CN102495830A - Quaternion Hartley approximate output method based on angular velocities for aircraft during extreme flight - Google Patents
Quaternion Hartley approximate output method based on angular velocities for aircraft during extreme flight Download PDFInfo
- Publication number
- CN102495830A CN102495830A CN2011103667742A CN201110366774A CN102495830A CN 102495830 A CN102495830 A CN 102495830A CN 2011103667742 A CN2011103667742 A CN 2011103667742A CN 201110366774 A CN201110366774 A CN 201110366774A CN 102495830 A CN102495830 A CN 102495830A
- Authority
- CN
- China
- Prior art keywords
- hartley
- quaternion
- pitching
- extreme flight
- lift
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Landscapes
- Navigation (AREA)
- Control Of Position, Course, Altitude, Or Attitude Of Moving Bodies (AREA)
Abstract
The invention discloses a quaternion Hartley approximate output method based on angular velocities for an aircraft during extreme flight, which is used for solving the technical problem of poor precision of quaternion outputted by existing inertial equipment when an aircraft is in extreme flight. The technical scheme includes that approximate description for a rolling angular velocity p, a pitching angular velocity q and a yawing angular velocity r is realized by the aid of a Hartley polynomial, a quaternion state transition matrix second-order approximant is directly obtained, a quaternion state transition matrix is also directly obtained, iterative computation precision of specified quaternion is guaranteed, and accordingly output precision of inertial equipment is improved when the aircraft is in extreme flight.
Description
Technical field
The present invention relates to a kind of attitude output intent of air craft carried inertial equipment, the approximate output intent of hypercomplex number Hartley when particularly relating to a kind of aircraft extreme flight based on angular velocity.
Background technology
Usually, the acceleration of rigid motion, angular velocity and attitude etc. all depend on inertial equipment output, and the output accuracy that therefore improves inertial equipment has clear and definite practical significance.The rigid motion differential equation is in most of the cases all adopted in spatial movements such as aircraft, torpedo, spacecraft; And the differential equation of portrayal rigid body attitude is a core wherein, is that pitching, lift-over and crab angle are described with three Eulerian angle usually, all resolves back output by pitching in the airborne inertial equipment, lift-over and yaw rate usually.When rigid body when the angle of pitch is ± 90 °, roll angle and crab angle can't definite values, it is excessive that error is found the solution in the zone of closing on this singular point simultaneously, causes intolerable error on the engineering and can not use; For fear of this problem, people adopt the method for restriction angle of pitch span, and this makes equation degenerate, attitude work entirely, thereby be difficult to be widely used in engineering practice.For this reason, people are based on the direct measured value of the pitching in the airborne inertial equipment, lift-over and yaw rate, and have adopted output flight attitudes such as direction cosine method, equivalent gyration vector method, hypercomplex number method.
Direction cosine method has been avoided Euler method " unusual " phenomenon, and calculating attitude matrix with direction cosine method does not have the equation degenerate problem, attitude work entirely; But need find the solution nine differential equations; Calculated amount is bigger, and real-time is relatively poor, can't satisfy the engineering practice requirement.Equivalence gyration vector method such as list appearance recursion, Shuangzi appearance gyration vector, three increment gyration vectors and four increment rotating vector methods and various correction algorithms on this basis and recursive algorithm etc.When studying rotating vector in the document, all be based on the algorithm that rate gyro is output as angle increment.Yet in actual engineering, the output of some gyros is angle rate signals, like optical fibre gyro, dynamic tuned gyroscope etc.When rate gyro was output as angle rate signal, the Algorithm Error of rotating vector method obviously increased.The hypercomplex number method is the most widely used method; This method is that the function of four Eulerian angle of definition calculates the boat appearance; Can effectively remedy the singularity of Euler method; As long as separate four differential equation of first order formula groups, analogy has tangible minimizing to cosine attitude matrix differential equation calculated amount, can satisfy in the engineering practice requirement to real-time.Its The common calculation methods has (Paul G.Savage.A Unified Mathematical Framework for Strapdown Algorithm Design [J] .Journal of guidance such as the card of finishing approximatioss, second order, fourth-order Runge-Kutta method and three rank Taylor expansion methods; Control; And dynamics; 2006,29 (2): 237-248).Finishing card approximatioss essence is list appearance algorithm, can not compensate by exchange error what limited rotation caused, and the algorithm drift under high current intelligence in the attitude algorithm can be very serious.When adopting fourth-order Runge-Kutta method to find the solution the hypercomplex number differential equation,, the trigonometric function value can occur to exceed ± 1 phenomenon, disperse thereby cause calculating along with the continuous accumulation of integral error.The Taylor expansion method also is restricted because of the deficiency of computational accuracy; Particularly for the aircraft maneuvering flight; The attitude orientation angular speed is all bigger usually; And the estimated accuracy of attitude proposed requirements at the higher level, and parameters such as hypercomplex number confirm that the error of bringing makes said method in most cases can not satisfy engineering precision.
Summary of the invention
The problem of inertial equipment output hypercomplex number low precision when overcoming existing aircraft extreme flight, the approximate output intent of hypercomplex number Hartley when the present invention provides a kind of aircraft extreme flight based on angular velocity.This method adopts the Hartley polynomial expression to lift-over, pitching, yaw rate p; Q, r carry out close approximation to be described, and directly obtains the hypercomplex number state-transition matrix; Can guarantee to confirm the iterative computation precision of hypercomplex number, thus inertial equipment output hypercomplex number precision when improving the aircraft extreme flight;
The technical solution adopted for the present invention to solve the technical problems is: the approximate output intent of hypercomplex number Hartley during a kind of aircraft extreme flight based on angular velocity is characterized in may further comprise the steps:
According to hypercomplex number continuous state equation
And discrete state equations
e(k+1)=Φ
e[(k+1)T,kT]e(k)
E=[e wherein
1, e
2, e
3, e
4]
T
Ф
e[(k+1) T, kT] is A
eState-transition matrix, T is the sampling period, in full symbol definition is identical;
P, q, r are respectively lift-over, pitching, the yaw rate that inertial equipment is directly measured; Eulerian angle
θ, ψ refers to lift-over, pitching, crab angle respectively;
State-transition matrix is according to approximant
And e (k+1)=Φ
e[(k+1) T, kT] e (k) obtains the time updating value of hypercomplex number;
Wherein
ξ
i(t)=cas(iωt)=cos(iωt)+sin(iωt),(i=-n,-n+1,…,-1,0,1,2,…,n)
ω is an angular frequency; Lift-over, pitching, yaw rate p, q, the Hartley expansion of r is respectively
p(t)=[p
-n…p
-1?p
0?p
1…p
n][ξ
-n(t)…ξ
-1(t)ξ
0(t)ξ
1(t)…ξ
n(t)]
T
q(t)=[q
-n…q
-1?q
0?q
1…q
n][ξ
-n(t)…ξ
-1(t)ξ
0(t)ξ
1(t)…ξ
n(t)]
T
r(t)=[r
-n…r
-1?r
0?r
1…r
n][ξ
-n(t)…ξ
-1(t)ξ
0(t)ξ
1(t)…ξ
n(t)]
T
The invention has the beneficial effects as follows: because the lift-over, pitching, the yaw rate p that adopt the Hartley polynomial expression that inertial equipment is directly exported; Q; R carries out close approximation to be described; It is approximant directly to have obtained hypercomplex number state-transition matrix second order, has guaranteed the iterative computation precision of definite hypercomplex number, thus inertial equipment output accuracy when having improved the aircraft extreme flight.
Below in conjunction with embodiment the present invention is elaborated.
Embodiment
According to hypercomplex number continuous state equation
And discrete state equations
e(k+1)=Φ
e[(k+1)T,kT]e(k)
In the formula, e=[e
1, e
2, e
3, e
4]
T
Ф
e[(k+1) T, kT] is A
eState-transition matrix, T is the sampling period,
P, q, r are respectively lift-over, pitching, yaw rate; Eulerian angle
θ, ψ refers to lift-over, pitching, crab angle respectively;
State-transition matrix is according to approximant
And e (k+1)=Φ
e[(k+1) T, kT] e (k) obtains the time updating value of hypercomplex number;
Wherein
ξ
i(t)=cas(iωt)=cos(iωt)+sin(iωt),(i=-n,-n+1,…,-1,0,1,2,…,n)
Lift-over, pitching, yaw rate p, q, the Hartley expansion of r is respectively
p(t)=[p
-n…p
-1?p
0?p
1…p
n][ξ
-n(t)…ξ
-1(t)ξ
0(t)ξ
1(t)…ξ
n(t)]
T
q(t)=[q
-n…q
-1?q
0?q
1…q
n][ξ
-n(t)…ξ
-1(t)ξ
0(t)ξ
1(t)…ξ
n(t)]
T
r(t)=[r
-n…r
-1?r
0?r
1…r
n][ξ
-n(t)…ξ
-1(t)ξ
0(t)ξ
1(t)…ξ
n(t)]
T
When inertial equipment is directly exported lift-over, pitching, yaw rate p, q, r adopt three rank to approach when describing, and the gained result is also near O (T
3), compare the O (T that finishes methods such as card approaches
2) precision will height.
Claims (1)
1. the approximate output intent of hypercomplex number Hartley during an aircraft extreme flight based on angular velocity is characterized in that may further comprise the steps:
According to hypercomplex number continuous state equation
And discrete state equations
e(k+1)=Φ
e[(k+1)T,kT]e(k)
E=[e wherein
1, e
2, e
3, e
4]
T
Ф
e[(k+1) T, kT] is A
eState-transition matrix, T is the sampling period, in full symbol definition is identical;
P, q, r are respectively lift-over, pitching, the yaw rate that inertial equipment is directly measured; Eulerian angle
θ, ψ refers to lift-over, pitching, crab angle respectively;
State-transition matrix is according to approximant
And e (k+1)=Φ
e[(k+1) T, kT] e (k) obtains the time updating value of hypercomplex number;
Wherein
ξ
i(t)=cas (i ω t)=cos (i ω t)+sin (i ω t), (i=-n ,-n+1 ... ,-1,0,1,2 ..., n) ω is an angular frequency; Lift-over, pitching, yaw rate p, q, the Hartley expansion of r is respectively
p(t)=[p
-n…p
-1?p
0?p
1…p
n][ξ
-n(t)…ξ
-1(t)ξ
0(t)ξ
1(t)…ξ
n(t)]
T
q(t)=[q
-n…q
-1?q
0?q
1…q
n][ξ
-n(t)…ξ
-1(t)ξ
0(t)ξ
1(t)…ξ
n(t)]
T
r(t)=[r
-n…r
-1?r
0?r
1…r
n][ξ
-n(t)…ξ
-1(t)ξ
0(t)ξ
1(t)…ξ
n(t)]
T
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN201110366774.2A CN102495830B (en) | 2011-11-17 | 2011-11-17 | Quaternion Hartley approximate output method based on angular velocities for aircraft during extreme flight |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN201110366774.2A CN102495830B (en) | 2011-11-17 | 2011-11-17 | Quaternion Hartley approximate output method based on angular velocities for aircraft during extreme flight |
Publications (2)
Publication Number | Publication Date |
---|---|
CN102495830A true CN102495830A (en) | 2012-06-13 |
CN102495830B CN102495830B (en) | 2015-03-25 |
Family
ID=46187655
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
CN201110366774.2A Expired - Fee Related CN102495830B (en) | 2011-11-17 | 2011-11-17 | Quaternion Hartley approximate output method based on angular velocities for aircraft during extreme flight |
Country Status (1)
Country | Link |
---|---|
CN (1) | CN102495830B (en) |
Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN104850127A (en) * | 2015-03-13 | 2015-08-19 | 哈尔滨工程大学 | Method for dynamic control of quad-rotor aircraft |
CN109855698A (en) * | 2017-11-30 | 2019-06-07 | 波音公司 | The combination of level gauging and maximum redundancy from individual compartment |
Citations (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN101029653A (en) * | 2007-04-05 | 2007-09-05 | 宫多乾 | Method and apparatus for eliminating runner opening vortex |
CN101846510A (en) * | 2010-05-28 | 2010-09-29 | 北京航空航天大学 | High-precision satellite attitude determination method based on star sensor and gyroscope |
CN102141613A (en) * | 2010-12-01 | 2011-08-03 | 北京空间机电研究所 | Method for determining signal-to-noise ratio of optical remote sensor by combining satellite orbit characteristics |
-
2011
- 2011-11-17 CN CN201110366774.2A patent/CN102495830B/en not_active Expired - Fee Related
Patent Citations (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN101029653A (en) * | 2007-04-05 | 2007-09-05 | 宫多乾 | Method and apparatus for eliminating runner opening vortex |
CN101846510A (en) * | 2010-05-28 | 2010-09-29 | 北京航空航天大学 | High-precision satellite attitude determination method based on star sensor and gyroscope |
CN102141613A (en) * | 2010-12-01 | 2011-08-03 | 北京空间机电研究所 | Method for determining signal-to-noise ratio of optical remote sensor by combining satellite orbit characteristics |
Cited By (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN104850127A (en) * | 2015-03-13 | 2015-08-19 | 哈尔滨工程大学 | Method for dynamic control of quad-rotor aircraft |
CN104850127B (en) * | 2015-03-13 | 2017-11-21 | 哈尔滨工程大学 | It is a kind of can dynamic manipulation quadrotor method |
CN109855698A (en) * | 2017-11-30 | 2019-06-07 | 波音公司 | The combination of level gauging and maximum redundancy from individual compartment |
Also Published As
Publication number | Publication date |
---|---|
CN102495830B (en) | 2015-03-25 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
CN112198885B (en) | Unmanned aerial vehicle control method capable of meeting autonomous landing requirement of maneuvering platform | |
CN102436437B (en) | Quaternion Fourier approximate output method in extreme flight of aircraft based on angular speed | |
CN102589553A (en) | Switching method for building aircraft motion model | |
CN117389312A (en) | Model-based three-dimensional tracking control method for counter roll of underwater vehicle | |
CN102495830A (en) | Quaternion Hartley approximate output method based on angular velocities for aircraft during extreme flight | |
CN102495831B (en) | Quaternion Hermitian approximate output method based on angular velocities for aircraft during extreme flight | |
CN102508819A (en) | Angular-speed-based quaternion Legendre approximate output method during extreme flying of aircraft | |
CN102495829B (en) | Quaternion Walsh approximate output method based on angular velocities for aircraft during extreme flight | |
CN102506864B (en) | Method for approximately outputting quaternion numbers with arbitrary step size in orthogonal series during extreme flight of aircraft | |
CN102506866B (en) | Angle speed-based Chebyshev approximate output method of quaternion numbers in ultimate flight of aircraft | |
CN102445202B (en) | Laguerre output method for rigid body space motion state | |
CN102506865B (en) | Four-ary number polynomial approximate output method during extreme aerobat flight based on angular velocity | |
CN102494688B (en) | Quaternion Laguerre approximate output method based on angular speed used during extreme flight of flying vehicle | |
CN102495825A (en) | Quaternion superlinear output method based on angular velocities for aircraft during extreme flight | |
CN102384747A (en) | Hartley output method of rigid body space motion states | |
CN102323990B (en) | Method for modeling pneumatic model for rigid body space motion | |
CN102508818B (en) | Arbitrary-step orthogonal series output method of space motion state of rigid body | |
CN102359790B (en) | Fourier outputting method for spatial movement state of rigid body | |
Jarrell et al. | Aircraft attitude, position, and velocity determination using sensor fusion | |
CN102359789B (en) | Arbitrary order output method for rigid body space motion state | |
CN102346729B (en) | Legendre output method for space motion space of rigid body | |
CN102445203B (en) | Emmett output method for rigid body space motion state | |
CN102323992B (en) | Polynomial type output method for spatial motion state of rigid body | |
CN102384746B (en) | Chebyshev output method for space motion state of rigid body | |
CN102508821B (en) | State output method for space motion of rigid body |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
C06 | Publication | ||
PB01 | Publication | ||
C10 | Entry into substantive examination | ||
SE01 | Entry into force of request for substantive examination | ||
C14 | Grant of patent or utility model | ||
GR01 | Patent grant | ||
CF01 | Termination of patent right due to non-payment of annual fee | ||
CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20150325 Termination date: 20191117 |