CN111797478A - A Strong Maneuvering Target Tracking Method Based on Variable Structure Multiple Models - Google Patents

Abstract

A strong maneuvering target tracking method based on variable structure multi-models relates to the field of target tracking, and aims at the problem that when a high-speed strong maneuvering target in an adjacent space is tracked, the target tracking accuracy is low, and the method comprises the following steps: constructing a dynamic tracking model set by using the dynamic characteristics of the target aircraft, and then acquiring a state equation set of a maneuvering target tracking system; step two: establishing a system measurement model, and obtaining a measurement equation and measurement noise of the system according to the established system measurement model; step three: and carrying out recursive estimation on the motion state and the pneumatic parameters of the target aircraft based on the state equation set of the system, the measurement equation of the system and the measurement noise. According to the method, the dynamic tracking model set is constructed based on the dynamic characteristics of the target aircraft, the description precision of target motion is improved, and the target tracking precision is improved by adopting an improved variable-structure multi-model tracking algorithm.

Description

A Strong Maneuvering Target Tracking Method Based on Variable Structure Multiple Models

technical field

The invention relates to the field of target tracking, in particular to a strong maneuvering target tracking method based on variable structure and multiple models.

Background technique

In the field of target tracking, Kalman filtering is usually used for tracking, and the algorithm is combined with the target motion model and measurement data to correct the measurement data. It mainly solves three problems: first, the measurement error of the observer, including constant deviation and random deviation, the instability and accuracy of the measurement data have been corrected in the target tracking algorithm; the second is the target's maneuvering, Since the target and the tracking party belong to different institutions, the maneuvering mode of the target cannot be accurately obtained, and its maneuvering has great randomness and uncertainty. During the tracking process, it is possible to identify whether the target has maneuvered according to the residual error, and provide a reference The third is that the sensor can only detect the position data of the target, and the speed and related parameter data of the target cannot be obtained. In the target tracking algorithm, the target state vector can be expanded, and then the estimated value of the relevant parameters can be obtained. Knowledge of target motion patterns also improves the accuracy of target tracking.

The field of near space refers to the airspace between 20 and 100 km from the ground. The flying speed of high-speed aircraft in this space can reach Mach 5 or more, and due to the characteristics of the thin atmosphere in the near space, the aircraft has a certain maneuverability, and its speed, acceleration parameters change drastically. This type of vehicle can achieve flexible maneuverability, rapid response and super penetration, and has strategic deterrence and actual combat application capabilities. It has important strategic significance for deterring strong enemies, controlling crises and winning wars. In the field of defense, traditional tracking algorithms have been unable to achieve accurate tracking, which is very difficult to track and predict ultra-high-speed targets in near space. Therefore, it is of great military and practical significance to carry out the research on the tracking algorithm of strong maneuvering targets in the near space.

At present, for the tracking of strong maneuvering targets, the commonly used models include the current statistical model, the Jerk model and other kinematic models. Near space tracking often uses a multi-model combination algorithm to perform fusion output and match the different maneuvering modes of the aircraft. Among the variable structure tracking algorithms, the IMM algorithm has the best tracking accuracy, but has certain limitations on the setting value of the tracking model; the variable structure multi-model algorithm (VSMM algorithm) based on directed graph switching can solve this problem, but in the model However, the delay problem is serious during switching; the adaptive variable structure algorithm (AGIMM algorithm) has flexible response and high tracking accuracy, but over-fitting will occur in the process of tracking and fitting, resulting in fast and unstable fitting results. resulting in a larger tracking error.

SUMMARY OF THE INVENTION

The purpose of the present invention is to propose a strong maneuvering target tracking method based on variable structure and multiple models, aiming at the problem of low target tracking accuracy when tracking high-speed strong maneuvering targets in the near space.

The technical scheme that the present invention takes in order to solve the above-mentioned technical problems is:

A strong maneuvering target tracking method based on variable structure multi-model, comprising the following steps:

Step 1: Use the dynamic characteristics of the target aircraft to build a dynamic tracking model set, and then obtain the state equation set of the maneuvering target tracking system;

Step 2: establish a system measurement model, and obtain the system measurement equation and measurement noise according to the established system measurement model;

Step 3: Based on the set of state equations of the system, the measurement equations of the system and the measurement noise, recursively estimate the motion state and aerodynamic parameters of the target aircraft.

Further, the specific steps of the step 1 are:

Step 11: According to the maneuvering characteristics of the target, select the aerodynamic parameters of the tracking model,

The aerodynamic parameters of the tracking model are:

Among them, C _L (α) and C _D (α) are aerodynamic parameters, C _L (α) is the lift coefficient, C _D (α) is the drag coefficient, S is the characteristic area of the target aircraft, m is the mass of the target aircraft, α _D , α _L are drag parameters and lift parameters;

Step 1 and 2: Use Gaussian white noise to model the variation characteristics of aerodynamic parameters, and obtain the state equation of the maneuvering target tracking system. The state equation of the maneuvering target tracking system is:

为弹道坐标系到探测系的转移矩阵，θ为速度倾角，σ为方位角，γ_v为速度倾侧角，ω_γ为倾侧角的高斯白噪声，ω_D，ω_L为气动参数的高斯白噪声，R为气动力，其中

S为目标飞行器的特征面积：Among them, ω _e is the angular velocity vector of the earth's rotation, g is the acceleration of gravity of the earth, r is the position vector of the target under the detection system, v is the speed of the target under the detection system,

is the transfer matrix from the ballistic coordinate system to the detection system, θ is the velocity inclination angle, σ is the azimuth angle, γ _v is the velocity inclination angle, ω _γ is the Gaussian white noise of the inclination angle, ω _D , ω _L is the Gaussian white noise of the aerodynamic parameters , R is the aerodynamic force, where

S is the characteristic area of the target aircraft:

Step 1 and 3: Take the velocity inclination angle γ _v in Step 1 and 2 as the model variable, and select different velocity inclination angles γ _v to construct the state equation set of the maneuvering target tracking system.

Further, the steps of obtaining the measurement equation and measurement noise of the system in the second step are as follows:

Step 21: Establish a detection coordinate system according to the requirements of the tracking task, and determine the position vector of the detector and the target in the detection coordinate system;

Step 22: According to the infrared detection principle, obtain the three-dimensional position coordinates of the target aircraft under the detector system;

Step 2 and 3: Using the three-dimensional position coordinates of the target aircraft under the detector system, analyze the positioning mean square error, and determine the measurement equation and measurement noise of the tracking system.

Further, in the step 21, the position vector of the detector and the target in the detection coordinate system is:

The position vector of the target in the detection coordinate system: r=(x, y, z);

The position vector of the detector in the detection coordinate system: S _l =(x _l , y _l , z _l ), where l represents the lth detector.

Further, the specific steps of the second and second steps are:

First, the vector of the detector pointing to the target is:

The detector detection angles α _l and β _l are expressed as:

Convert to get:

Using the least squares method to obtain the three-dimensional position coordinates of the target aircraft under the detector X=(x, y, z)

其中M为量测矩阵，X为状态量，Y为量测量。The least squares representation is:

Among them, M is the measurement matrix, X is the state quantity, and Y is the quantity measurement.

Further, the specific steps of determining the measurement equation of the tracking system and the measurement noise in the steps 2 and 3 are:

First, determine the relative position and angle relationship between the target and the detector according to the geometric principle:

x₁，y₁，z₁为第一个探测器在探测系下x、y、z三个方向的位置分量；x₂，y₂，z₂为第二个探测器在探测系下x、y、z三个方向的位置分量；Δκ＝κ₂-κ₁，

In the formula,

x ₁ , y ₁ , z ₁ are the position components of the first detector in the three directions of x, y, and z under the detection system; x ₂ , y ₂ , z ₂ are the x, y, and z directions of the second detector under the detection system. Position components in the three directions of y and z; Δκ=κ ₂ -κ ₁ ,

Then the noise R is obtained by measuring the noise formula. The measuring noise formula is:

in,

和

分别为探测器自身的位置坐标的均方差，

为目标定位均方差，

为探测器探测角α1的均方误差，

为探测器探测角α2的均方误差，

为探测器探测角β1的均方误差，

为探测器探测角β2的均方误差。In the above formula, c ₁ =κ ₂ (x ₂ -x ₁ )-(y ₂ -y ₁ ), c ₂ =-κ ₁ (x ₂ -x ₁ )+(y ₂ -y ₁ );

and

are the mean square error of the position coordinates of the detector itself,

is the mean square error of target positioning,

is the mean square error of the detector detection angle α1,

is the mean square error of the detector detection angle α2,

is the mean square error of the detector detection angle β1,

is the mean square error of the detector detection angle β2.

Further, in the step 3, the improved variable structure multi-model algorithm is used to perform recursive estimation on the motion state and aerodynamic parameters of the target aircraft; the specific steps of the improved variable structure multi-model algorithm are:

The first step, enter the interaction:

M为模型全体的集合，i,j表示第i,j个模型，

M is the set of all models, i,j represent the i,jth model,

Among them, p _ij is the transition probability of model i to j, and μ _i,j (k-1/k-1) is the mixing probability

The second step, filtering

进行卡尔曼滤波，Φ_j为状态转移矩阵，预测为：For the model M _j (k) with

Kalman filtering is performed, Φ _j is the state transition matrix, and the prediction is:

The prediction error covariance is:

Filter is:

The filtering covariance is:

The observation equation estimates, the Kalman gain is:

The third step, the model probability update

Among them, Λ _j (k)=N(r _j (k),0,S _j (k)), the likelihood function of mode j at time k, defines a variable r _j (k), the mean is 0, and the variance is S The Gaussian distribution of _j (k), Λ _j (k) is:

The fourth step, output interaction:

The fifth step, model set update:

Compute the maximum model probability:

u _max =max{u ₁ ,u ₂ ,u ₃ }

The corresponding model is set as model j, then the distance function is:

Tracking model adjustment, analogous to the principle of directed graph switching for model adjustment,

When u1 _max , if D ₁ (k)≥M, then

where G ₀ is the minimum grid spacing, k ₁ , k ₂ are adjustable parameters,

If D ₁ (k)<M, the model is updated according to the method of directed graph switching, that is

When u2 _max , if D ₂ (k)≥M, then

If D ₂ (k)<M, the model is updated according to the method of directed graph switching, that is,

When u3 _max , if D ₃ (k)≥M, then

If D ₃ (k)<M, the model is updated according to the method of directed graph switching, that is,

For the initialization of the state vector and covariance of the new activation model, the probability weighted combination of each model at the previous moment is used to initialize, namely:

The beneficial effects of the present invention are:

The present invention builds a dynamic tracking model set based on the dynamic characteristics of the target aircraft, improves the description accuracy of the target motion, and further improves the target tracking accuracy by using an improved variable-structure multi-model tracking algorithm, and the present invention detects the target maneuver for the model. And the corresponding probability is updated, which improves the robustness of the target maneuver.

Description of drawings

Figure 1 is a block diagram of the tracking principle of the variable structure multi-model algorithm;

Fig. 2 is the actual motion trajectory diagram of the target in the simulation example;

Fig. 3 is the change chart of the inclination angle of the actual moving speed of the target in the simulation example;

Fig. 4 is the tracking error diagram of the variable structure tracking algorithm in the weak maneuvering state;

Fig. 5 is the fitting error diagram of each algorithm to the target tilt angle in the weak maneuvering state;

Fig. 6 is the tracking error diagram of the variable structure tracking algorithm under strong maneuvering state;

Figure 7 is a graph of the fitting error of each algorithm to the target tilt angle in a strong maneuvering state.

Detailed ways

Specific implementation one:

The present embodiment is described in detail with reference to FIG. 1 . The goal of the present invention is to improve the tracking and positioning accuracy of high-speed and strong maneuvering targets in the near space, and combine the tracking principle to predict the aerodynamic parameters of the target and detect target maneuvering. By establishing the aircraft dynamics model, the aerodynamic characteristic parameters of the target are expanded into the target tracking state quantity, and the filter tracking is performed. The above-mentioned purpose of the invention is achieved through the following technical solutions:

In step 1 of the present invention, a dynamic tracking model set is constructed according to the dynamic characteristics of the target aircraft, and a state equation set of the maneuvering target tracking system is obtained.

In step 2 of the present invention, a system measurement model is established according to the principle and distribution of the detection device; the measurement equation and measurement noise of the system are obtained. The infrared appearance measurement is the azimuth angle of the target, which belongs to passive direction finding positioning, and the target is positioned by two or more infrared detectors.

In step 3 of the present invention, based on the state equation of the system, the measurement equation of the system and the measurement noise, an improved variable structure multi-model algorithm based on target maneuver detection is used to recursively estimate the motion state and control parameters of the target aircraft.

In the present invention, the dynamic tracking model set is constructed according to the dynamic characteristics of the target aircraft in step 1, and the specific method for obtaining the state equation set of the maneuvering target tracking system is:

Step 1-1. Analyze the maneuvering characteristics of the target and select the aerodynamic parameters of the tracking model:

In the free-gliding stage, the maneuvering of the aircraft mainly comes from aerodynamic force. The method is that the aerodynamic acceleration can be divided into drag acceleration, turning acceleration and climbing acceleration along the three directions of the ballistic system by pairing, namely:

的关系。飞行攻角α频繁且幅度较大的调整，会导致气动参数变化复杂、飞行器剧烈震荡，难以控制，通常滑翔过程中α的变化率很小，气动参数随攻角变化较为平缓，即短时间内参数变化较小，可作为状态量进行估计，故本文的跟踪模型中的气动参数设置为：It can be seen from this formula that the aerodynamic parameters C _L (α) and the aerodynamic parameters exist

Relationship. The frequent and large adjustment of the flight angle of attack α will lead to complex changes in aerodynamic parameters, the aircraft will vibrate violently, and it is difficult to control. Usually, the rate of change of α during the gliding process is very small, and the aerodynamic parameters change relatively smoothly with the angle of attack, that is, in a short period of time. The parameter changes are small and can be estimated as a state quantity, so the aerodynamic parameters in the tracking model in this paper are set as:

where S is the characteristic area of the target aircraft, and m is the mass of the target aircraft. α _D , α _L are drag parameters and lift parameters. Steps 1 and 2: Use Gaussian white noise to model the variation characteristics of aerodynamic parameters to obtain the state equation of the maneuvering target tracking system:

where γ _v is the velocity tilt angle, ω _γ is the Gaussian white noise of the tilt angle, ω _D , ω _L are the Gaussian white noise of the aerodynamic parameters, R is the aerodynamic force, and the expression is as follows:

In the present invention, the velocity inclination angle _γv is used as a model variable, and different _γv are selected to construct a maneuvering target tracking model set. Further, in the present invention, the specific method for obtaining the measurement equation of the system and the measurement noise described in step 2 is:

Step 2-1. Establish a detection system according to the requirements of the tracking task, and determine the position vector of the detector and the target in the detection coordinate system;

Step 2-2, according to the infrared detection principle, obtain the three-dimensional position coordinates of the target aircraft under the detector, and realize the positioning of the target aircraft;

Steps 2-3, the three-dimensional position coordinates of the target aircraft under the detector, analyze the positioning mean square error, and determine the measurement equation and measurement noise of the tracking system.

Further, in the present invention, in step 2-1, a detection coordinate system is established according to the position of the detector, and the position vector of the detector base point and the target under the detection coordinate system is determined;

The position vector of the target under the detection system: r=(x, y, z);

The position vector of the detector base point under the detection system: S _l = (x _l , y _l , z _l ), l represents the lth detector;

The vector directed by the detector to the target is: R _l =rS _l =(xx _l , yy _l , zz _l ).

Further, in the present invention, according to the infrared detection principle described in step 2-2, the three-dimensional position coordinates of the target aircraft under the detector are obtained, and the specific method for positioning the target aircraft is:

Let the distance between the target aircraft and the detector:

Since the detector detection angles α _l and β _l have:

Convert to get:

获得目标飞行器在探测器下的三维位置坐标X＝(x,y,z)。Using the least squares method there are:

Obtain the three-dimensional position coordinates X=(x, y, z) of the target aircraft under the detector.

Further, in the present invention, the specific method for determining the measurement noise of the tracking system described in steps 2-3 is:

Determined according to geometric principles:

其中，x₁，y₁，z₁为第一个探测器在探测系下x、y、z三个方向的位置分量；x₂，y₂，z₂为第二个探测器在探测系下x、y、z三个方向的位置分量；Δκ＝κ₂-κ₁，

通过测量噪声公式：In the formula,

Among them, x ₁ , y ₁ , z ₁ are the position components of the first detector in the three directions of x, y and z under the detection system; x ₂ , y ₂ , z ₂ are the position components of the second detector under the detection system Position components in the three directions of x, y, and z; Δκ=κ ₂ -κ ₁ ,

By measuring the noise formula:

Get the noise R, where,

和

分别为探测器自身的位置坐标的均方差，

为目标定位均方差，

为探测器探测角α1的均方误差，

为探测器探测角α2的均方误差，

为探测器探测角β1的均方误差，

为探测器探测角β2的均方误差。In the above formula, c ₁ =κ ₂ (x ₂ -x ₁ )-(y ₂ -y ₁ ), c ₂ =-κ ₁ (x ₂ -x ₁ )+(y ₂ -y ₁ );

and

are the mean square error of the position coordinates of the detector itself,

is the mean square error of target positioning,

is the mean square error of the detector detection angle α1,

is the mean square error of the detector detection angle α2,

is the mean square error of the detector detection angle β1,

is the mean square error of the detector detection angle β2.

Further, in step 3 of the present invention, an improved variable structure multi-model algorithm based on target maneuver detection is used to recursively estimate the motion state and aerodynamic parameters of the target aircraft:

Determine the filter initial state quantity and initial covariance:

为滤波器初始状态量，E(x₀)为目标飞行器的初始状态量均值；取均值

为初始协方差，x₀为目标飞行器的初始状态量；in,

is the initial state quantity of the filter, E(x ₀ ) is the mean value of the initial state quantity of the target aircraft; take the mean value

is the initial covariance, and x ₀ is the initial state quantity of the target aircraft;

The mathematical expectation of a matrix composed of random variables is defined as the matrix composed of the mathematical expectations of their individual elements, E(X)=μ. The covariance matrix of a multi-dimensional random variable is a symmetric matrix, which plays the role of the variance of a one-dimensional random variable in a certain sense. The covariance matrix C of X can be expressed as:

C=E((X-μ) ^T (X-μ))

则：Assume

but:

Cov(X₁,X₂)＝ρσ₁σ₁

Cov(X ₁ ,X ₂ )=ρσ ₁ σ ₁

Then the covariance matrix of (X ₁ , X ₂ ) is

Its probability density is:

The determinant of C is

The inverse matrix is

Write x=(x ₁ , x ₂ ),

Then there are:

So the probability density of (X ₁ , X ₂ ) can be expressed as:

If the probability density of n-dimensional random variable X=(X ₁ , X ₂ ,...X _n ) is:

j＝1,2…r，则在模型j的前提下，k时刻量测数据的似然函数为：Let n _j be the event for which model j is correct, with a prior probability

j=1,2...r, then under the premise of model j, the likelihood function of the measured data at time k is:

为滤波器j计算的新息残差

的概率密度，如下所示：in

innovation residual computed for filter j

The probability density of , as follows:

Then under the guidance of Bayesian theory, the posterior probability density of model j at time k is:

1. Variable structure multi-model algorithm

The first step, enter the interaction:

where p _ij is the transition probability for model i to transition to j. μ _i,j (k-1/k-1) mixing probability

The second step, filtering

进行卡尔曼滤波Corresponding model M _j (k) with

perform Kalman filter

predict:

Prediction error covariance:

Filter:

Filter covariance:

Observation equation estimate:

Kalman gain:

The third step, the model probability update

Λ _j (k)=N(r _j (k),0,S _j (k)), the likelihood function of mode j at time k, defines a variable r _j (k), the mean is 0, and the variance is S _j (k) Gaussian distribution (also called normal distribution).

The fourth step, output interaction

The fifth step, model set update

According to the model probability update, the corresponding model decision is further obtained, which depends on the set model transformation algorithm, which is a model adaptive process and is used for filtering at the next moment. For the initialization of the state vector and covariance of the new activation model, the probability weighted combination of each model at the previous moment is used to initialize, namely:

2. Improved variable structure multi-model method

The variable structure tracking algorithm has a good tracking effect for strong maneuvering problems. It mainly works on multiple tracking filters at the same time, and calculates their respective filter output probability according to the residuals and covariances of each filter. Finally, Combined with the interactive output results of each filter as the tracking data, this method usually uses the circular turning model as the filter tracking model, and this scheme uses the tilt angle of the target as the standard to distinguish each model. Its specific process is shown in Figure 1.

In this paper, aiming at the strong maneuvering flight target tracking, it is necessary to detect whether the target has strong maneuvering during the tracking process. Combined with the variable structure multi-model algorithm, the filtering innovation and its covariance in the target tracking process are used for discriminating detection. More past information should be forgotten at the maneuvering moment; more past information should be used at the non-maneuvering moment, and the model parameters should be closer to the real model by using the past information to adjust the model adaptively, and the tracking accuracy of the target non-maneuvering moment should be improved. The tracking result of the improved multi-model algorithm (GIMM algorithm) is between the IMM algorithm and the AGIMM algorithm, but compared with the IMM algorithm, it is not limited by the preset model. Compared with the AGIMM algorithm, there is no over-fitting phenomenon. Stablize.

The specific method is as follows:

In the filtering process, the innovation r _k+1|k and the innovation covariance S _k+1|k represent the error of one-step prediction. When there is a large error in the one-step prediction, it is very likely that the target has undergone a strong maneuver. At this time, the tracking system has not detected and adjusted accordingly. Therefore, after filtering at each moment, calculate: u_max=max(u _L , u _C , u _R ), and the model with the largest posterior probability represents the most suitable model at this moment. If it is still very large, it is considered that the aircraft has a strong maneuver. At this time, it is necessary to judge whether the aircraft has a strong maneuver, and calculate D(k)=r(k) ^T S(k) ^-1 r(k), r(k) Represents the innovation of the maximum probability model at time k; S(k) represents the innovation covariance of the maximum probability model at time k. Set the threshold value M reasonably. If D(k)>M, it is considered that the target has a strong maneuver.

The following is the specific content of this method:

After k filtering at a certain time, the innovation and its covariance corresponding to the maximum probability model are obtained.

Compute the maximum model probability:

u _max =max{u ₁ ,u ₂ ,u ₃ }

Its corresponding model is set to model j, then the distance function

Tracking model adjustments:

Model adjustment is analogous to the principle of directed graph switching.

When u1 _max , if D ₁ (k)≥M, then

Among them, G ₀ is the minimum grid spacing, and k ₁ and k ₂ are adjustable parameters.

If D ₁ (k)<M, the model is updated according to the method of directed graph switching, that is

When u2 _max , if D ₂ (k)≥M, then

If D ₂ (k)<M, the model is updated according to the method of directed graph switching, that is,

When u3 _max , if D ₃ (k)≥M, then

If D ₃ (k)<M, the model is updated according to the method of directed graph switching, that is,

Example:

The computer configuration adopted for the simulation in the embodiment of the present invention is as follows: the CPU is i7-8550U, the main frequency is 1.80GHz, and the memory is 8GB.

Simulation scene: The target is maneuvering in the near space, and the motion trajectory is shown in Figure 2. During this process, the attack angle of the target changes slowly. The target maneuvering situation is mainly realized according to the change of the target movement speed and the tilt angle. The change of the tilt angle is shown in the figure. 3 shown.

A variety of multi-model algorithms are combined with the target tracking dynamic model to achieve the tracking of strong maneuvering targets in the near space, and perform multiple Monte Carlo simulations. The following mainly analyzes and compares the accuracy, convergence speed and stability of each algorithm.

The target tracking state quantity is X=[xyzv _x v _y v _z α _D α _L ] ^T , the tilt angle γ _v is analogous to the angular velocity in the circular turning model as the multi-model distinguishing value, and the ckf filtering method is used to filter and track, and The velocity inclination angle used by each model is output interactively as an estimated value of the inclination angle, which is used as one of the judgment tracking accuracy.

The measurement adopts dual infrared detection. The origin of the infrared detection system is 5000m above the ground, which coincides with the local geographic coordinate system. The north-sky-east coordinate system is adopted. The distance between the two infrared detectors is 900km, and the detection distance of each infrared detector is 1100km. The angle error is 6×10 ^-4 rad.

The algorithm tracking performance index is expressed by the normalized position error (NPE), which is the ratio of the root mean square error (RMSE) of the position filter and the RMSE of the position measurement, which is specifically expressed as follows:

where M is the number of Monte Carlo simulations.

Simulation 1: Track the above target for 590-640s time period, at this time the target is in a weak maneuvering state, the tracking result is shown in Figure 4, and the tilt angle fitting error is shown in Figure 5. The following are the NEP error conditions:

Table 1 Comparison of simulation results

Simulation 2: Tracking the above target for 540-590s time period, the target is in a strong maneuvering state at this time, the tracking result is shown in Figure 6, and the tilt angle fitting error is shown in Figure 7. The following are the simulation results of the NEP error case:

Table 1 Tracking Results Comparison

It can be seen from the above simulation images and data that:

1) Tracking accuracy: when the target maneuverability is not strong, the tracking errors of the four variable-structure multi-model tracking methods all reach within 100 meters, and when strong maneuvering occurs, the tracking accuracy is also maintained at about 100 meters; comprehensive comparison, the GIMM algorithm is in the The comprehensive tracking accuracy is the best in weak maneuvering and strong maneuvering.

2) Convergence speed: The AGIMM algorithm has the fastest response in the case of strong maneuvering and can keep up with the maneuvering changes of the target, followed by the GIMM algorithm, but there is no big difference between the methods in terms of processing data time.

3) In terms of stability: in the filtering process, all four methods can be adjusted at any time according to the target maneuvering situation, and all of them can ensure that the tracking error is stable within a certain range, and there is no divergence.

This paper discusses the tracking problem of strong maneuvering aircraft in the near space, and combines the target dynamic model with the variable structure multi-model method to locate and track the target. While improving the tracking accuracy, the aerodynamic characteristics and maneuvering state of the target are obtained, which is of great help to cognitive target and trajectory prediction.

It can be seen from the above that the embodiment of the present invention realizes the problem of tracking the strong maneuvering aircraft in the near space. However, the above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. The present invention is also applicable to other related tracking problems. Any modifications, equivalent replacements and improvements made within the principles and spirit of the present invention are included within the protection scope of the present invention.

It should be noted that the specific embodiments are only explanations and descriptions of the technical solutions of the present invention, and cannot be used to limit the protection scope of the rights. Any changes made according to the claims and description of the present invention are only partial changes, which should still fall within the protection scope of the present invention.

Claims (7)

1. a strong maneuvering target tracking method based on variable structure multi-model, is characterized in that comprising the following steps: Step 1: Use the dynamic characteristics of the target aircraft to build a dynamic tracking model set, and then obtain the state equation set of the maneuvering target tracking system; Step 2: establish a system measurement model, and obtain the system measurement equation and measurement noise according to the established system measurement model; Step 3: Based on the set of state equations of the system, the measurement equations of the system and the measurement noise, recursively estimate the motion state and aerodynamic parameters of the target aircraft. 2. a kind of strong maneuvering target tracking method based on variable structure multi-model according to claim 1 is characterized in that the concrete step of described step 1 is: Step 11: According to the maneuvering characteristics of the target, select the aerodynamic parameters of the tracking model, The aerodynamic parameters of the tracking model are:

Among them, C _L (α) and C _D (α) are aerodynamic parameters, C _L (α) is the lift coefficient, C _D (α) is the drag coefficient, S is the characteristic area of the target aircraft, m is the mass of the target aircraft, α _D , α _L are drag parameters and lift parameters; Step 1 and 2: Use Gaussian white noise to model the variation characteristics of aerodynamic parameters, and obtain the state equation of the maneuvering target tracking system. The state equation of the maneuvering target tracking system is:

Among them, ω _e is the angular velocity vector of the earth's rotation, g is the acceleration of gravity of the earth, r is the position vector of the target under the detection system, v is the speed of the target under the detection system,

is the transfer matrix from the ballistic coordinate system to the detection system, θ is the velocity inclination angle, σ is the azimuth angle, γ _v is the velocity inclination angle, ω _γ is the Gaussian white noise of the inclination angle, ω _D , ω _L is the Gaussian white noise of the aerodynamic parameters , R is the aerodynamic force, where

S is the characteristic area of the target aircraft:

Step 1 and 3: Take the velocity inclination angle γ _v in Step 1 and 2 as the model variable, and select different velocity inclination angles γ _v to construct the state equation set of the maneuvering target tracking system. 3. a kind of strong maneuvering target tracking method based on variable structure multi-model according to claim 2, it is characterized in that the acquisition step of the measurement equation of system and measurement noise in described step 2 is specifically: Step 21: Establish a detection coordinate system according to the requirements of the tracking task, and determine the position vector of the detector and the target in the detection coordinate system; Step 22: According to the infrared detection principle, obtain the three-dimensional position coordinates of the target aircraft under the detector system; Step 2 and 3: Using the three-dimensional position coordinates of the target aircraft in the detector system, analyze the positioning mean square error, and determine the measurement equation and measurement noise of the tracking system. 4. a kind of strong maneuvering target tracking method based on variable structure multi-model according to claim 3, is characterized in that in described step 21, the position vector of detector and target under detection coordinate system is: The position vector of the target in the detection coordinate system: r=(x, y, z); The position vector of the detector in the detection coordinate system: S _l =(x _l , y _l , z _l ), where l represents the lth detector. 5. a kind of strong maneuvering target tracking method based on variable structure multi-model according to claim 4, is characterized in that the concrete steps of described step two two are: First, the vector of the detector pointing to the target is:

The detector detection angles α _l and β _l are expressed as:

Convert to get:

Using the least squares method to obtain the three-dimensional position coordinates of the target aircraft under the detector X=(x, y, z) The least squares representation is:

Among them, M is the measurement matrix, X is the state quantity, and Y is the quantity measurement. 6. a kind of strong maneuvering target tracking method based on variable structure multi-model according to claim 5, it is characterized in that the concrete steps of determining the measurement equation of tracking system and measurement noise in described step 23 are: First, determine the relative position and angle relationship between the target and the detector according to the geometric principle:

In the formula,

x ₁ , y ₁ , z ₁ are the position components of the first detector in the three directions of x, y, and z under the detection system; x ₂ , y ₂ , z ₂ are the x, y, and z directions of the second detector under the detection system. Position components in the three directions of y and z; Δκ=κ ₂ -κ ₁ ,

Then the noise R is obtained by measuring the noise formula. The measuring noise formula is:

in,

In the above formula, c ₁ =κ ₂ (x ₂ -x ₁ )-(y ₂ -y ₁ ), c ₂ =-κ ₁ (x ₂ -x ₁ )+(y ₂ -y ₁ );

and

are the mean square error of the position coordinates of the detector itself,

is the mean square error of target positioning,

is the mean square error of the detector detection angle α1,

is the mean square error of the detector detection angle α2,

is the mean square error of the detector detection angle β1,

is the mean square error of the detector detection angle β2. 7. a kind of strong maneuvering target tracking method based on variable structure multi-model according to claim 6, is characterized in that utilizes improved variable structure multi-model algorithm in described step 3 to carry out the movement state and aerodynamic parameter of target aircraft to carry out recursion. The specific steps of the improved variable structure multi-model algorithm are: The first step, enter the interaction:

M is the set of all models, i, j represent the i, jth model,

where p _ij is the transition probability of model i to j, and μ _i,j (k-1/k-1) is the mixing probability

The second step, filtering: For the model M _j (k) with

Kalman filtering is performed, Φ _j is the state transition matrix, and the prediction is:

The prediction error covariance is:

Filter is:

The filtering covariance is:

The observation equation estimates, the Kalman gain is:

The third step is to update the model probability:

Λ _j (k)=N(r _j (k), 0, S _j (k)), the likelihood function of mode j at time k, defines a variable r _j (k), the mean is 0, and the variance is S _j (k) Gaussian distribution (also called normal distribution).

The fourth step, output interaction:

The fifth step, model set update: Compute the maximum model probability: u _max =max{u ₁ , u ₂ , u ₃ } The corresponding model is set as model j, then the distance function is:

Tracking model adjustment, analogous to the principle of directed graph switching for model adjustment, When u1 _max , if D ₁ (k)≥M, then

where G ₀ is the minimum grid spacing, k ₁ , k ₂ are adjustable parameters, If D ₁ (k)<M, the model is updated according to the method of directed graph switching, that is

When u2 _max , if D ₂ (k)≥M, then

If D ₂ (k)<M, the model is updated according to the method of directed graph switching, that is,

When u3 _max , if D ₃ (k)≥M, then

If D ₃ (k)<M, the model is updated according to the method of directed graph switching, that is,

For the initialization of the state vector and covariance of the new activation model, the probability weighted combination of each model at the previous moment is used to initialize, namely:

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