CN114676877A - Maneuvering target track online prediction method based on dynamic sliding window identification - Google Patents
Maneuvering target track online prediction method based on dynamic sliding window identification Download PDFInfo
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Abstract
The invention provides a dynamic sliding window identification-based maneuvering target track online prediction method. The method comprises the following steps: firstly, establishing a dynamic sliding window with self-adaptive length adjustment, framing the maneuvering target track data acquired in real time on line, and endowing self-adaptive weight values to the data in the window; then calling a particle swarm algorithm to identify the kernel parameters of the Volterra series prediction model when the sliding window is updated every time, calling and adopting an equipartition grid method to initialize the position of the population for the first time, and then initializing the particle swarm by using the optimal position saved last time; and finally, performing online prediction on the maneuvering target track, and correcting the predicted value by using a residual error compensation method. Compared with the traditional trajectory prediction method, the method has the advantages that the latest trajectory data is selected as the training set through the dynamic sliding window, the online updating of model parameters is realized, the prediction accuracy is improved, meanwhile, the identification precision of the prediction model is improved and the calculation time is reduced by improving the initialization method of the particle swarm algorithm.
Description
Technical Field
The invention relates to the field of online prediction of a maneuvering target track, in particular to an online prediction method of the maneuvering target track based on dynamic sliding window identification.
Background
The track prediction refers to a process of reasonably predicting the future movement trend of a target through a maneuvering model or a prediction algorithm by combining historical track coordinate data according to current track points of the target measured by various sensors, and is widely applied to the fields of air-air confrontation, automatic driving, pedestrian tracking and the like. In recent years, with the improvement of the accuracy and precision of a sensor network for tracking a target, the track data of the target in an actual system can be updated online, while the traditional offline prediction algorithm cannot effectively utilize the track data received in real time, and the prediction result is no longer reliable along with the movement of the target. The online prediction algorithm can learn the motion rule of the maneuvering target in real time, online adjust the parameters of the prediction model, and predict the target track more quickly and accurately, so that the online prediction method has important significance in researching the maneuvering target track.
The methods for trajectory prediction are generally classified into two main categories. One type is a prediction algorithm based on an aerodynamic or kinematic model, and the algorithm needs to set parameters of a prediction model in advance according to the motion rule of a target, estimates and predicts the real-time state of the target in a recursion mode, and is suitable for target track prediction with various motion modes. However, for a moving target with high mobility, the prediction model is difficult to learn the moving characteristics of the moving target, and the problems of high modeling complexity or poor algorithm adaptability and the like are encountered, so that the prediction precision is reduced. The other type is an artificial intelligence algorithm based on target historical track data, the algorithm mainly utilizes big data to learn the motion characteristics of a maneuvering target, thereby training model parameters, constructing a track prediction model and predicting a target track with higher complexity. The literature [1] combines a convolution network and a long-term and short-term network to provide a four-dimensional flight trajectory prediction model, and the short-term trajectory prediction of an aircraft can be realized. Document [2] proposes a short-term online trajectory prediction method based on a GRU loop network, which realizes online prediction of a short-term flight trajectory by training network parameters in batch processing and updating the parameters online according to a real-time trajectory. However, the method needs a large enough data volume for training an accurate prediction model, and is often difficult to realize long-term online prediction.
Because the complex maneuvering target track has high nonlinear and time-varying characteristics, the track prediction of the maneuvering target can be realized by combining the chaos theory on the basis of the second method. Document [3] proposes a maneuvering target trajectory prediction algorithm for identifying a Volterra kernel coefficient based on an improved particle swarm algorithm, the prediction precision of a three-dimensional flight trajectory is high, but the algorithm does not consider the real-time prediction condition. Document [4] proposes a hybrid dynamic prediction algorithm, which introduces a sliding window method, trains prediction model parameters by using a least square method, and realizes online prediction of a complex system, but the least square method is easy to trap into a local extremum when searching, and has low identification precision. Aiming at the problems of low prediction precision, long time consumption and the like of the existing algorithm in the aspect of real-time trajectory prediction, the invention provides a dynamic sliding window strategy, can learn the trajectory characteristics of a maneuvering target in real time and realize on-line prediction, and meanwhile, aiming at the defects of complex calculation, slow convergence and the like of the existing algorithm in the process of identifying model parameters, the invention provides a method for initializing the population position by a grid, and the identification precision of a prediction model is increased.
The above-mentioned references are as follows:
[1]L.Ma and S.Tian.Hybrid CNN-LSTM model for aircraft 4D trajectory prediction.IEEE Access,vol.8,pp.134668–134680,2020.
[2]P.Han,W.Wang,Q.Shi and J.Yang.Real-time Short-Term Trajectory Prediction Based on GRU Neural Network.2019IEEE/AIAA 38th Digital Avionics Systems Conference(DASC),2019,pp.1-8.
[3] xi fei, xu an, Yu Xin, Li war Wu, Yang Ewu.
[4]M.Lv,X.Zhang,H.Chen,C.Ling and J.Li.An Accurate Online Prediction Model for Kiln Head Temperature Chaotic Time Series.IEEE Access,vol.8,pp. 44288-44299,2020.
Disclosure of Invention
The invention discloses a maneuvering target track online prediction method based on dynamic sliding window identification, which is characterized in that a dynamic sliding window method is provided, weighting value processing is carried out on data in a sliding window at the same time, the reliability of track data is increased, parameters of a Volterra series prediction model are identified online by using a particle swarm algorithm of an improved initialization method, the calculation consumption time is reduced, and finally a predicted value is corrected by combining a residual error compensation method, so that the track prediction precision is improved, and online accurate prediction of a maneuvering target track is realized.
In order to achieve the purpose, the invention adopts the following technical scheme:
the dynamic sliding window identification-based maneuvering target track online prediction method comprises the following steps: step 1: detecting the track data of the maneuvering target in real time, specifically:
setting a wireless sensor network to observe the position coordinate information of a maneuvering target in real time, representing the collected historical track data in a time series form, and recording as x (N), wherein N is 1,2, …, N; determining an embedding dimension m and a delay time tau of a reconstructed phase space by adopting an improved C-C method, reconstructing the historical track data to the m-dimensional phase space, and recording a multi-dimensional time sequence after reconstruction as X l，l＝1,2,…,M；
And 2, step: establishing a prediction model, specifically:
according to the embedding dimension m and the delay time tau of the reconstruction phase space in the step 1, establishing the following p-order Volterra series prediction model based on the phase space:
wherein the content of the first and second substances,
is a predicted value; h is0Is a constant term parameter; h isd(i1,i2,…,id) Is a Volterra kernel parameter of d order, i d0,1, …, m-1, d-1, 2, …, p; p is the model order; m is the embedding dimension; x (n-i)jτ) is a history track data sequence, N is 1,2, …, N, j is 1,2, …, d; τ is the delay time.
And step 3: establishing a dynamic sliding window, specifically:
determining the length of a fixed part of a dynamic sliding window according to the collected historical track data in the step 1, and recording the length as w; determining the length of a dynamic adjustment part of a sliding window according to the track characteristics of the maneuvering target and the prediction error of the algorithm, and recording as delta w; the length of the dynamic sliding window is formed by the fixed part and the dynamic adjusting part and is marked as W; for real-time moving maneuvering target, t is t1Starting time, sampling one track data into a sliding window at each time, and removing the earliest data in the window; predicting the track once at each moment; at t ═ tkAt the moment, the maneuvering target track coordinate data in the dynamic sliding window is recorded as x (j), wherein j is k, k +1, …, and k + W-1;
And 4, step 4: the length of the sliding window is dynamically adjusted, specifically:
determining the length of the dynamic adjustment part of the sliding window according to the step 3 by the track characteristics of the maneuvering target and the prediction error of the algorithm; from said t to t1Starting prediction at moment, setting a prediction time period as T, and dynamically adjusting the length of a sliding window before the period of each time is started; defining the average value fluctuation of the track data in the r-th time period as VrThe average absolute prediction error in the r-th time period is Er(ii) a Calculating the length delta w of a dynamic adjustment part according to the track data mean value fluctuation and the average absolute prediction error;
and 5: weighting the data in the sliding window, specifically:
selecting the latest maneuvering target track data on line according to the dynamic sliding window constructed in the step 3 and the step 4, performing phase space reconstruction on the data in the window by using the embedding dimension M and the delay time tau, and changing the data into an input data form of a Volterra series prediction model, wherein the input data form is marked as U (l), and l is 1,2, … and M; combining sigmoid function, giving weight to each data in the dynamic sliding window according to the increasing principle, and marking as alphal， l＝1,2,…,M；
Step 6: calling a particle swarm algorithm and setting initial parameters, specifically:
Obtaining the number of dynamic sliding windows with weights according to step 5Taking the data as training data of a particle swarm algorithm; the iteration times of the particle swarm optimization are set to start from the ite of 1, and the maximum iteration time is the itemaxThe population size is NP, the search space dimension is D, and the search upper limit is
The lower search limit is x.
And 7: setting a population initial position, specifically:
judging whether the particle swarm algorithm is called for the first time or not according to the dynamic sliding window and the initial parameters of the particle swarm algorithm obtained in the steps 5 and 6;
if so, initializing the population position by adopting an equipartition grid method: first, the search is capped
And the search lower limit x is divided into q +1 interval values I on averagek(ii) a Every interval value IkGrid vector expanded to D dimension
For the D-dimensional grid vector
Starting from dimension 1, the value I is added1Are sequentially replaced by IkK is 2,3, … q +1, and the remaining D-1 dimensions are still I1Recording the grid vector generated by each change until the D dimension; by analogy, all grid vectors
Repeating the above process; co-generating (q +1) × ((D × q) +1) a set of D-dimensional grid vectors using the method; substituting the grid vectors into a fitness function, selecting the NP-network grid vector with the minimum fitness value as a population initial position of the particle swarm algorithm, and recording the NP-network grid vector as the population initial position of the particle swarm algorithm 
Otherwise, use last guaranteeThe stored optimal position of the particle is taken as the initial position of the particle swarm calling the particle swarm algorithm at this time and recorded as the initial position
And 8: particle swarm identification optimization, specifically:
obtaining the initial position of the particle swarm according to the step 7
Simultaneous random initialization of particle group velocities
And starting loop iteration, and in the ith iteration, j: vector the position of the population
Substituting the weighted fitness function in sequence
In the case of 1,2, …, NP, the fitness value of the entire particle is calculated; obtaining the historical optimal position pbest of the ith particle according to the fitness valueiAnd the optimal historical position gbest of the j-th iteration of the population; evolving the population position according to the speed and position evolution rule; repeating the above process until the maximum iteration time ite is reachedmaxAnd storing the optimal position of the population.
And step 9: trajectory prediction, specifically:
and (4) taking the optimal particle position obtained in the step (8) as a parameter of the Volterra series prediction model, taking the data in the dynamic sliding window as input data of the prediction model, and calculating to obtain the time t-t of the maneuvering targetkSingle step track prediction value of time
Step 10: the residual compensation method corrects the predicted value, specifically:
sheet obtained according to step 9Step-by-step extrapolation prediction value 
Calculating the deviation between the actual value x (k) and the actual value x (k), recording as delta E (k), and storing a deviation vector with the maximum length being the length W of the dynamic sliding window, recording as delta E; using a recursive least square algorithm, wherein an input item is track coordinate data in the dynamic sliding window, an expected output item is the deviation vector delta E, and solving a predicted residual error compensation value res (k +1) at the next moment; adding the predicted residual compensation value res (k +1) of the next moment and the single-step predicted value of the prediction model of the next moment to obtain a corrected track predicted value, and recording the corrected track predicted value as
Step 11: and repeating the step 3 to the step 10 until the maneuvering target track is stopped being predicted.
Xl＝[x(l),x(l+τ),…,x(l+(m-1)τ)]T,l＝1,2,…,M
and M-N- (M-1) tau is the number of multi-dimensional space phase points after the historical track data sequence is reconstructed.
The length W of the dynamic sliding window in step 3 is calculated by the following method:
W＝w+Δw
wherein w is the length of the fixed part, and the size of the fixed part is determined by the collected data volume of the historical track; Δ w is the length of the dynamic adjustment section, the size of which is determined by the trajectory data characteristics and the prediction error fluctuation.
The length Δ w of the dynamic adjustment part of the sliding window in step 4 is calculated by the following method:
In the formula (I), the compound is shown in the specification,
wherein, λ and μ are smoothing factors for adjusting Δ w; delta (delta is more than or equal to 0 and less than or equal to 1) and epsilon (epsilon is more than or equal to 0 and less than or equal to 1) are set adjusting threshold values; z is a linear or branched memberrThe trace data in the r time period; var represents the variance; max and min represent the maximum and minimum values, respectively; Δ ejThe error is predicted for the trajectory during the r-th time period.
In step 5, the input data of the Volterra series prediction model is denoted as u (l), where l is 1,2, …, and M has the following specific form:
U(l)＝[1,x(l+(m-1)τ),…,x(l),x2(l+(m-1)τ),…,x2(l),…,xp(l)]T
wherein, M ═ W- (M-1) τ is the number of multidimensional space phase points after data reconstruction in the dynamic sliding window; m is the embedding dimension; τ is the delay time; and p is the order of a Volterra series prediction model.
Step 5, the self-adaptive weight alpha of each data in the sliding windowlThe following method is adopted for calculation:
in the formula (I), the compound is shown in the specification,
al＝1/(1+e(-10*l+5))
the weight of the trajectory data which is farther back in the dynamic sliding window is larger;
the search space dimension D in step 6 is calculated by the following method:
wherein p is the order of the Volterra series prediction model; m is the embedding dimension; c is a combination formula.
The interval value I in step 7kAnd the grid vector
Respectively adopting the following methods to calculate:
wherein the content of the first and second substances,
andxrespectively as an upper particle search limit and a lower particle search limit; q is a search space average value; d is the search space dimension.
Fitness value of the ith particle in step 8
The following method is adopted for calculation:
wherein alpha islIs the weight of the set I data; y (l) is a desired output item for the set of data; u (l) is the l-th set of input data; u shapeT(l) Transposed form of U (l);
is the position vector of the ith particle.
And 8, calculating the speed and position evolution rule of the ith particle of the particle swarm by adopting the following method:
wherein v isiIs the velocity of the ith particle; ω is the inertial weight of the particle; c. C1And c2Is a learning factor; r is1And r2Is [0,1 ]]Random numbers within the interval; pbesti(j) The historical optimal position of the ith particle in the jth iteration is taken as the position of the ith particle;
the position of the ith particle in the jth iteration is taken as the position of the ith particle; and gbest (j) is the optimal position of the group history of the j iteration.
In step 10, the maximum length is a deviation vector Δ E of the length W of the dynamic sliding window, and the specific form is as follows:
ΔE＝[Δe(k-W+1),Δe(k-W+2),…,Δe(k)]
wherein the content of the first and second substances,
w is the length of the dynamic sliding window.
The corrected predicted trajectory values in step 10
The following method is adopted for calculation:
wherein the content of the first and second substances,
the corrected predicted value is obtained;
a predicted value calculated for the Volterra prediction model; res (k +1) is t ═ tk+1And residual compensation value of the moment predicted value.
The invention has the beneficial effects that:
By the technical scheme, the invention provides the online mobile target track prediction method based on dynamic sliding window identification aiming at the problems of low prediction precision, long time consumption and the like of the existing online mobile target track prediction algorithm.
Firstly, in data processing, because all maneuvering modes of a target are difficult to obtain, track coordinate data of the maneuvering target can be obtained only through sensor network observation, in order to increase the reliability of the data, the invention provides a dynamic sliding window strategy with weight, real-time track data is obtained on line, and meanwhile, a prediction model parameter is updated before prediction every time, so that the prediction precision is improved, and online track prediction is realized;
secondly, in the aspect of model identification, because the standard particle swarm algorithm is difficult to obtain the optimal solution when identifying and predicting model parameters, and the identification process cannot be reproduced, in order to improve the identification effect of the model, the invention provides a space grid initialization method for identifying the parameters of the prediction model for the first time, and meanwhile, the stored optimal particle position is called to initialize the particle swarm when updating the model parameters, so that the identification time is reduced;
finally, in the aspect of track prediction, because the parameters of the prediction model are identified by adopting an online identification method combined with a dynamic sliding window, the prediction error is gradually increased due to long-term accumulation, in order to avoid the situation, the invention provides a residual error compensation method to correct the predicted value of each time, the corrected value is used as the final prediction result, and the track prediction precision is increased.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a diagram of a dynamic sliding window model according to the present invention.
FIG. 3 is a diagram of a sliding window weighting process of the present invention.
FIG. 4 is a schematic diagram of the residual error compensation method of the present invention
FIG. 5 is a diagram of the maneuver trajectory of the unmanned aerial vehicle
FIG. 6 is a diagram of the predicted deviation of the trajectory of the UAV under the method of the present invention
Detailed Description
The technical solutions of the present invention will be described clearly and completely with reference to the accompanying drawings, and it should be understood that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1: the maneuvering target track online prediction method based on dynamic sliding window identification comprises the following steps:
step 1: detecting the track data of the maneuvering target in real time, specifically:
setting a wireless sensor network to observe the position coordinate information of a maneuvering target in real time, representing the collected historical track data in a time series form, and recording as x (N), wherein N is 1,2, …, N; determining an embedding dimension m and a delay time tau of a reconstructed phase space by adopting an improved C-C method, reconstructing the historical track data to the m-dimensional phase space, and recording a multi-dimensional time sequence after reconstruction as XlThe concrete form is as follows:
Xl＝[x(l),x(l+τ),…,x(l+(m-1)τ)]T,l＝1,2,…,M
and M-N- (M-1) tau is the number of multi-dimensional space phase points after the historical track data sequence is reconstructed.
Step 2: establishing a prediction model, specifically:
according to the embedding dimension m and the delay time tau of the reconstruction phase space in the step 1, establishing the following p-order Volterra series prediction model based on the phase space:
wherein the content of the first and second substances,
is a predicted value; h is0Is a constant term parameter; h isd(i1,i2,…,id) Is a Volterra kernel parameter of d order, id0,1, …, m-1, d-1, 2, …, p; p is the model order; m is the embedding dimension; x (n-i)jτ) is a history track data sequence, N is 1,2, …, N, j is 1,2, …, d; τ is the delay time.
And 3, step 3: establishing a dynamic sliding window, specifically:
determining the length of a fixed part of a dynamic sliding window according to the collected historical track data in the step 1, and recording the length as w; determining the length of a dynamic adjustment part of a sliding window according to the track characteristics of the maneuvering target and the prediction error of the algorithm, and recording as delta w; the length of the dynamic sliding window is formed by the fixed part and the dynamic adjusting part and is marked as W; for real-time moving maneuvering target, t is t1Starting time, sampling one track data into a sliding window at each time, and removing the earliest data in the window; predicting the track once at each moment; at t ═ tkAt the moment, the maneuvering target track coordinate data in the dynamic sliding window is recorded as x (j), wherein j is k, k +1, …, and k + W-1; the dynamic sliding window model is shown in FIG. 2;
wherein, the length W of the dynamic sliding window in step 3 is calculated by the following method:
W＝w+Δw
wherein w is the length of the fixed part, and the size of the fixed part is determined by the collected data volume of the historical track; Δ w is the length of the dynamic adjustment section, the size of which is determined by the trajectory data characteristics and the prediction error fluctuation.
And 4, step 4: the length of the sliding window is dynamically adjusted, specifically:
The length of the dynamic adjustment part of the sliding window is determined by the track characteristics of the maneuvering target and the prediction error of the algorithm according to the step 3; from said t to t1Starting prediction at moment, setting a prediction time period as T, and dynamically adjusting the length of a sliding window before the period of each time is started; defining the average value fluctuation of the track data in the r-th time period as VrThe average absolute prediction error in the r-th time period is Er(ii) a Calculating the length delta w of a dynamic adjustment part according to the track data mean value fluctuation and the average absolute prediction error;
wherein, the length Δ w of the dynamic adjustment part of the sliding window in step 4 is calculated by the following method:
in the formula (I), the compound is shown in the specification,
wherein, λ and μ are smoothing factors for adjusting the magnitude of Δ w; delta (delta is more than or equal to 0 and less than or equal to 1) and epsilon (epsilon is more than or equal to 0 and less than or equal to 1) are set adjusting threshold values; zrThe trace data in the r time period; var represents the variance; max and min represent the maximum and minimum values, respectively; Δ ejThe error is predicted for the trajectory during the r-th time period.
And 5: weighting the data in the sliding window, specifically:
selecting the latest maneuvering target track data on line according to the dynamic sliding window constructed in the step 3 and the step 4, performing phase space reconstruction on the data in the window by using the embedding dimension M and the delay time tau, and changing the data into an input data form of a Volterra series prediction model, wherein the input data form is marked as U (l), and l is 1,2, … and M; combining sigmoid function, giving weight to each data in the dynamic sliding window according to the increasing principle, and marking as alpha l1,2, …, M; the sliding window weighting process is illustrated in fig. 3;
wherein, the input data of the Volterra series prediction model in step 5 is denoted as u (l), and l is 1,2, …, M, and the specific form is as follows:
U(l)＝[1,x(l+(m-1)τ),…,x(l),x2(l+(m-1)τ),…,x2(l),…,xp(l)]T
wherein, M ═ W- (M-1) τ is the number of multidimensional space phase points after data reconstruction in the dynamic sliding window; m is the embedding dimension; τ is the delay time; and p is the order of a Volterra series prediction model.
The respective data weights α within the sliding window in step 5lThe following method is adopted for calculation:
in the formula (I), the compound is shown in the specification,
al＝1/(1+e(-10*l+5))
the weight of the trajectory data which is farther back in the dynamic sliding window is larger;
step 6: calling a particle swarm algorithm and setting initial parameters, specifically:
obtaining dynamic sliding window data with weight according to the step 5, and taking the dynamic sliding window data as training data of the particle swarm algorithm; setting the iteration times of the particle swarm algorithm to start from ite to 1, wherein the maximum iteration time is itemaxThe population size is NP, the search space dimension is D, and the search upper limit is
The lower search limit is x.
Wherein, the search space dimension D in step 6 is calculated by the following method:
wherein p is the order of the Volterra series prediction model; m is the embedding dimension; c is a combination formula.
And 7: setting a population initial position, specifically:
Judging whether the particle swarm algorithm is called for the first time or not according to the dynamic sliding window and the initial parameters of the particle swarm algorithm obtained in the steps 5 and 6;
if so, initializing the population position by adopting an equipartition grid method: first limiting the search to an upper limit
And the search lower limit x is divided into q +1 interval values I on averagek(ii) a Every interval value IkGrid vector expanded to D dimension
For the D-dimensional grid vector
Starting from dimension 1, the value I is added1Are sequentially replaced by IkK is 2,3, … q +1, and the remaining D-1 dimensions are still I1Recording the grid vector generated by each change until the D dimension; thereby, the device is provided withAnalogizing, all grid vectors
Repeating the above process; co-generating (q +1) × ((D × q) +1) a set of D-dimensional grid vectors using the method; substituting the grid vectors into a fitness function, selecting the NP-network grid vector with the minimum fitness value as a population initial position of the particle swarm algorithm, and recording the NP-network grid vector as the population initial position of the particle swarm algorithm
Otherwise, using the optimal position of the particle saved last time as the initial position of the particle swarm calling the particle swarm algorithm, and recording the initial position as the initial position of the particle swarm calling the particle swarm algorithm
Wherein the interval value I in step 7kAnd the grid vector
Respectively calculated by the following methods
Wherein the content of the first and second substances,
and x is the upper and lower particle search limits, respectively; q is a search space average value; d is the search space dimension.
The D-dimensional grid vector in step 7
The generated new grid vector is in the following specific form:
where each column represents a new set of D-dimensional grid vectors, for a total of D × q sets.
And 8: particle swarm identification optimization, specifically:
obtaining the initial position of the particle swarm according to the step 7
Simultaneous random initialization of group velocities
And starting loop iteration, and in the ith iteration, j: vector the position of the population
Substituting the weighted fitness function in sequence
In the case of 1,2, …, NP, the fitness value of the entire particle is calculated; obtaining the historical optimal position pbest of the ith particle according to the fitness valueiAnd the optimal historical position gbest of the j-th iteration of the population; evolving the population position according to the speed and position evolution rule; repeating the above process until the maximum iteration time ite is reachedmaxAnd storing the optimal position of the population.
Wherein the fitness value of the ith particle in step 8
The following method is adopted for calculation:
wherein alpha islIs the weight of the set I data; y (l) desired output items for the l-th set of data; u (l) is the l groupInputting data; u shapeT(l) Transposed form of U (l);
is the position vector of the ith particle.
And 8, calculating the speed and position evolution rule of the ith particle of the particle swarm by adopting the following method:
Wherein v isiIs the velocity of the ith particle; ω is the inertial weight of the particle; c. C1And c2Is a learning factor; r is1And r2Is [0,1 ]]Random numbers within the interval; pbesti(j) The historical optimal position of the ith particle in the jth iteration is taken as the position of the ith particle;
the position of the ith particle in the jth iteration is taken as the position of the ith particle; and gbest (j) is the optimal position of the group history of the j iteration.
And step 9: trajectory prediction, specifically:
and (4) taking the optimal particle position obtained in the step (8) as a parameter of the Volterra series prediction model, taking the data in the dynamic sliding window as input data of the prediction model, and calculating to obtain the time t-t of the maneuvering targetkSingle step track prediction value of time
Step 10: the residual compensation method corrects the predicted value, specifically:
extrapolating the predicted value according to the single step obtained in the step 9
Calculating the deviation between the maximum length of the deviation vector and the true value x (k), recording the deviation as delta E (k), and storing the deviation vector with the maximum length as the length W of the dynamic sliding window as delta E; using a recursive least square algorithm, wherein an input item is track coordinate data in the dynamic sliding window, an expected output item is the deviation vector delta E, and a prediction residual compensation value res (k +1) at the next moment is solved; adding the predicted residual compensation value res (k +1) at the next moment and the single-step predicted value of the prediction model at the next moment to obtain a corrected track predicted value, and recording the corrected track predicted value as the track predicted value 
The residual compensation method is shown in fig. 4;
in step 10, the maximum length is a deviation vector Δ E of the length W of the dynamic sliding window, and the specific form is as follows:
ΔE＝[Δe(k-W+1),Δe(k-W+2),…,Δe(k)]
wherein, the first and the second end of the pipe are connected with each other,
w is the length of the dynamic sliding window.
The corrected predicted trajectory values in step 10
The following method is adopted for calculation:
wherein, the first and the second end of the pipe are connected with each other,
the corrected predicted value is obtained;
a predicted value calculated for the Volterra prediction model; res (k +1) is t ═ tk+1And residual compensation value of the moment predicted value.
Step 11: and repeating the steps 3 to 10 until the maneuvering target track is stopped being predicted.
By the technical scheme, the invention provides the online mobile target track prediction method based on dynamic sliding window identification aiming at the problems of low prediction precision, long time consumption and the like of the existing online mobile target track prediction algorithm.
Firstly, in data processing, because all maneuvering modes of a target are difficult to obtain, track coordinate data of the maneuvering target can be obtained only through sensor network observation, in order to increase the reliability of the data, the invention provides a dynamic sliding window strategy with weight, real-time track data is obtained on line, and meanwhile, a prediction model parameter is updated before prediction every time, so that the prediction precision is improved, and online track prediction is realized;
Secondly, in the aspect of model identification, because the standard particle swarm algorithm is difficult to obtain the optimal solution when identifying and predicting model parameters, and the identification process cannot be reproduced, in order to improve the identification effect of the model, the invention provides a space grid initialization method for identifying the parameters of the prediction model for the first time, and meanwhile, the stored optimal particle position is called to initialize the particle swarm when updating the model parameters, so that the identification time is reduced;
finally, in the aspect of track prediction, because the parameters of the prediction model are identified by adopting an online identification method combined with a dynamic sliding window, the prediction error is gradually increased due to long-term accumulation, in order to avoid the situation, the invention provides a residual error compensation method to correct the predicted value of each time, the corrected value is used as the final prediction result, and the track prediction precision is increased.
According to the method, the dynamic sliding window method is provided, the weighted value processing is carried out on the data in the window, the reliability of the track data is improved, then the particle swarm algorithm of the improved initialization method is used for identifying the Volterra series prediction model parameters on line, the calculation time consumption is reduced, finally the predicted value is corrected by combining the residual error compensation method, the track prediction precision is improved, and the online accurate prediction of the maneuvering target track is realized.
To verify the correctness and rationality of the above embodiment, fig. 5 shows a randomly generated model with three degrees of freedom for an unmanned aerial vehicleAnd (3) combining maneuver trajectories, wherein the sampling times are 300, and the sampling interval is 0.2s, and performing online prediction on the flight trajectories by using the method disclosed by the invention. Setting the initial length of the dynamic sliding window to be 20, and performing online single-step extrapolation prediction on the next 280 track coordinate points by adopting three-dimensional coordinate independent prediction. Calculating the delay time tau and the embedding dimension m of the algorithm by an improved C-C method, and respectively obtaining the X-dimension delay time tau of the three-degree-of-freedom maneuvering track of the unmanned aerial vehicle which is 5 and the embedding dimension m which is 2; y-dimension delay time τ ═ 6, and embedding dimension m ═ 2; the Z-dimension delay time τ is 6 and the embedding dimension m is 2. The order p of the Volterra series prediction model is selected to be 2. Setting the search space average value q of the particle swarm algorithm to be 29, and searching the upper limit
Search lower limit x is-5, inertia weight ω is 0.8, learning factor c1＝c2＝2。
Fig. 6 shows the predicted deviations of the unmanned aerial vehicle trajectory in three dimensions X, Y, Z, respectively, according to the method of the present invention, it can be seen that the online predicted trajectory of the maneuvering target obtained by the method of the present invention is basically consistent with the flying maneuvering trajectory of the unmanned aerial vehicle, the predicted deviations in the three dimensions fluctuate around the zero point, and the maximum predicted deviation does not exceed 1 m. The average single-step prediction time of the method is calculated to be about 0.043s, and for the sampling interval of the sensor to be 0.2s, the method provided by the invention can be used for realizing the online prediction of the maneuvering target moving in real time.
It needs to be further explained that:
the simulation experiment simulates the generation of real-time track data through a three-degree-of-freedom model of the unmanned aerial vehicle, the unmanned aerial vehicle is taken as a mass point, a ground coordinate system is taken as an inertia coordinate system, and then the motion model is as follows:
wherein x ist，ytAnd ztRespectively representing the horizontal and height coordinates of the unmanned aerial vehicle in an inertial coordinate system; v. oft，θtAnd psitRepresenting the speed, the climbing angle and the course angle of the unmanned aerial vehicle; phi is atRepresenting the roll angle; g is the acceleration of gravity; n isxtAnd nztRespectively representing horizontal overload and longitudinal overload; [ x ] oft,yt,zt,vt,θt,ψt]TAnd [ nxt,nzt,φt]TRespectively, the state variable and the control variable of the unmanned aerial vehicle.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (10)
1. The dynamic sliding window identification-based maneuvering target track online prediction method is characterized by comprising the following steps: the method comprises the following steps:
Step 1: detecting the track data of the maneuvering target in real time, specifically:
setting a wireless sensor network to observe the position coordinate information of a maneuvering target in real time, representing the collected historical track data in a time series form, and recording as x (N), wherein N is 1,2, …, N; determining an embedding dimension m and a delay time tau of a reconstructed phase space by adopting an improved C-C method, reconstructing the historical track data to the m-dimensional phase space, and recording a multi-dimensional time sequence after reconstruction as Xl，l＝1,2,…,M；
Step 2: establishing a prediction model, specifically:
according to the embedding dimension m and the delay time tau of the reconstruction phase space in the step 1, establishing the following p-order Volterra series prediction model based on the phase space:
wherein the content of the first and second substances,
is a predicted value; h is0Is a constant term parameter; h isd(i1,i2,…,id) Is a Volterra kernel parameter of d order, id0,1, …, m-1, d-1, 2, …, p; p is the model order; m is the embedding dimension; x (n-i)jτ) is a history track data sequence, N is 1,2, …, N, j is 1,2, …, d; τ is the delay time;
and step 3: establishing a dynamic sliding window, specifically:
determining the length of a fixed part of a dynamic sliding window according to the collected historical track data in the step 1, and recording the length as w; determining the length of a dynamic adjustment part of a sliding window according to the track characteristics of the maneuvering target and the prediction error of the algorithm, and recording as delta w; the length of the dynamic sliding window is formed by the fixed part and the dynamic adjusting part and is marked as W; for real-time moving maneuvering target, t is t 1Starting time, sampling one track data into a sliding window at each time, and removing the earliest data in the window; predicting the track once at each moment; at t ═ tkAt the moment, the maneuvering target track coordinate data in the dynamic sliding window is recorded as x (j), wherein j is k, k +1, …, and k + W-1;
and 4, step 4: the length of the sliding window is dynamically adjusted, specifically:
determining the length of the dynamic adjustment part of the sliding window according to the step 3 by the track characteristics of the maneuvering target and the prediction error of the algorithm; from said t to t1Starting prediction at moment, setting a prediction time period as T, and dynamically adjusting the length of a sliding window before the period of each time is started; defining the average value fluctuation of the track data in the r-th time period as VrThe average absolute prediction error in the r-th time period is Er(ii) a Calculating the length delta w of a dynamic adjustment part according to the track data mean value fluctuation and the average absolute prediction error;
and 5: weighting the data in the sliding window, specifically:
selecting the latest maneuvering target track data on line according to the dynamic sliding window constructed in the step 3 and the step 4, performing phase space reconstruction on the data in the window by using the embedding dimension M and the delay time tau, and changing the data into an input data form of a Volterra series prediction model, wherein the input data form is marked as U (l), and l is 1,2, … and M; combining sigmoid function, giving weight to each data in the dynamic sliding window according to the increasing principle, and marking as alpha l，l＝1,2,…,M；
And 6: calling a particle swarm algorithm and setting initial parameters, specifically:
obtaining dynamic sliding window data with weight according to the step 5, and taking the dynamic sliding window data as training data of the particle swarm algorithm; the iteration times of the particle swarm optimization are set to start from the ite of 1, and the maximum iteration time is the itemaxThe population size is NP, the search space dimension is D, and the search upper limit is
Lower limit of searchx；
And 7: setting a population initial position, specifically:
judging whether the particle swarm algorithm is called for the first time or not according to the dynamic sliding window and the initial parameters of the particle swarm algorithm obtained in the steps 5 and 6;
if so, initializing the population position by adopting an equipartition grid method: firstly, dividing the search upper limit x and the search lower limit x into q +1 interval values I on averagek(ii) a Every interval value IkGrid vector expanded to D dimension
For the D-dimensional grid vector
Starting from dimension 1, the value I is added1Are sequentially replaced by IkK is 2,3, … q +1, and the remaining D-1 dimensions are still I1Recording the grid vector generated by each change until the D dimension; by analogy, the instituteWith lattice vectors
Repeating the above process; co-generating (q +1) × ((D × q) +1) a set of D-dimensional grid vectors using the method; substituting the grid vectors into a fitness function, selecting the NP-network grid vector with the minimum fitness value as a population initial position of the particle swarm algorithm, and recording the NP-network grid vector as the population initial position of the particle swarm algorithm 
Otherwise, using the optimal position of the particle stored last time as the initial position of the particle swarm calling the particle swarm algorithm, and recording the initial position as the initial position of the particle swarm calling the particle swarm algorithm
And step 8: particle swarm identification optimization, specifically:
obtaining the initial position of the particle swarm according to the step 7
Simultaneous random initialization of group velocities
Starting loop iteration, and iterating for a turn j at the ite: vector the position of the population
Sequentially substituting into the weighted fitness function
Calculating the fitness value of the whole particle, wherein i is 1,2, …, NP; obtaining the historical optimal position pbest of the ith particle according to the fitness valueiAnd the optimal historical position gbest of the j-th iteration of the population; evolving the population position according to the speed and position evolution rule; repeating the above process until the maximum iteration time ite is reachedmaxStoring the optimal position of the population；
And step 9: trajectory prediction, specifically:
and (4) taking the optimal particle position obtained in the step (8) as a parameter of the Volterra series prediction model, taking the data in the dynamic sliding window as input data of the prediction model, and calculating to obtain the time t-t of the maneuvering targetkSingle step track prediction value of time
Step 10: the residual compensation method corrects the predicted value, specifically:
extrapolating the predicted value according to the single step obtained in the step 9 
Calculating the deviation between the actual value x (k) and the actual value x (k), recording as delta E (k), and storing a deviation vector with the maximum length being the length W of the dynamic sliding window, recording as delta E; using a recursive least square algorithm, wherein an input item is track coordinate data in the dynamic sliding window, an expected output item is the deviation vector delta E, and a prediction residual compensation value res (k +1) at the next moment is solved; adding the predicted residual compensation value res (k +1) at the next moment and the single-step predicted value of the prediction model at the next moment to obtain a corrected track predicted value, and recording the corrected track predicted value as the track predicted value
Step 11: and repeating the steps 3 to 10 until the maneuvering target track is stopped being predicted.
2. The dynamic sliding window identification-based maneuvering target trajectory online prediction method according to claim 1, characterized by: step 1, recording the reconstructed multidimensional time sequence as XlThe concrete form is as follows:
Xl＝[x(l),x(l+τ),…,x(l+(m-1)τ)]T,l＝1,2,…,M
and M-N- (M-1) tau is the number of multi-dimensional space phase points after the historical track data sequence is reconstructed.
3. The dynamic sliding window identification-based maneuvering target trajectory online prediction method according to claim 1, characterized by: the length W of the dynamic sliding window in step 3 is calculated by the following method:
W＝w+Δw
wherein w is the length of the fixed part, and the size of the fixed part is determined by the collected data volume of the historical track; Δ w is the length of the dynamic adjustment section, the size of which is determined by the trajectory data characteristics and the prediction error fluctuation.
4. The dynamic sliding window identification-based maneuvering target trajectory online prediction method according to claim 1, characterized by: the length Δ w of the dynamic adjustment part of the sliding window in step 4 is calculated by the following method:
in the formula (I), the compound is shown in the specification,
wherein, λ and μ are smoothing factors for adjusting the magnitude of Δ w; delta (0. ltoreq. delta. ltoreq.1) and epsilon (0. ltoreq. epsilon. ltoreq.1) as settingsA threshold value; z is a linear or branched memberrThe trace data in the r time period; var represents variance; max and min represent the maximum and minimum values, respectively; Δ ejThe error is predicted for the trajectory during the r-th time period.
5. The dynamic sliding window identification-based maneuvering target trajectory online prediction method according to claim 1, characterized by: in step 5, the input data of the Volterra series prediction model is denoted as u (l), where l is 1,2, …, and M has the following specific form:
U(l)＝[1,x(l+(m-1)τ),…,x(l),x2(l+(m-1)τ),…,x2(l),…,xp(l)]T
wherein, M ═ W- (M-1) τ is the number of multidimensional space phase points after data reconstruction in the dynamic sliding window; m is the embedding dimension; τ is the delay time; p is the Volterra series prediction model order;
step 5, the self-adaptive weight alpha of each data in the sliding windowlThe following method is adopted for calculation:
in the formula (I), the compound is shown in the specification,
al＝1/(1+e(-10*l+5))
wherein the later trajectory data in the dynamic sliding window has a greater weight.
6. The dynamic sliding window identification-based maneuvering target trajectory online prediction method according to claim 1, characterized by: the search space dimension D in step 6 is calculated by the following method:
wherein p is the order of the Volterra series prediction model; m is the embedding dimension; c is a combination formula.
7. The dynamic sliding window identification-based maneuvering target trajectory online prediction method according to claim 1, characterized by: interval value I in step 7kAnd the grid vector
Respectively adopting the following methods to calculate:
wherein the content of the first and second substances,
andxrespectively as an upper particle search limit and a lower particle search limit; q is a search space average value; d is the search space dimension.
8. The dynamic sliding window identification-based online trajectory prediction method for a mobile object according to claim 1, wherein: fitness value of the ith particle in step 8
The following method is adopted for calculation:
wherein alpha islIs the weight of the set I data; y (l) is a desired output item for the set of data; u (l) is the l-th set of input data; u shapeT(l) Transposed form of U (l);
is the position vector of the ith particle;
and 8, calculating the speed and position evolution rule of the ith particle of the particle swarm by adopting the following method:
Wherein v isiIs the velocity of the ith particle; ω is the inertial weight of the particle; c. C1And c2Is a learning factor; r is1And r2Is [0,1 ]]Random numbers within the interval; pbesti(j) The historical optimal position of the ith particle in the jth iteration is taken as the position of the ith particle;
the position of the ith particle in the jth iteration is taken as the position of the ith particle; and gbest (j) is the optimal position of the group history of the j iteration.
9. The dynamic sliding window identification-based maneuvering target trajectory online prediction method according to claim 1, characterized by: in step 10, the maximum length is a deviation vector Δ E of the length W of the dynamic sliding window, and the specific form is as follows:
ΔE＝[Δe(k-W+1),Δe(k-W+2),…,Δe(k)]
wherein the content of the first and second substances,
w is the length of the dynamic sliding window.
10. The dynamic sliding window identification-based maneuvering target trajectory online prediction method according to claim 1, characterized by: the corrected predicted trajectory values in step 10
The following method is adopted for calculation:
wherein the content of the first and second substances,
the corrected predicted value is obtained;
a predicted value calculated for the Volterra prediction model; res (k +1) is t ═ tk+1And residual compensation value of the moment predicted value.
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| CN115933787A (en) * | 2023-03-14 | 2023-04-07 | 西安英图克环境科技有限公司 | Indoor multi-terminal intelligent control system based on indoor environment monitoring |
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| CN115113038B (en) * | 2022-08-19 | 2022-12-30 | 国网江西省电力有限公司电力科学研究院 | Circuit breaker fault diagnosis method based on current signal phase space reconstruction |
| CN115933787A (en) * | 2023-03-14 | 2023-04-07 | 西安英图克环境科技有限公司 | Indoor multi-terminal intelligent control system based on indoor environment monitoring |
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