Air Target Trajectory Smoothing Method and System Based on Improved Cubic B-Spline Curve

Abstract

The present 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. First, a cubic B-spline curve of the original air target track data is constructed, and the target track data points are parameterized; then, a genetic algorithm is used for adaptive adjustment of the knot vector, and the least squares method is used to obtain the control vertices of the B-spline curve. Chromosomes are constructed based on the candidate genes at the knot distribution positions, and the air target overload limit and turning radius are used as the constraint conditions of the fitness function. The fitness function is used to find the optimal knot vector, so that the target track data can meet the requirements of the air target maneuverability during the smoothing process; the adjusted knot vector is used to smooth the target track. The present invention can make the smoothed target track data meet the aircraft maneuverability limit, and can retain the track detail features, which is convenient for the application in the processing of air target track data.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar data processing, and particularly relates to a method and system for smoothing the flight track of an airborne target based on an improved cubic B-spline curve. Background Technique

[0002] Affected by factors such as detection interruption, electromagnetic interference, terrain obstruction, and meteorological conditions, wild values and missing values inevitably appear in the received target track data, which do not meet the requirements of the aircraft's maneuverability, thus affecting the subsequent processing and application of the target track data. As an important link in data processing, track smoothing can significantly improve the accuracy of target track data. Therefore, before analyzing and applying the target track data, how to smooth it is the primary task.

[0003] Currently, the main track smoothing algorithms include filtering methods, high-degree polynomial methods, B-spline curve methods, etc. Among them, the filtering method mainly includes α-β filtering algorithms, Kalman filtering algorithms, etc. First, a motion model of the aircraft needs to be established, and then each track point is filtered to obtain new track points. Since the smoothed airborne target track belongs to an aircraft type with a relatively complex motion situation, the established motion model cannot adapt to the aircraft's motion state in real time. In addition, the smoothing effect is not good for the case of continuous data jitter. The high-degree polynomial method: High-degree polynomials are prone to the Runge phenomenon at the endpoints of the domain interval, and their coefficients are also very sensitive to small changes in the data. The B-spline curve method: A mathematical method that uses smooth parametric curve segments to approximate a polyline polygon, without the need to construct a motion model of the aircraft; compared with high-degree polynomials, the degree of the B-spline curve is not high, the calculation amount is small, and a cubic B-spline curve is usually selected for interpolation fitting. Moreover, the first-order and second-order derivatives of the B-spline curve are continuous, meeting the requirements of the continuous change of the ground speed and overload of the airborne target. For smoothing the track with a cubic B-spline curve, the key lies in the selection of the knot vector. If the number of knots is small, a large amount of track details will be lost, and the flight law of the aircraft cannot be correctly reflected; if the number of knots is too large, it will cause redundancy and increase the calculation amount. Therefore, how to determine the knot vector to balance the calculation amount and the aircraft's maneuverability has become an urgent problem to be solved. Summary of the Invention

[0004] To this end, the present invention provides a method and system for smoothing the flight track of an airborne target based on an improved cubic B-spline curve. By using a genetic algorithm to adaptively adjust the knot vector of the cubic B-spline curve to obtain the optimal knot vector, and then completing the smoothing process of the airborne target track, the smoothed target track data can meet the aircraft maneuverability limit, and can retain the track detail features, which is convenient for the application in the processing of airborne target track data.

[0005] According to the design solution provided by the present invention, a method for smoothing the air target track based on an improved cubic B-spline curve is provided, including the following contents:

[0006] Construct a cubic B-spline curve for the original air target track data and parameterize the target track data points;

[0007] For the parameterized curve knot vector, use the genetic algorithm to adaptively adjust the knot vector. Among them, in the adaptive adjustment, use the least squares method to obtain the control vertices of the B-spline curve, construct chromosomes based on the candidate genes of the knot distribution positions, and use the air target overload limit and turning radius as the constraint conditions of the fitness function. Use the fitness function to find the optimal knot vector so that the target track data can meet the requirements of the air target maneuverability during the smoothing process;

[0008] Use the adjusted knot vector to smooth the target track.

[0009] As the method for smoothing the air target track based on the improved cubic B-spline curve in the present invention, further, the constructed k-th order B-spline curve equation is expressed as: where d i is the control vertex, i = 0, 1,... n, N i,k is the k-th order B-spline basis function, u is the knot vector, and n is the number of knots.

[0010] As the method for smoothing the air target track based on the improved cubic B-spline curve in the present invention, further, in the parameterization of the target track data points, the uniform parameterization method is used for parameterization processing, where the parameterization processing process is expressed as: i = 0, 1, 2,..., m - 1, i is the knot number, and m is the number of original data points.

[0011] As the method for smoothing the air target track based on the improved cubic B-spline curve in the present invention, further, for the parameterized curve knot vector, use the genetic algorithm for adaptive adjustment, including: First, convert the domain of definition of the curve to the canonical parameter domain, set the knot values at both ends of the knot vector, and determine the range of knots inside the curve; Then, use the genetic algorithm to adaptively adjust the knot vector inside the curve.

[0012] As the method for smoothing the air target track based on the improved cubic B-spline curve of the present invention, further, use the least squares method to obtain the control vertices of the B-spline curve, including the following contents: First, through endpoint interpolation, make the boundary track data points the same as the control vertices; Then, apply the least squares method principle to construct a linear equation system with the internal control vertices as unknowns based on the track data point objective function; Then, use the linear equation system and obtain all the control vertices of the cubic B-spline curve through the knot vector.

[0013] As the air target trajectory smoothing method based on the improved cubic B-spline curve of the present invention, further, the constructed linear equation system is expressed as: (N T N)D = N T R, where N represents the B-spline curve basis function scalar matrix of (m - 2)×(n - 2), and R and D respectively represent the coefficient matrices, r i = q i - q0N 0,k (u i ) - q m-1 N n-1,k (u i ), i = 1, 2,..., m - 2, d i is the control vertex, N i,k is the k-th B-spline basis function, u i is the knot vector with serial number i, m is the number of original data points, q i is the trajectory data point.

[0014] As the air target trajectory smoothing method based on the improved cubic B-spline curve of the present invention, further, the fitness function is expressed as: where a is the overload limit vector, r is the turning radius of the circular motion of the air target, χ is the chi-square value used to represent the deviation degree between the observed value and the inferred value, AIC and BIC are two penalty information criteria used to balance the complexity of the cubic B-spline curve and the excellent smoothness of the curve, and n is the number of control vertices, m is the number of original data points, X j is the original data, d i is the control vertex, N i,k is the k-th B-spline basis function, u i is the knot vector with serial number i.

[0015] Further, the present invention also provides an air target trajectory smoothing system based on the improved cubic B-spline curve, including: a data point parameterization module, a knot vector adaptive adjustment module, and a curve smoothing processing module, where,

[0016] The data point parameterization module is used to construct the cubic B-spline curve of the original trajectory data of the air target and parameterize the target trajectory data points;

[0017] The node vector adaptation and adjustment module is used to adaptively adjust the node vector of the curve after parameterization by using the genetic algorithm. In the adaptive adjustment, the control vertices of the B-spline curve are obtained by using the least squares method, the chromosome is constructed based on the candidate genes of the node distribution positions, the overload limit and turning radius of the airborne target are used as the constraint conditions of the fitness function, and the fitness function is used to find the optimal node vector so that the target track data can meet the maneuverability requirements of the airborne target during the smoothing process;

[0018] The curve smoothing processing module is used to smooth the target track by using the adjusted node vector.

[0019] The beneficial effects of the present invention:

[0020] Under the conditions of aircraft dynamics constraints, the present invention uses the fitness function of the genetic algorithm to adaptively adjust the curve node vector and obtain the optimal cubic B-spline node vector, so that the smoothed target track can meet the maneuverability limitations of the aircraft while retaining the detailed features of the track, improving the quality and accuracy of the target track data, and facilitating the practical application in scenarios such as target track planning. Description of the drawings

[0021] Figure 1 Schematic diagram of the air target track smoothing process based on the improved cubic B-spline curve in the embodiment;

[0022] Figure 2 Schematic diagram of the air target track smoothing algorithm process in the embodiment;

[0023] Figure 3 Schematic diagram of the comparison before and after smoothing the track longitude and latitude in the embodiment;

[0024] Figure 4 Schematic diagram of the comparison before and after smoothing the track altitude in the embodiment;

[0025] Figure 5 Schematic diagram of the change trend before and after smoothing the track ground speed and overload in the embodiment;

[0026] Figure 6 Schematic diagram of the iterative diagram of the track adaptive adjustment node vector in the embodiment;

[0027] Figure 7 Schematic diagram of the node vector distribution diagram after the track adaptive adjustment in the embodiment. Detailed implementation manners

[0028] To make the purpose, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below in conjunction with the drawings and technical solutions.

[0029] B-spline curves have characteristics such as intuitiveness, convex hull property, locality, and convexity preservation. Modifying the control vertices locally will not affect the trend of the entire curve, and it can approximate the characteristic polygon better, obtaining a relatively smooth target flight path and effectively eliminating the angle between flight path segments. For the embodiments of this case, see Figure 1 As shown, a method for smoothing the flight path of an aerial target based on an improved cubic B-spline curve is provided, including:

[0030] S101. Construct a cubic B-spline curve for the original flight path data of the aerial target and parameterize the flight path data points;

[0031] S102. For the knot vector of the parameterized curve, use the genetic algorithm to adaptively adjust the knot vector. Among them, in the adaptive adjustment, use the least squares method to obtain the control vertices of the B-spline curve, construct chromosomes based on the candidate genes of the knot distribution positions, take the overload limit and turning radius of the aerial target as the constraint conditions of the fitness function, and use the fitness function to find the optimal knot vector so that the target flight path data can meet the requirements of the maneuverability of the aerial target during the smoothing process;

[0032] S103. Use the adjusted knot vector to smooth the target flight path.

[0033] Use the genetic algorithm to adaptively adjust the B-spline knot vector; treat the knots as variables and solve using the genetic algorithm, transforming a continuous non-linear variable optimization problem with multiple local optima into a discrete combinatorial optimization problem; use the genetic algorithm fitness function that conforms to the aircraft dynamics constraints to adaptively adjust the knot vector of the cubic B-spline curve, so that the smoothed target flight path data meets the aircraft maneuverability limitations, and can retain the details of the flight path, can complete the smoothing of the target flight path under the condition of the least number of knot vectors, will not cause knot redundancy, reduce the calculation amount, improve the quality and accuracy of the target flight path data, and facilitate applications in scenarios such as flight path planning.

[0034] Assume that m flight path data points q i ∈R, i = 0,..., m - 1 are obtained. A known curve p(u) is needed to approximate the target flight path data points, and this curve is the smoothed target flight path. The equation of a k-th order B-spline curve can be expressed as:

[0035]

[0036] In the formula, d i (i = 0, 1,... n) are the control vertices, and N i,k (i = 0, 1,..., n) are the k-th order B-spline basis functions. Its standard algorithm is the De Boor-Cox recurrence formula:

[0037]

[0038] In the formula, N i,k in (u), i represents the serial number, k is the degree of the B-spline curve, and u i is the knot vector U{u i}, i = 0, 1,..., n + p + 1.

[0039] To determine the i-th k-th degree B-spline N i,k (u), u i , u i+1 ,..., u i+k+1 a total of k + 2 knots are required. The N i,k (u) of the k-th degree B-spline curve can be recursively obtained from two N i,k-1 (u) of degree k - 1 and N i+1,k-1 (u).

[0040] In order to reflect the properties of the target track to be smoothed as much as possible, it is also necessary to parameterize the data points. Since the sampling points of the air target track data are uniformly sampled except for the influence of detection interruption. Therefore, in the embodiments of this case, the uniform parameterization method can be used to parameterize the track data points, and its formula can be expressed as:

[0041]

[0042] As a preferred embodiment, further, for the knot vector of the parameterized curve, an adaptive adjustment is performed using the genetic algorithm, including: First, the domain of definition of the curve is converted into a canonical parameter domain, the knot values at both ends of the knot vector are set, and the range of internal knots of the curve is determined; then, the genetic algorithm is used to adaptively adjust the internal knot vector of the curve.

[0043] To facilitate the control of the shape of the curve endpoints, referring to the geometric properties of the endpoints of the same-degree Bezier curve, the multiplicity at both ends of the knot vector is taken as k + 1. First, the domain of definition of the curve is converted into a canonical parameter domain, that is, u ∈ [u k , u n+1 = [0, 1], then the knot values at both ends of the knot vector are u0 = u1 =... = u k = 0; u n+1 = u n+2 =... = u n+k+1 = 1, so the only thing left to determine is {u k+1 , u k+2 ,..., u n} these internal knots.

[0044] For these unknown internal nodes, the genetic algorithm is used for adaptive adjustment. Chromosomes are constructed by considering candidate genes for the node distribution positions, and a new fitness function is designed under the constraints of aircraft dynamics. Based on this, the optimal node vector is found, so that the target track data is smoothed and at the same time meets the maneuverability requirements of the aircraft. This method does not require any subjective factors, such as the error tolerance or the smoothing factor, and the iterative search for the nodes at the initial positions of the quantities

[0045] Further, in the embodiments of this case, the least square method is used to obtain the control vertices of the B-spline curve, which includes the following contents: First, through endpoint interpolation, the boundary track data points are made the same as the control vertices; then, the principle of the least square method is applied, and a linear equation system with the internal control vertices as unknowns is constructed according to the track data point objective function; then, all the control vertices of the cubic B-spline curve are obtained by using the linear equation system and the node vector.

[0046] When the node vector is determined, the control vertices of the B-spline curve are calculated by the least square method (the control vertices determine the shape of the B-spline curve). First, a B-spline curve with endpoint interpolation is adopted, that is, the two boundary track data points are the same as the control vertices. Therefore, only n - 2 internal control vertices need to be solved. Applying the standard least square principle, satisfying q0 = p(0), q m-1 = p(1), that is, the track data points q i (i = 1, 2,..., m - 2) are approximated in the least square sense, and its objective function is:

[0047]

[0048] To minimize the objective function f, its derivative with respect to the n - 2 control vertices should be zero, that is:

[0049]

[0050] Thus, a linear equation system with n - 2 control vertices as unknowns and containing n - 2 equations can be obtained:

[0051] (N T N)D = N T R (6)

[0052] Here N is the scalar matrix of the B-spline curve basis functions of (m - 2)×(n - 2):

[0053]

[0054] The expressions of the coefficient matrices R and D in formula (7) are as follows:

[0055]

[0056]

[0057] Wherein, r i = q i - q0N 0,k (u i ) - q m-1 N n-1,k (u i )i = 1, 2,..., m - 2.

[0058] The above two coefficient matrices can be obtained through the knot vector, and all control vertices of the cubic B-spline curve can be obtained by substituting them into Equation (7).

[0059] The genetic algorithm (GA) is a stochastic global optimization algorithm that simulates the process of survival of the fittest in nature. Through operations such as selection, crossover, and mutation, the solution to the problem evolves in competition to obtain a satisfactory solution. In the embodiments of this case, in the optimal selection of the knot vector using the genetic algorithm, the encoding method of the genetic algorithm is first determined. Since the real number encoding method and the decimal encoding method cannot adjust the position of the knots, and the binary encoding method can flexibly adjust the distribution position and quantity of the knots, therefore, in the embodiments of this case, the binary encoding method can be selected.

[0060] First, use a chromosome bit string H = h1h2h3...h L to replace the internal knots in the knot vector U, where L is the length of the chromosome. Then, according to the length of the chromosome, the parameterized air target trajectory data is divided into L + 1 equal parts. The gene at the i-th position in H corresponds to the internal point

[0061] When h i = 1, the corresponding internal point v i ∈U; if h i = 0, then Therefore, each chromosome represents a unique knot vector U. In addition, 0 and 1 in the chromosome appear in a certain proportion, denoted as the knot rate η.

[0062] The population randomly generated by the genetic algorithm may not meet the requirements of the search space. In order to effectively and adaptively adjust the knot vector and discard inappropriate knot vectors, the fitness function can be redesigned under the constraints of the aircraft's maneuverability and curve smoothing effect.

[0063] In the chi-square test, the degree of deviation between the actual observed value and the theoretical inferred value of the test sample is examined. The chi-square value of the statistic represents the degree of deviation between the actual observed value and the theoretical inferred value. The larger the chi-square value, the greater the deviation; the smaller the chi-square value, the smaller the deviation; the complexity of the calculation model does not need to be considered.

[0064]

[0065] In the formula, X is the original track data, and Y is the data after smoothing.

[0066] In the penalty information criterion, in order to better balance the complexity of the cubic B-spline curve and the goodness of this curve for smoothing the target track data, the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) are selected. By simply balancing the accuracy, the optimal smoothing model is found, which includes two terms: the first term is the accuracy of the model function, and the second term is the penalty for minimizing the number of free parameters in the formula. The expression is as follows:

[0067]

[0068] In the formula, n is the number of control vertices, m is the number of original data points, and X j is the original data. The smaller the values of AIC and BIC, the better the fitness, that is, the better the selection of the knot vector. Since the genetic algorithm is convenient for finding the maximum value, the minimum value problem needs to be transformed into the solution of the maximum value problem.

[0069] Considering the flyability of the track after smoothing, it is necessary to meet the limitations of the aircraft's maneuverability, including the maximum allowable overload and the turning radius. Due to the structure of the aircraft and the pilot's physical endurance, the overload of the aircraft generally does not exceed 9G, and the angle of attack, sideslip angle, and rudder deflection angle of the aircraft are also important factors restricting the flight performance of the aircraft and are closely related to the overload. In addition, without considering factors such as wind force, wind direction, aircraft fuselage width, airway width, and aircraft controllability, the turning radius of the aircraft generally should not be less than three times the aircraft length. Therefore, the overload limit and turning radius of the aircraft are used as two constraint conditions in the fitness function.

[0070] The B-spline curve of the air target track is a smooth curve, and x(t), y(t), and z(t) respectively represent the smooth curve functions in the three directions of longitude, latitude, and altitude:

[0071]

[0072] Regarding the air target track as the motion track of a particle in space, the ground velocity vector and overload vector of the particle can be given by the first and second derivatives of the function in Equation (12):

[0073]

[0074] The overload value of the air target at each track point can be obtained from Equation (13):

[0075]

[0076] The overload vector a can be decomposed into a tangential overload a τ and a normal overload a n in two parts. Among them, the normal overload a n i.e., the centripetal overload. According to Newton's second law, the centripetal overload is generated by the centripetal force. In circular motion, its relationship with the speed is:

[0077]

[0078] In the formula, r is the radius of circular motion; a τ is the projection of a on v, then:

[0079] |a τ | = (v·a) / |v| (16)

[0080] Then:

[0081]

[0082] Calculate the turning radius of the target from (15) and (17):

[0083]

[0084] In the formula, (v·a) = x'(t)x″(t) + y'(t)y″(t) + z'(t)z″(t).

[0085] Intuitively, the entire arc length of the cubic B-spline curve is the entire flight path of the aircraft, and it is required that the curvature radius of each point on the curve should be greater than or equal to the minimum turning radius of the aircraft, which is equivalent to judging by overload. If it is satisfied then it is considered to meet the aircraft flight restriction conditions; if not, the knot vector of the cubic B-spline needs to be adjusted, and this step is realized by the adaptive adjustment of the genetic algorithm.

[0086] Combining the above constraint conditions, the fitness function that meets the track smoothing can be expressed as:

[0087]

[0088] Because the chi-square test value, AIC, and BIC are all the smaller the better for the smoothing effect, while the genetic algorithm is to find the maximum value of the model, so take the opposite here. At the same time, under the aircraft dynamics constraint conditions, the fitness function is not necessarily the larger the better. Although it can better approximate the original target track, it cannot achieve the smoothing effect of the track. Therefore, the maximum fitness function value that can meet the aircraft dynamics constraint conditions can be selected.

[0089] In the design of the genetic algorithm, the selection operator is implemented in two ways. For each iteration process, the optimal chromosome in the parent generation is directly inherited to the next generation using the elitist retention strategy, and the remaining chromosomes are selected by roulette wheel, ensuring that chromosomes with higher fitness values have a greater chance of being selected than those with lower fitness values, improving the efficiency of the algorithm to adjust the node vector and avoiding the abandonment of excellent chromosomes. Select an appropriate crossover probability and perform crossover in a single-point crossover manner, calculate the fitness value of the new chromosome, and compare it with the fitness value of its parent chromosome; and cross the number of chromosomes in this generation until the original population size is restored. For the chromosome c to be mutated determined by the mutation probability Pm in the parent population, after randomly determining the position of its mutated gene, perform a complement operation on this gene to generate a new chromosome e. Then compare the fitness values of the two chromosomes before and after mutation, and retain the chromosome with the larger fitness value as the offspring chromosome to ensure that the population does not degenerate. In addition to the selection of the selection, crossover, and mutation operators, it is also necessary to determine the population size K, the chromosome length L, the node rate η, the crossover probability Pc, and the mutation probability Pm. K represents the size of the search space for each iteration of the algorithm. If K is too small, the search space of the algorithm is too small, and the algorithm may stop iterating before finding the optimal node vector and fall into a local optimum; if K is too large, the computational amount will increase. L determines the number of final nodes. A larger L indicates that the initial chromosome contains more nodes, which is beneficial to searching for the global optimal solution, but the computational amount will be relatively large. Generally, it is more appropriate to select two-thirds of the number of original track data points. η determines the number of internal nodes in the initial population. Pc and Pm are not limited to the parameter range of the standard genetic algorithm.

[0090] In the specific algorithm implementation, refer to Figure 2 As shown, the optimal cubic B-spline node vector is adaptively adjusted through the genetic algorithm. Then, the control vertices of the cubic B-spline curve are inversely calculated using the least squares method, and the smoothed target track is calculated in combination with the spline basis function, so that the smoothed target track meets the maneuverability limitations of the aircraft and retains the detailed features of the track, improving the quality and accuracy of the target track.

[0091] Furthermore, based on the above method, an embodiment of the present invention also provides an air target track smoothing system based on an improved cubic B-spline curve, including: a data point parameterization module, a node vector adaptive adjustment module, and a curve smoothing processing module, where,

[0092] The data point parameterization module is used to construct a cubic B-spline curve of the original track data of the air target and parameterize the target track data points;

[0093] The node vector adaptation and adjustment module is used to adaptively adjust the node vector of the parameterized curve using the genetic algorithm. In the adaptive adjustment, the control vertices of the B-spline curve are obtained using the least squares method, and the chromosome is constructed based on the candidate genes of the node distribution positions. The overload limit and turning radius of the airborne target are used as the constraint conditions of the fitness function, and the fitness function is used to find the optimal node vector to make the target track data meet the maneuverability requirements of the airborne target during the smoothing process;

[0094] The curve smoothing processing module is used to smooth the target track using the adjusted node vector.

[0095] To verify the effectiveness of the solution in this case, the following further explanations are made in combination with the experimental data:

[0096] Taking a certain type of aircraft as an example, the maximum available overload limit is 9G, the maximum flight speed is 604 m / s, and the aircraft length is 15.09 m. The target track data is from the adsbexchange public website, and the data contains multiple information such as flight number, icao number, longitude, latitude, altitude, speed, heading, and climb rate, which can provide support for analyzing the maneuverability of the aircraft. As shown in Figure 3 the original track data of the airborne target, it can be seen that there are many burrs on the track, which does not meet the maneuverability requirements of the aircraft. Therefore, in order to better utilize the data, the improved cubic B-spline curve in this case is used to smooth the track data of the airborne target, improving the quality and accuracy of the data so that the track meets the maneuverability requirements of the aircraft.

[0097] The instance simulation is programmed and implemented in the MATLAB2020b environment. The node vector of the cubic B-spline curve is adaptively adjusted using the genetic algorithm. The parameter selection in the genetic algorithm is as follows: population size η = 20; chromosome length L = 100 (appropriately adjusted according to the number of track points, generally two-thirds of the number of track points); knot ratio η = 0.6; number of iterations 200 times; crossover probability Pc = 0.8; mutation probability Pm = 0.5.

[0098] Figures 3 to 5 The result graph of the track smoothing is shown. Figure 3 、 4 For the comparison of the longitude, latitude, and altitude of the target track before and after smoothing under the condition of adaptive node distribution, it can be seen that the target track smoothed by the improved cubic B-spline curve has no burrs, the track shape is smooth, and the detailed features of the original target track are retained, which is more in line with the actual movement of the aircraft during flight; Figure 5 For the overload of the aircraft after smoothing under the condition of adaptive node distribution, it does not exceed the limit of the aircraft's maneuverability, and the change trend is consistent with the change trend of the speed.

[0099] Figure 6It is an iterative graph of adaptively adjusting the knot vector of the cubic B-spline curve by the genetic algorithm. As the number of iterations increases, the fitness function value gradually converges, and the number of knots is also determined accordingly. Figure 7 It is the distribution diagram of the optimal knot vector output after the adaptive adjustment by the genetic algorithm.

[0100] Further verified by the above experimental data, in the solution of this case, by using the fitness function in the genetic algorithm to adaptively adjust and find the optimal cubic B-spline knot vector under the conditions of aircraft dynamics constraints, the smoothed target flight path can meet the maneuverability limitations of the aircraft, and retain the detailed features of the flight path, which can improve the quality and accuracy of the target flight path.

[0101] Unless otherwise specifically stated, 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.

[0102] Each embodiment in this specification is described in a progressive manner. The key point of each embodiment is to illustrate the differences from other embodiments. The same or similar parts among the embodiments can be referred to each other. For the system disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the description of the method part.

[0103] The units and method steps of each example described in combination with the embodiments disclosed herein can be implemented by electronic hardware, computer software, or a combination of the two. To clearly illustrate the interchangeability of hardware and software, the composition and steps of each example have been generally described according to functions in the above description. Whether these functions are executed in a hardware or software manner depends on the specific application and design constraints of the technical solution. Those of ordinary skill in the art can use different methods to implement the described functions for each specific application, but such implementation is not considered to exceed the scope of the present invention.

[0104] Those of ordinary skill in the art can understand that all or part of the steps in the above method can be completed by instructing relevant hardware through a program, and the program can be stored in a computer-readable storage medium, such as a read-only memory, a magnetic disk, or an optical disc, etc. Optionally, all or part of the steps of the above embodiments can also be implemented using one or more integrated circuits. Correspondingly, each module / unit in the above embodiments can be implemented in the form of hardware or in the form of a software functional module. The present invention is not limited to any specific form of combination of hardware and software.

[0105] Finally, it should be noted that the above-described embodiments are only specific embodiments of the present invention, which are used to illustrate the technical solutions of the present invention, rather than limiting it. The protection scope of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that any person skilled in the art within the technical scope disclosed by the present invention can still modify the technical solutions recorded in the foregoing embodiments, or can easily think of changes, or make equivalent replacements for some of the technical features; and these modifications, changes or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered by the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. An air target track smoothing method based on improved cubic B-spline curve, characterized in that, It includes the following content: Construct a cubic B-spline curve for the original track data of airborne targets and parameterize the target track data points; For the parameterized curve knot vector, the genetic algorithm is used for adaptive adjustment of the knot vector. In the adaptive adjustment, the least squares method is used to obtain the control vertices of the B-spline curve. Chromosomes are constructed based on the candidate genes of the knot distribution positions. The overload limit and turning radius of the airborne target are used as the constraint conditions of the fitness function, and the fitness function is used to find the optimal knot vector so that the target trajectory data can meet the maneuverability requirements of the airborne target during the smoothing process. The fitness function is expressed as: a is the overload limit vector, r is the turning radius of the airborne target's circular motion, χ is the chi-square value used to represent the deviation degree between the observed value and the inferred value, AIC and BIC are two penalty information criteria used to balance the complexity of the cubic B-spline curve and the goodness of curve smoothing, and n is the number of control vertices, m is the number of original data points, X j is the original data, d i is the control vertex, N i,k is the k-th B-spline basis function, u i is the knot vector with the serial number i; Use the adjusted knot vector to smooth the target track.

2. The method for smoothing the air target track based on the improved cubic B-spline curve according to claim 1, wherein, The constructed k-th B-spline curve equation is expressed as: where d i is the control vertex, i = 0, 1,... n, N i,k is the k-th B-spline basis function, u is the knot vector, and n is the number of knots.

3. The method for smoothing the air target track based on the improved cubic B-spline curve according to claim 1 or 2, characterized in that, In the parameterization of the target track data points, a uniform parameterization method is used for parameterization. The parameterization process is expressed as follows: i is the node serial number, and m is the number of original data points.

4. The air target track smoothing method based on an improved cubic B-spline curve according to claim 1, wherein For the knot vector of the parameterized curve, use the genetic algorithm for adaptive adjustment, including: First, convert the domain of the curve to the canonical parameter domain, set the knot values at both ends of the knot vector, and determine the range of internal knots of the curve; Then, use the genetic algorithm to adaptively adjust the internal knot vector of the curve.

5. The method for smoothing the air target track based on the improved cubic B-spline curve according to claim 4, characterized in that, Use the least squares method to obtain the control vertices of the B-spline curve, including the following content: First, through endpoint interpolation, make the boundary track data points the same as the control vertices; Then, apply the least squares principle and construct a linear equation system with the internal control vertices as unknowns based on the track data point objective function; Then, use the linear equation system and obtain all the control vertices of the cubic B-spline curve through the knot vector.

6. The method for smoothing the air target track based on the improved cubic B-spline curve according to claim 5, wherein The constructed system of linear equations is expressed as: (N T N)D = N T R, where N represents the scalar matrix of B-spline curve basis functions of (m - 2)×(n - 2), and R and D represent the coefficient matrices respectively, r i = q i -q0N 0,k (u i ) - q m-1 N n-1,k (u i ), i = 1, 2,..., m - 2, d i is the control vertex, N i,k is the k-th B-spline basis function, u i is the knot vector with serial number i, m is the number of original data points, q i is the track data point.

7. An air target track smoothing system based on an improved cubic B-spline curve, characterized in that, It includes: a data point parameterization module, a knot vector adaptive adjustment module, and a curve smoothing processing module, where The data point parameterization module is used to construct a cubic B-spline curve for the original track data of airborne targets and parameterize the target track data points; The node vector adaptation and adjustment module is used to adaptively adjust the curve node vector after parameterization by using the genetic algorithm. In the adaptive adjustment, the control vertices of the B-spline curve are obtained by using the least squares method, the chromosome is constructed based on the candidate genes of the node distribution positions, the overload limit and turning radius of the airborne target are used as the constraint conditions of the fitness function, and the fitness function is used to find the optimal node vector so that the target track data can meet the maneuverability requirements of the airborne target while in the smoothing process; the fitness function is expressed as: α is the overload limit vector, r is the turning radius of the airborne target's circular motion, χ is the chi-square value used to represent the deviation degree between the observed value and the inferred value, AIC and BIC are two penalty information criteria used to balance the complexity of the cubic B-spline curve and the goodness of curve smoothing, and n is the number of control vertices, m is the number of original data points, X j is the original data, d i is the control vertex, N i,k is the k-th B-spline basis function, u i is the node vector with the serial number i; The curve smoothing processing module is used to smooth the target track using the adjusted knot vector.

8. An electronic device, characterized in that, It includes a processor, a communication interface, a memory, and a communication bus. Among them, the processor, the communication interface, and the memory complete mutual communication through the communication bus; The memory is used to store computer programs; The processor is used to execute the programs stored on the memory and implement the method steps described in any one of claims 1 to 6 when the programs are executed.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, and when the computer program is executed by the processor, it implements the method steps described in any one of claims 1 to 6.

Images