CN113342059B - Multi-unmanned aerial vehicle tracking mobile radiation source method based on position and speed errors - Google Patents

Multi-unmanned aerial vehicle tracking mobile radiation source method based on position and speed errors Download PDF

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CN113342059B
CN113342059B CN202110599746.9A CN202110599746A CN113342059B CN 113342059 B CN113342059 B CN 113342059B CN 202110599746 A CN202110599746 A CN 202110599746A CN 113342059 B CN113342059 B CN 113342059B
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radiation source
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张娟
朱少光
张林让
丁彤
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Xidian University
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    • G05D1/12—Target-seeking control
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/10—Simultaneous control of position or course in three dimensions
    • G05D1/101—Simultaneous control of position or course in three dimensions specially adapted for aircraft
    • G05D1/104—Simultaneous control of position or course in three dimensions specially adapted for aircraft involving a plurality of aircrafts, e.g. formation flying
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Abstract

The invention discloses a method for tracking a mobile radiation source by multiple unmanned aerial vehicles based on position and speed errors, which solves the problem of tracking the mobile radiation source when the unmanned aerial vehicles have the position and speed errors in a two-dimensional space. The method comprises the following implementation steps: randomly selecting one unmanned aerial vehicle as a host machine, and the other unmanned aerial vehicles as auxiliary machines; calculating the TDOA measured value and the FDOA measured value of the arrival time difference between each auxiliary machine and the main machine; calculating the difference value between the distance between each auxiliary machine and the radiation source and the distance between the main machine and the radiation source and the change rate of the difference value; estimating a position vector and a velocity vector of a radiation source when the main unmanned aerial vehicle and the auxiliary unmanned aerial vehicle have state errors; updating a radiation source state vector; calculating the optimal course angles of the main unmanned aerial vehicle and the auxiliary unmanned aerial vehicle; each drone autonomously selects a single step flight trajectory. The invention utilizes the position and speed errors of the unmanned aerial vehicle and plans the optimal flight path of the unmanned aerial vehicle, has simple geometric positioning model, improves the tracking performance and can be used for positioning and tracking the mobile radiation source.

Description

Multi-unmanned aerial vehicle tracking mobile radiation source method based on position and speed errors
Technical Field
The invention belongs to the technical field of communication, and further relates to a method for tracking a mobile radiation source by multiple unmanned aerial vehicles based on position and speed errors in the technical field of target tracking. The invention utilizes a plurality of unmanned aerial vehicles to position the moving radiation source which moves at a constant speed on the ground, thereby realizing the tracking of the radiation source.
Background
The main task of the multiple unmanned aerial vehicles for passive positioning and tracking of the mobile radiation source is that the multiple unmanned aerial vehicles only receive electromagnetic signals emitted by the radiation source to perform data fusion processing and analysis, and positioning and tracking of the mobile radiation source are achieved. With the development of information science and communication technology, a large number of positioning and tracking methods for moving radiation source tracking exist. However, due to objective factors such as the position and speed error of the unmanned aerial vehicle and unknown real state vector of the radiation source, it still faces a great challenge to accurately track the moving radiation source in real time.
The university of Shandong in the patent document "a high-precision positioning method of unmanned aerial vehicle based on TDOA and FDOA" (patent application No. 202011132782.6, application publication No. CN 112444776A) discloses a target tracking method based on multiple receiving stations. The method is implemented by receiving TDOA measurements and FDOA measurements with a receiving station in space and equating them to range-difference measurements and range-difference-rate-of-change measurements; performing joint estimation on the position coordinates of the receiving station to construct a vector to be estimated; constructing corresponding range difference measurement values, range difference change rate measurement values and expressions between the receiving station position measurement values and the vectors to be estimated; solving a nonlinear weighted least square optimization model of the cost error function; solving the optimal closed-form solution of the vector to be estimated by Taylor series combined iteration; and obtaining the position and the speed of the target when the iteration termination condition is met. The method has the defects that when the multi-observation station is used for tracking the target, the tracking condition of the receiving station and the unmanned aerial vehicle in the motion state cannot be reflected, and when the radiation source is far away from the unmanned aerial vehicle, accurate tracking cannot be realized.
Weijia Wang, Peng Bai, Yuning Wang, Xiaoolong Liang and Jianianing Zhang disclose a TDOA/FDOA-based target tracking method in the published paper "Optimal Sensor Deployment and Velocity Configuration With Hybrid TDOA and FDOA measures" (IEEE Acess,2019,7: 109181-. Firstly, receiving an electromagnetic signal from a target by an unmanned aerial vehicle to establish an observation model and an error variance model; secondly, solving a Fisher information matrix of the positioning error under the model, and analyzing the optimal configuration of the unmanned aerial vehicle and the target; and finally, optimizing the flight path of the unmanned aerial vehicle by taking the FIM and the posterior error covariance matrix as target functions and fully considering the flight performance constraint of the unmanned aerial vehicle and the cooperative constraint condition of the unmanned aerial vehicle, so as to realize the tracking of the moving target. However, the method still has the defects that the unmanned aerial vehicles are small in size and strong in maneuverability, random errors of positions and speeds of the unmanned aerial vehicles are not negligible, and the errors affect the positioning accuracy of the target.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method for tracking and moving a radiation source by multiple unmanned aerial vehicles based on position and speed errors, and aims to solve the problems of tracking conditions when the unmanned aerial vehicles and the radiation source are in a motion state and accurate tracking and moving of the radiation source when the unmanned aerial vehicles have random position and speed errors.
The idea for realizing the aim of the invention is that when the distance between the radiation source and the unmanned aerial vehicle is far, the flying track of the unmanned aerial vehicle is optimized to realize the accurate positioning of the mobile radiation source, thereby solving the tracking problem when the unmanned aerial vehicle and the radiation source are both in motion state.
The technical scheme for realizing the aim of the invention comprises the following steps:
(1) randomly selecting one unmanned aerial vehicle as a host machine, and the other unmanned aerial vehicles as auxiliary machines;
(2) calculating TDOA (time Difference of arrival) measurement value of each auxiliary machine and each main machine:
(2a) calculating the arrival time of the radiation source signal to the main unmanned aerial vehicle and the auxiliary unmanned aerial vehicle;
(2b) calculating the difference value between the arrival time of the radiation source signal to the main unmanned aerial vehicle and the arrival time of the radiation source signal to each auxiliary unmanned aerial vehicle by using an arrival time difference formula;
(3) calculating an arrival frequency Difference FDOA (frequency Difference of arrival) measured value of each auxiliary machine and the main machine by using an arrival frequency Difference formula;
(4) calculating the difference between the distance between each auxiliary machine and the radiation source and the distance between the main machine and the radiation source and the change rate of the difference:
(4a) calculating the difference between the distance between each auxiliary machine and the radiation source and the distance between the main machine and the radiation source;
(4b) calculating the change rate of the distance between each auxiliary machine and the radiation source and the difference value of the distance between the main machine and the radiation source;
(5) estimating the position vector and the velocity vector of the radiation source when the main unmanned aerial vehicle and the auxiliary unmanned aerial vehicle have state random errors by using the following formula:
Figure BDA0003092475840000021
Figure BDA0003092475840000022
wherein s represents the position vector of the radiation source in the x-axis and y-axis two-dimensional space when the main unmanned aerial vehicle and the auxiliary unmanned aerial vehicle have state random errors, U represents a diagonal matrix, and U is diag (sgn (ω)2(1:2)-u1) Diag denotes the diagonal matrix sign, sgn denotes the sign discrimination function, ω2(1) Representing the value, ω, corresponding to the position of the radiation source in two dimensions on the x-axis2(2) Representing the value corresponding to the position of the radiation source in two dimensions on the y-axis, T representing the transposition operation, u1Indicating the existence state of the main and auxiliary unmanned aerial vehiclesThe position vector of the host in the two-dimensional space of the x axis and the y axis when the machine has errors,
Figure BDA0003092475840000031
representing the velocity vector, omega, of the radiation source in the x-axis and y-axis two-dimensional space when the main unmanned aerial vehicle and the auxiliary unmanned aerial vehicle have state random errors2(3) Representing the corresponding value, omega, of the speed of movement of the radiation source in two dimensions on the x-axis2(4) Representing the corresponding value of the motion speed of the radiation source on the y-axis in a two-dimensional space,
Figure BDA0003092475840000032
representing the velocity vector of the main machine in the x-axis and y-axis two-dimensional space when the main unmanned aerial vehicle and the auxiliary unmanned aerial vehicle have state random errors;
(6) the radiation source state vector is updated as follows:
Figure BDA0003092475840000033
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003092475840000034
representing the updated state vector of the radiation source,
Figure BDA0003092475840000035
representing the state vector of the radiation source before updating, K representing the observation gain of the extended Kalman filter, zkRepresenting an observation vector, the elements in which are composed of corresponding observations produced by the primary and secondary unmanned aerial vehicle observation radiation sources, HkRepresents the nonlinear observation function of the main unmanned aerial vehicle and the auxiliary unmanned aerial vehicle to the radiation source
Figure BDA0003092475840000036
Performing Taylor series expansion to obtain a measurement matrix;
(7) calculating the optimal course angles of the main unmanned aerial vehicle and the auxiliary unmanned aerial vehicle according to the following formula:
Figure BDA0003092475840000037
wherein the content of the first and second substances,
Figure BDA0003092475840000038
is shown as
Figure BDA0003092475840000039
Taking the value of psi (k) at the minimum, psi (k) representing the vector consisting of the flight heading angles of all the main and auxiliary drones, u (k) representing the state vectors of the main and auxiliary drones at the time k, trance representing the operation of finding the trace of the matrix, J representing the Fisher information matrix of the radiation source,-1representing inversion operation, wherein u (k +1) represents state vectors of the main unmanned aerial vehicle and the auxiliary unmanned aerial vehicle at the moment of k + 1;
(8) each drone autonomously selects a single step flight trajectory according to the following formula:
Figure BDA00030924758400000310
wherein x isi(k +1) represents a value corresponding to the position of the ith unmanned aerial vehicle on the x axis in the two-dimensional space at the moment of k +1, and yi(k +1) represents a value corresponding to the position of the ith unmanned aerial vehicle on the y axis in the two-dimensional space at the moment of k +1, and xi(k) The value, y, corresponding to the position of the ith unmanned aerial vehicle on the x axis in the k-time two-dimensional spacei(k) The method comprises the steps of representing a value corresponding to the position of the ith unmanned aerial vehicle on the y axis in the two-dimensional space at the moment k, v representing the flight speed of the ith unmanned aerial vehicle, T representing the sampling time interval of the ith unmanned aerial vehicle during the flight of a tracking radiation source, cos representing cosine operation, sin representing sine operation,
Figure BDA0003092475840000041
indicating the flight heading angle of the ith drone at time k.
Compared with the prior art, the invention has the following advantages:
firstly, the invention overcomes the problem of poor tracking performance of the prior art when the unmanned aerial vehicle and the radiation source are both in a motion state by optimizing the flight path of the unmanned aerial vehicle when the radiation source is far away from the unmanned aerial vehicle, so that the invention has high-efficiency tracking capability in tracking the moving radiation source.
Secondly, the invention utilizes the random error of the position and the speed of the unmanned aerial vehicle to track the mobile radiation source, and overcomes the problem that the random error of the position and the speed of the unmanned aerial vehicle influences the positioning precision due to small volume and strong maneuverability of a plurality of unmanned aerial vehicles in the prior art, so that the invention has higher positioning performance and can accurately track the mobile radiation source.
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FIG. 1 is a flow chart of the present invention;
FIG. 2 is a diagram showing the results of a simulation experiment according to the present invention.
Detailed Description
The invention is described in further detail below with reference to the figures and specific examples.
The steps of carrying out the present invention are further described with reference to fig. 1.
Step 1, randomly selecting one unmanned aerial vehicle as a host and the rest unmanned aerial vehicles as auxiliary machines.
Step 2, calculating the TDOA measured value of the arrival time difference between each auxiliary machine and the main machine:
and calculating the arrival time of the radiation source signal to the main unmanned aerial vehicle and the auxiliary unmanned aerial vehicle.
The arrival time of the radiation source signal to each unmanned aerial vehicle is calculated according to the following formula:
ti＝ri o/c
wherein, tiIndicate the time that the radiation source signal was received to ith unmanned aerial vehicle, i indicates the serial number of unmanned aerial vehicle, and i is 1,2, …, M, and M indicates the total number of unmanned aerial vehicle, ri oThe actual distance between the ith unmanned aerial vehicle and the radiation source is shown, and c represents the propagation speed of the electromagnetic signals.
Calculating the difference value between the arrival time of the radiation source signal to the main unmanned aerial vehicle and the arrival time of the radiation source signal to each auxiliary unmanned aerial vehicle by using the following arrival time difference formula:
Figure BDA0003092475840000051
wherein, tj1The difference value of the time when the jth auxiliary machine receives the radiation source signal and the time when the main machine receives the radiation source signal is shown,
Figure BDA0003092475840000052
representing the actual distance, r, of the jth auxiliary machine from the radiation source1 oRepresenting the actual distance, Δ t, of the host from the radiation sourcej1The measurement error of TDOA is shown, j represents the serial number of the slave, and j is 2, …, M.
And 3, calculating the arrival frequency difference FDOA measured value of each auxiliary machine and the main machine by using the following arrival frequency difference formula:
Figure BDA0003092475840000053
wherein f isj1Represents the FDOA measured value of the j-th frame slave machine and the main machine,
Figure BDA0003092475840000054
showing the actual distance change rate of the j-th auxiliary machine and the radiation source,
Figure BDA0003092475840000055
representing the actual rate of change of distance, f, of the host from the source0Representing the frequency at which the radiation source emits an electromagnetic signal,
Figure BDA0003092475840000056
indicating measurement error of FDOA.
Step 4, calculating the difference value between the distance between each auxiliary machine and the radiation source and the distance between the main machine and the radiation source and the change rate of the difference value:
and calculating the difference between the distance between each auxiliary machine and the radiation source and the distance between the main machine and the radiation source.
The difference value between the distance between each auxiliary machine and the radiation source and the distance between the main machine and the radiation source is calculated by the following formula:
Figure BDA0003092475840000057
wherein r isj1Representing the difference between the distance between the jth auxiliary machine and the radiation source and the distance between the main machine and the radiation source, nj1Representing a gaussian distribution with a mean value of 0.
And calculating the change rate of the distance between each auxiliary machine and the radiation source and the difference value of the distance between the main machine and the radiation source.
The calculation of the change rate of the difference value between the distance between each auxiliary machine and the radiation source and the distance between the main machine and the radiation source is obtained by the following formula:
Figure BDA0003092475840000058
wherein the content of the first and second substances,
Figure BDA0003092475840000059
showing the change rate of the difference value of the distance between the jth auxiliary machine and the radiation source and the distance between the main machine and the radiation source,
Figure BDA00030924758400000510
representing a gaussian distribution with a mean value of 0.
And 5, estimating the position vector and the velocity vector of the radiation source when the main unmanned aerial vehicle and the auxiliary unmanned aerial vehicle have state random errors by using the following formula:
Figure BDA0003092475840000061
Figure BDA0003092475840000062
wherein s represents the position vector of the radiation source in the x-axis and y-axis two-dimensional space when the main unmanned aerial vehicle and the auxiliary unmanned aerial vehicle have state random errors, U represents a diagonal matrix, and U is diag (sgn (ω)2(1:2)-u1) Diag denotes a diagonal matrix sign, sgn denotes sign discriminationFunction, ω2(1) Representing the value, ω, corresponding to the position of the radiation source on the x-axis in two-dimensional space2(2) Representing the value corresponding to the position of the radiation source in two dimensions on the y-axis, T representing the transposition operation, u1The position vector of the main machine in the x-axis and y-axis two-dimensional space when the main unmanned aerial vehicle and the auxiliary unmanned aerial vehicle have state random errors is represented,
Figure BDA0003092475840000063
representing the velocity vector, omega, of the radiation source in the x-axis and y-axis two-dimensional space when the main unmanned aerial vehicle and the auxiliary unmanned aerial vehicle have state random errors2(3) Representing the corresponding value, omega, of the speed of movement of the radiation source in two dimensions on the x-axis2(4) Representing the corresponding value of the motion speed of the radiation source on the y-axis in a two-dimensional space,
Figure BDA0003092475840000064
and representing the velocity vector of the main machine in the x-axis and y-axis two-dimensional space when the main unmanned aerial vehicle and the auxiliary unmanned aerial vehicle have state random errors.
Step 6, updating the state vector of the radiation source according to the following formula:
Figure BDA0003092475840000065
wherein the content of the first and second substances,
Figure BDA0003092475840000066
representing the updated state vector of the radiation source,
Figure BDA0003092475840000067
representing the state vector of the radiation source before updating, K representing the observation gain of the extended Kalman filter, zkRepresenting an observation vector, the elements in which are composed of corresponding observations produced by the primary and secondary unmanned aerial vehicle observation radiation sources, HkRepresents the nonlinear observation function of the main unmanned aerial vehicle and the auxiliary unmanned aerial vehicle to the radiation source
Figure BDA0003092475840000068
Is subjected to Taylor series expansion to obtainThe measurement matrix of (2).
And 7, calculating the optimal course angles of the main unmanned aerial vehicle and the auxiliary unmanned aerial vehicle according to the following formula:
Figure BDA0003092475840000069
wherein the content of the first and second substances,
Figure BDA00030924758400000610
is shown as
Figure BDA00030924758400000611
Taking the value of psi (k) at the minimum, psi (k) representing the vector consisting of the flight heading angles of all the primary and secondary drones, u (k) representing the state vectors of the primary and secondary drones at time k, trance representing the operation of finding the traces of the Matrix, J representing the Fisher Information Matrix (Fisher Information Matrix) of the radiation source,-1the inversion operation is represented, and u (k +1) represents the state vectors of the main unmanned aerial vehicle and the auxiliary unmanned aerial vehicle at the moment of k + 1.
Step 8, each unmanned aerial vehicle autonomously selects a single-step flight track according to the following formula:
Figure BDA0003092475840000071
wherein x isi(k +1) represents a value corresponding to the position of the ith unmanned aerial vehicle on the x axis in the two-dimensional space at the moment of k +1, and yi(k +1) represents a value corresponding to the position of the ith unmanned aerial vehicle on the y axis in the two-dimensional space at the moment of k +1, and xi(k) The value corresponding to the position of the ith unmanned aerial vehicle on the x axis in the k moment two-dimensional space, yi(k) The method comprises the steps of representing a value corresponding to the position of the ith unmanned aerial vehicle on the y axis in the two-dimensional space at the moment k, v representing the flight speed of the ith unmanned aerial vehicle, T representing the sampling time interval of the ith unmanned aerial vehicle during the flight of a tracking radiation source, cos representing cosine operation, sin representing sine operation,
Figure BDA0003092475840000072
indicating the ith unmanned plane at time kAnd (4) flight course angle.
The effect of the present invention will be further explained with the simulation experiment.
1. Simulation experiment conditions are as follows:
the hardware test platform of the simulation experiment of the invention is as follows: the processor is a CPU intel Core i7-7700, the main frequency is 3.6GHz, and the memory is 16 GB.
The software platform of the simulation experiment of the invention is as follows: windows 7 flagship edition, 64-bit operating system and MATLAB R2018 b.
The simulation experiment scene of the invention is set as follows: the four unmanned aerial vehicles cooperate to position and track a radiation source which moves at a uniform speed on the ground, and the initial position vector of the radiation source is s ═ 11000,5000]Tm, velocity vector of
Figure BDA0003092475840000073
The position coordinates of the four unmanned aerial vehicles are u1＝[2000，2000]T m,u2＝[2000,1000]T m，u3＝[1000,2000]T m，u4＝[1000,1000]Tm, the flying speed of the unmanned aerial vehicle is 80m/s, the initial course angle is pi/2, the first unmanned aerial vehicle is selected as a host, the rest unmanned aerial vehicles are auxiliary machines, the sampling time is 80s, the sampling time interval is 1s, and the TDOA measured noise variance is sigmar0.06, the path loss exponent is 0.6, and the covariance matrix of the drone position error is
Figure BDA0003092475840000074
Figure BDA0003092475840000075
Covariance matrix of unmanned aerial vehicle speed error is
Figure BDA0003092475840000076
3. Simulation content simulation result analysis:
the simulation experiment of the invention is to adopt the position and speed random error and arrival time/frequency difference combined positioning method of the unmanned aerial vehicle to track the mobile radiation source and carry out the simulation experiment on the track optimization of four unmanned aerial vehicles.
The effect of the present invention will be described in one step with reference to the simulation diagram of fig. 2.
Fig. 2(a) is a graph of the optimal flight trajectories of four unmanned aerial vehicles, and four curves in the graph are obtained by calculating the optimal course angle of each unmanned aerial vehicle in the four unmanned aerial vehicles in step 7 and then selecting the corresponding optimal course angle for each unmanned aerial vehicle in step 8. The abscissa in fig. 2(a) represents the movement of the position coordinate of each waypoint along the x-axis for each drone flight trajectory in two-dimensional space by a corresponding value, and the ordinate represents the movement of the position coordinate of each waypoint along the y-axis for each drone flight trajectory in two-dimensional space by a corresponding value, in meters. In fig. 2(a), the curve indicated by triangle-dashed line-triangle represents the optimal flight trajectory of the master, the curve indicated by square-dashed line-square represents the optimal flight trajectory of the slave 1, the curve indicated by circle-dashed line-circle represents the optimal flight trajectory of the slave 2, and the curve indicated by diamond-dashed line-diamond represents the optimal flight trajectory of the slave 3.
Fig. 2(b) is a flight trajectory graph of four unmanned aerial vehicles during no-flight-path planning, that is, a motion trajectory graph of the unmanned aerial vehicle during flying toward an estimated radiation source all the time, and the four curves in fig. 2(b) are obtained by calculating position coordinates of the radiation source through the step 5 of the invention, then calculating an azimuth angle of the position of each unmanned aerial vehicle and the position of the radiation source, and selecting a corresponding azimuth angle for each unmanned aerial vehicle. The abscissa in fig. 2(b) represents the value of the movement of the position coordinate of each waypoint in each unmanned aerial vehicle flight trajectory along the x-axis in two-dimensional space, and the ordinate represents the value of the movement of the position coordinate of each waypoint in each unmanned aerial vehicle flight trajectory along the y-axis in two-dimensional space in meters m. In fig. 2(b), the curve indicated by triangle-dashed line-triangle represents the flight path of the master, the curve indicated by square-dashed line-square represents the flight path of the slave 1, the curve indicated by circle-dashed line-circle represents the flight path of the slave 2, and the curve indicated by diamond-dashed line-diamond represents the flight path of the slave 3.
Fig. 2(c) is a tracking trajectory of the radiation source at the time of optimal trajectory optimization, and the abscissa in fig. 2(c) represents a value corresponding to a shift of the position coordinate of each waypoint in the motion trajectory of the radiation source along the x-axis in a two-dimensional space, and the ordinate represents a value corresponding to a shift of the position coordinate of each waypoint in the motion trajectory of the radiation source along the y-axis in a two-dimensional space, in units of meters m. The curve marked by diamond-dashed-diamond in fig. 2(c) represents the actual motion trajectory of the radiation source, and the curve marked by circle-dashed-circle represents the tracking trajectory of the radiation source. The curve marked by circle-dotted line-circle represents the tracking trajectory of the radiation source, which is obtained by calculating the position vector of the radiation source in step 5 and then updating the position vector of the radiation source in step 6.
Fig. 2(d) is a tracking trajectory of the radiation source in the non-track optimization, and the abscissa in fig. 2(d) represents a value corresponding to a movement of the position coordinate of each waypoint in the motion trajectory of the radiation source along the x-axis in the two-dimensional space, and the ordinate represents a value corresponding to a movement of the position coordinate of each waypoint in the motion trajectory of the radiation source along the y-axis in the two-dimensional space, and the unit is meter m. In fig. 2(d), the curve marked by diamond-dashed-diamond represents the actual motion trajectory of the radiation source, and the curve marked by circle-dashed-circle represents the tracking trajectory of the radiation source. The curve marked with circle-dashed line-circle indicates that the tracking trajectory of the radiation source is calculated by using step 5 of the invention,
fig. 2(e) is a root mean square error plot of the radiation source position for optimal and no-track planning, which is obtained by the error of the radiation source position vector calculated in step 5 of the present invention and the actual position vector of the radiation source. The abscissa in fig. 2(e) represents the time of flight in seconds and the ordinate represents the root mean square error of the radiation source position in meters m. The curve marked by circle-dashed line-circle in fig. 2(e) represents the root mean square error of the radiation source position in the non-track planning, and the curve marked by square-dashed line-square represents the root mean square error of the radiation source position in the optimal track planning.
Fig. 2(f) is a root mean square error plot of the radiation source speed for optimal and no-track planning, obtained from the error of the radiation source speed vector calculated in step 5 of the present invention and the actual speed vector of the radiation source. The abscissa in fig. 2(f) represents the time of flight in seconds and the ordinate represents the root mean square error of the radiation source velocity in meters per second m/s. The curve marked with circle-dashed-circle in fig. 2(f) represents the root mean square error of the radiation source speed in the case of no-track planning, and the curve marked with diamond-dashed-diamond represents the root mean square error of the radiation source speed in the case of optimal track planning.
As can be seen from comparison between fig. 2(c) and fig. 2(d), the tracking trajectory of the radiation source gradually deviates from the motion trajectory of the radiation source during the no-track planning, and the tracking trajectory of the radiation source almost tends to be consistent with the actual motion trajectory by optimizing the track of the unmanned aerial vehicle, which indicates that the tracking performance can be improved by optimizing the track of the unmanned aerial vehicle.
As can be seen from fig. 2(e) and 2(f), the positioning accuracy can be further improved by using the random error of the position and speed of the drone and optimizing the flight path of the drone.

Claims (6)

1. A method for tracking a mobile radiation source by multiple unmanned aerial vehicles based on position and speed errors is characterized in that the unmanned aerial vehicles are used as observation stations and carry passive detection equipment, and under the condition of considering random errors of the positions and the speeds of the unmanned aerial vehicles, the mobile radiation source is positioned and tracked by means of a nonlinear filtering algorithm, and the method comprises the following steps:
(1) randomly selecting one unmanned aerial vehicle as a host machine, and the other unmanned aerial vehicles as auxiliary machines;
(2) calculating the TDOA measured value of the arrival time difference between each auxiliary machine and the main machine:
(2a) calculating the arrival time of the radiation source signal to the main unmanned aerial vehicle and the auxiliary unmanned aerial vehicle;
(2b) calculating the difference value between the arrival time of the radiation source signal to the main unmanned aerial vehicle and the arrival time of the radiation source signal to each auxiliary unmanned aerial vehicle by using an arrival time difference formula;
(3) calculating an arrival frequency difference FDOA measured value of each auxiliary machine and the main machine by using an arrival frequency difference formula;
(4) calculating the difference between the distance between each auxiliary machine and the radiation source and the distance between the main machine and the radiation source and the change rate of the difference:
(4a) calculating the difference between the distance between each auxiliary machine and the radiation source and the distance between the main machine and the radiation source;
(4b) calculating the change rate of the distance between each auxiliary machine and the radiation source and the difference value of the distance between the main machine and the radiation source;
(5) estimating the position vector and the velocity vector of the radiation source when the main unmanned aerial vehicle and the auxiliary unmanned aerial vehicle have state random errors by using the following formula:
Figure FDA0003092475830000011
Figure FDA0003092475830000012
wherein s represents the position vector of the radiation source in the x-axis and y-axis two-dimensional space when the main unmanned aerial vehicle and the auxiliary unmanned aerial vehicle have state random errors, U represents a diagonal matrix, and U is diag (sgn (ω)2(1:2)-u1) Diag denotes the diagonal matrix sign, sgn denotes the sign discrimination function, ω2(1) Representing the value, ω, corresponding to the position of the radiation source on the x-axis in two-dimensional space2(2) Representing the value corresponding to the position of the radiation source in two dimensions on the y-axis, T representing the transposition operation, u1The position vector of the main machine in the x-axis and y-axis two-dimensional space when the main unmanned aerial vehicle and the auxiliary unmanned aerial vehicle have state random errors is represented,
Figure FDA0003092475830000013
representing the velocity vector, omega, of the radiation source in the x-axis and y-axis two-dimensional space when the main unmanned aerial vehicle and the auxiliary unmanned aerial vehicle have state random errors2(3) Representing the corresponding value, omega, of the speed of movement of the radiation source in two dimensions on the x-axis2(4) Representing the corresponding value of the motion speed of the radiation source on the y-axis in a two-dimensional space,
Figure FDA0003092475830000014
representing the velocity vector of the main machine in the x-axis and y-axis two-dimensional space when the main unmanned aerial vehicle and the auxiliary unmanned aerial vehicle have state random errors;
(6) the radiation source state vector is updated as follows:
Figure FDA0003092475830000021
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003092475830000022
representing the updated state vector of the radiation source,
Figure FDA0003092475830000023
representing the state vector of the radiation source before updating, K representing the observation gain of the extended Kalman filter, zkRepresenting an observation vector, the elements in which are composed of corresponding observations produced by the primary and secondary unmanned aerial vehicle observation radiation sources, HkRepresents the nonlinear observation function of the main unmanned aerial vehicle and the auxiliary unmanned aerial vehicle to the radiation source
Figure FDA0003092475830000024
Performing Taylor series expansion to obtain a measurement matrix;
(7) calculating the optimal course angle of the main unmanned aerial vehicle and the auxiliary unmanned aerial vehicle according to the following formula:
Figure FDA0003092475830000025
wherein the content of the first and second substances,
Figure FDA0003092475830000026
is shown as
Figure FDA0003092475830000027
Taking the value of psi (k) at the minimum, psi (k) representing the vector consisting of the flight heading angles of all the main and auxiliary drones, u (k) representing the state vectors of the main and auxiliary drones at the time k, trance representing the operation of finding the trace of the matrix, J representing the Fisher information matrix of the radiation source,-1representing inversion operation, wherein u (k +1) represents state vectors of the main unmanned aerial vehicle and the auxiliary unmanned aerial vehicle at the moment of k + 1;
(8) each drone autonomously selects a single step flight trajectory according to the following formula:
Figure FDA0003092475830000028
wherein x isi(k +1) represents a value corresponding to the position of the ith unmanned aerial vehicle on the x axis in the two-dimensional space at the moment of k +1, and yi(k +1) represents a value corresponding to the position of the ith unmanned aerial vehicle on the y axis in the two-dimensional space at the moment of k +1, and xi(k) The value, y, corresponding to the position of the ith unmanned aerial vehicle on the x axis in the k-time two-dimensional spacei(k) The method comprises the steps of representing a value corresponding to the position of the ith unmanned aerial vehicle on the y axis in the two-dimensional space at the moment k, v representing the flight speed of the ith unmanned aerial vehicle, T representing the sampling time interval of the ith unmanned aerial vehicle during the flight of a tracking radiation source, cos representing cosine operation, sin representing sine operation,
Figure FDA0003092475830000029
indicating the flight heading angle of the ith drone at time k.
2. The method of claim 1, wherein the step (2a) of calculating the arrival time of the radiation source signal to each drone is obtained by the following formula:
ti＝ri o/c
wherein, tiIndicate the time that the radiation source signal was received to ith unmanned aerial vehicle, i indicates the serial number of unmanned aerial vehicle, and i is 1,2, …, M, and M indicates the total number of unmanned aerial vehicle, ri oThe actual distance between the ith unmanned aerial vehicle and the radiation source is shown, and c represents the propagation speed of the electromagnetic signals.
3. The method of claim 2, wherein the time difference of arrival formula in step (2b) is as follows:
Figure FDA0003092475830000031
wherein, tj1The difference value of the time when the jth auxiliary machine receives the radiation source signal and the time when the main machine receives the radiation source signal is shown,
Figure FDA0003092475830000032
representing the actual distance, r, of the jth auxiliary machine from the radiation source1 oRepresenting the actual distance, Δ t, of the host from the radiation sourcej1The measurement error of TDOA is shown, j represents the serial number of the slave, and j is 2, …, M.
4. The method of claim 3, wherein the frequency difference of arrival formula in step (3) is as follows:
Figure FDA0003092475830000033
wherein f isj1Represents the FDOA measured value of the j-th frame slave machine and the main machine,
Figure FDA0003092475830000034
showing the actual distance change rate of the j-th auxiliary machine and the radiation source,
Figure FDA0003092475830000035
representing the actual rate of change of distance, f, of the host from the source0Representing the frequency at which the radiation source emits an electromagnetic signal,
Figure FDA0003092475830000036
indicating measurement error of FDOA.
5. The method of claim 3, wherein the step (4a) of calculating the difference between the distance between each auxiliary machine and the radiation source and the distance between the main machine and the radiation source is obtained by the following formula:
Figure FDA0003092475830000037
wherein r isj1Representing the difference between the distance between the jth auxiliary machine and the radiation source and the distance between the main machine and the radiation source, nj1Representing a gaussian distribution with a mean of 0.
6. The method of claim 4, wherein the calculating of the variation rate of the difference between the distance between each auxiliary machine and the radiation source and the distance between the main machine and the radiation source in step (4b) is obtained by the following formula:
Figure FDA0003092475830000041
wherein the content of the first and second substances,
Figure FDA0003092475830000042
showing the change rate of the difference value of the distance between the jth auxiliary machine and the radiation source and the distance between the main machine and the radiation source,
Figure FDA0003092475830000043
representing a gaussian distribution with a mean value of 0.
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