781689880000201
Figure BDA0002781689880000202
Figure BDA0002781689880000203
(4) The measurement equation with velocity as observation is:
Figure BDA0002781689880000204
H＝[I2×2 02×13]
step 4, after the rotary modulation forward navigation fine alignment is finished, setting the initial value posture and position of the reverse navigation algorithm as the posture and position of the forward navigation finish time, and changing the model parameters into a small error model parameter system to carry out rotary modulation reverse navigation fine alignment;
as shown in fig. 3, the specific steps of step 4 include:
(1) calculating the starting time t of backward navigation in forward navigationreSampling a gyroscope in a forward algorithm, negating a gyroscope constant drift and an earth rotation angular rate symbol, setting an initial value posture and a position of a reverse navigation algorithm as a posture and a position of a forward navigation ending moment, negating a speed symbol of the forward navigation ending moment as a speed of the reverse navigation initial moment, and changing a model parameter into a small-error model parameter;
(2) the sampling data is processed reversely, so that reverse navigation calculation and Kalman filtering from the reverse navigation starting moment to the coarse alignment starting moment can be realized, and the misalignment angle is estimated until the coarse alignment starting moment t0。
Reverse navigation solution in the forward and reverse navigation processes, the attitude matrices of the two processes at the same time are equal, the position coordinates are also equal, and the speeds are equal in magnitude but opposite in sign.
In this embodiment, during the reverse navigation alignment, the gyro sampling and the earth rotation angle rate symbol in the forward navigation are inverted, and the initial value of the reverse navigation algorithm is set as
Figure BDA0002781689880000205
Figure BDA0002781689880000206
And performing reverse navigation calculation on the sampled data:
the reverse navigation attitude updating formula is as follows:
Figure BDA0002781689880000211
the reverse navigation speed updating formula is as follows:
Figure BDA0002781689880000212
the reverse navigation position updating formula is as follows:
Figure BDA0002781689880000213
Figure BDA0002781689880000214
Figure BDA0002781689880000215
wherein the content of the first and second substances,
m represents the last forward navigation end time;
p represents the pth reverse resolving moment, and p-1 represents the next reverse navigation data moment of the pth moment;
Figure BDA0002781689880000216
Figure BDA0002781689880000217
Figure BDA0002781689880000218
in the reverse navigation fine alignment process, the updating of the system state variables is also carried out according to the reverse sequence. And calculating a continuous time state transition matrix F according to a reverse navigation result, negating the speed of the state variable and the gyro drift symbol, and calculating according to a Kalman filter precisely aligned with the forward navigation.
Step 5, filtering to the initial time t of coarse alignment in the reverse navigation Kalman0Adjusting the error model parameters again, enabling the alignment program to enter rotary modulation precision alignment, sampling a gyroscope in a forward algorithm, adopting symbols of forward calculation for gyroscope constant drift and earth rotation angular rate symbols, setting an initial value attitude and position of a reverse navigation algorithm as the attitude and position of a forward navigation ending moment, negating a speed symbol of the reverse navigation ending moment as the speed of the forward navigation initial moment, starting forward calculation and Kalman filtering on sampling data from a rough alignment starting moment, carrying out rotary modulation precision alignment, estimating a misalignment angle until the reverse navigation starting moment tre(ii) a Performing fixed point smoothing filtering in the reverse navigation process, and performing online smoothing on the filtered state vector by fully utilizing all observation values in the measurement period to realize the optimized estimation of the state variable;
the method for performing fixed point smoothing filtering processing in the reverse navigation process in the step 5 comprises the following steps:
the fixed point on-line smoothing filtering is to carry out on-line smoothing processing on a filtering state vector by fully utilizing all observation values during measurement on the basis of conventional Kalman filtering estimation, thereby realizing the optimized estimation of state variables and improving the alignment precision of a system.
At the initial moment, the state estimate is obtained by a Kalman filter
Figure BDA0002781689880000221
Sum state error mean square error matrix PkThe fixed point smoothing algorithm firstly gives an initial value to the smooth state estimation value and the prediction covariance matrix according to a Kalman filtering result:
Figure BDA0002781689880000222
when the Kalman filtering time k is more than or equal to the smooth time j, calculating a smooth gain matrix by using the following formula
Figure BDA0002781689880000223
Fixed point state smoothing estimate
Figure BDA0002781689880000224
And its covariance
Figure BDA0002781689880000225
Figure BDA0002781689880000226
Where the superscript s denotes fixed-point smoothing filtering.
Step 6, repeatedly executing the operation times of the step 4 and the step 5, repeatedly utilizing the navigation data and the external reference information in the alignment time, and determining the repeated calculation times according to the calculation capability and the alignment time length of the navigation computer;
step 7, after the rotational modulation forward navigation fine alignment of the step 6 is completed, performing information fusion by using misalignment angle state quantity and state estimation mean square error obtained by forward and reverse navigation calculation, and finally obtaining global optimal estimation of the misalignment angle state, thereby improving the alignment precision of the system;
the calculation formula of the step 7 is as follows:
Figure BDA0002781689880000231
Figure BDA0002781689880000232
wherein the content of the first and second substances,
Figure BDA0002781689880000233
representing the local estimation, P, of the same state vector X obtained from a plurality of forward and backtracking null correction processesiRepresenting the mean square error of state estimation, N representing the sum of times of forward navigation or backtracking zero-speed correction process, and calculating the mean square error of all the state estimationThe state information estimated in the forward zero-speed correction process and the backtracking zero-speed correction process is fused to obtain the global optimal estimation of the state
Figure BDA0002781689880000234
Global estimation error PgLess than any local error Pi。
Step 8, after the information fusion after the step 7 is completed, from treThe forward navigation fine alignment is carried out from the moment until the alignment end time teThe misalignment angle and velocity information are partially feedback corrected during alignment.
The partial feedback correction method in the step 8 comprises the following steps:
suppose PrealFor estimation of true values of navigation parameters, PcalcuFor calculating values, X, of navigation parameterspThe estimated value of the Kalman filter is
Figure BDA0002781689880000235
Wherein, Pc′alcu＝(Pcalcu-α·Xp)，X′p＝(1-α)Xp，α∈[0,1]The method is a partial feedback coefficient, namely, a state estimation value of the Kalman filter is partially fed back to an inertial navigation calculation value, so that the calculation value is closer to a true value, the rest part is continuously kept in the Kalman filter, alpha is 0 and represents no feedback, alpha is 1 and represents full feedback, alpha is more than 0 and less than 1, partial feedback is performed, an error state is changed into a small amount through partial feedback correction, the linearity of an error system is kept, the convergence speed of the Kalman filter is higher, the state estimation is more accurate, and meanwhile, the calculation value in the alignment process is smoother.
Part of the feedback coefficients take the form:
Figure BDA0002781689880000236
wherein, TsTime interval, τ e, representing the partial feedback correction of the Kalman filter(0, + ∞) is the time constant of partial feedback correction, and according to the needs of the system, the larger tau is, the smaller each feedback quantity is, and the smoother the navigation parameter is.
The system performs partial feedback corrections during both forward navigational alignment and reverse navigational alignment.
It should be emphasized that the embodiments described herein are illustrative and not restrictive, and thus the present invention includes, but is not limited to, the embodiments described in the detailed description, and that other embodiments derived from the teachings of the present invention by those skilled in the art are also within the scope of the present invention.

Claims (8)

1. An alignment method based on rotation modulation, characterized in that: the method comprises the following steps:
step 1, after a system is electrified and receives a starting command, carrying out rotation modulation around an azimuth axis based on a rotation modulation strategy;
step 2, in the rotation modulation process of the step 1, the system adopts an indirect coarse alignment scheme based on an inertial system to perform coarse rotation modulation alignment;
step 3, after the coarse alignment of the rotation modulation is finished, the system carries out the fine alignment of the rotation modulation forward navigation;
step 4, after the rotary modulation forward navigation fine alignment is finished, setting the initial value posture and position of a reverse navigation algorithm as the posture and position of the forward navigation finish time, and changing the model parameters into a small-error model parameter system to carry out rotary modulation reverse navigation fine alignment;
step 5, filtering to the initial time t of coarse alignment in the reverse navigation Kalman0Adjusting the parameters of the error model again, enabling the alignment program to enter rotation modulation precise alignment, sampling the gyroscope in the forward algorithm, adopting symbols calculated in the forward direction for the gyroscope constant drift and the earth rotation angular rate symbols, and setting the initial attitude and position of the reverse navigation algorithm asTaking the inverse of the speed sign of the backward navigation ending moment as the speed of the forward navigation initial moment, carrying out forward calculation and Kalman filtering on the sampled data from the rough alignment starting moment, carrying out rotary modulation precise alignment, and estimating the misalignment angle until the backward navigation starting moment tre(ii) a Performing fixed point smoothing filtering in the reverse navigation process, and performing online smoothing on the filtered state vector by fully utilizing all observation values during measurement to realize the optimal estimation of the state variable;
step 6, repeatedly executing the operation times of the step 4 and the step 5, repeatedly utilizing the navigation data and the external reference information in the alignment time, and determining the repeated calculation times according to the calculation capability and the alignment time length of the navigation computer;
step 7, after the rotational modulation forward navigation fine alignment of the step 6 is completed, performing information fusion by using misalignment angle state quantity and state estimation mean square error obtained by forward and reverse navigation calculation, and finally obtaining global optimal estimation of the misalignment angle state, thereby improving the alignment precision of the system;
step 8, after the information fusion after the step 7 is completed, from treThe forward navigation fine alignment is carried out from the moment until the alignment end time teThe misalignment angle and velocity information are partially feedback corrected during alignment.
2. The alignment method based on rotation modulation according to claim 1, wherein: the specific steps of the step 1 comprise:
(1) alignment start time t0The IMU is in a static state relative to the carrier, the IMU is in an electric zero position of the indexing mechanism, at the moment, an IMU coordinate system is coincident with an inertial navigation carrier coordinate system, and tsAt the moment IMU starts
Figure FDA0002781689870000021
Is rotated 180 deg. about the azimuth axis relative to the carrier, wherein trThe rotation time of the turntable is long, and the IMU is positioned at an electrical 180-degree position of the indexing mechanism at the moment;
(2) the IMU is then stationary relative to the carrier for a period of time tsThe IMU is around the azimuth axis
Figure FDA0002781689870000022
Is rotated 180 deg. relative to the carrier, while the IMU is located in the null position of the indexing mechanism, and then the IMU is stationary relative to the inertial frame for a period ts；
(3) The IMU is then rotated about the azimuth axis
Figure FDA0002781689870000023
Is rotated 180 deg. relative to the carrier, the IMU is now located at the electrical-180 deg. position of the indexing mechanism, the IMU is stationary relative to the inertial frame, the stationary duration is ts；
(4) Then IMU to
Figure FDA0002781689870000024
Is rotated by 180 DEG around the azimuth axis relative to the inertial navigation coordinate system, the IMU is located at the electrical zero position of the indexing mechanism, and then the IMU is stationary relative to the inertial navigation coordinate system for a period of time tsTo this end, the IMU completes a rotational modulation period TrRotation of (2);
wherein:
b, a carrier coordinate system, defining the right front upper part as positive, and assuming that inertial navigation is superposed with the carrier system;
a p system-IMU coordinate system, wherein the p system of the indexing mechanism in the electric zero position is a b system of a right front upper coordinate system of the inertial navigation carrier;
p0system-initial moment IMU inertial system, coinciding with IMU coordinate system at initial alignment start moment, then non-rotating with respect to inertial space;
n is a navigation coordinate system, namely a northeast geographic coordinate system;
n0system-initial moment navigation inertial system, coinciding with initial alignment start instant navigation coordinate system, then no rotation with respect to inertial space;
Figure FDA0002781689870000031
the attitude-angle relationship of the IMU coordinate system output by the angle-measuring device with respect to the carrier coordinate system
Figure FDA0002781689870000032
3. The alignment method based on rotation modulation according to claim 1, wherein: indirect coarse alignment of the inertial system of step 2
Figure FDA0002781689870000033
The key point of indirect coarse alignment of the inertial system is to find p0Is related to n0Conversion of systems, i.e. constant-value matrices
Figure FDA0002781689870000034
The method comprises the following specific steps:
(1)
Figure FDA0002781689870000035
is solved for
Figure FDA0002781689870000036
Due to the fact that
Figure FDA0002781689870000037
Is constant, i.e. n is relative to n0The rotation of the shaft is fixed to the shaft,
therefore, the temperature of the molten metal is controlled,
Figure FDA0002781689870000038
wherein L is latitude, omegaieIs the angular velocity of the earth's rotation,
Figure FDA0002781689870000039
is a component of the earth in the geographic system of rotational angular velocity,
Figure FDA0002781689870000041
(2)
Figure FDA0002781689870000042
is solved for
Figure FDA0002781689870000043
Figure FDA0002781689870000044
The initial value of attitude quaternion is the measured value of the gyroscope
Figure FDA0002781689870000045
Real-time attitude matrix obtained by utilizing attitude updating algorithm
Figure FDA0002781689870000046
Angular rate by gyroscope
Figure FDA0002781689870000047
The integral yields an equivalent rotation vector, i.e.
Figure FDA0002781689870000048
Wherein, for the gyroscope output by the angular increment, phi is the angular increment information output by the gyroscope in real time;
the rotation angle phi is | phi |;
the rotation direction u is equal to phi/phi;
converting the equivalent rotation vector into a quaternion:
Figure FDA0002781689870000049
wherein m represents the current time, and m-1 represents the last time;
the quaternion of the current moment can be obtained
Figure FDA00027816898700000410
Converting quaternion of current time into quaternion of current time
Figure FDA00027816898700000411
Figure FDA00027816898700000412
(3)
Figure FDA00027816898700000413
Is solved for
Gravity acceleration vector is in n0Is projected as
Figure FDA00027816898700000414
Wherein, gn＝[0 0 -g]TFor the component of the gravity acceleration vector under the navigation system, we can obtain:
Figure FDA0002781689870000051
specific force of accelerometer
Figure FDA0002781689870000052
At p0The projection is as follows:
Figure FDA0002781689870000053
by passing
Figure FDA0002781689870000054
A relationship between the gravity acceleration and the specific force of the accelerometer can be established; general formula
Figure FDA0002781689870000055
Are simultaneously left-multiplied on two sides
Figure FDA0002781689870000056
To obtain
Figure FDA0002781689870000057
Namely, it is
Figure FDA0002781689870000058
Wherein the content of the first and second substances,
Figure FDA0002781689870000059
in order to be equivalent to the accelerometer measurement error,
Figure FDA00027816898700000510
is the specific force output of the accelerometer,
Figure FDA00027816898700000511
is shown in p0Measuring errors and linear acceleration interference by an accelerometer of the system;
therefore, only two matrix equations are established by obtaining the gravity and specific force measurement values at two moments, and the two matrix equations can be solved through a double-vector attitude determination algorithm
Figure FDA00027816898700000512
Because the inertia system indirect coarse alignment algorithm has relatively weak capacity of resisting line shaking interference in a short time, in order to reduce the influence of the line shaking interference, the above formula is integrated and recorded in the initial alignment process
Figure FDA00027816898700000513
Then there is
Figure FDA00027816898700000514
Usually take t2＝2t1，t1Modulating the period T for rotationr，t2＝tcIs the coarse alignment end time;
by adopting a mode of carrying out quadratic integration on the acceleration information in the inertia space, the following results can be obtained:
Figure FDA0002781689870000061
according to a double-vector attitude determination algorithm, the method can obtain
Figure FDA0002781689870000062
(4)
Figure FDA0002781689870000063
Is solved for
P of the indexing mechanism at the electric zero position is a system b of a right front upper coordinate system of the strapdown inertial navigation carrier, and the IMU winds around z in the alignment processpHas a rotation angle of theta (t) of
Figure FDA0002781689870000064
And theta (t) is obtained in real time from an angle measuring device in a control loop of the indexing mechanism.
4. The alignment method based on rotation modulation according to claim 1, wherein: the specific method of the step 3 comprises the following steps: constructing an attitude matrix by using the rough initial attitude obtained by the rough alignment, carrying out forward navigation fine alignment, and estimating by using a Kalman filter through a misalignment angle of a misalignment angle error model until the reverse navigation initial time treThe reverse navigation starting time t can be determined according to the computing power and the alignment time length of the navigation computerre。
5. The alignment method based on rotation modulation according to claim 1, wherein: the specific steps of the step 4 comprise:
(1) calculating the starting time t of backward navigation in forward navigationreSampling a gyroscope in a forward algorithm, carrying out gyroscope constant drift and earth rotation angular rate symbol negation, setting an initial value posture and position of a reverse navigation algorithm as a posture and position of a forward navigation ending moment, and negating a speed symbol of the forward navigation ending moment as a speed of the reverse navigation initial moment;
(2) the sampling data is processed in reverse direction, so that reverse navigation calculation and Kalman filtering from the start time of reverse navigation to the start time of coarse alignment can be realized, and the misalignment angle is estimated until the start time t of coarse alignment0。
6. The alignment method based on rotation modulation according to claim 1, wherein: the method for performing fixed point smoothing filtering processing in the reverse navigation process in the step 5 comprises the following steps:
at the initial moment, the state estimate is obtained by a Kalman filter
Figure FDA0002781689870000071
Sum state error mean square error matrix PkThe fixed point smoothing algorithm is first based on KalmanAnd the filtering result gives an initial value to the smooth state estimation value and the prediction covariance matrix:
Figure FDA0002781689870000072
when the Kalman filtering time k is more than or equal to the smooth time j, calculating a smooth gain matrix by using the following formula
Figure FDA0002781689870000073
Fixed point state smoothing estimate
Figure FDA0002781689870000074
And its covariance
Figure FDA0002781689870000075
Figure FDA0002781689870000076
Where the superscript s denotes fixed-point smoothing filtering.
7. The alignment method based on rotation modulation according to claim 1, wherein: the calculation formula of the step 7 is as follows:
Figure FDA0002781689870000077
Figure FDA0002781689870000078
wherein the content of the first and second substances,
Figure FDA0002781689870000079
representing the forward zero-speed correction process and the backtracking zero-speed correction process from multiple timesObtained local estimates, P, of the same state vector XiRepresenting the mean square error of state estimation, N representing the sum of times of forward navigation or backtracking zero-speed correction process, and fusing state information estimated in all the forward zero-speed correction and backtracking zero-speed correction processes to obtain the global optimal estimation of state
Figure FDA00027816898700000710
Global estimation error PgLess than any local error Pi。
8. The alignment method based on rotation modulation according to claim 1, wherein: the partial feedback correction method in the step 8 comprises the following steps:
suppose PrealFor estimation of true values of navigation parameters, PcalcuFor calculating values, X, of navigation parameterspThe estimated value of the Kalman filter is
Figure FDA0002781689870000081
Wherein, P'calcu＝(Pcalcu-α·Xp)，X′p＝(1-α)Xp，α∈[0,1]The method is a partial feedback coefficient, namely, a state estimation value of the Kalman filter is partially fed back to an inertial navigation solution value, so that the solution value is closer to a true value, the rest part is continuously kept in the Kalman filter, alpha is 0 and represents no feedback, alpha is 1 and represents full feedback, alpha is more than 0 and less than 1, partial feedback is performed, the error state is changed into a small amount through partial feedback correction, the linearity of an error system is kept, the convergence speed of the Kalman filter is higher, the state estimation is more accurate, and meanwhile, the solution value in the alignment process is smoother;
part of the feedback coefficients take the form:
Figure FDA0002781689870000082
wherein, TsThe time interval of the partial feedback correction of the Kalman filter is represented, tau epsilon (0, and ∞) is a time constant of the partial feedback correction, and is set according to the needs of the system, the larger tau is, the smaller feedback quantity each time is, and the smoother navigation parameters are.
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CN113959462B (en) * 2021-10-21 2023-09-12 北京机电工程研究所 Quaternion-based inertial navigation system self-alignment method
CN114894222A (en) * 2022-07-12 2022-08-12 深圳元戎启行科技有限公司 External parameter calibration method of IMU-GNSS antenna and related method and equipment

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