CN116858287A - Polar region inertial navigation initial alignment method based on earth coordinate system - Google Patents
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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
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
- G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
- G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
- G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
- G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
- G01C21/18—Stabilised platforms, e.g. by gyroscope
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
- G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
- G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
- G01C21/183—Compensation of inertial measurements, e.g. for temperature effects
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
- G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/42—Determining position
- G01S19/48—Determining position by combining or switching between position solutions derived from the satellite radio beacon positioning system and position solutions derived from a further system
- G01S19/49—Determining position by combining or switching between position solutions derived from the satellite radio beacon positioning system and position solutions derived from a further system whereby the further system is an inertial position system, e.g. loosely-coupled
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- Navigation (AREA)
Abstract
The application provides a polar region inertial navigation initial alignment method based on an earth coordinate system, which comprises the following steps: collecting the output of an accelerometer and a gyroscope in inertial navigation; performing coarse alignment on the inertial navigation to obtain a posture transformation matrix of the inertial navigation at any moment; and based on the attitude transformation matrix, carrying out fine alignment on the inertial navigation by utilizing the output, and obtaining the aligned attitude, speed and position of the inertial navigation. The application has simple calculated amount, strong anti-interference capability and high reliability, and can be used in any place around the world.
Description
Technical Field
The application belongs to the technical field of inertial navigation, and particularly relates to a polar region inertial navigation initial alignment method based on an earth coordinate system.
Background
As human activity in polar regions increases, polar navigation is increasingly important. Because of the advantages of complete autonomy, strong anti-interference capability, high reliability, etc., inertial navigation systems are widely used. The initial alignment technology specially used for determining the initial attitude of the inertial navigation system has the most important influence on the navigation precision, and is one of the most important technologies in the inertial navigation field. In polar regions, due to the rapid convergence of meridians, the horizontal component of the earth's rotational angular velocity also decreases dramatically, and conventional initial alignment methods based on the "east-north-day" geographic coordinate system are difficult to use properly. For this reason, various navigation coordinate systems suitable for polar regions have been developed, for example: a traveling azimuth coordinate system, a pseudo-earth coordinate system, an abscissa system, a grid coordinate system, and the like. And initial alignment techniques were developed based thereon. But the above mentioned coordinate systems all belong to a local horizontal coordinate system. The coordinate system has specific mathematical singular points, and the global navigation is realized by two or more navigation coordinate systems. Switching between different navigational coordinate systems may cause abrupt changes in the navigational filter as the carrier traverses the polar region. The earth coordinate system has no mathematical singular points and has global navigation capability. Furthermore, compared with a local horizontal coordinate system, the calculation amount of the inertial navigation updating algorithm based on the regional coordinate system is simpler. Therefore, the application adopts the earth coordinate system as the navigation coordinate system to study the polar region initial alignment technology.
Disclosure of Invention
In order to solve the technical problems, the application provides an inertial navigation initial alignment technology which can be used in any place (including polar regions) around the world.
In order to achieve the above object, the present application provides an initial alignment method of polar region inertial navigation based on an earth coordinate system, comprising:
collecting the output of an accelerometer and a gyroscope in inertial navigation;
performing coarse alignment on the inertial navigation to obtain a posture transformation matrix of the inertial navigation at any moment;
and based on the attitude transformation matrix, carrying out fine alignment on the inertial navigation by utilizing the output, and obtaining the aligned attitude, speed and position of the inertial navigation.
Optionally, coarsely aligning the inertial navigation includes:
based on a satellite navigation system, acquiring an initial attitude transformation matrix of the inertial navigation by utilizing a specific force differential equation;
and acquiring the attitude transformation matrix of the inertial navigation at any moment based on the initial attitude transformation matrix.
Optionally, the specific force differential equation is:
wherein ,representing the projection of the velocity of the carrier relative to the inertial space in the earth's system, f b Acceleration vector representing accelerometer output, +.>Projection of the earth's subsurface representing the earth's gravity, < +.>Representing an initial gesture transformation matrix->Representing the earth rotation angular velocity vector,/->Representing the derivative of the velocity of the carrier with respect to the inertial space projected in the earth,representing from the initial time to t k Angular transformation matrix of the earth system with respect to the inertial space at moment +.>From t k The time to initial time carrier is an angular transformation matrix relative to the inertial space.
Optionally, the attitude transformation matrix of the inertial navigation at any moment is:
wherein ,representing t k Posture transformation matrix from b line to e line at moment, < >>An attitude transformation matrix representing the initial time from b-line to e-line, < >>Representing from the initial time to t k Time e is a transformation matrix, ">From t k The transformation matrix of the b system from the moment to the initial moment, b system represents the carrier coordinate system and e system represents the earth coordinate system.
Optionally, obtaining the initial pose transformation matrix of the inertial navigation includes:
preprocessing the specific force differential equation to obtain a preset equation;
integrating the preset equation;
based on the preset equation after the integration processing, acquiring the initial attitude transformation matrix of the inertial navigation by utilizing a multi-vector attitude determination algorithm.
Optionally, the preset equation is:
wherein ,from t k The earth system is transformed into a matrix of angles relative to the inertial space from moment to initial moment.
Optionally, fine-aligning the inertial navigation includes:
based on the gesture transformation matrix, calculating the output to acquire the initial gesture, speed and position of the inertial navigation;
constructing an inertial navigation error model based on the initial attitude, speed and position of the inertial navigation; estimating the inertial navigation error model based on a Kalman filter to obtain an estimated error;
and compensating the attitude transformation matrix based on the estimation error to finish the precise alignment of the inertial navigation.
Optionally, the initial attitude, velocity and position of the inertial navigation are respectively:
wherein ,representing the initial pose of inertial navigation,>representing the initial speed of inertial navigation, +.>Representing the initial position of inertial navigation,>representing the position of the carrier in the earth's coordinate system.
Optionally, the inertial navigation error model is:
wherein X represents an error state,representing misalignment angle vector, +.>Representing a velocity error vector, ">Representing a position error vector, ">Indicating gyro constant drift +.>Representing accelerometer constant zero bias, F representing state transition matrix,>derivative representing error state +.>Representing the angular velocity of the output of a triaxial gyroscope in inertial navigation,/->Representing acceleration of the triaxial accelerometer output in inertial navigation, G representing noise distribution matrix, W representing process noise vector,/->Representing system observation noise, Z representing observation vector, representing inertial navigation pure inertial solution attitude matrix +.>Transpose of->A position vector representing an inertial navigation pure inertial solution,position vector representing GPS elevation,>posture matrix representing inertial navigation pure inertial solution, < >>Representing a position error vector, I 3×3 Representing a third order identity matrix.
Optionally, the method for compensating the gesture transformation matrix comprises the following steps:
wherein ,representing the corrected inertial navigation attitude matrix, +.>Representing the estimated misalignment angle vector of the Kalman filter, x represents the inverse symmetric matrix operation,/and->Indicating corrected inertial velocity, +.>Indicating the corrected inertial navigation position.
Compared with the prior art, the application has the following advantages and technical effects: the existing inertial navigation system taking an east-north-sky geographic coordinate system as a reference coordinate system has a coefficient term of tan (L) (L represents latitude) when navigation calculation is performed, so that the navigation algorithm has singular calculation at the north-south pole of the earth (latitude 90 degrees) or near the north-south pole, and does not have global navigation capability. The measures taking the earth coordinate system as the reference coordinate system can overcome the defects, and the navigation calculation at any position of the world can not face the problem of singular calculation, so that the method has the global navigation capability. Meanwhile, the application adopts an alignment mode of rough alignment and fine alignment, and the initial attitude of inertial navigation can be roughly calculated under any maneuvering state in the rough alignment stage under the assistance of GPS. In the fine alignment stage, a Kalman filter is utilized to estimate the residual navigation error, and as the fine alignment stage adopts the Liqun correlation theory to obtain a constant error model, compared with the traditional error model, the fine alignment method based on the constant error model can work under the condition of larger initial attitude error and has higher convergence rate.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the application. In the drawings:
FIG. 1 is a diagram illustrating relationships between different coordinate systems according to an embodiment of the present application;
FIG. 2 is a schematic diagram of a coarse alignment process according to an embodiment of the present application;
fig. 3 is a schematic diagram of a fine alignment process according to an embodiment of the present application.
Detailed Description
It should be noted that, without conflict, the embodiments of the present application and features of the embodiments may be combined with each other. The application will be described in detail below with reference to the drawings in connection with embodiments.
It should be noted that the steps illustrated in the flowcharts of the figures may be performed in a computer system such as a set of computer executable instructions, and that although a logical order is illustrated in the flowcharts, in some cases the steps illustrated or described may be performed in an order other than that illustrated herein.
The application provides a polar region inertial navigation initial alignment method based on an earth coordinate system, which comprises the following steps:
collecting the output of an accelerometer and a gyroscope in inertial navigation;
performing coarse alignment on inertial navigation to obtain an attitude transformation matrix of the inertial navigation at any moment;
based on the gesture transformation matrix, the output is utilized to precisely align the inertial navigation, and the gesture, the speed and the position of the aligned inertial navigation are obtained.
Further, performing coarse alignment on inertial navigation includes:
based on a satellite navigation system, acquiring an initial attitude transformation matrix of inertial navigation by utilizing a specific force differential equation;
based on the initial attitude transformation matrix, acquiring an attitude transformation matrix of inertial navigation at any moment.
Further, obtaining the initial pose transformation matrix of inertial navigation includes:
preprocessing a differential equation of the contrast force to obtain a preset equation;
integrating the preset equation;
based on a preset equation after integral processing, an initial attitude transformation matrix of inertial navigation is obtained by utilizing a multi-vector attitude determination algorithm.
Further, fine alignment of inertial navigation includes:
based on the gesture transformation matrix, calculating the output to acquire the initial inertial navigation gesture, speed and position;
based on the initial inertial navigation posture, speed and position, constructing an inertial navigation error model; estimating an inertial navigation error model based on a Kalman filter to obtain an estimated error;
based on the estimation error, the attitude transformation matrix is compensated, and the precise alignment of inertial navigation is completed.
The technical scheme of the embodiment is as follows:
collecting the output of three accelerometers and three gyroscopes in inertial navigation;
under the assistance of a satellite navigation system, constructing vectors of different lines by utilizing a specific force differential equation, and then carrying out vector attitude determination to determine the rough initial attitude of inertial navigation; this process is called a coarse alignment process;
calculating the output of the inertial navigation system on the basis of the initial gesture obtained by rough alignment and the speed and position information provided by the satellite navigation system; then an error model of the inertial navigation system is established, and the error of the inertial navigation system is estimated and compensated by using a Kalman filter so as to obtain more accurate attitude, speed and position information; this process is referred to as a fine alignment process.
The detailed steps of this embodiment are:
step 1: acquiring outputs of a gyroscope and an accelerometer:
defining gyroscope outputs asAccelerometer output +.>Where b denotes the carrier coordinate system and i denotes the inertial coordinate system. /> and />Gyroscope angular velocity outputs representing the X-axis, Y-axis and Z-axis respectively; /> and />The accelerometer specific force outputs are shown for the X-axis, Y-axis and Z-axis, respectively.
Step 2: as shown in fig. 2, a coarse alignment phase is entered to obtain a coarse initial pose:
for convenience of the following description, the relevant coordinate system is defined as follows. The inertial coordinate system is defined as the i-system, which remains stationary relative to the inertial space. The earth coordinate system is defined as the e-system, which rotates with the rotation of the earth. The "east-north-day" geographic coordinate system is defined as the g-system. The carrier coordinate system is defined as the b-system. The relationship between the coordinate systems is shown in fig. 1:
according to the chain rule of the matrix, the inertial navigation attitude matrix at any moment can be decomposed into:
wherein Representing t k And the attitude transformation matrix from b system to e system at the moment. />The posture transformation matrix from b series to e series at the initial time is shown. />Representing from the initial time to t k Time e is a transformation matrix, ">From t k The transition matrix from time b to initial time b.
and />The recursive calculation formula of (c) is as follows:
wherein T represents the sampling period,representing the earth rotation angular velocity vector,/->Representing t k-1 Angular velocity vector output by moment gyroscope, I 3×3 Representing a third order identity matrix, x represents the inverse symmetric matrix operation.
As can be seen from the above formula, and />Can be easily calculated directly, thus, if an initial posture transformation matrix +.>Then the posture transformation matrix at any time +.>Can be obtained.
The following equation can be readily derived from the differential equation of specific force:
wherein ,representing the projection of the velocity of the carrier relative to the inertial space in the earth's system, f b Acceleration vector (also called specific force) representing accelerometer output +.>A projection of the earth's gravitational force in the earth's subsurface. The rearrangement formula (4) can be obtained: (right side of differential equation of specific force +.>Move to the left and multiply by +.>)
To reduce the effect of noise, the integration operation is performed simultaneously on both ends of equation (5):
may be obtained by a satellite navigation system. Since each instant of time a different alpha (t k) and β(tk ) Therefore, the initial posture matrix can be obtained by using any multi-vector posture determining algorithm aiming at the formula (6)>Combination->Andcalculating to obtain an attitude transformation matrix at any moment>Of course, the gesture transformation matrix obtained in this step is inaccurate, and has more errors, and the navigation errors are estimated next.
Step 3: after coarse alignment, the inertial navigation solution obtains the gesture, the speed and the position
First, the differential equations for attitude, velocity and position of the inertial navigation system are as follows:
representing the position of the carrier in the earth's coordinate system. After the initial attitude matrix obtained in the coarse alignment stage and the initial speed and initial position information provided by the satellite navigation system are utilized, the subsequent carrier attitude, speed and position can be continuously integrated and calculated by utilizing a fourth-order Dragon-Kutta method by combining a differential equation.
Step 4: an inertial navigation error model is built, and the inertial navigation error is estimated by adopting Kalman filtering:
the application introduces the Liquus theory to build the inertial navigation error model. First, the attitude, speed and position of inertial navigation are built into a special European group.
According to the group error definition and the left invariant feature of satellite navigation observables, constructing a left invariant group error as follows:
wherein "-" represents physical quantities calculated by inertial navigation and contains errors.
According to the logarithmic mapping relation between the Li group and the Li algebra vector space, carrying out logarithmic linearization on the group error to obtain a new navigation error vector as follows:
the differential equation for deriving the error vector on both sides of (15) - (16) simultaneously is as follows:
error of gyroscopeAnd accelerometer error δf b Set to a form of constant Gaussian noise
wherein Indicating a constant drift of the gyroscope,/->Representing accelerometer constant zero bias, +.>Representing gyroscope noise +.>Representing accelerometer noise.
So far, the inertial navigation error state equation can be obtained:
position information provided by satellite navigation systemAnd position information calculated by inertial navigation +.>And taking the difference to obtain a navigation error observation equation.
wherein Representing system observation noise, Z representing observation vector, representing inertial navigation pure inertial solution attitude matrix +.>Transpose of->Position vector representing inertial pure inertial solution, < >>Position vector representing GPS elevation,>posture matrix representing inertial navigation pure inertial solution, < >>Representing a position error vector, I 3×3 Representing a third order identity matrix, x representing the error state.
(23) And (26) form a complete state space model. The navigation error can be estimated by adopting a standard Kalman filter to obtain an estimation result and />
Step 5: compensating the inertial navigation error according to the estimation result of the inertial navigation error;
according to the definition of the navigation error vector, the compensation method is obtained as follows:
wherein ,representing the corrected inertial navigation attitude matrix, +.>Representing the estimated misalignment angle vector of the Kalman filter, x represents the inverse symmetric matrix operation,/and->Indicating corrected inertial velocity, +.>Indicating the corrected inertial navigation position.
Thus, accurate inertial navigation output can be obtained, including accurate attitude, speed and position information. Steps 3 to 5 are performed at each instant after the coarse alignment is combined. Steps 3 to 5 are both fine alignment processes, as shown in fig. 3.
The present application is not limited to the above-mentioned embodiments, and any changes or substitutions that can be easily understood by those skilled in the art within the technical scope of the present application are intended to be included in the scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.
Claims (10)
1. The polar region inertial navigation initial alignment method based on the earth coordinate system is characterized by comprising the following steps of:
collecting the output of an accelerometer and a gyroscope in inertial navigation;
performing coarse alignment on the inertial navigation to obtain a posture transformation matrix of the inertial navigation at any moment;
and based on the attitude transformation matrix, carrying out fine alignment on the inertial navigation by utilizing the output, and obtaining the aligned attitude, speed and position of the inertial navigation.
2. The initial alignment method of polar region inertial navigation based on the earth coordinate system of claim 1, wherein performing coarse alignment on the inertial navigation comprises:
based on a satellite navigation system, acquiring an initial attitude transformation matrix of the inertial navigation by utilizing a specific force differential equation;
and acquiring the attitude transformation matrix of the inertial navigation at any moment based on the initial attitude transformation matrix.
3. The polar region inertial navigation initial alignment method based on the earth coordinate system according to claim 2, wherein the specific force differential equation is:
wherein ,representing the projection of the velocity of the carrier relative to the inertial space in the earth's system, f b Acceleration vector representing accelerometer output, +.>Projection of the earth's subsurface representing the earth's gravity, < +.>Representing an initial gesture transformation matrix->Representing the earth rotation angular velocity vector,/->Derivative representing the projection of the velocity of the carrier with respect to the inertial space in the earth system, < >>Representing from the initial time to t k Angular transformation matrix of the earth system with respect to the inertial space at moment +.>From t k The time to initial time carrier is an angular transformation matrix relative to the inertial space.
4. The polar region inertial navigation initial alignment method based on the earth coordinate system according to claim 2, wherein the attitude transformation matrix of the inertial navigation at any moment is:
wherein ,representing t k Posture transformation matrix from b line to e line at moment, < >>An attitude transformation matrix representing the initial time from b-line to e-line, < >>Representing from the initial time to t k Time e is a transformation matrix, ">From t k The transformation matrix of the b system from the moment to the initial moment, b system represents the carrier coordinate system and e system represents the earth coordinate system.
5. The polar region inertial navigation initial alignment method based on the earth coordinate system according to claim 2, wherein obtaining the initial pose transformation matrix of the inertial navigation comprises:
preprocessing the specific force differential equation to obtain a preset equation;
integrating the preset equation;
based on the preset equation after the integration processing, acquiring the initial attitude transformation matrix of the inertial navigation by utilizing a multi-vector attitude determination algorithm.
6. The polar region inertial navigation initial alignment method based on the earth coordinate system according to claim 5, wherein the preset equation is:
wherein ,from t k The earth system is transformed into a matrix of angles relative to the inertial space from moment to initial moment.
7. The initial alignment method of polar region inertial navigation based on an earth coordinate system of claim 1, wherein the fine-alignment of the inertial navigation comprises:
based on the gesture transformation matrix, calculating the output to acquire the initial gesture, speed and position of the inertial navigation;
constructing an inertial navigation error model based on the initial attitude, speed and position of the inertial navigation; estimating the inertial navigation error model based on a Kalman filter to obtain an estimated error;
and compensating the attitude transformation matrix based on the estimation error to finish the precise alignment of the inertial navigation.
8. The polar region inertial navigation initial alignment method based on the earth coordinate system according to claim 1, wherein the initial attitude, velocity and position of the inertial navigation are respectively:
wherein ,representing the initial pose of inertial navigation,>representing the initial speed of inertial navigation, +.>Indicating the initial position of the inertial navigation,representing the position of the carrier in the earth's coordinate system.
9. The polar region inertial navigation initial alignment method based on the earth coordinate system according to claim 7, wherein the inertial navigation error model is:
wherein X represents an error state,representing misalignment angle vector, +.>Representing a velocity error vector, ">Representing a position error vector, ">Indicating constant drift, v of gyro b Representing accelerometer constant zero bias, F representing state transition matrix,>derivative representing error state +.>Representing the angular velocity of the output of a triaxial gyroscope in inertial navigation,/->Representing acceleration of the triaxial accelerometer output in inertial navigation, G representing noise distribution matrix, W representing process noise vector,/->Representing system observation noise, Z representing observation vector, representing inertial navigation pure inertial solution attitude matrix +.>Transpose of->Position vector representing inertial pure inertial solution, < >>Position vector representing GPS elevation,>posture matrix representing inertial navigation pure inertial solution, < >>Representing a position error vector, I 3×3 Representing a third order identity matrix.
10. The polar region inertial navigation initial alignment method based on the earth coordinate system according to claim 1, wherein the method for compensating the attitude transformation matrix is as follows:
wherein ,representing the corrected inertial navigation attitude matrix, +.>Representing the estimated misalignment angle vector of the Kalman filter, x represents the inverse symmetric matrix operation,/and->Indicating corrected inertial velocity, +.>Indicating the corrected inertial navigation position.
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| CN103791918A (en) * | 2014-02-10 | 2014-05-14 | 哈尔滨工程大学 | Polar region moving base alignment method for naval vessel strapdown inertial navigation system |
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| CN114111843A (en) * | 2021-11-24 | 2022-03-01 | 东南大学 | Initial alignment method for optimal movable base of strapdown inertial navigation system |
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