CN112162244A - Event trigger target tracking method under correlated noise and random packet loss environment - Google Patents

Abstract

The invention discloses an event-triggered target tracking method under a correlated noise and random packet loss environment, and belongs to the technical field of target tracking. The invention describes the observation of a sensor to a target in a radar system as a linear discrete time dynamic system, then carries out target tracking based on an improved Kalman filtering estimation method, introduces a transmission packet loss variable to simulate a random packet loss process during target estimation, considers the measurement noise of the sensor, the system noise at the previous moment and the current moment and the limitation of network bandwidth and energy, and introduces an event trigger parameter to simulate whether the measurement data is fused or not. The method reduces redundant measurement transmission, improves the precision of target tracking estimation, saves network bandwidth and transmission energy consumption, has the characteristics of small operand, low energy consumption and the like, can be directly used for tracking estimation of a real target, is simple to implement, and has potential value in a plurality of application fields such as target tracking, integrated navigation, fault detection and control and the like.

Description

An event-triggered target tracking method in correlated noise and random packet loss environment

technical field

The invention belongs to the technical field of radar target tracking in the aspect of information processing, and relates to an event-triggered Kalman filter estimation method in a noise correlation and random packet loss environment.

Background technique

Radar means "Radio Detection and Ranging", that is, the use of radio methods to find targets and determine their spatial position. Therefore, radar is also called "radiolocation". The radar is generally divided into two parts: the radar front-end and the radar terminal. The radar front-end includes an antenna, a transmitter, a receiver and a signal preprocessor. The transmitter generates the required intensity of radiation pulse power and is fed to the antenna. To obtain a larger observation distance, the receiver amplifies the weak echo signal to a level sufficient for signal processing, and then calculates the position, time, size, energy amplitude and other information of the observation target through signal processing; the radar terminal includes control The unit, the display unit and the signal processing unit realize the control of the front end of the radar, receive and display the radar image sent by the front end of the radar, receive the target trace information sent by the front end of the radar, and track and display the target track.

Although radar is accurate in estimating and tracking targets, it is inevitable that there will be some inherent noise, which will undoubtedly have an impact on the received signal. Long-term use of radar makes the noise more and more diverse and complex, and it is more and more difficult to process. At the same time, in the process of information transmission, the tracking target information may be lost due to the instability of the communication link. At present, the commonly used classical filtering estimation methods do not fully consider the interference of noise correlation and packet loss to the system, which will lead to poor tracking effect.

The two-way data transmission between the radar front end and the terminal is carried out through the wireless sensor network. Since the network bandwidth and transmission capacity in the wireless sensor network are very limited, efficient bandwidth and energy utilization are very important. The event triggering mechanism can reduce network transmission bandwidth occupation and save data transmission energy consumption on the premise of ensuring target tracking accuracy. Therefore, it has received extensive attention.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a target tracking and positioning method based on wireless sensor data in a radar system, which considers the unreliability of the communication link in the transmission process, simulates the process of random packet loss, and considers the sensor measurement noise and The system noise at the previous moment and the current moment, as well as the limited network bandwidth and energy, use an event-triggered Kalman filter estimation method in the environment of correlated noise and random packet loss to achieve sensor target tracking.

The invention provides an event-triggered target tracking method in the environment of correlated noise and random packet loss, which is used for target tracking of a radar system. The observation of a target by a sensor in the radar system is described as a linear discrete-time dynamic system, and then Target tracking based on improved Kalman filter estimation method. The method of the present invention comprises the following steps:

方差为

的高斯分布；目标状态包括目标的位置和速度；设传感器观测目标时的系统噪声是均值为零、协方差为Q_k的高斯白噪声，Q_k的初始值为Q₀；设传感器目标状态和系统噪声之间的估计误差协方差矩阵初始值为

设传输丢包变量λ_k服从参数为p的伯努利分布；Step 1: Obtain the initial data of the tracked target, and set the initial target state to conform to the mean value.

The variance is

The target state includes the position and velocity of the target; it is assumed that the system noise when the sensor observes the target is Gaussian white noise with zero mean and covariance Q _k , and the initial value of Q _k is Q ₀ ; let the sensor target state and The initial value of the estimated error covariance matrix between system noise is

Let the transmission packet loss variable _λk obey the Bernoulli distribution with parameter p;

Step 2, at time k, obtain the observation data z _k and the observation transition matrix C _k of the sensor during time (k-1,k]; k is a positive integer;

Step 3: Introduce the transmission packet loss variable λ _{k at time k} to simulate the packet loss process. When λ _k = 1, the observed data arrives normally; when λ _k = 0, the observed data is lost, and the packet loss and normal conditions are obtained respectively. probability distribution of observed noise;

与状态预测误差协方差矩阵P_k|k-1；Step 4: Calculate the target state prediction matrix at the current k time according to the estimated value of the target state at time k-1

with the state prediction error covariance matrix P _k|k-1 ;

与状态预测误差协方差矩阵P_k|k-1，计算传感器的事件触发参数γ_k；当γ_k＝1时，测量数据z_k被传输到远程估计器，当γ_k＝0时，测量数据z_k不会被传输到远程估计器；Step 5, at time k, use the observation data z _k obtained in step 2 and the target state prediction matrix calculated in step 4

and the state prediction error covariance matrix P _k|k-1 , calculate the event trigger parameter γ _k of the sensor; when γ _k =1, the measurement data z _k is transmitted to the remote estimator, when γ _k =0, the measurement data z _k will not be transmitted to the remote estimator;

与状态预测误差协方差矩阵P_k|k-1、以及步骤5计算的传感器的事件触发参数γ_k，计算k时刻的目标状态估计矩阵

状态估计误差协方差矩阵P_k|k，系统噪声估计矩阵

系统噪声估计误差协方差矩阵

以及状态和系统噪声间的估计误差协方差矩阵

Step 6, at time k, use the observation data z _k obtained in step 2, the transmission packet loss variable λ _k obtained in step 3, and the target state prediction matrix calculated in step 4

Calculate the target state estimation matrix at time k with the state prediction error covariance matrix P _k|k-1 and the event trigger parameter γ _k of the sensor calculated in step 5

State estimation error covariance matrix P _k|k , system noise estimation matrix

System Noise Estimation Error Covariance Matrix

and the estimated error covariance matrix between state and system noise

以及状态估计误差协方差矩阵P_k|k，可以得到任意k,k＝1,2,…时刻对目标跟踪的结果。Step 7, assign k+1 to k, repeat steps 2 to 6, and output the target state estimation matrix at time k calculated in step 6

And the state estimation error covariance matrix P _k|k , the result of tracking the target at any time k, k=1, 2, ... can be obtained.

In the step 3, the probability distribution of the observation noise v _k under the observation value transmission packet loss variable λ _k at time k is expressed as:

Among them, N(0, R _k ) represents a normal distribution with a standard deviation of 0 and a variance of R _k , and R _k represents the observation error variance matrix at time k; N(0, σ ² I) represents a standard deviation of 0 and a variance of 0. is the normal distribution of σ ² I, the parameter σ→∞, I represents the identity matrix.

和状态预测误差协方差矩阵P_k|k-1，如下：In the step 4, at the transmission time k, the target state prediction matrix is calculated according to the target state estimation matrix at time k-1.

and the state prediction error covariance matrix P _k|k-1 , as follows:

P_k-1|k-1分别表示k-1时刻的目标状态估计矩阵和状态估计误差协方差矩阵，

A_k-1表示k-1时刻的系统状态转移矩阵，上角标T表示转置；

表示k-1时刻系统噪声的估计值，

表示k-1时刻系统噪声的估计误差协方差矩阵，

表示k-1时刻的系统状态和系统噪声之间的估计误差协方差矩阵，

in,

P _k-1|k-1 represents the target state estimation matrix and the state estimation error covariance matrix at time k-1, respectively,

A _k-1 represents the system state transition matrix at time k-1, and the superscript T represents the transposition;

represents the estimated value of the system noise at time k-1,

represents the estimated error covariance matrix of the system noise at time k-1,

represents the estimated error covariance matrix between the system state and system noise at time k-1,

In the step 5, the method for calculating the event trigger parameter γ _k of the sensor is:

新息的协方差矩阵

以及增益矩阵分别为：First, calculate the difference between the observed data measured at time k and the predicted value of the observed data based on the state at time k-1 to obtain the innovation

innovation covariance matrix

and the gain matrix are:

表示上一时刻系统噪声和当前k时刻观测噪声的协方差阵。新息的协方差矩阵

是一个半正定矩阵，计算

的特征值

m是z_k的维数，并将其表示为对角阵的形式：in,

Represents the covariance matrix of the system noise at the previous moment and the observation noise at the current k moment. innovation covariance matrix

is a positive semi-definite matrix, calculate

eigenvalues of

m is the dimension of z _k and represents it in the form of a diagonal matrix:

Calculate the unitary matrix U _k using the following formula:

则进一步得到归一化且去相关性的矩阵

Then, let the matrix

Then further normalized and de-correlated matrices are obtained

其中，||·||_∞表示矩阵的无穷范数，θ为事件触发的阈值，θ≥0。Finally, get the event trigger parameters of the sensor

Among them, ||·|| _∞ represents the infinity norm of the matrix, θ is the threshold of event triggering, θ≥0.

与P_k|k，计算如下：In the step 6, the target state estimation matrix and the state estimation error covariance matrix at time k are respectively:

and P _k|k , calculated as follows:

以及状态和系统噪声间的估计误差协方差矩阵：Calculate the system noise estimation matrix at time k, the system noise estimation error covariance matrix, and the gain matrix of the system noise

and the estimated error covariance matrix between state and system noise:

Among them, γ _k represents the event trigger parameter, λ _k represents the transmission packet loss variable, and S _k represents the covariance matrix of the system noise and the observation noise at time k;

分布

distributed

distributed

Compared with the prior art, the advantages and positive effects of the present invention are:

(1) The present invention adopts an event-triggered transmission mechanism, which reduces redundant measurement transmissions compared with traditional time-triggered transmissions, saves network bandwidth and transmission energy consumption on the premise of ensuring target estimation accuracy, and has the advantages of small computational complexity and low energy consumption. It can make more effective and full use of data with the lowest energy consumption;

(2) The method of the present invention considers the relevant noise, overcomes the complex environment in which the system noise at the previous moment is related to the observation noise at the current moment, and the system noise at the current moment is related to the observation noise at the current moment, and improves the accuracy of target tracking estimation;

(3) The present invention considers the data packet loss problem caused by the unreliability of the communication link during the transmission process of the system, simulates the random packet loss process, and improves the accuracy of target tracking estimation;

(4) The improved Kalman filter estimation algorithm used in the method of the present invention can obtain the optimal solution in the sense of the minimum variance of the target observation error, and can effectively realize the target tracking estimation;

(5) The method of the present invention has strong anti-noise and anti-interference ability, and can improve the tracking and positioning accuracy of the system;

(6) The method of the present invention can be directly used for tracking estimation of real targets, and the method is simple to implement, easy to popularize, and has potential value in many application fields such as target tracking, integrated navigation, fault detection and control.

Description of drawings

1 is a schematic flowchart of an event-triggered target tracking method with correlated noise and random packet loss according to the present invention;

2 is a schematic diagram of the relationship between the average sensor communication rate and the event trigger threshold in the simulated method of the present invention;

Fig. 3 is the position and velocity root mean square error comparison diagram of the inventive method of computer simulation under different thresholds;

Fig. 4 is a comparison diagram of the position and velocity root mean square error of the inventive method of computer simulation and the KF algorithm that considers packet loss but ignores noise correlation;

5 is a comparison diagram of the position and velocity root mean square errors of the method of the present invention simulated by the computer and the KF algorithm that considers noise correlation but ignores packet loss.

Detailed ways

The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

Under the environment of correlated noise and random packet loss, the method of the invention is based on a class of linear discrete-time dynamic systems, with radar target tracking as the background and obtaining high-precision target information as the goal, to study the event-triggered Kalman filter state estimation problem.

In the embodiment of the present invention, the hardware environment and software configuration for implementing the method of the present invention are as follows:

Hardware environment: computer; correlator;

Software configuration: Windows 7/8//9/10; any language environment software such as matlab or C language or C++.

The linear discrete-time dynamic system in which the sensor observes the target can be described as

x _k+1 =A _k x _k +ω _k , k=0,1,2,…

z _k =C _k x _k +v _k

是k时刻的系统状态向量，是一个n维实数向量；R代表实数；s_k和

分别表示在k时刻时被跟踪目标的位置和速度，系统状态即目标状态；A_k∈R^n×n是k时刻的系统状态转移矩阵，是一个n×n维的实数矩阵；ω_k是k时刻的过程噪声，设它是均值为零，协方差为Q_k的高斯白噪声，初始Q_k＝Q₀；z_k∈R^m是传感器在k时刻的测量值，是一个m维实数向量；C_k∈R^m×n是k时刻的测量转移矩阵，是一个m×n维的实数矩阵。v_k是k时刻的观测噪声，设v_k是均值为零，协方差为

的白噪声，并且

其中δ_kl是克罗内克函数。测量噪声v_k与当前时刻系统噪声ω_k和上一时刻系统噪声ω_k-1相关。v_l表示l时刻的观测噪声，R_k表示k时刻的观测误差方差矩阵，S_k表示当前k时刻系统噪声和观测噪声的协方差阵，

表示上一时刻系统噪声和当前时刻观测噪声的协方差阵。in,

is the system state vector at time k, which is an n-dimensional real number vector; R represents a real number; s _k and

respectively represent the position and velocity of the tracked target at time k, and the system state is the target state; A _k ∈R ^n×n is the system state transition matrix at time k, which is an n×n-dimensional real number matrix; ω _k is k The process noise at time, let it be Gaussian white noise with zero mean and covariance Q _k , initial Q _k = Q ₀ ; z _k ∈ R ^m is the measurement value of the sensor at time k, which is an m-dimensional real vector; C _k ∈R ^m×n is the measurement transition matrix at time k, which is a real matrix with m×n dimensions. v _k is the observation noise at time k, let v _k be zero mean, and the covariance is

white noise, and

where δ _kl is the Kronecker function. The measurement noise v _k is related to the system noise ω k at the current moment and the system noise ω _{k -1} at the previous moment. v _l represents the observation noise at time l, R _k represents the observation error variance matrix at time k, S _k represents the covariance matrix of the current system noise and observation noise at time k,

Represents the covariance matrix of the system noise at the previous moment and the observation noise at the current moment.

方差为

的高斯分布，并且和ω_k、v_k相互独立，k为正整数。The initial state x ₀ is the mean

The variance is

The Gaussian distribution of , and ω _k , v _k are independent of each other, and k is a positive integer.

As shown in FIG. 1 , the method for event-triggered target tracking in a correlated noise and random packet loss environment provided by the present invention is divided into the following 8 steps for description.

及方差

初始系统噪声方差矩阵Q₀以及目标状态和系统噪声间的估计误差协方差矩阵初始值为

其中，

为n维实向量，

是n维矩阵，且

是正定矩阵，Q₀∈R^n×n是n维矩阵，

是n维矩阵，设传输丢包变量λ_k服从参数为p的伯努利分布。其中，

代表目标状态估计误差，

代表系统噪声估计误差。Step 1. Obtain the initial data of the sensor observation target, including obtaining the mean value of the initial state vector

and variance

The initial system noise variance matrix Q ₀ and the estimated error covariance matrix between the target state and the system noise are

in,

is an n-dimensional real vector,

is an n-dimensional matrix, and

is a positive definite matrix, Q ₀ ∈ R ^n×n is an n-dimensional matrix,

is an n-dimensional matrix, and the transmission packet loss variable λ _k is assumed to obey the Bernoulli distribution with parameter p. in,

represents the target state estimation error,

represents the system noise estimation error.

以及当前时刻系统噪声和当前时刻观测噪声的协方差阵S_k。Step 2. For time k, k=1, 2,..., input the transmission packet loss variable λ _k , input the event trigger threshold θ , input the system state matrix A _k and the system noise variance matrix Q _k ; input (k-1,k ] The observation data z _k and the observation matrix C _k from the sensor obtained at the moment, the observation noise variance matrix R _k , the covariance matrix of the system noise at the previous moment and the observation noise at the current moment

and the covariance matrix S _k of the system noise at the current moment and the observation noise at the current moment.

The setting values of the relevant parameters involved in the method of the present invention and the conditions that need to be satisfied are as follows:

λ _k : transmission packet loss variable, a quantity used to describe whether the transmission is lost or not, obeys the Bernoulli distribution with parameter p, 0<p<1;

θ: Threshold value of event trigger, a quantity used to describe the trigger threshold value, θ≥0;

z _k : the observation amount of the sensor, its dimension is m, the value range: m≤n;

A _k : The system state transition matrix, which is used to describe the amount of transition between states. Value range: full rank matrix of eigenvalues in the unit circle, if the dimension of the target state is n, then A _k ∈ R ^n×n ;

C _k : observation transition matrix, used to describe the dimension of observation data and observation data, its dimension is m, namely C _k ∈ R ^m×n ;

Q _k : system noise variance matrix, used to describe the system modeling error, its dimension is n×n, in general, it is a non-negative definite matrix;

R _k : the observation error variance matrix, used to describe the observation error deviation, its dimension is m×m, and the value range is a non-negative definite matrix;

上一时刻系统噪声和当前时刻观测噪声的协方差，用于描述上一时刻系统噪声和当前时刻观测噪声相关性，其维数为n×m，取值范围为非负定矩阵；

The covariance of the system noise at the previous moment and the observation noise at the current moment is used to describe the correlation between the system noise at the previous moment and the observation noise at the current moment. Its dimension is n×m, and the value range is a non-negative definite matrix;

S _k : the covariance of the system noise at the current moment and the observation noise at the current moment, used to describe the correlation between the system noise at the current moment and the observation noise at the current moment, its dimension is n×m, and the value range is a non-negative definite matrix;

I: represents the identity matrix;

I _n : represents an n-dimensional unit matrix;

p(x|y): represents the probability of occurrence of x under the condition y;

N(μ,σ): represents a normal distribution with a standard deviation of μ and a variance of σ.

Step 3. At the measurement transmission time k, k=1, 2, ..., the packet loss process is simulated by transmitting the packet loss variable λ _k , and the probability distribution of the packet loss and the observed noise under normal conditions is obtained as follows:

Among them, p(v _k |λ _k ) represents the probability distribution of the observation noise v _k under the transmission packet loss variable λ _k at time k, and the parameter σ→∞. When λ _k =1, the observation value z _k can arrive normally; when λ _k =0, the observation value is lost.

和目标状态预测误差协方差矩阵P_k|k-1：Step 4. At the measurement transmission time k, k=1, 2, 3, ..., use the following formula to calculate the target state prediction matrix

and the target state prediction error covariance matrix P _k|k-1 :

表示基于上一时刻系统状态预测的当前k时刻的目标状态，P_k|k-1表示预测的误差协方差矩阵，

和P_k-1|k-1分别表示k-1时刻目标状态估计矩阵和状态估计误差协方差矩阵，当k＝1时，

表示k-1时刻系统噪声的估计值，

表示k-1时刻系统噪声的估计误差协方差矩阵，

表示k-1时刻的系统状态和系统噪声之间的估计误差协方差矩阵，当k＝1时，

in,

represents the target state at the current k moment predicted based on the system state at the previous moment, P _k|k-1 represents the predicted error covariance matrix,

and P _k-1|k-1 represent the target state estimation matrix and the state estimation error covariance matrix at time k-1, respectively. When k=1,

represents the estimated value of the system noise at time k-1,

represents the estimated error covariance matrix of the system noise at time k-1,

Represents the estimated error covariance matrix between the system state and system noise at time k-1, when k=1,

和P_k|k-1，利用下式计算传感器的事件触发参数γ_k：Step 5. At time k, k=1, 2, ..., use the observation data z _k and related parameters input in step 2, and the calculated

and P _k|k-1 , the event trigger parameter γ _k of the sensor is calculated using the following formula:

及新息的协方差矩阵

与增益矩阵K_k分别为：new interest

and the covariance matrix of innovation

and the gain matrix K _k are:

表示k时刻测量的真实观测数据与基于k-1时刻状态预测的观测数据之间的差值。Among them, the new

It represents the difference between the real observation data measured at time k and the observation data predicted based on the state at time k-1.

是一个半正定矩阵，求得

的特征值

m是z_k的维数，并将其表示为对角阵Λ_k的形式because

is a positive semi-definite matrix, we get

eigenvalues of

m is the dimension of z _k and expresses it in the form of a diagonal matrix Λ _k

Calculate the unitary matrix U _k ∈R ^m×m that holds the equation using:

Define the matrix H _k ∈ R ^m×m as

Further normalized and decorrelated matrices are obtained

确定传感器的事件触发参数：Then, according to the matrix

Determine the event trigger parameters for the sensor:

where ||·|| _∞ denotes the infinite norm of the matrix, when _{γk =} 1, the measurement value zk of the sensor can be transmitted to the remote estimator, that is, the fusion center; otherwise, when _γk = 0, the fusion The center will not receive measurements.

和P_k|k-1以及步骤5计算出的Kalman滤波事件触发条件，利用下式计算状态估计矩阵

和相应的估计误差协方差矩阵P_k|k：Step 6. At time k, k=1, 2, ..., using the observation data z _k input in step 2 and related parameters, step 3 calculates the random packet loss parameter,

and P _k|k-1 and the Kalman filter event trigger condition calculated in step 5, use the following formula to calculate the state estimation matrix

and the corresponding estimated error covariance matrix P _k|k :

Calculate the white noise estimator as:

表示k时刻对系统噪声的估计值，

表示系统噪声的增益矩阵，

表示系统噪声的估计误差协方差矩阵，λ_k表示k时刻观测值传输丢包变量，上角标T表示转置。γ_k表示传感器的事件触发参数。in,

represents the estimated value of the system noise at time k,

is the gain matrix representing the system noise,

Represents the estimated error covariance matrix of system noise, λ _k represents the transmission packet loss variable of the observation value at time k, and the superscript T represents the transpose. γ _k represents the event trigger parameter of the sensor.

Filtered error covariance matrix between system state and system noise:

表示k时刻的系统状态与系统噪声之间的滤波误差协方差矩阵，

表示k时刻的系统噪声与系统状态之间的滤波误差协方差矩阵。

represents the filter error covariance matrix between the system state at time k and the system noise,

Represents the filter error covariance matrix between the system noise and the system state at time k.

Among them, the distribution of β(θ) and Q(θ) is as follows:

和P_k|k，作为雷达系统在当前k时刻对目标跟踪的结果。Step 7: At time k, k=1, 2, ..., output x _k|k and P _k|k , that is, obtain the estimated value of the state of the sensor and the estimated error covariance matrix obtained at time k. The x _k|k and P _k|k output in step 7 are calculated in step 6.

and P _k|k , as the result of the radar system tracking the target at the current k time.

Step 8. When the next time k+1 is reached, assign k+1 to k, and then repeat steps 2 to 7 to track the Kalman filter of the target at the next moment, and obtain the estimated value of the target state and the error covariance matrix. .

The effectiveness of the method of the present invention will be tested by simulation experiments below.

A single-sensor radar tracking system can be described by the following equation:

z _k =Cx _k +v _k ,k=1,2,...,L

v _k =η _k +β ₁ ξ _k-1 +β ₂ ξ _k

其中s_k是跟踪目标在kT时刻的位置，

是kT时刻的速度。假设ξ_k∈R是零均值，协方差为

的高斯白噪声。Γ_k＝[T 1]^T是噪声转移矩阵。z_k是传感器的量测向量，C＝[10]。v_k是量测噪声，传感器的量测噪声与上一时刻和当前时刻系统噪声ξ_k-1和ξ_k相关。相关性由β₁和β₂的值决定。η_k是高斯噪声，并且它的均值为零，协方差为

并独立于ξ_k,k＝1,2,…。初始值为

ω₀＝[0 0]^T，

Where T=0.01 represents the sampling period. L=300 is the measured length of the estimated signal x. state vector

where _sk is the position of the tracking target at time kT,

is the velocity at time kT. Assuming that ξ _k ∈ R is zero mean, the covariance is

Gaussian white noise. Γ _k =[T 1] ^T is the noise transfer matrix. z _k is the measurement vector of the sensor, C=[10]. v _k is the measurement noise, and the measurement noise of the sensor is related to the system noise ξ _k-1 and ξ _k at the previous moment and the current moment. The correlation is determined by the values _of β1 and _β2 . η _k is Gaussian noise, and its mean is zero, and the covariance is

and independent of ξ _k , k=1,2,…. The initial value is

ω ₀ =[0 0] ^T ,

它是系统噪声ω_k＝Γ_kξ_k对应的协方差矩阵，测量噪声协方差为

ω_k-1和v_k之间的协方差为

而

是ω_k和v_k之间的协方差矩阵。systematic error variance matrix

It is the covariance matrix corresponding to the system noise ω _k =Γ _k ξ _k , and the measured noise covariance is

The covariance between ω _k-1 and v _k is

and

is the covariance matrix between ω _k and v _k .

To compare the effects of different thresholds on the estimation performance under event-triggered conditions, four different thresholds are randomly set, which are θ=0, θ=0.5, θ=0.8 and θ=1.0. Among them, when θ=0, the event trigger degenerates into a time trigger, that is, the estimator can receive the measurement value of the corresponding sensor at each moment.

The purpose of the experiment of the present invention is to estimate the target by the sensor, give the state estimation of the state x _k , and compare the influence of ignoring the correlation noise and the packet loss on the estimation result in the case of correlated noise and random packet loss.

并且β₁＝6，β₂＝6，因此，测量噪声与上一时刻系统噪声和当前时刻系统噪声相关。传输丢包变量的参数p＝0.1。本发明进行了1000次蒙特卡洛仿真并观察所提算法的有效性。仿真结果如图2～5所示。Assume

And β ₁ =6, β ₂ =6, therefore, the measurement noise is related to the system noise at the previous moment and the system noise at the current moment. The parameter p=0.1 for the transmission packet loss variable. The present invention conducts 1000 Monte Carlo simulations and observes the effectiveness of the proposed algorithm. The simulation results are shown in Figures 2-5.

The average communication rate of the sensor of the improved Kalman filter algorithm proposed in the present invention is defined as follows

Figure 2 shows the relationship between the event trigger threshold θ and the average sensor communication rate γ. It can be seen that with the increase of the event trigger threshold, the communication rate of the sensor decreases continuously.

FIG. 3 shows the statistical simulation curves of the position and velocity root mean square error (RMSE) of the Kalman filtering method under different trigger thresholds in the method of the present invention (KFO for short). It can be seen from FIG. 3 that, under a smaller trigger threshold, the state estimation effect of the method of the present invention is always better than that under a larger trigger threshold. The dotted line in the figure represents θ=1.0, the solid line represents θ=0.8, the dotted line represents θ=0.5, and the dotted line represents θ=0.

Fig. 4 shows the statistical simulation curve of the RMSE of the method of the present invention considering noise correlation and packet loss (KFO for short) and the KF algorithm considering packet loss but not noise correlation (KFN for short), including the root mean square error of position and velocity, The event trigger threshold θ=0.5 is set. In the figure, the solid line represents the method of the present invention, and the dotted line represents the comparison method. It can be seen that when θ=0.5, the root mean square error curve of the KF algorithm in the method of the present invention is lower than that considering packet loss but not considering noise correlation. The root mean square error curve of the KF algorithm (KFN) shows that the KF algorithm considering the noise correlation is effective, and ignoring the noise correlation will reduce the state estimation accuracy.

Fig. 5 shows the statistical simulation curve of the RMSE of the method of the present invention considering noise correlation and packet loss and the KF algorithm (KFD for short) considering noise correlation but not packet loss, including the root mean square error of position and velocity, wherein the set event Trigger threshold θ=0.5. In the figure, the solid line represents the method of the present invention, and the dashed line represents the comparison method. It can be seen that when θ=0.5, the root mean square error curve of the KF algorithm in the method of the present invention is lower than considering the noise correlation but not considering the packet loss. The root mean square error curve of the KF algorithm (KFD) shows that the KF algorithm considering packet loss is effective, and ignoring packet loss will reduce the accuracy of state estimation.

Table 1 shows the time-averaged velocity and position RMSE of the KFO, KFN, and KFD algorithms at different trigger thresholds.

Table 1 Time-averaged RMSE under different thresholds θ in different situations

It can be seen that KFO outperforms the other two algorithms when θ takes the same value. Note that when θ=0 it means that all raw sensor measurements are transmitted and the system degenerates to a time-triggered system. Therefore, the method of the present invention has the best estimation performance when θ=0. As θ increases, the estimation accuracy of the method of the present invention decreases. But no matter what conditions, the method of the present invention is optimal.

In a word, it can be seen from the above simulation that the method of the present invention has a good simulation effect, and the Kalman filtering algorithm used considering noise correlation and packet loss is better than the Kalman filtering algorithm that ignores one of the two, and can improve the Target tracking and positioning accuracy.

Claims (5)

1. An event trigger target tracking method under the environment of related noise and random packet loss is used for target tracking of a radar system, target observation by a sensor is described as a linear discrete time dynamic system, and a target state comprises the position and the speed of a target; characterized in that the method comprises the following steps:

step 1, acquiring initial data of a tracked target, and setting a target initial state x₀In accordance with a mean value of

Variance of

(ii) a gaussian distribution of; when the sensor is set to observe the target, the system noise is 0 in mean value and Q in covariance_kWhite gaussian noise, Q_kIs Q₀(ii) a Setting the initial value of the covariance matrix of the estimation error between the target state and the system noise as

Set transmission packet loss variable lambda_kObeying a bernoulli distribution with a parameter p;

step 2, at the moment k, acquiring that the sensor is at (k-1, k)]Observed data z of time_kAnd observation transfer matrix C_k(ii) a k is a positive integer;

step 3, at the moment k, a variable lambda of packet loss is transmitted_kSimulating the packet loss process as λ_kWhen 1, the observed data arrives normally, when λ_kWhen the packet loss is equal to 0, the observation data is lost, and probability distribution of the packet loss and the observation noise under the normal condition is respectively obtained;

step 4, according to the target state estimation value at the k-1 moment, calculating a target state prediction matrix at the current k moment

Covariance matrix P with state prediction error_k|k-1；

Step 5, at the time k, the observation data z obtained in the step 2 is used_kAnd step 4, calculating a target state prediction matrix

Covariance matrix P with state prediction error_k|k-1Calculating the event triggering parameter gamma of the sensor_k(ii) a When gamma is_kWhen 1, measurement data z_kIs transmitted to a remote estimator when gamma is_kWhen 0, the measured data z_kWill not be transmitted to the remote estimator;

step 6, at the time k, the observation data z obtained in the step 2 is used_kThe product obtained in step 3Random packet loss variable lambda_kAnd 4, calculating a target state prediction matrix

Covariance matrix P with state prediction error_k|k-1And the event triggering parameter gamma of the sensor calculated in step 5_kCalculating the target state estimation matrix at the time k

State estimation error covariance matrix P_k|kSystem noise estimation matrix

Covariance matrix of system noise estimation error

And covariance matrix of estimation error between state and system noise

Step 7, assigning k +1 to k, repeating the steps 2-6, and outputting the target state estimation matrix of the k moment calculated in the step 6

And a state estimation error covariance matrix P_k|kAnd obtaining the target tracking result at any time.

2. The method according to claim 1, wherein in step 3, the packet loss variable λ is transmitted at the observation at time k_kObserved noise v of_kThe probability distribution is expressed as

Wherein, N (0, R)_k) Denotes a standard deviation of 0 and a variance of R_kNormal ofDistribution, R_kRepresenting an observation error variance matrix at time k; n (0, sigma)²I) Denotes a standard deviation of 0 and a variance of σ²Normal distribution of I, parameter σ → ∞, I representing the identity matrix.

3. The method of claim 1, wherein in step 4, at transmission time k, the target state prediction matrix is calculated from the target state estimation matrix at time k-1

Sum state prediction error covariance matrix P_k|k-1The following are:

wherein ,

P_k-1|k-1respectively representing the target state estimation matrix and the state estimation error covariance matrix at time k-1,

A_k-1representing a system state transition matrix at the moment of k-1, wherein an upper corner mark T represents transposition;

representing an estimate of the system noise at time k-1,

an estimation error covariance matrix representing the system noise at time k-1,

representing the covariance matrix of the estimation error between the system state and the system noise at time k-1,

representing the covariance matrix of the estimation error between the system noise and the system state at time k-1,

4. the method of claim 1, wherein in step 5, the event triggering parameter γ of the sensor is calculated_kThe method comprises the following steps:

first, the difference between the observed data measured at time k and the predicted value of the observed data based on the state at time k-1, i.e., the innovation, is calculated

And covariance matrix of innovation

And a gain matrix K_kRespectively as follows:

wherein ,

representing a covariance matrix of system noise at the last moment and observation noise at the current k moment; covariance matrix of innovation

Is a semi-positive definite matrix, calculating

Characteristic value of

m is z_kAnd expressed in the form of a diagonal matrix:

calculating the unitary matrix U using the equation_k：

Then, a matrix is set

A normalized and decorrelated matrix is further obtained

Finally, obtaining event trigger parameters of the sensor

Wherein | · | purple sweet_∞And representing the infinite norm of the matrix, wherein theta is a threshold value triggered by the event, and theta is more than or equal to 0.

5. The method of claim 1, wherein in step 6, the target state estimation matrix and the state estimation error covariance matrix at time k are respectively

And P_k|kThe calculation is as follows:

calculating the system noise estimated value at the k moment

Covariance matrix of system noise estimation error, gain matrix of system noise

And an estimation error covariance matrix between the system state and the system noise:

wherein ,γ_kDenotes an event trigger parameter, λ_kIndicating transmission packet loss variable, S_kA covariance matrix representing the system noise and the observation noise at time k;

distribution of

Distribution of

θ is the threshold for event triggering.

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