CN112525191B - Airborne distributed POS transfer alignment method based on relative strapdown calculation - Google Patents

Airborne distributed POS transfer alignment method based on relative strapdown calculation Download PDF

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CN112525191B
CN112525191B CN202110180736.1A CN202110180736A CN112525191B CN 112525191 B CN112525191 B CN 112525191B CN 202110180736 A CN202110180736 A CN 202110180736A CN 112525191 B CN112525191 B CN 112525191B
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subsystem
attitude
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vector
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CN112525191A (en
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李建利
曲春宇
刘刚
房建成
朱庄生
宫晓琳
揭绍锋
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Beihang University
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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
    • G01C21/165—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 combined with non-inertial navigation instruments
    • 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
    • G01C21/005—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 with correlation of navigation data from several sources, e.g. map or contour matching
    • 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
    • G01C21/20—Instruments for performing navigational calculations
    • 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
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • 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
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/40—Means for monitoring or calibrating
    • G01S7/4004—Means for monitoring or calibrating of parts of a radar system

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Abstract

The invention discloses an airborne distributed POS (point of sale) transfer alignment method based on relative strapdown calculation, and aims to improve the measurement precision of airborne distributed POS spatial motion information in a dynamic environment. The method comprises the following steps: constructing a pseudo single sample rotation vector by using angular velocities output by the gyroscope at the current and the previous N sampling moments of the main subsystem and a rotation vector error compensation coefficient deduced based on conical motion, and solving a relative attitude quaternion in real time based on the rotation vector to realize updating of the relative attitude; meanwhile, a relative velocity and position updating algorithm is established according to the space position vector relation of the main subsystem and the subsystem, and the relative velocity and position updating is realized by utilizing the specific force and the relative posture output by the accelerometer of the main subsystem and the subsystem; and finally, establishing a transfer alignment state model and a measurement model based on a relative strapdown resolving error differential equation and the three-dimensional relative position and three-dimensional relative attitude measured by the fiber bragg grating, and performing transfer alignment by adopting a linear Kalman filtering estimation method to obtain high-precision motion information.

Description

Airborne distributed POS transfer alignment method based on relative strapdown calculation
Technical Field
The invention relates to an airborne distributed POS transfer alignment method based on relative strapdown resolving, belongs to the field of aerial remote sensing, can improve the measurement accuracy of airborne distributed POS motion information and is applied to motion compensation of distributed imaging loads such as a flexible baseline array antenna SAR and the like.
Background
A Distributed Position and attitude measurement System (DPOS) is an important device for acquiring motion parameters such as Position, speed, attitude and the like of multiple nodes in an onboard high-resolution earth observation System. The distributed POS mainly comprises a high-precision main position and attitude Measurement system (main POS), a plurality of low-precision sub-Inertial Measurement Units (IMUs), a navigation computer and a set of post-processing software. The main POS is composed of a high-precision main IMU and a Global Navigation Satellite System (GNSS), the main IMU is generally installed in an engine cabin or an engine belly, the sub IMUs are generally installed on wings on two sides, and the main IMU and the sub IMUs are fixedly connected with imaging loads respectively to provide high-precision position, posture and other motion information for the distributed multi-node imaging loads.
In the flying process of the aircraft, due to the influence of gust, turbulence and engine vibration, the wing generates flexural deformation which changes along with time, so that the precision of transfer alignment can be influenced, and the imaging precision is further influenced. Aiming at the problem, related scholars provide a transfer alignment method based on relative strapdown resolving error differential equations, and flexible deformation measurement can be realized. However, the deformation of the wing will cause relative motion, even cone motion, between the main system and the sub system, and inevitably bring irreplaceable errors in the process of resolving the relative attitude, so that the measurement accuracy of the relative attitude is seriously affected, and further the measurement accuracy of the relative speed and the relative position is affected, and the measurement accuracy of the spatial motion information of the distributed POS is reduced.
Disclosure of Invention
The invention provides a relative strapdown resolving-based airborne distributed POS transfer alignment method aiming at the technical problem of non-commutative errors generated by airborne distributed POS due to flexible deformation.
In order to achieve the above purpose, the invention provides the following technical scheme:
the invention relates to an airborne distributed POS transfer alignment method based on relative strapdown resolving, which comprises the following steps:
(1) establishing a relative attitude updating algorithm based on a pseudo-single-sample rotation vector: and establishing a pseudo-single-sample rotation vector by using angular velocities output by the gyroscope at the current and previous N sampling moments of the main subsystem, deriving a rotation vector error compensation coefficient by adopting typical conical motion, and obtaining a relative attitude quaternion in real time by solving the rotation vector, thereby realizing updating of the relative attitude.
(2) Establishing a relative speed updating algorithm: and a vector equation among the main system, the subsystems and the relative positions of the main subsystem and the subsystems is established according to the vector relation of the spatial positions of the main subsystem and the subsystems, a second derivative is solved relative to an inertial coordinate system to obtain a relative velocity differential equation, and a numerical solution is solved for the relative velocity differential equation based on specific force information and relative attitude information measured by an accelerometer of the main subsystem and the subsystems, so that the relative velocity is updated.
(3) Establishing a relative position updating algorithm: and establishing a relative position differential equation based on a differential relation between the relative position and the relative speed, and solving the numerical solution of the relative position differential equation by utilizing the solved relative speed to realize the update of the relative position.
(4) Establishing a transfer alignment algorithm: establishing a transfer alignment state model and a measurement model based on a relative strapdown resolving error differential equation and three-dimensional relative positions and three-dimensional relative postures measured by the fiber bragg gratings, performing transfer alignment by adopting a linear Kalman filtering estimation method, and performing feedback correction on a relative strapdown resolving result to obtain high-precision motion information.
The principle of the invention is as follows: constructing a pseudo single sample rotation vector by using angular velocities output by the gyroscope at the current and the previous N sampling moments of the main subsystem and a rotation vector error compensation coefficient deduced based on typical conical motion, and solving a relative attitude quaternion in real time based on the rotation vector to realize updating of a relative attitude; meanwhile, a relative velocity and relative position updating algorithm is established according to the vector relation of the spatial positions of the main subsystem and the subsystem, and the relative velocity and the relative position are updated by utilizing the specific force and the posture information output by the accelerometer of the main subsystem and the subsystem; finally, establishing a transfer alignment state model and a measurement model based on a relative strapdown resolving error propagation formula and three-dimensional relative positions and three-dimensional relative postures measured by the fiber bragg gratings, and performing transfer alignment by adopting a linear Kalman filtering estimation method to obtain high-precision motion information; the relative strapdown resolving error propagation formula is obtained by simultaneously obtaining a relative attitude error differential equation, a relative speed error differential equation and a relative position error differential equation.
Compared with the prior art, the invention has the beneficial effects that:
according to the airborne distributed POS transfer alignment method based on relative strapdown calculation, the irreplaceable error under the flexible deformation condition can be reduced, the relative attitude drift is restrained, and the measurement precision of the spatial motion information of the distributed POS is improved. Meanwhile, the relative attitude updating algorithm based on the pseudo-single-subsample rotation vector is adopted, so that the problem of quantization error caused by high-frequency sampling is solved without increasing sampling frequency and reducing the requirement of a hardware system while inhibiting the non-exchangeable error.
Drawings
In order to more clearly illustrate the embodiments of the present application or technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments described in the present invention, and other drawings can be obtained by those skilled in the art according to the drawings.
Fig. 1 is a flowchart of a method provided in an embodiment of the present invention.
Fig. 2 is a diagram illustrating a relationship between an attitude update period and an angular velocity sampling period according to an embodiment of the present invention.
Fig. 3 is a spatial position vector diagram of a main subsystem according to an embodiment of the present invention.
Detailed Description
In order to make the technical solutions of the present invention better understood by those skilled in the art, the present invention will be further described in detail with reference to the accompanying drawings and examples. It is to be understood that the embodiments described are only a few embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, the specific method of the present invention is as follows:
1. and establishing a relative attitude updating algorithm based on the pseudo-single-sample rotation vector. And establishing a pseudo-single-sample rotation vector by using angular velocities output by the gyroscope at the current and previous N sampling moments of the main subsystem, deriving a rotation vector error compensation coefficient by adopting typical conical motion, and obtaining a relative attitude quaternion in real time by solving the rotation vector, thereby realizing updating of the relative attitude. The method comprises the following specific steps:
assume that it is currentt k Time subsystem carrier coordinate systems(k) Coordinate system of main system carrierm(k)，t k+1 Time subsystem carrier coordinate systems(k+1) Coordinate system of main system carrierm(k+1). Note the books(k) Tos(k+1) Is a rotational quaternion ofq(h)，m(k) Tos(k) Is a rotational quaternion ofQ(t k )，m(k+1) Tos(k+1) Is a rotational quaternion ofQ(t k+1)，m(k) Tom(k+1) Is a rotational quaternion ofp(h) Wherein, in the step (A),h= t k+1-t k . Then the relationship is expressed as the following quaternion:
Figure DEST_PATH_IMAGE001
（1）
in the attitude update periodh= t k+1-t k The coordinate system of the main system carrier changes very slowly due to the position change, and the approximation is that
Figure 968547DEST_PATH_IMAGE002
The above formula can be rewritten as:
Figure DEST_PATH_IMAGE003
（2）
wherein:
Figure 412166DEST_PATH_IMAGE004
（3）
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE005
is composed ofs(k) Tos(k+1) The equivalent rotation vector of (a) is,
Figure 845422DEST_PATH_IMAGE006
. For convenience of description, willQ(t k ) AndQ(t k+1) Are respectively called ast k Andt k+1the relative attitude quaternion at the time of day,q(h) The attitude change quaternion in the period of time.
Because the traditional attitude updating algorithm based on the multi-subsample rotation vector algorithm puts higher requirements on the acquisition frequency of the system, increases the hardware burden and even generates quantization errors, the current and previous attitude updating algorithms are adopted to reduce the data acquisition frequencyNThe pseudo-single-subsample rotation vector relative attitude updating algorithm of the angular velocity at each sampling moment is as follows:
Figure DEST_PATH_IMAGE007
（4）
in the formula (I), the compound is shown in the specification,
Figure 61769DEST_PATH_IMAGE008
in order to update the rotation vector after the update,
Figure DEST_PATH_IMAGE009
for the current sampling instantt k And the next moment of time (t k +h) The relative angular increment of (a) is,G j j is more than or equal to 1 and less than or equal to N for the cone error compensation coefficient to be solved,ω j()is prepared from (a)t k -jh) The relative angular velocity of the moment of time,ωfor the current sampling instantt k Relative angular velocity of (d). Attitude update periodhAnd angular velocity sampling period deltaTEqual as shown in fig. 2.
Generally, for attitude updating of an inertial navigation system, cone motion is the worst working environment condition, which can cause severe drift of a mathematical platform, so that the non-commutative error of the algorithm is generally researched by adopting typical cone motion when the rotating vector algorithm is optimized. Setting the motion of the subsystem relative to the main system as a coordinate system around the subsystem carrierxConical movement of the axis rotation (amplitude ofαAngular frequency is Ω), which can be expressed as:
Figure 682106DEST_PATH_IMAGE010
（5）
according to the relation between the quaternion and the rotation vector, the attitude quaternion of the conical motion is as follows:
Figure DEST_PATH_IMAGE011
（6）
according to equation (6) and the quaternion differential equation:
Figure 929417DEST_PATH_IMAGE012
（7）
the corresponding angular velocity output under the condition of the available conical motion is as follows:
Figure DEST_PATH_IMAGE013
（8）
in the attitude update period according to equations (3) and (6)hThe inner attitude change quaternion can be expressed as:
Figure 341812DEST_PATH_IMAGE014
（9）
in the attitude update period according to equation (3)hThe equivalent rotation vector of the inner cone motion can be expressed as:
Figure DEST_PATH_IMAGE015
（10）
from equation (10), (b) ()t k -jh) Relative angular velocity vector of time:
Figure 586849DEST_PATH_IMAGE016
（11）
as can be seen from the above formula, the relative angular velocity vector is obtained onlyxThe component of the axis is a non-periodic term, and the other two axial directions are periodic terms with the same frequency as cone motion, and the influence of the periodic terms can be not considered in error analysis. Due to the fact that
Figure DEST_PATH_IMAGE017
Is constant, therefore, the relative angular velocity increment at the current time can be expressed as:
Figure 84695DEST_PATH_IMAGE018
（12）
for simplicity, let the conic error compensation term be as follows:
Figure DEST_PATH_IMAGE019
（13）
if only the non-periodic term is considered and the trigonometric function is approximated, the following results are obtained:
Figure 870117DEST_PATH_IMAGE020
（14）
order toλ=ΩhThe first two terms of equation (14) are subjected to taylor expansion to obtain:
Figure DEST_PATH_IMAGE021
（15）
in the formula, coefficient
Figure 752666DEST_PATH_IMAGE022
Figure DEST_PATH_IMAGE023
Form a column vectorC。
Similarly, taylor expansion of the last term of equation (14) results in:
Figure 230921DEST_PATH_IMAGE024
（16）
in the formula, coefficient
Figure DEST_PATH_IMAGE025
Figure 216063DEST_PATH_IMAGE026
Form a matrixACoefficient to be solvedG j (1≤j≤N) Form a column vectorG。
By comparing equations (15) and (16), it can be found that when two equations are usedλ j+21(1≤j≤N) When the coefficients of (a) are the same, i.e. the following formula is satisfied, the error of the algorithm is minimal:
Figure 100002_DEST_PATH_IMAGE027
（17）
at the same time, the user can select the desired position,Nthe larger, the residual aboutλError of term (2)N+3) The higher the order, the smaller the algorithm error, butNThe actual selection of (a) must also take into account other requirements such as real-time performance of the computer.
Since the direct input quantity of the formula (4) is the relative angular velocity between the main subsystem and the sub-system, the pseudo-single-sample rotation vector relative attitude update algorithm can be rewritten as the final form as follows:
Figure 336335DEST_PATH_IMAGE028
（18）
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE029
is shown assIs prepared byt-jh) The relative angular velocity of the main subsystem and the subsystem is not more than 1 at any momentj≤N；
Figure 333110DEST_PATH_IMAGE030
Is a subsystem gyroscope int k -jh) The original angular velocity output at the time of day,
Figure DEST_PATH_IMAGE031
is at presentt k Time of daymIs tied tosA relative attitude matrix of the system is determined,
Figure 982266DEST_PATH_IMAGE032
is at at-jh) Time of daymIs tied tosRelative attitude matrix of series, 1 ≦j≤N，
Figure DEST_PATH_IMAGE033
Can be prepared byt k -jh) Time of daymIs tied tosQuaternion of relative attitude of system
Figure 189125DEST_PATH_IMAGE034
Obtaining:
Figure DEST_PATH_IMAGE035
（19）
select the rightNAfter the specific value of (a), the coefficient to be solved can be obtained by the formula (17)G j And is substituted into the formula (18) to obtain an updated rotation vector
Figure 310490DEST_PATH_IMAGE036
And substituting into the formula (2) to obtaint k+1Quaternion of relative attitude at time
Figure DEST_PATH_IMAGE037
And further realized according to the following formulat k+1Updating the three-dimensional posture at the moment:
Figure 161772DEST_PATH_IMAGE038
（20）
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE039
are respectively updatedt k+1And (3) relative pitch angle, relative roll angle and relative course angle among the main subsystems at the moment.
2. A relative velocity update algorithm is established. And a vector equation among the main system, the subsystems and the relative positions of the main subsystem and the subsystems is established according to the vector relation of the spatial positions of the main subsystem and the subsystems, a second derivative is solved relative to an inertial coordinate system to obtain a relative velocity differential equation, and a numerical solution is solved for the relative velocity differential equation based on specific force information and relative attitude information measured by an accelerometer of the main subsystem and the subsystems, so that the relative velocity is updated. The method comprises the following specific steps:
influenced by the distributed POS flexible lever armt k At the moment, the relative position of the subsystem with respect to the main systemRAnd relative velocityVIs no longer fixed but is constantly changing with deflection. Defining the position vector of the primary system in the inertial system asR m The position vector of the subsystem in the inertial coordinate system isR s As shown in FIG. 3, the lever arms between the main subsystems have the following vector relationship:
Figure 981829DEST_PATH_IMAGE040
（21）
for the relative inertial coordinate system of equation (21)iThe first derivative is calculated, and:
Figure DEST_PATH_IMAGE041
(22) in the formula (I), the compound is shown in the specification,
Figure 410405DEST_PATH_IMAGE042
gyroscope at current t for main systemkThe original angular velocity output at any moment;
for formula (22) relative inertial frameiThe first derivative is calculated, and:
Figure DEST_PATH_IMAGE043
（23）
specific force equation of main subsystem measurement:
Figure 341321DEST_PATH_IMAGE044
（24）
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE045
、
Figure 578267DEST_PATH_IMAGE046
are respectively the currentt k The specific force measured by the master system at the momentmProjection of the system, specific force measured by the subsystemsProjection of the system;
Figure DEST_PATH_IMAGE047
and
Figure 38067DEST_PATH_IMAGE048
are respectively the currentt k Time master subsystem universal gravitation acceleration in geographical coordinate systemeDue to the small distance of the main subsystem,
Figure DEST_PATH_IMAGE049
(ii) a And bring this formula into the above formula, order
Figure 225378DEST_PATH_IMAGE050
WhereinVIs at presentt k The relative speed of the time main subsystem is shown as follows:
Figure DEST_PATH_IMAGE051
（25）
project the above formula tom isThe following can be obtained:
Figure 694406DEST_PATH_IMAGE052
(26)
due to the fact that
Figure DEST_PATH_IMAGE053
Relative speed of the main subsystem, not obtained by direct measurementV m May be expressed in another form, such that:
Figure 520279DEST_PATH_IMAGE054
(27)
taking equation (26) into formula (22) to obtain the first derivative with respect to the inertial frame, the differential equation of absolute velocity of the subsystem with respect to the main system can be obtained:
Figure DEST_PATH_IMAGE055
(28)
solving the speed differential equation in the formula (28) to obtain a numerical solution, and realizing the relative speed between the main system and the sub system according to the formula (27)V m Update to obtaint k+1Three-dimensional relative velocity between time master subsystemsV m (t k+1)。
3. A relative position update algorithm is established. And establishing a relative position differential equation based on a differential relation between the relative position and the relative speed, and solving the numerical solution of the relative position differential equation by utilizing the solved relative speed to realize the update of the relative position. The method comprises the following specific steps:
the relative position can be obtained by integrating the relative velocity, and thus the relative position differential equation can be expressed as:
Figure 416560DEST_PATH_IMAGE056
(29)
projecting formula (29) in the coordinate system of the main system carriermThe following can be obtained:
Figure DEST_PATH_IMAGE057
(30)
the differential equation of the relative position in the formula (30) is solved to obtain a numerical solution, so that the relative position between the main subsystems can be realizedR m Update to obtaint k+1Three-dimensional relative position between time master subsystemsR m (t k+1)。
4. A transfer alignment algorithm is established. Establishing a transfer alignment state model and a measurement model based on a relative strapdown resolving error propagation formula and three-dimensional relative positions and three-dimensional relative postures measured by the fiber bragg gratings, performing transfer alignment by adopting a linear Kalman filtering estimation method, and performing feedback correction on relative strapdown resolving results to obtain high-precision motion information. The method comprises the following specific steps:
relative attitude matrix due to flexural deformation of lever arms
Figure 554149DEST_PATH_IMAGE058
Is a time-varying matrix with the following differential equation:
Figure DEST_PATH_IMAGE059
(31)
Figure 826868DEST_PATH_IMAGE060
(32)
Figure DEST_PATH_IMAGE061
(33)
in the formula (I), the compound is shown in the specification,
Figure 366302DEST_PATH_IMAGE062
、
Figure DEST_PATH_IMAGE063
the rotation angular rates of the carrier of the main inertial navigation system and the sub inertial navigation system respectively,
Figure 60300DEST_PATH_IMAGE064
is composed ofsIs relative tomThe angular rate of rotation of the system ismThe projection in the system is determined by the distance between the projection and the optical system,
Figure 826131DEST_PATH_IMAGE065
、
Figure DEST_PATH_IMAGE066
、
Figure 699278DEST_PATH_IMAGE067
are respectively as
Figure DEST_PATH_IMAGE068
、
Figure 562060DEST_PATH_IMAGE069
、
Figure DEST_PATH_IMAGE070
Is used to generate the inverse symmetric matrix. The relative attitude differential equation can be obtained by the simultaneous equations (31) to (33):
Figure 737827DEST_PATH_IMAGE071
(34)
defining an actual relative attitude matrix calculated by a relative strapdown calculation algorithm as
Figure DEST_PATH_IMAGE072
Whereinm' for calculating the coordinate system of the main system carrier, anmThe systems differ by a small angle transformation, namely:
Figure 53270DEST_PATH_IMAGE073
(35)
in the formula (I), the compound is shown in the specification,µis composed ofmDeviation of systemmDeviation angle of the system.
Taking the inertial device error of the subsystem into consideration, and transposing two sides of the formula (34) to obtain:
Figure DEST_PATH_IMAGE074
(36)
in the formula (I), the compound is shown in the specification,
Figure 995687DEST_PATH_IMAGE075
is the output value of the main system gyro,
Figure DEST_PATH_IMAGE076
is composed of
Figure 656519DEST_PATH_IMAGE077
The anti-symmetric matrix is a matrix of a plurality of symmetric matrices,
Figure DEST_PATH_IMAGE078
is a subsystem gyro output value, which can be expressed as
Figure 331083DEST_PATH_IMAGE079
，
Figure DEST_PATH_IMAGE080
For subsystem gyro drift atsThe projection of the system is obtained by substituting equation (34) and equation (36) into equation (35) to obtain a relative attitude error differential equation:
Figure 664981DEST_PATH_IMAGE081
(37)
definition of
Figure DEST_PATH_IMAGE082
，
Figure 817614DEST_PATH_IMAGE083
，
Figure DEST_PATH_IMAGE084
Because of the error in the subsystem accelerometer output specific force, the relative velocity and position differential equations can be expressed as:
Figure 451726DEST_PATH_IMAGE085
(38)
Figure DEST_PATH_IMAGE086
(39)
projecting equations (38) and (39) ontomBy subtracting equations (28) and (30) from each other, differential equations for the relative velocity and relative position errors are obtained:
Figure 297192DEST_PATH_IMAGE087
(40)
Figure DEST_PATH_IMAGE088
(41)
simultaneous equations (37), (40) and (41) can yield the error propagation equation for relative navigation:
Figure 790490DEST_PATH_IMAGE089
(42)
Figure DEST_PATH_IMAGE090
(43)
Figure 803271DEST_PATH_IMAGE091
(44)
and solving an error propagation formula according to the relative strapdown, so as to obtain a state model of transfer alignment. Taking the state vector as:
Figure DEST_PATH_IMAGE092
(45)
in the formula (I), the compound is shown in the specification,δФ x ,δФ y ,δФ z is the relative attitude error angle of the main subsystem,δU x ,δU y ,δU z is the absolute value of the relative velocity error of the main subsystem,δR x ,δR y ,δR z in order to account for the relative position error of the main subsystem,ε bx ,ε by ,ε bz is the random constant drift of the subsystem gyro + bx , ▽ by , ▽ bz Is a random constant bias for the subsystem accelerometer.
The state model can be described as:
Figure 229573DEST_PATH_IMAGE093
(46)
in the formula (I), the compound is shown in the specification,Ain order to be a matrix of the system,Bthe matrix is driven for the system noise,Wthe system noise includes the random constant drift of the gyroscope and the random constant bias of the accelerometer, namely:
Figure DEST_PATH_IMAGE094
(47)
system matrixAComprises the following steps:
Figure 183622DEST_PATH_IMAGE095
(48)
system noise driving matrixBComprises the following steps:
Figure DEST_PATH_IMAGE096
(49)
the transfer alignment is carried out by adopting a relative position and relative attitude matching mode, and the measurement vector of the transfer alignment is as follows:
Figure 288851DEST_PATH_IMAGE097
(50)
in the formula (I), the compound is shown in the specification,Z 1for the relative position to match the measurement vector,Z 2the measurement vectors are matched for relative pose.
To build the transfer alignment measurement model, a transfer alignment coordinate system needs to be specified:mis connected withsAre respectively a main subsystem carrier coordinate system,αis the nominal coordinate system of the subsystem, and in the initial state,αis connected withmThe two layers are overlapped with each other,ηis composed ofαDeviation of systemmAttitude angle of the system, corresponding to the attitude matrix of
Figure DEST_PATH_IMAGE098
；ξIs composed ofsDeviation of systemαThe mounting error angle of the system, corresponding to a mounting error matrix of
Figure 783286DEST_PATH_IMAGE099
；µIs composed ofmDeviation of systemmThe misalignment angle of the system, the corresponding misalignment angle matrix is
Figure DEST_PATH_IMAGE100
；βIs composed ofsDeviation of systemmThe attitude angle of the system, the corresponding relative attitude calculation matrix of the main subsystem is
Figure 267357DEST_PATH_IMAGE101
. The following relationship can be obtained from the assumption of small angular deformation:
Figure DEST_PATH_IMAGE102
(51)
Figure 454625DEST_PATH_IMAGE103
(52)
Figure DEST_PATH_IMAGE104
(53)
Figure 787429DEST_PATH_IMAGE105
(54)
the following relationship holds according to the coordinate transformation principle:
Figure DEST_PATH_IMAGE106
(55)
substituting equations (51) - (54) into equation (55) can result in:
Figure 288817DEST_PATH_IMAGE107
(56)
ignoring the second order product fraction yields:
Figure DEST_PATH_IMAGE108
(57)
according to the three-dimensional relative attitude obtained by calculationβ c Three-dimensional relative attitude measured by fiber gratingβ M Establishing a measurement vector matched with the relative attitude:
Figure 424133DEST_PATH_IMAGE109
(58)
from the calculated three-dimensional relative position
Figure DEST_PATH_IMAGE110
Three-dimensional relative position to fiber grating measurement
Figure 782302DEST_PATH_IMAGE111
Establishing a relative position matching measurement vector:
Figure DEST_PATH_IMAGE112
(59)
establishing a transfer alignment measurement model according to a transfer alignment measurement vector expression:
Figure 330963DEST_PATH_IMAGE113
(60)
Figure DEST_PATH_IMAGE114
(61)
in the formula (I), the compound is shown in the specification,Hin order to measure the matrix, the measurement matrix is,Vin order to measure the noise, the noise is measured,Vthe measurement noise determined by the relative position and attitude of the fiber grating measurements.
The system represented by the established state model and the established measurement model is continuous, and in order to facilitate the linear Kalman filtering recursion calculation in a computer, the continuous model in the transfer alignment needs to be converted into a discrete form.
Discretizing the state model and the measurement model to obtain:
Figure 167201DEST_PATH_IMAGE115
(62)
in the formula (I), the compound is shown in the specification,X k is composed ofkOf time of daynThe state of the dimension is changed into a variable,Z k is composed ofkOf time of daymDimension measurementThe amount of the compound (A) is,
Figure DEST_PATH_IMAGE116
is composed ofk-1 tokMoment system one-step state transition matrix, Γk-1Driving a noise matrix for the system, characterized byk-1 tokThe system noise at each moment respectively influenceskThe degree of each of the states at a time,W k-1is composed ofk-The system at time 1 excites a noise sequence,V k is composed ofkOf time of daymThe noise sequence is measured in dimension.
Figure 625864DEST_PATH_IMAGE117
Can be expressed as:
Figure DEST_PATH_IMAGE118
(63)
in the formula (I), the compound is shown in the specification,Tin order to be the period of the filtering,A k-1is composed ofk-The system matrix at time 1.
Γk-1Can be expressed as:
Figure 500409DEST_PATH_IMAGE119
(64)
in the formula, is the filter periodGThe matrix is driven for process noise.
Kalman filtering requirementW k AndV k is a zero-mean white noise sequence which is uncorrelated with each other, and therefore has the following relationship:
Figure DEST_PATH_IMAGE120
(65)
in the formula (I), the compound is shown in the specification,R k andQ k the measurement noise variance matrix and the system noise variance matrix, respectively, may be determined based on statistical properties of the process noise and the measurement noise.
According to the distanceScattered state transition matrix
Figure 677312DEST_PATH_IMAGE121
System noise driving matrix gammak-1Measuring matrixH k =HAnd system noise and measurement noise variance matrixQ k AndR k transfer alignment recursive calculation can be completed by using a discrete Kalman filtering equation, and feedback correction is performed on the relative strapdown resolving result to obtain high-precision motion information.
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: it is to be understood that modifications may be made to the technical solutions described in the foregoing embodiments, or equivalents may be substituted for some of the technical features thereof, but such modifications or substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims (3)

1. An airborne distributed POS transfer alignment method based on relative strapdown calculation is characterized by comprising the following steps:
(1) establishing a relative attitude updating algorithm based on a pseudo-single-sample rotation vector: establishing a pseudo-single sample rotation vector by using angular velocities output by the gyroscope at the current and the previous N sampling moments of the main subsystem, deriving a rotation vector error compensation coefficient by adopting typical conical motion, and obtaining a relative attitude quaternion in real time by solving the rotation vector, thereby realizing updating of a relative attitude;
(2) establishing a relative speed updating algorithm: establishing a vector equation among the main system, the subsystems and the relative positions of the main subsystem and the subsystems according to the vector relation of the spatial positions of the main subsystem and the subsystems, solving a second derivative relative to an inertial coordinate system to obtain a relative velocity differential equation, and solving a numerical solution of the relative velocity differential equation based on specific force information and relative attitude information measured by an accelerometer of the main subsystem and the subsystems so as to realize relative velocity updating;
(3) establishing a relative position updating algorithm: establishing a relative position differential equation based on a differential relation between the relative position and the relative speed, and solving the position differential equation by utilizing the solved relative speed to solve a numerical solution to realize relative position updating;
(4) establishing a transfer alignment algorithm: establishing a transfer alignment state model and a measurement model based on a relative strapdown resolving error propagation formula and three-dimensional relative positions and three-dimensional relative postures measured by the fiber bragg gratings, performing transfer alignment by adopting a linear Kalman filtering estimation method, and performing feedback correction on relative strapdown resolving results to obtain high-precision motion information; the relative strapdown resolving error propagation formula is obtained by simultaneously obtaining a relative attitude error differential equation, a relative speed error differential equation and a relative position error differential equation;
the specific scheme for establishing the relative attitude updating algorithm based on the pseudo-single-sample rotation vector in the step (1) is as follows:
assume that it is currentt k Time subsystem carrier coordinate systems(k) Coordinate system of main system carrierm(k)，t k+1 Time subsystem carrier coordinate systems(k+1) Coordinate system of main system carrierm(k+1) Memory for recordings(k) Tos(k+1) Is a rotational quaternion ofq(h)，m(k) Tos(k) Is a rotational quaternion ofQ(t k )，m(k+1) Tos(k+1) Is a rotational quaternion ofQ(t k+1)，m(k) Tom(k+1) Is a rotational quaternion ofp(h) Wherein, in the step (A),h= t k+1- t k then, the following quaternion expression relationship is given:
Figure 585184DEST_PATH_IMAGE001
in the attitude update periodh= t k+1- t k Approximately consider that
Figure 874083DEST_PATH_IMAGE002
The above formula can be rewritten as:
Figure 178025DEST_PATH_IMAGE003
wherein the content of the first and second substances,
Figure 249887DEST_PATH_IMAGE004
in the formula (I), the compound is shown in the specification,
Figure 955674DEST_PATH_IMAGE005
is composed ofs(k) Tos(k+1) The equivalent rotation vector of (a) is,
Figure 353158DEST_PATH_IMAGE006
for convenience of description, willQ(t k ) AndQ(t k+1) Are respectively called ast k Andt k+1the relative attitude quaternion at the time of day,q(h) A quaternion of attitude change in the period of time;
establishing a relative attitude updating algorithm based on a pseudo-simple-sample rotation vector in the step (1), and adopting current and previousNThe pseudo-single-subsample rotation vector relative attitude updating algorithm of the angular velocity at each sampling moment is as follows:
Figure 941134DEST_PATH_IMAGE007
in the formula (I), the compound is shown in the specification,
Figure 82265DEST_PATH_IMAGE008
in order to update the rotation vector after the update,
Figure 173718DEST_PATH_IMAGE009
is at presentSampling timet k And the next moment of time (t k +h) The relative angular increment of (a) is,G j j is more than or equal to 1 and less than or equal to N for the cone error compensation coefficient to be solved,ω (j)is prepared from (a)t k -jh) The relative angular velocity of the moment in time,ωfor the current sampling instantt k Relative angular velocity of (d), attitude update periodhAnd angular velocity sampling period deltaTEqual;
because the direct input quantity of the above formula is the relative angular velocity between the main subsystem and the sub-system, the pseudo-single-sample rotation vector relative attitude updating algorithm is rewritten into the final form as follows:
Figure 7682DEST_PATH_IMAGE010
in the formula (I), the compound is shown in the specification,
Figure 20637DEST_PATH_IMAGE011
is shown assIs prepared byt k -jh) The relative angular velocity of the main subsystem and the subsystem is not more than 1 at any momentj≤N；
Figure 965459DEST_PATH_IMAGE012
Is a subsystem gyroscope int k -jh) The original angular velocity output at the time of day,
Figure 114681DEST_PATH_IMAGE013
is at presentt k Time of daymIs tied tosA relative attitude matrix of the system is determined,
Figure 916284DEST_PATH_IMAGE014
is at at k -jh) Time of daymIs tied tosA relative attitude matrix of the system is determined,
Figure 410676DEST_PATH_IMAGE015
by (a)t k -jh) Time of daymIs tied tosQuaternion of relative attitude of system
Figure 628031DEST_PATH_IMAGE016
Obtaining:
Figure 162917DEST_PATH_IMAGE017
；
the relative speed updating algorithm in the step (2) comprises the following contents:
defining a position vector of the host system in the inertial coordinate system asR m The position vector of the subsystem in the inertial coordinate system isR s The relative position of the subsystem with respect to the main system isRThe lever arms between the main subsystems have the following vector relationship:
Figure 135421DEST_PATH_IMAGE018
relative inertial coordinate systemiThe first derivative is calculated, and:
Figure 122969DEST_PATH_IMAGE019
in the formula (I), the compound is shown in the specification,
Figure 940752DEST_PATH_IMAGE020
gyroscope for main system is currentlyt k The original angular velocity output at any moment;
relative inertial coordinate systemiThe first derivative is calculated, and:
Figure 64566DEST_PATH_IMAGE021
specific force equation of main subsystem measurement:
Figure 145654DEST_PATH_IMAGE022
in the formula (I), the compound is shown in the specification,
Figure 417236DEST_PATH_IMAGE023
、
Figure 507551DEST_PATH_IMAGE024
are respectively the currentt k The specific force measured by the master system at the momentmProjection of the system, specific force measured by the subsystemsProjection of the system;
Figure 485872DEST_PATH_IMAGE025
and
Figure 65758DEST_PATH_IMAGE026
are respectively the currentt k Time master subsystem universal gravitation acceleration in geographical coordinate systemeThe projection of (a) is performed,
Figure DEST_PATH_IMAGE027
(ii) a Order to
Figure 627232DEST_PATH_IMAGE028
WhereinVIs at presentt k The relative speed of the time main subsystem is shown as follows:
Figure 255660DEST_PATH_IMAGE029
project the above formula tom isThe following can be obtained:
Figure 354066DEST_PATH_IMAGE030
due to the fact that
Figure 776957DEST_PATH_IMAGE031
Relative speed of the main subsystem, not obtained by direct measurementV m Expressed in another form, let:
Figure 23130DEST_PATH_IMAGE032
the differential equation of the absolute velocity of the subsystem relative to the main system can be obtained:
Figure 189669DEST_PATH_IMAGE033
solving the velocity differential equation in the above formula and based on the value
Figure 142582DEST_PATH_IMAGE034
Realizing the relative speed between the main system and the sub systemV m Update to obtaint k+1Three-dimensional relative velocity between time master subsystemsV m (t k+1)。
2. The relative strapdown solution based airborne distributed POS delivery alignment method according to claim 1, wherein the relative position update algorithm of step (3) comprises the following:
the relative position is obtained by integrating the relative velocity, and therefore the relative position differential equation is expressed as:
Figure 533112DEST_PATH_IMAGE035
projecting the above formula on a main system carrier coordinate systemmThe following can be obtained:
Figure 1002DEST_PATH_IMAGE036
numerical solution to the differential equation of relative position in the above equationRealizing the relative position between the main subsystem and the sub-systemR m Update to obtaint k+1Three-dimensional relative position between time master subsystemsR m (t k+1)。
3. The relative strapdown solution based onboard distributed POS transfer alignment method of claim 1, wherein the transfer alignment algorithm of step (4) comprises the following: and (3) obtaining a state model of transfer alignment according to a relative strapdown resolving error propagation formula, wherein the state vector is:
Figure 502391DEST_PATH_IMAGE037
in the formula (I), the compound is shown in the specification,δФ x ,δФ y ,δФ z is the relative attitude error angle of the main subsystem,δU x ,δU y ,δU z is the absolute value of the relative velocity error of the main subsystem,δR x ,δR y ,δR z in order to account for the relative position error of the main subsystem,ε bx ,ε by ,ε bz is a random constant drift of the subsystem gyroscope bx , ▽ by , ▽ bz A random constant bias for the subsystem accelerometer;
the state model is described as:
Figure 372127DEST_PATH_IMAGE038
in the formula (I), the compound is shown in the specification,Ain order to be a matrix of the system,Bthe matrix is driven for the system noise,Wthe system noise includes the random constant drift of the gyroscope and the random constant bias of the accelerometer, namely:
Figure 136820DEST_PATH_IMAGE039
system matrixAComprises the following steps:
Figure 826428DEST_PATH_IMAGE040
system noise driving matrixBComprises the following steps:
Figure 414665DEST_PATH_IMAGE041
the transfer alignment is carried out by adopting a relative position and relative attitude matching mode, and the measurement vector of the transfer alignment is as follows:
Figure 342169DEST_PATH_IMAGE042
in the formula (I), the compound is shown in the specification,Z 1for the relative position to match the measurement vector,Z 2matching the measurement vector for the relative pose;
according to the three-dimensional relative attitude obtained by calculationβ c Three-dimensional relative attitude measured by fiber gratingβ M Establishing a measurement vector matched with the relative attitude:
Figure 277764DEST_PATH_IMAGE043
in the formula (I), the compound is shown in the specification,ηis composed ofαDeviation of systemmThe attitude angle of the system is determined,ξis composed ofsDeviation of systemαThe angle of the installation error of the system,mis connected withsAre respectively a main subsystem carrier coordinate system,αis the subsystem nominal coordinate system;
from the calculated three-dimensional relative position
Figure 923509DEST_PATH_IMAGE044
Three-dimensional relative position to fiber grating measurement
Figure 32279DEST_PATH_IMAGE045
Establishing a relative position matching measurement vector:
Figure 814291DEST_PATH_IMAGE046
establishing a transfer alignment measurement model according to a transfer alignment measurement vector expression:
Figure 186366DEST_PATH_IMAGE047
Figure DEST_PATH_IMAGE048
in the formula (I), the compound is shown in the specification,Hin order to measure the matrix, the measurement matrix is,Vin order to measure the noise, the noise is measured,Vthe measurement noise determined by the relative position and attitude of the fiber grating measurements.
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