CN115755961A - Air target track smoothing method and system based on improved cubic B-spline curve - Google Patents
Air target track smoothing method and system based on improved cubic B-spline curve Download PDFInfo
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Abstract
The invention belongs to the technical field of radar data processing, and particularly relates to an air target track smoothing method and system based on an improved cubic B-spline curve, wherein the cubic B-spline curve of original track data of an air target is constructed firstly, and a target track data point is parameterized; carrying out node vector self-adaptive adjustment by using a genetic algorithm, obtaining a control vertex of a B spline curve by using a least square method, constructing a chromosome according to candidate genes of a node distribution position, taking overload limitation and turning radius of an aerial target as constraint conditions of a fitness function, and searching for an optimal node vector by using the fitness function so that target track data can meet the maneuvering performance requirement of the aerial target in the smoothing process; and smoothing the target track by using the adjusted node vector. The method can ensure that the smoothed target track data meets the maneuvering performance limit of the airplane, can keep track detail characteristics, and is convenient for application in processing the aerial target track data.
Description
Technical Field
The invention belongs to the technical field of radar data processing, and particularly relates to an aerial target track smoothing method and system based on an improved cubic B-spline curve.
Background
The target track data are influenced by factors such as detection interruption, electromagnetic interference, terrain interference, meteorological conditions and the like, so that wild values and vacancy values inevitably appear in the receiving process of the target track data, the maneuvering performance requirements of the airplane are not met, and the subsequent processing and application of the target track data are influenced. Track smoothing is an important link of data processing, and can significantly improve the precision of target track data, so how to smooth the target track data before analyzing and applying the target track data is the primary work.
At present, the track smoothing algorithm mainly comprises a filtering method, a high-order polynomial method, a B-spline curve method and the like. Wherein, the filtering method: the method mainly comprises an alpha-beta filtering algorithm, a kalman filtering algorithm and the like. Firstly, a motion model of the airplane needs to be established, and then each track point is subjected to filtering processing to obtain a new track point. Because the smooth aerial target track belongs to a model with a complex motion condition, the established motion model cannot adapt to the motion state of the airplane in real time, and the smooth effect is poor for the condition of continuous data jumping. High order polynomial method: the high order polynomial redefines the end points of the domain interval easily causing the dragon lattice phenomenon, and the coefficients thereof are sensitive to small changes of data. B spline curve method: a mathematical mode that smooth parameter curve segments approach a polygonal line polygon is utilized, and a motion model of the airplane does not need to be constructed; compared with a high-order polynomial, the B-spline curve has low times and small calculation amount, and a cubic B-spline curve is usually selected for interpolation fitting. And the first-order derivative and the second-order derivative of the B spline curve are continuous, and the requirements of the aerial target on the ground speed and the overload continuous change are met. And for a cubic B-spline curve smooth track, the key point lies in the selection of the nodal vectors. If the number of the nodes is small, a large amount of flight path details can be lost, and the flight rule of the airplane cannot be correctly reflected; if the number of nodes is too large, redundancy will be caused, and the amount of calculation will be increased. Therefore, how to determine the node vector to balance the calculation amount and the airplane maneuvering performance becomes an urgent problem to be solved.
Disclosure of Invention
Therefore, the invention provides an aerial target track smoothing method and system based on an improved cubic B spline curve, which can be used for obtaining an optimal node vector by adaptively adjusting the node vector of the cubic B spline curve through a genetic algorithm, further completing the smoothing treatment of the aerial target track, enabling the smoothed target track data to meet the aircraft maneuvering performance limitation, and reserving track detail characteristics, thereby facilitating the application in the aerial target track data processing.
According to the design scheme provided by the invention, the method for smoothing the aerial target track based on the improved cubic B-spline curve comprises the following steps:
constructing a cubic B-spline curve of the original flight path data of the aerial target, and parameterizing the target flight path data point;
aiming at the parameterized curve node vector, performing node vector adaptive adjustment by using a genetic algorithm, wherein in the adaptive adjustment, a control vertex of a B spline curve is obtained by using a least square method, a chromosome is constructed according to candidate genes of a node distribution position, the overload limit and the turning radius of an aerial target are used as constraint conditions of a fitness function, and the optimal node vector is searched by using the fitness function, so that target track data can meet the maneuvering performance requirement of the aerial target in the smoothing process;
and smoothing the target track by using the adjusted node vector.
As the method for smoothing the aerial target track based on the improved cubic B-spline curve, further, the k-order B-spline curve equation is expressed as follows:
wherein d is i To control the vertices, i =0, 1.. N, N i,k Is a k-th order B-spline basis function, u is a node vector, and n is the number of nodes.
As the method for smoothing the aerial target track based on the improved cubic B-spline curve, the target track data point is further parameterized uniformlyThe parameterization method carries out parameterization, wherein the parameterization process is represented as:
i =0,1, 2.,. M-1, i is the node number, m is the number of raw data points.
As the air target track smoothing method based on the improved cubic B spline curve, the method further performs self-adaptive adjustment by utilizing a genetic algorithm aiming at the parameterized curve node vector, and comprises the following steps: firstly, converting a definition domain of a curve into a standard parameter domain, setting node values at two ends of a node vector, and determining a node range in the curve; and then, carrying out self-adaptive adjustment on the node vector in the curve by using a genetic algorithm.
As the air target track smoothing method based on the improved cubic B-spline curve, further, the control vertex of the B-spline curve is obtained by using a least square method, and the method comprises the following contents: firstly, enabling a boundary track data point to be the same as a control vertex through endpoint interpolation; then, a linear equation set with an internal control vertex as an unknown quantity is constructed according to a track data point target function by applying a least square principle; then, all control vertices of the cubic B-spline curve are obtained by using the system of linear equations and through the nodal vectors.
As the method for smoothing the aerial target track based on the improved cubic B-spline curve, further, the constructed linear equation system is expressed as follows: (N) T N)D＝N T R, wherein N represents (m-2) x (N-2) B spline curve basis function scalar matrix, R and D respectively represent coefficient matrix,
r i ＝q i -q 0 N 0,k (u i )-q m-1 N n-1,k (u i )，i＝1,2,...,m-2，d i to control the vertex, N i,k Is a k-th order B-spline basis function, u i Is a node vector with sequence number i, m is the number of original data points, q i Are track data points.
As a base of the inventionIn the method for improving the aerial target track smoothing of the cubic B-spline curve, further, the fitness function is expressed as:
wherein a is an overload limiting vector, r is a turning radius of the circular motion of the aerial target, χ is a chi-square value used for representing the deviation degree between an observed value and an inferred value, AIC and BIC are two punishment information standards used for balancing the complexity of a cubic B-spline curve and the smoothness and the goodness of the curve, and
n is the number of control vertices, m is the number of original data points, X j As raw data, d i To control the vertex, N i,k Is a k-th order B-spline basis function, u i Is a node vector with sequence number i.
Further, the present invention also provides an aerial target track smoothing system based on the improved cubic B-spline curve, comprising: a data point parameterization module, a node vector adaptation adjusting module and a curve smoothing processing module, wherein,
the data point parameterization module is used for constructing a cubic B-spline curve of the original flight path data of the aerial target and parameterizing the target flight path data point;
the node vector adaptive adjustment module is used for carrying out node vector adaptive adjustment by using a genetic algorithm aiming at a parameterized curve node vector, wherein in the adaptive adjustment, a control vertex of a B spline curve is obtained by using a least square method, a chromosome is constructed according to candidate genes of a node distribution position, the overload limit and the turning radius of an aerial target are used as constraint conditions of a fitness function, and the fitness function is used for searching an optimal node vector, so that target track data can meet the maneuvering performance requirement of the aerial target in the smoothing process;
and the curve smoothing module is used for smoothing the target track by using the adjusted node vector.
The invention has the beneficial effects that:
according to the method, under the condition of aircraft dynamics constraint, a genetic algorithm fitness function is used for carrying out self-adaptive adjustment on curve node vectors and obtaining the optimal cubic B spline node vector, so that the smooth target track can meet the maneuvering performance limitation of the aircraft, the detailed characteristics of the track are reserved, the quality and the precision of target track data are improved, and the practical application in scenes such as target track planning is facilitated.
Description of the drawings:
FIG. 1 is a schematic flow chart of the aerial target track smoothing process based on the improved cubic B-spline curve in the embodiment;
FIG. 2 is a flow chart of an aerial target track smoothing algorithm in an embodiment;
FIG. 3 is a schematic diagram showing the comparison between the smoothness of the track latitude and longitude in the embodiment;
FIG. 4 is a schematic diagram showing the comparison of the track height smoothness before and after the embodiment;
FIG. 5 is a schematic diagram of the track-to-ground speed and the change trend before and after the overload smoothing in the embodiment;
FIG. 6 is an iteration diagram of a track adaptive adjustment node vector in the embodiment;
FIG. 7 is a vector distribution diagram of nodes after adaptive track adjustment in the embodiment.
The specific implementation mode is as follows:
in order to make the objects, technical solutions and advantages of the present invention clearer and more obvious, the present invention is further described in detail below with reference to the accompanying drawings and technical solutions.
The B-spline curve has the characteristics of intuition, convex hull, locality, convexity protection and the like, local modification of control vertexes cannot lead the trend of the whole curve, the characteristic polygon is more approximate, a smoother target track can be obtained, and the included angle between track sections can be effectively eliminated. In an embodiment of the present disclosure, referring to fig. 1, a method for smoothing an aerial target track based on an improved cubic B-spline curve is provided, including:
s101, constructing a cubic B spline curve of original flight path data of an aerial target, and parameterizing a target flight path data point;
s102, carrying out adaptive adjustment on the node vectors by using a genetic algorithm aiming at the parameterized curve node vectors, wherein in the adaptive adjustment, a control vertex of a B spline curve is obtained by using a least square method, a chromosome is constructed according to candidate genes of a node distribution position, the overload limit and the turning radius of an aerial target are used as constraint conditions of a fitness function, and the optimal node vectors are searched by using the fitness function, so that target track data can meet the maneuvering performance requirements of the aerial target in the smoothing process;
and S103, smoothing the target track by using the adjusted node vector.
B spline node vectors are adjusted in a self-adaptive mode by utilizing a genetic algorithm; processing nodes as variables, solving by using a genetic algorithm, and converting a continuous nonlinear variable optimization problem with a plurality of local optima into a discrete combination optimization problem; the node vectors of the cubic B-spline curve are adaptively adjusted by utilizing a genetic algorithm fitness function which accords with aircraft dynamics constraints, so that the smoothed target track data meets aircraft maneuvering performance limits, track detail characteristics can be reserved, the target track can be smoothed under the condition of least node vectors, node redundancy is avoided, the calculated amount is reduced, the target track data quality and precision are improved, and the application in scenes such as track planning is facilitated.
Suppose that m track data points q are acquired i E.g., R, i = 0.. No., m-1, a known curve p (u) is needed to approximate the target track data point, which is the smoothed target track. An equation for a k-th order B-spline curve can be expressed as:
in the formula, d i (i =0,1,. N) is the control vertex, N i,k (i =0, 1.. Eta., n) is a k-th order B-spline basis function. The standard algorithm is a Deboolean-Cox (Debor-Cox) recurrence formula:
in the formula, N i,k In (u), i represents the number, k is the number of times of the B-spline curve, and u i Is a node vector U { U } i },i＝0,1,...,n+p+1。
To determine the ith k-th B-spline N i,k (u) if necessary u i ,u i+1 ,...,u i+k+1 Total k +2 nodes, N of k-th order B-spline curve i,k (u) N which may be substituted by two k-1 times i,k-1 (u) and N i+1,k-1 (u) recursion.
In order to reflect the nature of the smoothed target trajectory as much as possible, the data points also need to be parameterized. Because the sampling point of the aerial target track data removes the influence of detection interruption and is uniformly sampled. Therefore, in the embodiment of the present disclosure, a uniform parameterization method may be used to parameterize the track data point, and the formula may be expressed as:
as a preferred embodiment, further, the adaptive adjustment is performed on the parameterized curve node vector by using a genetic algorithm, and the adaptive adjustment includes: firstly, converting a definition domain of a curve into a standard parameter domain, setting node values at two ends of a node vector, and determining a node range in the curve; and then, carrying out self-adaptive adjustment on the node vector in the curve by using a genetic algorithm.
In order to facilitate the control of the shape of the curve end point, the end point geometric property of the Bezier curve of the same time is used for reference, and the repetition degree of two ends of the node vector is taken as k +1. First, the definition domain of the curve is converted into a canonical parameter domain, even if u ∈ [ ] k ,u n+1 ]＝[0,1]Then the node values at both ends of the node vector are u 0 ＝u 1 ＝...＝u k ＝0；u n+1 ＝u n+2 ＝...＝u n+k+1 =1, so that only u remains to be determined k+1 ,u k+2 ,...,u n These inner nodes.
And carrying out self-adaptive adjustment on the unknown internal nodes by using a genetic algorithm. A chromosome is constructed by considering candidate genes of node distribution positions, a new fitness function is designed under the constraint of aircraft dynamics, and an optimal node vector is found, so that the maneuvering performance requirements of the aircraft are met on the basis of smoothness of target track data. The method does not require any subjective factors such as fault tolerance or smoothing factor, and node iterative search of initial positions of quantities
Further, in the embodiment of the present disclosure, the obtaining of the control vertex of the B-spline by using the least square method includes the following steps: firstly, enabling boundary track data points to be the same as control vertexes through endpoint interpolation; then, a linear equation set with an internal control vertex as an unknown quantity is constructed according to a track data point target function by applying a least square principle; then, all control vertices of the cubic B-spline curve are obtained by the node vectors using the system of linear equations.
When the node vector is determined, the control vertex of the B-spline curve is back-calculated by using the least square method (the control vertex determines the shape of the B-spline curve). Firstly, a B-spline curve with endpoint interpolation is adopted, namely, the data points of the two boundary tracks are the same as the control vertex. Therefore, only n-2 internal control vertices need to be solved. Using standard least square principle to satisfy q 0 ＝p(0),q m-1 = p (1), i.e. track data point q i (i =1, 2.. Lam.m-2) is approximated in the least-squares sense with an objective function of:
to minimize the objective function f, its derivative with respect to n-2 control vertices should be zero, i.e.:
thus, a linear system of equations with n-2 control vertices as unknowns and containing n-2 equations can be obtained:
(N T N)D＝N T R (6)
where N is a B-spline curve basis function scalar matrix of (m-2) × (N-2):
the coefficient matrices R and D in equation (7) are expressed as follows:
in the formula, r i ＝q i -q 0 N 0,k (u i )-q m-1 N n-1,k (u i )i＝1,2,...,m-2。
The two coefficient matrixes can be obtained through the node vectors, and all control vertexes of the cubic B-spline curve can be obtained by substituting the coefficient matrixes into the formula (7).
Genetic Algorithm (GA) is a random global optimization Algorithm, which simulates the process of excellence and disqualification in nature, and the solution of the problem is evolved in competition through the operations of operators such as selection, intersection, mutation and the like so as to obtain a satisfactory solution. In the embodiment of the scheme, in the optimal selection of the node vector by using the genetic algorithm, the coding mode of the genetic algorithm is determined firstly, and the binary coding mode can flexibly adjust the distribution position and the number of the nodes because the positions of the nodes cannot be adjusted by the real number coding mode and the decimal coding mode, so the embodiment of the scheme can select the binary coding mode.
Firstly, a chromosome bit string H = H is used 1 h 2 h 3 ...h L Instead of an internal partial node in the node vector U, L is the chromosome length. Then, the parameterized aerial target trajectory data is divided into L +1 equal parts according to the length of the chromosome. The i-th gene in H corresponds to an internal point
When h is generated i If =1, then the corresponding internal partial point v i E is U; if h i If not =0, then
Each chromosome therefore represents a unique one of the node vectors U. In addition, 0 and 1 appear in a certain ratio in the chromosome and are denoted as a node ratio η.
The population randomly generated by the genetic algorithm does not necessarily meet the requirement of a search space, and in order to effectively adjust the node vector in a self-adaptive manner and discard an improper node vector, a fitness function can be redesigned under the constraint of aircraft dynamics according to the maneuvering performance and the curve smoothing effect of the aircraft.
In chi-square verification, the deviation degree between the actual observed value and the theoretical inferred value of a sample is tested, the statistic chi-square value represents the deviation degree between the actual observed value and the theoretical inferred value, and the larger the chi-square value is, the larger the deviation is; the smaller the chi-square value is, the smaller the deviation is; the complexity of the computational model need not be taken into account.
In the formula, X is original track data, and Y is smoothed data.
In the penalty Information standard, in order to better balance the complexity of the cubic B-spline curve and the excellence of the curve in smoothing target track data, an Akaike Information Criterion (AIC) and a Bayesian Information Criterion (BIC) are selected and adopted. By simply balancing the precision, optimal smooth models are found, which include two terms: the first term is the accuracy of the model function and the second term is the penalty of minimizing the number of free parameters in the equation. The expression is as follows:
wherein n is the number of control vertices, m is the number of original data vertices, X j Is the original data. The smaller the values of AIC and BIC, the better the fitness, i.e. the better the node vector is selected. Because the genetic algorithm is convenient to find the maximum value, the minimum value problem needs to be converted into the solution of the maximum value problem.
Given the flyability of the smoothed flight path, it is desirable to meet the constraints on the maneuverability of the aircraft, including maximum allowable overload and turning radius. Due to the structure of the airplane and the bearing capacity of the body of a pilot, the overload of the airplane cannot exceed 9G generally, and the attack angle, the sideslip angle and the deflection angle of the airplane are also important factors for limiting the flight performance of the airplane and are closely related to the overload. In addition, the turning radius of the aircraft should generally not be less than three times the aircraft length, regardless of factors such as wind power, wind direction, aircraft fuselage width, channel width, and aircraft maneuverability. The overload limit and the turning radius of the aircraft are taken as two constraints in the fitness function.
The B spline curve of the aerial target track is a smooth curve, and x (t), y (t) and z (t) respectively represent curve functions after the smoothness in three directions of longitude and latitude:
considering the aerial target track as the motion trajectory of the particles in space, the ground velocity vector and the overload vector of the particles can be given by the first and second derivatives of the function in equation (12):
the overload value of the aerial target at each track point can be obtained by the formula (13):
the overload vector a can be decomposed intoTangential overload a τ And normal overload a n Two parts. Wherein the normal overload a n Namely centripetal overload, which is generated by centripetal force and has a relation with velocity in circular motion, can be obtained according to newton's second law:
wherein r is the radius of the circular motion; a is a τ For the projection of a on v, then:
|a τ |＝(v·a)/|v| (16)
then:
the target turning radius is calculated from (15) and (17):
in the formula (I), the compound is shown in the specification,
(v·a)＝x'(t)x″(t)+y'(t)y″(t)+z'(t)z″(t)。
intuitively, the whole arc length of the cubic B-spline curve is the whole range of the airplane, and the curvature radius of each point on the curve is required to be larger than or equal to the minimum turning radius of the airplane, which is equivalent to overload judgment. If it is satisfied with
Determining that the aircraft flight restriction condition is met; if not, the node vector of the cubic B spline needs to be adjusted, and the step is realized by self-adaptive adjustment of a genetic algorithm.
By combining the above constraint conditions, the fitness function that meets the track smoothness can be expressed as:
the inverse is taken because the chi-square test value, AIC and BIC are smaller values and the smoothing effect is the best, and the genetic algorithm is to find the maximum value of the model. Meanwhile, under the constraint condition of aircraft dynamics, the fitness function is not necessarily larger and better, although the original target track can be better approximated, the track smoothing effect cannot be achieved. Therefore, the maximum fitness function value that can satisfy the aircraft dynamics constraints can be selected.
In genetic algorithm design, operator selection is realized by two methods. Aiming at each iteration process, the optimal chromosome in the parent is directly inherited to the next generation by an elite retention strategy, and the rest chromosomes are selected by adopting a roulette mode, so that the probability that the chromosome with a high fitness value is drawn is greater than that of the chromosome with a low fitness value, the efficiency of adjusting the node vector by an algorithm is improved, and the excellent chromosomes are prevented from being discarded. Selecting proper cross probability, carrying out cross in a single-point cross mode, calculating to obtain the fitness value of the new chromosome, and comparing the fitness value with the fitness value of the parent chromosome; and crossover the number of chromosomes in the current generation until the original population size is restored. After randomly determining the position of a variant gene of a chromosome c to be variant determined by the variant probability Pm in a parent population, complementing the gene to generate a new chromosome e. And then comparing the fitness values of the two chromosomes before and after mutation, reserving the chromosome with the larger fitness value, and using the chromosome as a progeny chromosome to ensure that the population cannot be degenerated. Besides the selection of selection, crossing and mutation operators, the size K of the population, the length L of the chromosome, the node rate eta, the crossing probability Pc and the mutation probability Pm are also required to be determined. K represents the space size searched by each iterative algorithm, if the K is too small, the space searched by the algorithm is too small, the algorithm stops iteration before the optimal node vector is not found, and the algorithm falls into local optimization; if K is too large, the amount of calculation increases. L determines the number of final nodes, and if L is larger, the number of the nodes contained in the initial chromosome is larger, so that the global optimal solution can be searched, but the calculated amount is larger, and generally two thirds of the number of the original track data points is more suitable for selection. η determines the number of internal nodes in the initial population. Pc and Pm are not limited to the parameter ranges of standard genetic algorithms.
In the specific algorithm implementation, referring to fig. 2, an optimal cubic B-spline nodal vector is obtained through self-adaptive adjustment of a genetic algorithm, a control vertex of a cubic B-spline curve is back-calculated by using a least square method, and a smoothed target track is calculated by combining a spline basis function, so that the smooth target track meets the maneuvering performance limit of the airplane, the detailed characteristics of the track are retained, and the quality and the precision of the target track are improved.
Further, based on the above method, an embodiment of the present invention further provides an aerial target track smoothing system based on an improved cubic B-spline curve, including: a data point parameterization module, a node vector adaptation adjusting module and a curve smoothing module, wherein,
the data point parameterization module is used for constructing a cubic B-spline curve of the original flight path data of the aerial target and parameterizing the target flight path data point;
the node vector adaptive adjustment module is used for carrying out node vector adaptive adjustment by utilizing a genetic algorithm aiming at the parameterized curve node vector, wherein in the adaptive adjustment, a control vertex of a B spline curve is obtained by utilizing a least square method, a chromosome is constructed according to candidate genes of a node distribution position, the overload limit and the turning radius of an aerial target are used as constraint conditions of a fitness function, and the fitness function is utilized to search an optimal node vector, so that target track data can meet the maneuvering performance requirement of the aerial target in the smoothing process;
and the curve smoothing processing module is used for smoothing the target track by using the adjusted node vector.
To verify the validity of the protocol, the following further explanation is made with reference to the test data:
taking a certain type of airplane as an example, the maximum available overload limit is 9G, the maximum flying speed is 604m/s, and the airplane length is 15.09m. The target track data is from an adsbexchange public website, and the data comprises flight number, icao number, longitude and latitude height, speed, course, climbing rate and other information, and can provide support for analyzing the maneuvering performance of the airplane. From the raw flight path data of the aerial target as shown in fig. 3, it can be seen that many burrs exist on the flight path, which do not meet the maneuvering performance requirements of the aircraft. Therefore, in order to better utilize data, the cubic B spline curve is improved to smooth the aerial target track data, and the quality and the precision of the data are improved, so that the track meets the requirement of the maneuverability of the airplane.
Example simulations were programmed in the MATLAB2020b environment. And adaptively adjusting the node vector of the cubic B spline curve by means of a genetic algorithm, wherein the parameters in the genetic algorithm are selected as follows: population size η =20; chromosome length L =100 (appropriately adjusted according to the difference of the track point number, generally two thirds of the track point number); pitch ratio η =0.6; the iteration times are 200; cross probability Pc =0.8; the mutation probability Pm =0.5.
FIGS. 3-5 show graphs of the results of track smoothing. FIGS. 3 and 4 are the comparison between the longitude and latitude and the height of the target track before and after the node self-adaptive distribution condition, so that the target track which slides out of the improved cubic B-spline curve is free of burrs, the track shape is smooth, the detail characteristics of the original target track are retained, and the motion of the original target track is more consistent with the motion of the actual airplane during flying; FIG. 5 shows that the smoothed aircraft is overloaded under the adaptive distribution of nodes, the mobility limit of the aircraft is not exceeded, and the variation trend is consistent with the speed variation trend.
Fig. 6 is an iterative diagram of a genetic algorithm adaptively adjusting a cubic B-spline curve node vector, and as the number of iterations increases, the fitness function value gradually converges, and the number of nodes is also determined accordingly. FIG. 7 is an optimal node vector distribution diagram output after adaptive adjustment of a genetic algorithm.
Through further verification of the experimental data, in the scheme, the fitness function in the genetic algorithm is used for adaptively adjusting and searching the optimal cubic B-spline node vector under the condition of aircraft dynamics constraint, so that the target track sliding out flatly can meet the maneuvering performance limit of the aircraft, the detailed characteristics of the track are reserved, and the quality and the precision of the target track can be improved.
Unless specifically stated otherwise, the relative steps, numerical expressions, and values of the components and steps set forth in these embodiments do not limit the scope of the present invention.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The elements of the various examples and method steps described in connection with the embodiments disclosed herein may be embodied in electronic hardware, computer software, or combinations of both, and the components and steps of the examples have been described in a functional generic sense in the foregoing description for clarity of hardware and software interchangeability. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the technical solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
Those skilled in the art will appreciate that all or part of the steps of the above methods can be implemented by a program instructing relevant hardware, and the program can be stored in a computer readable storage medium, such as: read-only memory, magnetic or optical disk, and the like. Alternatively, all or part of the steps of the foregoing embodiments may also be implemented by using one or more integrated circuits, and accordingly, each module/unit in the foregoing embodiments may be implemented in the form of hardware, and may also be implemented in the form of a software functional module. The present invention is not limited to any specific form of combination of hardware and software.
Finally, it should be noted that: the above-mentioned embodiments are only specific embodiments of the present invention, which are used for illustrating the technical solutions of the present invention and not for limiting the same, and the protection scope of the present invention is not limited thereto, although the present invention is described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: any person skilled in the art can modify or easily conceive the technical solutions described in the foregoing embodiments or equivalent substitutes for some technical features within the technical scope of the present disclosure; such modifications, changes or substitutions do not depart from the spirit and scope of the embodiments of the present invention, and they should be construed as being included therein. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (10)
1. An aerial target track smoothing method based on an improved cubic B-spline curve is characterized by comprising the following steps:
constructing a cubic B-spline curve of the original flight path data of the aerial target, and parameterizing the target flight path data point;
aiming at the parameterized curve node vector, carrying out node vector self-adaptive adjustment by using a genetic algorithm, wherein in the self-adaptive adjustment, a control vertex of a B spline curve is obtained by using a least square method, a chromosome is constructed according to candidate genes of a node distribution position, the overload limit and the turning radius of an aerial target are used as constraint conditions of a fitness function, and the optimal node vector is searched by using the fitness function, so that target track data can meet the maneuvering performance requirement of the aerial target in the smoothing process;
and smoothing the target track by using the adjusted node vector.
2. The aerial target track smoothing method based on the improved cubic B-spline curve as claimed in claim 1, wherein the k-th order B-spline curve equation is constructed as follows:
wherein, d i To control the vertices, i =0,1,. N, N i,k Is a k-th order B-spline basis function, u is a node vector, and n is the number of nodes。
3. The aerial target track smoothing method based on the improved cubic B-spline curve as claimed in claim 1 or 2, wherein in parameterizing the target track data points, a uniform parameterization method is adopted for parameterization, wherein the parameterization process is represented as:
i is the node serial number, and m is the number of original data points.
4. The improved cubic B-spline curve-based aerial target track smoothing method as claimed in claim 1, wherein the adaptive adjustment is performed by using a genetic algorithm for the parameterized curve node vector, and comprises: firstly, converting a definition domain of a curve into a standard parameter domain, setting node values at two ends of a node vector, and determining a node range in the curve; and then, carrying out self-adaptive adjustment on the node vector in the curve by using a genetic algorithm.
5. The method for smoothing aerial target track based on the improved cubic B-spline curve of claim 4, wherein the control vertex of the B-spline curve is obtained by a least square method, and the method comprises the following steps: firstly, enabling boundary track data points to be the same as control vertexes through endpoint interpolation; then, a least square method principle is applied, and a linear equation set with an internal control vertex as an unknown quantity is constructed according to a track data point target function; then, all control vertices of the cubic B-spline curve are obtained by using the system of linear equations and through the nodal vectors.
6. The improved cubic B-spline curve-based aerial target track smoothing method as recited in claim 5, wherein the constructed linear equation system is expressed as: (N) T N)D＝N T R, wherein N represents (m-2) x (N-2) B spline curve basis function scalar matrix, R and D respectively represent coefficient matrix,
r i ＝q i -q 0 N 0,k (u i )-q m-1 N n-1,k (u i )，i＝1,2,...,m-2，d i to control the vertex, N i,k Is a k-th order B-spline basis function, u i Is a node vector with sequence number i, m is the number of original data points, q i Are track data points.
7. The improved cubic B-spline curve-based aerial target track smoothing method as claimed in claim 1, wherein the fitness function is expressed as:
wherein a is an overload limiting vector, r is the turning radius of the circular motion of the aerial target, χ is a chi-square value used for representing the deviation degree between an observed value and an inferred value, AIC and BIC are two punishment information standards used for balancing the complexity of a cubic B-spline curve and the smoothness and the superiority of the curve, and
n is the number of control vertices, m is the number of original data points, X j As raw data, d i To control the vertex, N i,k Is a k-th order B-spline basis function, u i Is a node vector with sequence number i.
8. An aerial target track smoothing system based on an improved cubic B-spline curve, comprising: a data point parameterization module, a node vector adaptation adjusting module and a curve smoothing processing module, wherein,
the data point parameterization module is used for constructing a cubic B-spline curve of the original flight path data of the aerial target and parameterizing the target flight path data point;
the node vector adaptive adjustment module is used for carrying out node vector adaptive adjustment by utilizing a genetic algorithm aiming at the parameterized curve node vector, wherein in the adaptive adjustment, a control vertex of a B spline curve is obtained by utilizing a least square method, a chromosome is constructed according to candidate genes of a node distribution position, the overload limit and the turning radius of an aerial target are used as constraint conditions of a fitness function, and the fitness function is utilized to search an optimal node vector, so that target track data can meet the maneuvering performance requirement of the aerial target in the smoothing process;
and the curve smoothing processing module is used for smoothing the target track by using the adjusted node vector.
9. The electronic equipment is characterized by comprising a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory are communicated with each other through the communication bus;
a memory for storing a computer program;
a processor for executing the program stored in the memory and for performing the method steps of any one of claims 1 to 7 when the program is executed.
10. A computer-readable storage medium, characterized in that a computer program is stored in the computer-readable storage medium, which computer program, when being executed by a processor, carries out the method steps of any one of claims 1 to 7.
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