CN107300697A - Moving target UKF filtering methods based on unmanned plane - Google Patents
Moving target UKF filtering methods based on unmanned plane Download PDFInfo
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- 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
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Abstract
The invention discloses a kind of moving target UKF filtering methods based on unmanned plane, position, speed and acceleration one-step prediction value of the current target in earth right angle coordinate system are exported according to target movement model first；Then using unmanned aerial vehicle onboard sensor senses target oblique distance, azimuth and angle of pitch angle value as variable is measured, built with reference to carrier aircraft navigation equipment outgoing position, posture angle value and measure non-linear measurement equation between variable and state variable；Finally by UKF filtering methods fusion output target optimum state value.This method had both simplified derivation process complicated in mixed proportion, and the target tracking accuracy in rectangular coordinate system is improved again, with good practical significance.
Description
Technical Field
The invention relates to the technical field of unmanned aerial vehicle target positioning, in particular to a moving target UKF filtering method based on an unmanned aerial vehicle.
Background
For a moving target, in order to achieve high-precision track tracking capability, an accurate target motion model (system state equation) and a system measurement model must be established. However, the establishment of the target model and the metrology model depends largely on the coordinate system selected by itself. The target model and the measurement model are mostly established in a rectangular earth coordinate system, wherein the target model comprises CV, CA, a time correlation model, a current statistical model and the like. The state variables are the position, the speed and the acceleration of the target in the rectangular coordinate system of the earth, and the measured values are measured by using coordinate values of the target in the rectangular coordinate system of the earth, which are calculated by a target positioning algorithm. On one hand, the measurement value of the filter in use is mixed with a very large target positioning algorithm error due to the result of indirect calculation, so that the statistical property of the error is required, and the target positioning precision is not improved; another aspect is that the uncertainty of the measurement noise is increased because the error value is related to the distance of the target from the drone and is not a constant one.
To improve the accuracy of the system measurement equation, it is necessary to establish direct measurement values (R, α, lambda) by sensorsTThe (target slope, azimuth angle and pitch angle) are nonlinear measurement equations of measurement variables, and the system measurement noise variance matrix is directly obtained from the sensor, so that the accuracy of the measurement model is greatly improved. Currently, the main solution to this problem is a hybrid coordinate system solution toAnd establishing a linear measurement equation and a conversion relation between the rectangular coordinate system and the spherical coordinate system for the state variable under the spherical coordinate system. However, the method involves first and second order derivation of a strong nonlinear function, and the process is complex and cumbersome and is not good, so that a simple and effective system measurement equation conforming to the characteristics of the unmanned aerial vehicle is necessary to be established.
Disclosure of Invention
The invention aims to solve the technical problem that the precision of a system is not high due to inaccuracy of a noise model caused by separation of a positioning model and a filter in a traditional target tracking scheme, and provides a moving target UKF filtering method based on an unmanned aerial vehicle.
The invention adopts the following technical scheme for solving the technical problems:
a moving target UKF filtering method based on an unmanned aerial vehicle comprises the following steps:
step 1), arranging an infrared photoelectric pod and a radar on an unmanned aerial vehicle, wherein the infrared photoelectric pod is used for measuring the distance of a moving target relative to the unmanned aerial vehicle, and the radar is used for measuring the azimuth angle and the pitch angle of the moving target relative to the unmanned aerial vehicle;
step 2), measuring the moving target by utilizing an infrared photoelectric pod and a radar on the unmanned aerial vehicle to obtain the distance, the azimuth angle and the pitch angle (R, α, lambda) of the moving target relative to the unmanned aerial vehicleTWherein, R is the distance of the moving target relative to the unmanned aerial vehicle, α is the azimuth angle of the moving target relative to the unmanned aerial vehicle, and λ is the pitch angle of the moving target relative to the unmanned aerial vehicle;
step 3), a uniform acceleration mathematical model of the moving target is established according to the kinematics principle, and the system state equation is as follows:
Xk＝Φk,k-1Xk-1+Gk-1Wk-1
wherein,
Xkis the state quantity at the moment k of the moving object, Xk-1The state quantity at the moment of moving object k-1,
Wk-1is white Gaussian noise with zero mean value of the state equation at the moment of k-13×3Is a unit matrix, and T is a sampling period;
step 4), the nonlinear measurement equation of the moving target is Zk＝h(Xk)+VkWherein, h (X)k) As a function of the measurement, VkIs zero mean Gaussian white noise measured at the time of k, and the variance is R, Zk＝[R,α,λ]T；
Establishing a relation between a rectangular coordinate system of the moving target in the ground and a coordinate system of the moving target relative to a sensor base of the unmanned aerial vehicle:
obtaining coordinate values (x, y, z) of a rectangular coordinate system of the earth of the moving target by adopting a homogeneous coordinate conversion method) To base coordinate system coordinate value (x)b,yb,zb) Is converted into a matrixWherein:
hsis the unmanned aerial vehicle height, RNIs the curvature radius of the fourth prime circle, lambdasLatitude of unmanned plane, αsIs the longitude of the drone or the drone,is the roll angle, theta, of the unmanned aerial vehicleasIs the pitch angle, psi, of the droneasIs the yaw angle of the drone,is the roll angle, Delta theta, of the base of the measuring apparatusbaIs the pitch angle, delta psi, of the base of the measuring devicebaIs measuring the yaw angle of the equipment base;
coordinate value (x) of moving object relative to sensor base coordinate systemb,yb,zb) Target measurement value with sensor pair (R, α, lambda)TThe relationship between them is as follows:
then combining the transformation matricesThe nonlinear relation h (X) of (R, α, lambda) and (X, y, z) is obtained by operationk)；
Step 5), UKF filtering
Step 5.1), according to the state quantity of the moving target at the moment of k-1And covariance Pk-12n +1 symmetrical Sigma sampling points are constructed, and 2n +1 is the number of the sampling points;
step 5.2), combining a system state equation of the moving target uniform acceleration mathematical model to obtain a moving target state equation at the moment k and a one-step predicted value of covariance;
step 5.3), calculating the coordinate value of the moving target and a one-step predicted value of the measurement value;
step 5.4), calculating an auto-covariance matrixInter-cooperation variance matrixAnd a kalman filter gain;
and 5.5) updating the coordinates and covariance of the moving target.
As a further optimization scheme of the unmanned aerial vehicle-based moving target UKF filtering method, in the step 5.1), 2n +1 symmetrical Sigma sampling points are constructed according to the following formula:
wherein χ represents the state quantity passing through the nonlinear measurement function h (X)k)+VkThe subscript of χ represents the sample point sequence and time; gamma ═2(n + k) -n, k are preset threshold values, wherein the distance between a sampling point and the mean value is determined; kappa is more than or equal to 0 to ensure the semi-positive character of the variance matrix.
As a further optimization scheme of the unmanned aerial vehicle-based moving target UKF filtering method, in the step 5.2), a one-step predicted value of a moving target state equation and covariance at the moment k is obtained according to the following formula:
as a further optimization scheme of the unmanned aerial vehicle-based moving target UKF filtering method of the present invention, in the step 5.3), a one-step predicted value of the coordinate value and the measurement value of the moving target is calculated by the following formulas:
wherein,
as a further optimization scheme of the unmanned aerial vehicle-based moving target UKF filtering method, in the step 5.4), an auto-covariance matrix is calculated by the following formulaInter-cooperation variance matrixAnd kalman filter gain:
in the formula, RkThe variance of the noise is measured for time k.
β is a parameter related to the prior distribution of the state vectors.
As a further optimization scheme of the unmanned aerial vehicle-based moving target UKF filtering method, in the step 5.5), the target coordinates and covariance update are calculated by the following formulas:
compared with the prior art, the invention adopting the technical scheme has the following technical effects:
the invention directly takes three parameters of the target pitch distance, the azimuth angle and the pitch angle as measurement variables, thereby reducing the workload when the noise characteristics are measured by statistics to a great extent and improving the accuracy of the noise model. Compared with a hybrid coordinate system, the system state variables are unified, the problem of state variable conversion in the hybrid coordinate system does not exist, the target nonlinear measurement equation constructed by combining the characteristics of the unmanned aerial vehicle does not relate to the second order derivation of a strong nonlinear equation, and the complexity of the model is greatly reduced. The final simulation result verifies the rapid convergence performance and the high-precision performance of the model.
Drawings
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a graph of X-axis position error in the present invention;
FIG. 3 is a Y-axis position error map of the present invention;
FIG. 4 is a Z-axis position error map of the present invention;
FIG. 5 is a graph of X-axis velocity error in the present invention;
FIG. 6 is a Y-axis velocity error plot of the present invention;
FIG. 7 is a Z-axis velocity error plot of the present invention;
FIG. 8 is a graph of X-axis acceleration error in the present invention;
FIG. 9 is a Y-axis acceleration error plot of the present invention;
FIG. 10 is a Z-axis acceleration error plot of the present invention.
Detailed Description
The technical scheme of the invention is further explained in detail by combining the attached drawings:
the invention mainly relates to a moving target UKF filtering method based on an unmanned aerial vehicle, and a design flow chart of the scheme is shown in an attached figure 1. The method utilizes sensors such as a radar and an infrared photoelectric pod as measurement means to obtain measurement information such as the distance, the azimuth angle and the pitch angle of a target relative to the sensors, and establishes a nonlinear measurement equation by taking the measurement information as input quantity and combining with self information of the unmanned aerial vehicle obtained by an unmanned aerial vehicle airborne navigation device. Meanwhile, a target predicted value is obtained through the target motion model, and unscented Kalman filtering is performed by combining the nonlinear measurement equation and the target motion model to obtain a target state quantity with high precision at the current moment.
The invention comprises the following steps:
step 1), arranging an infrared photoelectric pod and a radar on an unmanned aerial vehicle, wherein the infrared photoelectric pod is used for measuring the distance of a moving target relative to the unmanned aerial vehicle, and the radar is used for measuring the azimuth angle and the pitch angle of the moving target relative to the unmanned aerial vehicle;
step 2), measuring the moving target by utilizing an infrared photoelectric pod and a radar on the unmanned aerial vehicle to obtain the distance, the azimuth angle and the pitch angle (R, α, lambda) of the moving target relative to the unmanned aerial vehicleTWherein, R is the distance of the moving target relative to the unmanned aerial vehicle, α is the azimuth angle of the moving target relative to the unmanned aerial vehicle, and λ is the pitch angle of the moving target relative to the unmanned aerial vehicle;
step 3), establishing a uniform acceleration mathematical model of the moving target according to a kinematics principle, wherein a system state equation is as follows:
Xk＝Φk,k-1Xk-1+Gk-1Wk-1(1)
wherein,
Xkis the state quantity at the moment k of the moving object, Xk-1Being the state quantity at the moment k-1 of the moving object, phik,k-1Is the system state transition matrix from time k-1 to time k, Gk-1Is the k-1 time system noise matrix, Wk-1Is zero mean Gaussian white noise of a system at the moment of k-1, the variance is Q, T is a sampling period, I3×3Is a third order identity matrix. The target acceleration transformation quantity is used as system noise interference, and the tracking capability of the system on the maneuvering target is improved.
Step 4), the nonlinear measurement equation of the moving target is made to be
Zk＝h(Xk)+Vk(2)
Wherein, h (X)k) As a function of the measurement, VkIs zero mean Gaussian white noise measured at the time of k, and the variance is R, Zk＝[R,α,λ]TDistance, azimuth and pitch angle information of the target relative to the radar. Since the state variable is based on the rectangular coordinate system of the earth, whereas the measured variable is based on the coordinate system of the sensor base, a relation between the two is required to be constructed. The relationship between the above two coordinate systems is calculated according to the following formula.
Recording the coordinates of the target in a rectangular coordinate system of the earth as (x, y, z), and the coordinates of the target in a sensor base coordinate system of the unmanned aerial vehicle as (x)b,yb,zb)，The transformation matrix from the earth rectangular coordinate system to the base coordinate system expressed by the homogeneous coordinate system is expressed, so that the moving target is in the earth rectangular coordinate systemThe relationship between the angular coordinate system and the relative unmanned aerial vehicle sensor base coordinate system of the moving target is as follows:
obtaining coordinate values (x, y, z) of a rectangular coordinate system of the earth of the moving target to coordinate values (x) of a coordinate system of a base by adopting a homogeneous coordinate conversion methodb,yb,zb) The transformation matrix of (a) is:
wherein,is a transformation matrix from a geodetic rectangular coordinate system (G system) to a geographic system (S system),is a transformation matrix from a geographic system (S system) to a carrier system (A system),is a transformation matrix from the carrier system (system A) to the base system (system B).
The following are obtained separatelyAnd
wherein, αs,λs,hsRespectively, the latitude, longitude and altitude of the earth, e is the earth reference ellipseFirst eccentricity of the ball, RNThe curvature radius of the unitary mortise ring.
Wherein phi isas,θas,ψasRespectively a roll angle, a pitch angle and a yaw angle of the carrier.
Wherein,Δθba,Δψbarespectively roll angle, pitch angle and yaw angle of the shock absorber.
Coordinate value (x) of moving object relative to sensor base coordinate systemb,yb,zb) Target measurement value with sensor pair (R, α, lambda)TThe relationship between them is as follows:
then combining the transformation matricesCalculating to obtain a nonlinear relation h (X) of (R, α, lambda) and (X, y, z)k)。
Step 5), UKF filtering
Step 5.1), calculating sampling points
Target state quantity according to k-1 timeAnd covariance Pk-12n +1 symmetric Sigma sample points were constructed as follows：
Wherein χ represents the state quantity passing through the nonlinear measurement function h (X)k)+VkThe subscript of χ represents the sample point sequence and time; gamma ═2(n + k) -n, k are preset threshold values, wherein the distance between a sampling point and the mean value is determined; kappa is more than or equal to 0 to ensure the semi-positive character of the variance matrix.
Step 5.2), establishing a time updating equation
The moving target state updating equation and the covariance one-step predicted value at the moment k obtained by the system state equation (1) are respectively as follows:
step 5.3), calculating the target coordinate value and one-step predicted value of the quantity measurement
Obtaining a one-step predicted sampling point χ of the k-1 moment relative to the k moment through the sampling point obtained by the calculation of the formula (9) and a measurement equation (2)k/k-1Target coordinate value prediction valueAnd measuring the one-step predicted valueAs shown in the following formula:
wherein,
step 5.4), substituting the formulas (12) and (13) into the following formula to obtain the self-covariance matrixSum cross covariance matrixComprises the following steps:
(14) in the formula, RkThe variance of the noise is measured for time k.
β is a parameter related to the prior distribution of the state vectors.
Kalman filter gains are obtained by equations (14) and (15)
Step 5.5), updating the target coordinate and covariance
Substituting the quantities obtained by expressions (16), (13), (14) and (15) into expressions (17) and (18) below to obtain the state quantity and covariance update equation
And (3) substituting the moving target state equation established in the step (3) and the system measurement equation established in the step (4) into the step (5) for filtering treatment, so that the target state quantity with more accurate k moment can be obtained, and the algorithm can be used for calculating in a circulating manner, so that the accurate positioning of the target at each moment can be obtained according to the measurement value of the target directly by the sensor.
FIG. 2 is a comparison graph of the X-axis direction position error after UKF filtering and linear Kalman filtering.
FIG. 3 is a comparison graph of Y-axis direction position errors after UKF filtering and linear Kalman filtering, respectively.
FIG. 4 is a Z-axis direction position error comparison graph after UKF filtering and linear Kalman filtering respectively.
FIG. 5 is a graph comparing X-axis velocity errors after UKF filtering and linear Kalman filtering, respectively.
FIG. 6 is a Y-axis direction velocity error comparison graph after UKF filtering and linear Kalman filtering, respectively.
FIG. 7 is a Z-axis velocity error comparison graph after UKF filtering and linear Kalman filtering, respectively.
FIG. 8 is a comparison graph of X-axis direction acceleration errors after UKF filtering and linear Kalman filtering, respectively.
FIG. 9 is a comparison graph of acceleration errors in the Y-axis direction after UKF filtering and linear Kalman filtering, respectively.
FIG. 10 is a comparison graph of Z-axis direction acceleration errors after UKF filtering and linear Kalman filtering, respectively.
As can be seen from fig. 2 to fig. 10, at the initial time, the improved UKF filtering method and the kalman filtering method have the same positioning and tracking accuracy, but as time goes on, the error difference starts to be gradually highlighted, and the farther the target is from the unmanned aerial vehicle, the more obvious the difference is, the more prominent the performance is particularly in terms of speed and acceleration, and the improved algorithm has higher accuracy.
It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
The above-mentioned embodiments, objects, technical solutions and advantages of the present invention are further described in detail, it should be understood that the above-mentioned embodiments are only illustrative of the present invention and are not intended to limit the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (6)
1. A moving target UKF filtering method based on an unmanned aerial vehicle is characterized by comprising the following steps:
step 1), arranging an infrared photoelectric pod and a radar on an unmanned aerial vehicle, wherein the infrared photoelectric pod is used for measuring the distance of a moving target relative to the unmanned aerial vehicle, and the radar is used for measuring the azimuth angle and the pitch angle of the moving target relative to the unmanned aerial vehicle;
step 2), measuring the moving target by utilizing an infrared photoelectric pod and a radar on the unmanned aerial vehicle to obtain the distance, the azimuth angle and the pitch angle of the moving target relative to the unmanned aerial vehicle (R,α,λ)TWherein, R is the distance of the moving target relative to the unmanned aerial vehicle, α is the azimuth angle of the moving target relative to the unmanned aerial vehicle, and λ is the pitch angle of the moving target relative to the unmanned aerial vehicle;
step 3), a uniform acceleration mathematical model of the moving target is established according to the kinematics principle, and the system state equation is as follows:
Xk＝Φk,k-1Xk-1+Gk-1Wk-1
wherein,
Xkis the state quantity at the moment k of the moving object, Xk-1The state quantity at the moment of moving object k-1,Wk-1is white Gaussian noise with zero mean value of the state equation at the moment of k-13×3Is a unit matrix, and T is a sampling period;
step 4), the nonlinear measurement equation of the moving target is Zk＝h(Xk)+VkWherein, h (X)k) As a function of the measurement, VkIs zero mean Gaussian white noise measured at the time of k, and the variance is R, Zk＝[R,α,λ]T；
Establishing a relation between a rectangular coordinate system of the moving target in the ground and a coordinate system of the moving target relative to a sensor base of the unmanned aerial vehicle:
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obtaining coordinate values (x, y, z) of a rectangular coordinate system of the earth of the moving target to coordinate values (x) of a coordinate system of a base by adopting a homogeneous coordinate conversion methodb,yb,zb) Is converted into a matrixWherein:
<mrow> <msubsup> <mi>C</mi> <mi>g</mi> <mi>s</mi> </msubsup> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>h</mi> <mi>s</mi> </msub> <mo>-</mo> <msub> <mi>R</mi> <mi>N</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>cos&lambda;</mi> <mi>s</mi> </msub> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <msub> <mi>sin&lambda;</mi> <mi>s</mi> </msub> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>sin&lambda;</mi> <mi>s</mi> </msub> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <msub> <mi>cos&lambda;</mi> <mi>s</mi> </msub> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>cos&alpha;</mi> <mi>s</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>sin&alpha;</mi> <mi>s</mi> </msub> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>sin&alpha;</mi> <mi>s</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>cos&alpha;</mi> <mi>s</mi> </msub> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mrow> <msub> <mi>R</mi> <mi>N</mi> </msub> <msup> <mi>e</mi> <mn>2</mn> </msup> <msub> <mi>sin&lambda;</mi> <mi>s</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> </mrow>
hsis the unmanned aerial vehicle height, RNIs the curvature radius of the fourth prime circle, lambdasLatitude of unmanned plane, αsIs the longitude of the drone or the drone,is the roll angle, theta, of the unmanned aerial vehicleasIs the pitch angle, psi, of the droneasIs the yaw angle of the drone,is the roll angle, Delta theta, of the base of the measuring apparatusbaIs the pitch angle, delta psi, of the base of the measuring devicebaIs measuring the yaw angle of the equipment base;
coordinate value (x) of moving object relative to sensor base coordinate systemb,yb,zb) Target measurement value with sensor pair (R, α, lambda)TThe relationship between them is as follows:
<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mi>R</mi> <mo>=</mo> <msqrt> <mrow> <msubsup> <mi>x</mi> <mi>b</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>y</mi> <mi>b</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>z</mi> <mi>b</mi> <mn>2</mn> </msubsup> </mrow> </msqrt> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&alpha;</mi> <mo>=</mo> <mi>a</mi> <mi>r</mi> <mi>c</mi> <mi>t</mi> <mi>a</mi> <mi>n</mi> <mfrac> <msub> <mi>x</mi> <mi>b</mi> </msub> <msub> <mi>y</mi> <mi>b</mi> </msub> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&lambda;</mi> <mo>=</mo> <mi>arcsin</mi> <mfrac> <msub> <mi>z</mi> <mi>b</mi> </msub> <msqrt> <mrow> <msubsup> <mi>x</mi> <mi>b</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>y</mi> <mi>b</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>z</mi> <mi>b</mi> <mn>2</mn> </msubsup> </mrow> </msqrt> </mfrac> </mrow> </mtd> </mtr> </mtable> </mfenced>
then combining the transformation matricesThe nonlinear relation h (X) of (R, α, lambda) and (X, y, z) is obtained by operationk)；
Step 5), UKF filtering
Step 5.1), according to the state quantity of the moving target at the moment of k-1And covariance Pk-12n +1 symmetrical Sigma sampling points are constructed, and 2n +1 is the number of the sampling points;
step 5.2), combining a system state equation of the moving target uniform acceleration mathematical model to obtain a moving target state equation at the moment k and a one-step predicted value of covariance;
step 5.3), calculating the coordinate value of the moving target and a one-step predicted value of the measurement value;
step 5.4), calculating an auto-covariance matrixInter-cooperation variance matrixAnd a kalman filter gain;
and 5.5) updating the coordinates and covariance of the moving target.
2. The unmanned aerial vehicle-based moving target UKF filtering method of claim 1, wherein in step 5.1), 2n +1 symmetric Sigma sampling points are constructed according to the following formula:
<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&chi;</mi> <mrow> <mn>0</mn> <mo>,</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&chi;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mrow> <mo>(</mo> <msqrt> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mi>&gamma;</mi> <mo>)</mo> <msub> <mi>P</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mrow> </msqrt> <mo>)</mo> </mrow> <mi>i</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&chi;</mi> <mrow> <mi>i</mi> <mo>+</mo> <mi>n</mi> <mo>,</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mrow> <mo>(</mo> <msqrt> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mi>&gamma;</mi> <mo>)</mo> <msub> <mi>P</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mrow> </msqrt> <mo>)</mo> </mrow> <mi>i</mi> </msub> </mrow> </mtd> </mtr> </mtable> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>n</mi> </mrow>
wherein χ represents the state quantity passing through the nonlinear measurement function h (X)k)+VkThe subscript of χ represents the sample point sequence and time; gamma ═2(n + k) -n, k are preset threshold values, wherein the distance between a sampling point and the mean value is determined; kappa is more than or equal to 0 to ensure the semi-positive character of the variance matrix.
3. The UKF filtering method for moving target based on UAV of claim 2, wherein in step 5.2), the one-step predicted value of the state equation and covariance of moving target at time k is obtained according to the following formula:
<mrow> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>&Phi;</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mrow>
<mrow> <msub> <mi>P</mi> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>&Phi;</mi> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <msub> <mi>P</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <msubsup> <mi>&Phi;</mi> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mi>T</mi> </msubsup> <mo>+</mo> <msub> <mi>G</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <msub> <mi>Q</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <msubsup> <mi>G</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mi>T</mi> </msubsup> <mo>.</mo> </mrow>
4. the UKF filtering method for moving target based on UAV of claim 3, wherein in step 5.3), the one-step predicted value of coordinate value and measurement value of moving target is calculated by the following formula:
<mrow> <msubsup> <mi>&chi;</mi> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mi>j</mi> </msubsup> <mo>=</mo> <msub> <mi>&Phi;</mi> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <msubsup> <mi>&chi;</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mi>j</mi> </msubsup> </mrow>
<mrow> <msubsup> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mo>&prime;</mo> </msubsup> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mn>2</mn> <mi>n</mi> </mrow> </munderover> <msubsup> <mi>W</mi> <mi>j</mi> <mi>m</mi> </msubsup> <msubsup> <mi>&chi;</mi> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mi>j</mi> </msubsup> </mrow>
<mrow> <msubsup> <mi>Z</mi> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mi>j</mi> </msubsup> <mo>=</mo> <mi>h</mi> <mrow> <mo>(</mo> <msubsup> <mi>&chi;</mi> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mi>j</mi> </msubsup> <mo>)</mo> </mrow> </mrow>
<mrow> <msubsup> <mover> <mi>Z</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mo>&prime;</mo> </msubsup> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mn>2</mn> <mi>n</mi> </mrow> </munderover> <msubsup> <mi>W</mi> <mi>j</mi> <mi>m</mi> </msubsup> <msubsup> <mi>Z</mi> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mi>j</mi> </msubsup> </mrow>
wherein,
<mrow> <msubsup> <mi>W</mi> <mn>0</mn> <mi>m</mi> </msubsup> <mo>=</mo> <mfrac> <mi>&gamma;</mi> <mrow> <mi>&gamma;</mi> <mo>+</mo> <mi>n</mi> </mrow> </mfrac> <mo>,</mo> <msubsup> <mi>W</mi> <mi>j</mi> <mi>m</mi> </msubsup> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <mi>&gamma;</mi> <mo>+</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>,</mo> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mn>2</mn> <mi>n</mi> <mo>.</mo> </mrow>
5. the UKF filtering method for moving target based on UAV of claim 4, wherein in step 5.4), the auto-covariance matrix is calculated by the following formulaInter-cooperation variance matrixAnd kalman filter gain:
<mrow> <msub> <mi>P</mi> <mrow> <msub> <mover> <mi>z</mi> <mo>^</mo> </mover> <mi>k</mi> </msub> <msub> <mover> <mi>z</mi> <mo>^</mo> </mover> <mi>k</mi> </msub> </mrow> </msub> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mn>2</mn> <mi>n</mi> </mrow> </munderover> <mrow> <msubsup> <mi>W</mi> <mi>j</mi> <mi>c</mi> </msubsup> <mo>&lsqb;</mo> <msubsup> <mi>Z</mi> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mi>j</mi> </msubsup> <mo>-</mo> <msubsup> <mover> <mi>Z</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mo>&prime;</mo> </msubsup> <mo>&rsqb;</mo> <msup> <mrow> <mo>&lsqb;</mo> <msubsup> <mi>Z</mi> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mi>j</mi> </msubsup> <mo>-</mo> <msubsup> <mover> <mi>Z</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mo>&prime;</mo> </msubsup> <mo>&rsqb;</mo> </mrow> <mi>T</mi> </msup> </mrow> <mo>+</mo> <msub> <mi>R</mi> <mi>k</mi> </msub> </mrow>
<mrow> <msub> <mi>P</mi> <mrow> <msub> <mi>x</mi> <mi>k</mi> </msub> <msub> <mi>z</mi> <mi>k</mi> </msub> </mrow> </msub> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mn>2</mn> <mi>n</mi> </mrow> </munderover> <msubsup> <mi>W</mi> <mi>j</mi> <mi>c</mi> </msubsup> <mo>&lsqb;</mo> <msubsup> <mi>&chi;</mi> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mi>j</mi> </msubsup> <mo>-</mo> <msubsup> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mo>&prime;</mo> </msubsup> <mo>&rsqb;</mo> <msup> <mrow> <mo>&lsqb;</mo> <msubsup> <mi>Z</mi> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mi>j</mi> </msubsup> <mo>-</mo> <msubsup> <mover> <mi>Z</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mo>&prime;</mo> </msubsup> <mo>&rsqb;</mo> </mrow> <mi>T</mi> </msup> </mrow>
<mrow> <msubsup> <mi>W</mi> <mn>0</mn> <mi>c</mi> </msubsup> <mo>=</mo> <mfrac> <mi>&gamma;</mi> <mrow> <mi>&gamma;</mi> <mo>+</mo> <mi>n</mi> </mrow> </mfrac> <mo>+</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>&epsiv;</mi> <mn>2</mn> </msup> <mo>+</mo> <mi>&beta;</mi> <mo>,</mo> <msubsup> <mi>W</mi> <mi>j</mi> <mi>c</mi> </msubsup> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <mi>&gamma;</mi> <mo>+</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>,</mo> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mn>2</mn> <mi>n</mi> <mo>,</mo> <mi>&beta;</mi> <mo>&GreaterEqual;</mo> <mn>0</mn> </mrow>
<mrow> <mi>K</mi> <mo>=</mo> <msub> <mi>P</mi> <mrow> <msub> <mi>x</mi> <mi>k</mi> </msub> <msub> <mi>z</mi> <mi>k</mi> </msub> </mrow> </msub> <msubsup> <mi>P</mi> <mrow> <msub> <mover> <mi>z</mi> <mo>^</mo> </mover> <mi>k</mi> </msub> <msub> <mover> <mi>z</mi> <mo>^</mo> </mover> <mi>k</mi> </msub> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mrow>
in the formula, RkThe variance of the noise is measured for time k.
β is a parameter related to the prior distribution of the state vectors.
6. The UKF filtering method for moving target based on UAV of claim 5, wherein in step 5.5), the target coordinates and covariance update are calculated by the following formula:
<mrow> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>k</mi> </msub> <mo>=</mo> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi>K</mi> <mrow> <mo>(</mo> <msub> <mi>Z</mi> <mi>k</mi> </msub> <mo>-</mo> <msubsup> <mover> <mi>Z</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mo>&prime;</mo> </msubsup> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>P</mi> <mi>k</mi> </msub> <mo>=</mo> <msub> <mi>P</mi> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>KP</mi> <mrow> <msub> <mover> <mi>z</mi> <mo>^</mo> </mover> <mi>k</mi> </msub> <msub> <mover> <mi>z</mi> <mo>^</mo> </mover> <mi>k</mi> </msub> </mrow> </msub> <msup> <mi>K</mi> <mi>T</mi> </msup> <mo>.</mo> </mrow>3
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN108362288A (en) * | 2018-02-08 | 2018-08-03 | 北方工业大学 | Polarized light S L AM method based on unscented Kalman filtering |
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| CN108490927A (en) * | 2018-01-24 | 2018-09-04 | 天津大学 | A kind of Target Tracking System and tracking applied to pilotless automobile |
| CN108267731A (en) * | 2018-02-01 | 2018-07-10 | 郑州轻工业学院 | The construction method of unmanned plane target tracking system and application |
| CN108267731B (en) * | 2018-02-01 | 2020-03-31 | 郑州轻工业学院 | Construction method and application of unmanned aerial vehicle target tracking system |
| CN108362288A (en) * | 2018-02-08 | 2018-08-03 | 北方工业大学 | Polarized light S L AM method based on unscented Kalman filtering |
| CN108362288B (en) * | 2018-02-08 | 2021-05-07 | 北方工业大学 | Polarized light SLAM method based on unscented Kalman filtering |
| CN109581302B (en) * | 2018-12-12 | 2021-04-16 | 北京润科通用技术有限公司 | Vehicle-mounted radar data tracking method and system |
| CN109581302A (en) * | 2018-12-12 | 2019-04-05 | 北京润科通用技术有限公司 | A kind of trailer-mounted radar data tracking method and system |
| CN110632941A (en) * | 2019-09-25 | 2019-12-31 | 北京理工大学 | Trajectory generation method for target tracking of unmanned aerial vehicle in complex environment |
| CN110824453A (en) * | 2020-01-10 | 2020-02-21 | 四川傲势科技有限公司 | Unmanned aerial vehicle target motion estimation method based on image tracking and laser ranging |
| CN111722213A (en) * | 2020-07-03 | 2020-09-29 | 哈尔滨工业大学 | Pure distance extraction method for motion parameters of maneuvering target |
| CN111722213B (en) * | 2020-07-03 | 2023-11-03 | 哈尔滨工业大学 | Pure distance extraction method for maneuvering target motion parameters |
| CN113076634A (en) * | 2021-03-24 | 2021-07-06 | 哈尔滨工业大学 | Multi-machine cooperative passive positioning method, device and system |
| CN113076634B (en) * | 2021-03-24 | 2023-04-07 | 哈尔滨工业大学 | Multi-machine cooperative passive positioning method, device and system |
| CN113743475A (en) * | 2021-08-10 | 2021-12-03 | 中国电子科技集团公司第二十七研究所 | Real-time multi-source data fusion method based on UKF |
| CN113743475B (en) * | 2021-08-10 | 2024-05-17 | 中国电子科技集团公司第二十七研究所 | UKF-based real-time multi-source data fusion method |
| CN113390421A (en) * | 2021-08-17 | 2021-09-14 | 武汉理工大学 | Unmanned aerial vehicle positioning method and device based on Kalman filtering |
| CN113390421B (en) * | 2021-08-17 | 2021-12-10 | 武汉理工大学 | Unmanned aerial vehicle positioning method and device based on Kalman filtering |
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