CN107729585A - A kind of method that noise covariance to unmanned plane is estimated - Google Patents
A kind of method that noise covariance to unmanned plane is estimated Download PDFInfo
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Abstract
The invention provides a kind of method that noise covariance to unmanned plane is estimated, the state estimation equation after unmanned plane kinetic model is linearized using extended Kalman filter combination controlled quentity controlled variable and observation；Coefficient matrix, kalman gain and the new breath that state estimation equation after the linearisation is obtained are updated to the covariance matrix for obtaining being formed in auto-covariance least-squares algorithm with the desired value newly ceased and the new estimate for ceasing the auto-covariance matrix that desired value is formed, determine planning algorithm by more than half, obtain the covariance of process noise and measure the covariance of noise.It is high to process noise covariance Q and the estimation accuracy for measuring noise covariance R by the method estimated the noise covariance of unmanned plane in the present invention.Meanwhile the evaluation method provides numeric reference for operating personnel, so general operation personnel are more convenient quick in debugging process noise covariance Q and measurement noise covariance R.
Description
Technical field
The present invention relates to unmanned air vehicle technique field, is carried out more specifically to a kind of noise covariance to unmanned plane
The method of estimation.
Background technology
UAV referred to as " unmanned plane ", is manipulated using radio robot and the presetting apparatus provided for oneself
Not manned aircraft, its is widely used, is widely used in dual-use field, such as air-borne early warning, agricultural, geology, gas
As industries such as, electric power, rescue and relief work, video captures.As the unmanned plane manipulated using self-contained program's control device, it has strong
Coupling, non-linear, control difficulty characteristic, Dynamic Modeling are complex.The interference that the control and manipulation of unmanned plane face
Including：The external disturbance torque such as gravity, and system in unmanned plane kinetic model make the observation in sound and measurement equation
The interference from unmanned plane therein such as noise, above multi-source, which disturbs, to be needed to be estimated by high-precision model and algorithm,
So as to reach high-precision control.
However, in the prior art, processing unmanned plane process noise and the filtering algorithm for measuring noise, such as Kalman's filter
Ripple, when noise characteristic is unknown, typically using empirical value or the covariance matrix value of noise is obtained by the method for debugging, i.e.
In the prior art, the association of the covariance to the process noise in unmanned plane kinetic model and the observation noise in measurement equation
Variance is required to that by debugging optimum efficiency can be reached.Therefore, following defect is left in the prior art：The covariance square of noise
Battle array needs to obtain by empirical value or the method for debugging, it is necessary to which more experienced operating personnel, operating personnel
Ask higher, and if the given noise covariance deviation of debugging it is excessive, can directly result in filter value recursion it is a certain during, very
Increasingly deviate actual value into whole process, cause filtering divergence, cause the flight of unmanned plane to deviate objective result.
Odelson can effectively estimate the association of noise in the auto-covariance Least Square Theory method proposed in 2003
Variance matrix, save the time of debugging.Auto-covariance Least Square Theory algorithm is usually used in the noise estimation of chemical industry at present,
Not yet it is used for unmanned plane field.Rajamani et al. proposed the linear time-varying auto-covariance for nonlinear system in 2011
Least square method.Process noise and observation noise of the present invention by above method combination unmanned plane kinetic model to unmanned plane
Estimated.
The content of the invention
The technology of the present invention solves problem：Overcome existing processing unmanned plane process noise and measure the filtering of noise
In algorithm, when noise characteristic is unknown, it is necessary to obtain the covariance matrix value of noise using empirical value or by the method for debugging,
The problem of requiring higher to operating personnel, and easily causing deviation, design one kind can be automatically to caused by process noises and observation
Covariance matrix value carries out the evaluation method of valuation.
The technical solution adopted for the present invention to solve the technical problems is：A kind of noise covariance to unmanned plane is provided to enter
The method of row estimation, it is characterised in that using auto-covariance Least Square Theory method to the mistake in unmanned plane kinetic model
The characteristic of observation noise in journey noise and measurement equation is estimated, is comprised the following steps：
S1, establish unmanned plane kinetic model；
S2, using extended Kalman filter combination controlled quentity controlled variable and observation unmanned plane kinetic model is linearized to obtain
State estimation equation after linearisation；And obtained according to the state estimation equation after the linearisation coefficient matrix, Kalman
Gain and new breath；
S3, by the coefficient matrix, the kalman gain and it is described it is new breath be updated to auto-covariance least square calculate
The covariance matrix that is formed with the desired value that newly ceases and the auto-covariance matrix formed with new breath desired value are obtained in method
Estimate；
S4, the covariance matrix formed using the desired value of the new breath and the self tuning side formed with new breath desired value
The estimate of poor matrix, by Semidefinite Programming algorithm, obtain the covariance of process noise and measure the covariance of noise.
Further, the step S1 further comprises following steps：
The line equation of motion that S11, the unmanned plane kinetic model are established in earth axes and in body axis system
The rotation equation of middle foundation is：
Wherein, m is the quality of unmanned plane, and X is the position vector of unmanned plane,For the acceleration of unmanned plane, T is rotation
Thrust caused by the wing, M are torque caused by rotor, and J is the rotary inertia of unmanned plane, and ω is the angular speed that unmanned plane rotates,
The angular acceleration rotated for unmanned plane, G are the gravity that unmanned plane is subject to, and F is the air drag that unmanned plane is subject to,
Wherein, L is rotor centers to X-axis or the distance of Y-axis, Ω1、Ω2、Ω3、Ω4The rotating speed of respectively four blades,
B, d is respectively the tension coefficient and torque coefficient of blade；
S12, the angle between axis X and horizontal plane is defined as pitching angle theta, come back as just；By axis X in level
Projection and X on faceEAngle between axle is defined as yaw angleHead right avertence is just；By axis Z and pass through body X-axis
Angle between vertical guide is defined as roll angle φ, and the right rolling of unmanned plane is just, these three angles is Eulerian angles；
OrderThen the coordinate conversion matrix from body axis system to earth axes is
Then the kinetic model of unmanned plane is written as
Wherein,Respectively unmanned plane is in earth axes XE,YE,ZEAcceleration on direction of principal axis； Respectively unmanned plane is in body axis system X, Y, the angular acceleration in Z-direction；Ixx、Iyy、IzzRespectively unmanned plane is around machine
Body coordinate system X-axis, Y-axis, the rotary inertia of Z axis, Ffx、Ffy、FfzComponents of the respectively F on the axle of body axis system three, [ωx,
ωy,ωz] it is components of the ω on the axle of body axis system three, [ωx,ωy,ωz] as follows with the relation of Eulerian angles
Further, the step S2 further comprises following steps：
S21, the general type for being written as the state equation of system and measurement equation：
Wherein, xkFor quantity of state, ykFor the observed quantity, the observed quantity obtains from sensor, ukFor the control
Amount, the controlled quentity controlled variable is by being manually set, wkFor the process noise, vkFor the measurement noise；wk~N (0, Q) and vk~N (0,
R it is) uncorrelated, its state is estimated by equation (5), obtained
Wherein, LkFor the Kalman filtering gain, the new breath is
S22, the equation (5) existedPlace linearizes
Wherein, Ak, Bk, Gk, CkIt is the coefficient matrix,
State estimation equation after S23, the linearisation is：
Further, the step S3 further comprises following steps：
S31, it is described form auto-covariance matrix with the desired value that newly ceases,
S32, with [R (N)]sWith the estimate of the auto-covariance matrix formed with new breath desired valueDifference two models
Several square minimum optimization aims,
Wherein,
Further, when estimating the noise covariance that line moves, by the Eulerian angles and four blades
Rotating speed as the controlled quentity controlled variable.
Further, when the noise covariance of diagonal motion is estimated, using the rotating speed of four blades as institute
State controlled quentity controlled variable.
One or more technical schemes provided by the invention, have at least the following technical effects or advantages：
The process noise of unmanned plane and process moulding can be estimated by auto-covariance Least Square Theory method,
Reduce in the prior art, the covariance matrix value of debugging process noise and observation noise is wanted to empirical value and operating personnel
Ask, accurate valuation section can be provided to operating personnel, save the time of debugging, while ensure that system is caused and seen
Survey the accuracy of noise.
Brief description of the drawings
In order to illustrate more clearly about the embodiment of the present invention or technical scheme of the prior art, below will be to embodiment or existing
There is the required accompanying drawing used in technology description to be briefly described, it should be apparent that, drawings in the following description are only this
The embodiment of invention, for those of ordinary skill in the art, on the premise of not paying creative work, can also basis
The accompanying drawing of offer obtains other accompanying drawings.
Fig. 1 is the method schematic that the noise covariance of unmanned plane in the present invention is estimated；
Fig. 2 is the schematic diagram of earth axes and body axis system in the present invention；
Fig. 3 is X in earth axes of the present inventionEThe position curve of direction of principal axis；
Fig. 4 is X in earth axes of the present inventionEThe rate curve of direction of principal axis；
Fig. 5 is Y in earth axes of the present inventionEThe position curve of direction of principal axis；
Fig. 6 is Y in earth axes of the present inventionEThe rate curve of direction of principal axis；
Fig. 7 is Z in earth axes of the present inventionEThe position curve of direction of principal axis；
Fig. 8 is Z in earth axes of the present inventionEThe rate curve of direction of principal axis；
Fig. 9 is roll angle φ of the present invention change curve；
Figure 10 is rolling angular rate of change of the present inventionChange curve；
Figure 11 is the change curve of pitching angle theta of the present invention；
Figure 12 is Elevation angle changing rate of the present inventionChange curve；
Figure 13 is yaw angle of the present inventionChange curve；
Figure 14 is present invention driftage angular rate of changeChange curve；
Embodiment
As shown in figure 1, the method schematic estimated of noise covariance of the unmanned plane for the present invention, first, this hair
It is bright including：Step S1, unmanned plane kinetic model is established, step S2, using extended Kalman filter combination controlled quentity controlled variable u and is led to
The observation h (x) for crossing sensor acquisition linearizes unmanned plane kinetic model；Step S3, the coefficient square that linearisation is obtained
Battle array A, B, C, G, kalman gain L and new breath y substitutions obtain new breath from linear time-varying-auto-covariance least-squares algorithm
Desired value form auto-covariance matrix [R (N)]sWith the estimate of the auto-covariance matrix with new breath desired value compositionStep
Rapid S4, the desired value that acquisition is newly ceased form auto-covariance matrix [R (N)]sWith the self tuning side formed with new breath desired value
The estimate of poor matrixSubstitute into semi definite programming algorithm, try to achieve process noise covariance Q and measure noise covariance R.
Step S1 includes, as shown in Fig. 2 for four rotor wing unmanned aerial vehicles of X-shaped, establishes earth axes and body coordinate
System is as shown in Figure 2.Body axis system B-XYZ：Origin takes the barycenter in unmanned plane, and coordinate system is connected with body.X-axis is set with fuselage
The longitudinal axis of meter is parallel, and in the symmetrical plane in unmanned plane, is directing forwardly；Y-axis is pointed to right perpendicular to unmanned plane symmetrical plane
Side；Z axis is and downwardly directed perpendicular to X-axis in unmanned plane symmetrical plane.Whole coordinate system meets the eulerian coordinate system right hand and determined
Then.Earth axes E-XEYEZE：Coordinate system, X using east northeastEAxle points to north, YEAxle points in the east, and ZEAxle vertically to
Under.
In the case of the air drag F that pulling force T and unmanned plane caused by only consideration unmanned plane gravity G, rotor are subject to, S1
Further comprise step S11, the kinetic model for establishing unmanned plane is as follows.The line equation of motion is established in earth axes respectively
It is as follows with rotation equation is established in body axis system：
Wherein, m is the quality of unmanned plane, and X is the position vector of unmanned plane,For the acceleration of unmanned plane, M is rotation
Torque caused by the wing, J are the rotary inertia of unmanned plane, and ω is the angular speed that unmanned plane rotates,The angle rotated for unmanned plane adds
Speed,
Wherein, L is rotor centers to X-axis or the distance of Y-axis, Ω1、Ω2、Ω3、Ω4The rotating speed of respectively four blades,
B, d is respectively the tension coefficient and torque coefficient of blade.
S1 further comprises step S12, the angle between axis X and horizontal plane is defined as into pitching angle theta, coming back is
Just；By axis X projections in the horizontal plane and XEAngle between axle is defined as yaw angleHead right avertence is just；By body
Angle between axle Z and the vertical guide for passing through body X-axis is defined as roll angle φ, and the right rolling of unmanned plane is just.These three angles are
Eulerian angles.
OrderThen the coordinate conversion matrix from body axis system to earth axes is
Then the kinetic model of unmanned plane is written as
Wherein,Respectively unmanned plane is in earth axes XE,YE,ZEAcceleration on direction of principal axis； Respectively unmanned plane is in body axis system X, Y, the angular acceleration in Z-direction；Ixx、Iyy、IzzRespectively unmanned plane
Around body axis system X-axis, Y-axis, Z axis rotary inertia, Ffx、Ffy、FfzComponents of the respectively F on the axle of body axis system three,
[ωx,ωy,ωz] it is components of the ω on the axle of body axis system three, [ωx,ωy,ωz] as follows with the relation of Eulerian angles
Step S2 further comprises the general type that the state equation of system and measurement equation are written as by S21：
Its state is estimated, wherein, xkFor quantity of state, ykFor the observed quantity, the observed quantity obtains from sensor
Take, ukFor the controlled quentity controlled variable, the controlled quentity controlled variable is by being manually set, wkFor the process noise, vkFor the measurement noise；wk~N
(0, Q) and vk~N (0, R) is uncorrelated, and its state is estimated by equation (1), obtained
Wherein, LkFor Kalman filtering gain, new breath
Step S2 further comprises S22, and the equation (5) is existedPlace linearizes
Wherein, Ak, Bk, Gk, CkIt is the coefficient matrix,
Step S2 further comprises S23, and the state estimation equation after linearisation is
State estimation error is expressed as
And
Then
Step S3 further comprises S31, and auto-covariance matrix is formed with the desired value newly ceased
Step S3 further comprises S31, withWith estimating for the auto-covariance matrix formed with new breath desired value
EvaluationDifference two norms square minimum optimization aim
Wherein,
Embodiment one
Due to the equation group that unmanned plane kinetic model is one 12 dimension, covariance Least Square Theory algorithm is used
When estimating the noise covariance in model, to shorten program runtime, respectively to line motion and the noise association side in angular movement
Difference is estimated.Each parameter value is as shown in table 1 in the model used during emulation.
The parameter value of table 1
| Parameter name | Parameter value | Parameter name | Parameter value |
| Unmanned plane quality m | 1.5kg | Gravity acceleration g | 9.79m/s2 |
| X-axis rotary inertia Ixx | 0.024kg·m2 | Y-axis rotary inertia Iyy | 0.024kg·m2 |
| Z-axis rotary inertia Izz | 0.112kg·m2 | L | 0.232m |
| Blade tension coefficient b | 1.0643×10-5 | Blade torque coefficient d | 2.3528×10-7 |
| Coefficient of air resistance k | -0.2334 |
1. line moves
State equation is the line equation of motion of unmanned plane kinetic model in line motion, i.e.,
Wherein, state variable is X=[x, y, z, u, v, w]T.Using the rotating speed of Eulerian angles and four motors as controlled quentity controlled variable,
[φ, θ, φ]=[0,0,0], [Ω1,Ω2,Ω3,Ω4]=[588.9737,588.9737,588.9737,588.9737].Shape
State amount initial value isAnd it is as follows to set measurement equation
It is Q=2.5 × 10 to add covariance in online motion model-5Zero mean Gaussian white noise, in observational equation
Addition covariance is R=10-3I6×6White Gaussian noise, the sight of 10 seconds is generated with the fixed step size of 0.001 second using ODE45 functions
Survey data.
First, coefficient matrix is obtained using expanded Kalman filtration algorithm bonding state equation, controlled quentity controlled variable and observation data
And kalman gain.Then, the auto-covariance of new breath desired value composition is provided using the theory of auto-covariance least-squares algorithm
The estimate for the auto-covariance matrix that matrix and new breath desired value are formed.Finally, formula is solved using semi definite programming method
(14) optimal problem in, obtain required process noise covariance Q and measure noise covariance R.
2. angular movement
State equation is the angular motion equation of unmanned plane kinetic model in angular movement, i.e.,
Wherein, state variable isControlled quentity controlled variable is the rotating speed of four motors in angular movement, [Ω1,
Ω2,Ω3,Ω4]=[481.5,481.5,481.5,481.5].
Quantity of state initial value isIt is as follows to set measurement equation
It is Q=2.5 × 10 to add covariance in online motion model-5Zero mean Gaussian white noise, in observational equation
Addition covariance is R=10-3I6×6White Gaussian noise, the sight of 10 seconds is generated with the fixed step size of 0.001 second using ODE45 functions
Survey data.The process of covariance estimation is identical in being moved with line.
The simulation result of embodiment one is as follows：
1. line moves
It is set to 0.1 second using sampling time during covariance Least Square Theory algorithm, Q initial estimate is set to 8
×10-3, R initial estimate is set to 3 × 10-3I6×6, the result that covariance Least Square Theory method program recognizes to obtain is
2. angular movement
The sampling time is set to 0.1 second when being emulated using covariance Least Square Theory algorithm, and Q initial estimate is equal
It is set to 3 × 10-3, R initial estimate is set to 3 × 10-3I6×6, the result for recognizing to obtain is
The noise characteristic estimated in line motion and angle movement model is substituted into EKF and is filtered, is obtained
To filtered each variable curve and each variable actual value, observation comparison diagram as shown in figs. 3-14, depicted in Fig. 3-14
Observation, actual value and the use filtered value of EKF of each state variable.The scattered point of grey is each in figure
The observation of variable, the solid line of black is actual value.As can be seen that due to process noise and observation noise be present, observation is deposited
In error.The process noise covariance Q and measurement noise covariance R that covariance Least Square Theory algorithm is recognized to obtain
Substitute into expanded Kalman filtration algorithm and be filtered, obtained the filtered value that black dotted lines represent in figure.Although filtering
Value afterwards still suffers from error, but has been sufficiently close to actual value, illustrates that covariance Least Square Theory algorithm is estimated to obtain
Covariance it is more accurate.
In summary, by the method estimated the noise covariance of unmanned plane in the present invention, to process noise
Covariance Q and the estimation accuracy height for measuring noise covariance R.Meanwhile the evaluation method provides numerical value ginseng for operating personnel
Examine, so general operation personnel are more convenient quick in debugging process noise covariance Q and measurement noise covariance R.
Claims (6)
1. a kind of method that noise covariance to unmanned plane is estimated, it is characterised in that comprise the following steps：
S1, establish unmanned plane kinetic model；
S2, using extended Kalman filter combination controlled quentity controlled variable and observation the unmanned plane kinetic model is linearized to obtain
State estimation equation after linearisation；And obtained according to the state estimation equation after the linearisation coefficient matrix, Kalman
Gain and new breath；
S3, by the coefficient matrix, the kalman gain and it is described it is new breath be updated in auto-covariance least-squares algorithm
Obtain the estimation of covariance matrix and the auto-covariance matrix formed with new breath desired value formed with the desired value newly ceased
Value；
S4, the covariance matrix formed using the desired value of the new breath and the auto-covariance square formed with new breath desired value
The estimate of battle array, by Semidefinite Programming algorithm, obtain the covariance of process noise and measure the covariance of noise.
2. according to the evaluation method in claim 1, it is characterised in that the step S1 further comprises following steps：
The line equation of motion and built in body axis system that S11, the unmanned plane kinetic model are established in earth axes
Vertical rotation equation is：
Wherein, m is the quality of unmanned plane, and X is the position vector of unmanned plane,For the acceleration of unmanned plane, T produces for rotor
Raw thrust, M are torque caused by rotor, and J is the rotary inertia of unmanned plane, and ω is the angular speed that unmanned plane rotates,For nothing
The angular acceleration of man-machine rotation, G are the gravity that unmanned plane is subject to, and F is the air drag that unmanned plane is subject to,
Wherein, L is rotor centers to X-axis or the distance of Y-axis, Ω1、Ω2、Ω3、Ω4The rotating speed of respectively four blades, b, d points
Not Wei blade tension coefficient and torque coefficient；
S12, the angle between axis X and horizontal plane is defined as pitching angle theta, come back as just；By axis X in the horizontal plane
Projection and XEAngle between axle is defined as yaw angleHead right avertence is just；By axis Z and the vertical by body X-axis
Angle between face is defined as roll angle φ, and the right rolling of unmanned plane is just, these three angles is Eulerian angles；
OrderThen the coordinate conversion matrix from body axis system to earth axes is
Then the kinetic model of unmanned plane is written as
Wherein,Respectively unmanned plane is in earth axes XE,YE,ZEAcceleration on direction of principal axis； Point
Not Wei unmanned plane in body axis system X, Y, the angular acceleration in Z-direction；Ixx、Iyy、IzzRespectively unmanned plane is around body coordinate
It is X-axis, Y-axis, the rotary inertia of Z axis, Ffx、Ffy、FfzComponents of the respectively F on the axle of body axis system three, [ωx,ωy,ωz]
For components of the ω on the axle of the body axis system three, [ωx,ωy,ωz] as follows with the relation of Eulerian angles
。
3. according to the evaluation method in claim 1, it is characterised in that the step S2 further comprises following steps：
S21, according to kalman filtering theory, the general type that the state equation of system and measurement equation are written as：
Wherein, xkFor quantity of state, ykFor the observed quantity, the observed quantity obtains from sensor, ukFor the controlled quentity controlled variable, institute
Controlled quentity controlled variable is stated by being manually set, wkFor the process noise, vkFor the measurement noise；wk~N (0, Q) and vk~N (0, R) is no
Correlation, its state is estimated by equation (5), obtained
Wherein, LkFor the Kalman filtering gain, the new breath is
S22, the equation (5) existedPlace linearizes
Wherein, Ak, Bk, Gk, CkIt is the coefficient matrix,
State estimation equation after S23, the linearisation is：
。
4. according to the evaluation method in claim 1, it is characterised in that the step S3 further comprises following steps：
S31, it is described form auto-covariance matrix with the desired value that newly ceases,
S32, with [R (N)]sWith the estimate that auto-covariance matrix is formed with the desired value newly ceasedDifference two norms
Square minimum optimization aim,
Wherein,
5. according to the evaluation method in claim 2, it is characterised in that when estimating the noise covariance that line moves,
Using the rotating speed of the Eulerian angles and four blades as the controlled quentity controlled variable.
6. according to the evaluation method in claim 2, it is characterised in that when the noise covariance of diagonal motion is estimated,
Using the rotating speed of four blades as the controlled quentity controlled variable.
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