阅读说明：本技术 一种结合三边测量和u变换的传感器网络目标跟踪方法 (Sensor network target tracking method combining trilateration and U transformation ) 是由 赵宣植 张康 张文 于 2021-02-25 设计创作，主要内容包括：本发明涉及一种结合三边测量和U变换的传感器网络目标跟踪方法,属于信号融合技术领域。本发明提出将UT变换与三边测量方法结合,获得目标位置的统计量,再将其作为卡尔曼滤波的虚拟观测实现动态目标的跟踪。本发明与现有技术相比,主要解决了线性高斯系统不适用,线性化处理带来的误差,跟踪结果不稳定,以及诸如粒子滤波算法中粒子退化,样本贫化等问题。本方法通过引入UT变换,利用UT变换来最终获得目标位置信息的统计量,该方法具有较低的测量误差和时间复杂度,跟踪效果较好。本文得出的结论可为无线传感器网络定位与跟踪技术的实际应用提供参考。(The invention relates to a sensor network target tracking method combining trilateration and U transformation, and belongs to the technical field of signal fusion. The invention provides a method for tracking a dynamic target by combining UT transformation and trilateration to obtain the statistic of the target position, and then using the statistic as the virtual observation of Kalman filtering to realize the tracking of the dynamic target. Compared with the prior art, the method mainly solves the problems that a linear Gaussian system is not suitable for use, errors are caused by linearization processing, a tracking result is unstable, and the problems such as particle degradation and sample depletion in a particle filter algorithm are solved. The method finally obtains the statistic of the target position information by introducing UT transformation and utilizing the UT transformation, and has lower measurement error and time complexity and better tracking effect. The conclusion drawn herein can provide reference for practical application of wireless sensor network location and tracking technology.)

1. A sensor network target tracking method combining trilateration and U transformation is characterized in that: target information statistics is obtained through a UT conversion method and is used as filtering virtual observation to achieve dynamic target tracking, and meanwhile tracking performance is improved. The method comprises the following specific steps:

(1) the positioning principle of the trilateral algorithm is that the distances between a mobile node and 3 non-collinear beacon nodes are measured in sequence, the positions of the 3 beacon nodes are taken as the circle centers, and the corresponding distances are taken as the radius to make 3 circles. If the distance measurement is error-free, the 3 circles intersect at one point, namely the position coordinate of the mobile node;

(2) trilateration is a distance-based positioning algorithm. The algorithm is described as follows: assuming that the coordinates of the target position are (x, y), the coordinates of the three points a, B, and C are known as (xa, ya), (xb, yb), (xc, yc), respectively. Their distances to the target are da, db and dc, respectively. The following equation can be obtained;

(3) formula (1) minus formula (3), formula (2) minus formula (3), and simultaneous equations;

(4) when a filtering method is adopted for tracking and positioning of the wireless sensor network, nonlinear transformation is required. UT transforms are a new approach to the problem of nonlinear transforms. Trilateration and U-transform are combined to convert tracking from nonlinear filtering to linear filtering. Based on the previous three-side positioning method model, the formula in (3) can be rewritten as follows;

(5) hypothetical distance observationsIs the true distance d_a,d_b,d_cWith observation noise epsilon_a,ε_b,ε_cThe superposition of (a) and (b) is as follows;

(6) if observing the noise ε_a,ε_b,ε_cIs independent 0 mean Gaussian distribution with variance ofThree actual distances d_a,d_b,d_cChanging into a Gaussian random vector;

wherein the content of the first and second substances,

and it is known that A, B, C are not collinear and are available;

(7) then, the mean value and the variance of the target position (x, y) can be obtained through UT transformation;

(8) and finally, taking the mean value and the covariance of [ x, y ] as virtual observation of trilateral positioning of the sensor network, and combining Kalman filtering to realize positioning and tracking.

2. The method of claim 1 wherein in step (7), the step of UT transforming is as follows:

assuming that the nonlinear function α is f (β), the input variable β is an n-dimensional random state vector, and the average value is known asVariance is P_β. The first and second moments of the function y can be calculated by UT transform techniques. The main process is as follows:

2.1 the random State vector is n-dimensional, so 2n +1 sample points s are calculated_iAnd corresponding weight w_i；

In the above formula, λ is a fine tuning parameter, and the sample point can be further approximated to the state distribution of the true value by adjusting the size of the parameter. The parameter lambda can be used for adjusting the size of the high-order sample moment and the distance from the sample point to the mean value. Representing the ith column square root matrix. And the weight valueThe normalization requirement is met;

2.2, each sampling point is substituted into a nonlinear equation to obtain a transformed point set;

and 2.3, the mean and the variance of the transformed nonlinear function can be estimated by using the weighted new sample points. As shown in the following formula;

3. the method according to step 8) of claim 1, wherein the kalman filtering algorithm comprises the following steps:

3.1 time update:

pre-estimating state variables

Pre-estimation of state variance

3.2 Observation update:

computing kalman gain

Updating state variables

Updating state variance

Technical Field

The invention relates to a target tracking method of a sensor network, which is a method for combining UT transformation and trilateration and belongs to the technical field of information fusion.

Background

In a wireless sensor network, Target Tracking (Target Tracking) is one of the most important and classical applications. The need for target tracking is becoming increasingly strong, whether in the military or civilian fields. Research in this field of application is emerging as a multidisciplinary cross-curriculum, and the aspects involved include signal processing, network architecture, distributed algorithms, and mems (micro electro Mechanical systems) sensor technologies, among others. Due to the easy distributability of the sensor network, the sensors can be arranged in areas without advanced infrastructure preparation, and tasks such as environment monitoring, safety monitoring, battlefield information acquisition and the like are injected. Outdoor target tracking usually utilizes satellites to survey, but indoor and other remote areas have weak satellite signals and cannot timely and effectively position and track targets. The sensor has the characteristics of small volume, light weight, mobility, convenience in deployment, strong real-time performance and the like, and is suitable for being applied to various fields of military affairs, environmental monitoring, medical treatment and the like.

The current tracking filter algorithm mainly comprises linear filtering and nonlinear filtering. The former is most studied and in practice the most commonly used is kalman filtering. For a nonlinear non-Gaussian model, good filtering effect can be obtained based on extended Kalman filtering and unscented Kalman filtering of Kalman filtering, and an effective solution is provided by a particle filtering algorithm. There is a three-dimensional underwater target tracking algorithm proposed in the literature, which tracks a target by using a modified extended kalman gain. There are documents that implement the tracking of the sensor network to the target by applying methods such as particle filtering and UIF. However, problems such as particle degradation and sample depletion exist in the particle filter algorithm, and it is a great challenge to further accelerate the practical process of the wireless sensor network to research a filter algorithm with better comprehensive performance.

Disclosure of Invention

In view of the problems that a linear Gaussian system is not suitable, errors caused by linearization processing are not stable, tracking results are not stable, particle degradation and sample depletion in a particle filter algorithm are solved, the invention aims to provide the sensor network target tracking method combining trilateration and U transformation. The method can provide reference for practical application of the wireless sensor network positioning and tracking technology.

The technical scheme of the invention is as follows: a sensor network target tracking method combining trilateration and U transformation comprises the following specific steps:

(1) the positioning principle of the trilateral algorithm is that the distances between a mobile node and 3 non-collinear beacon nodes are measured in sequence, the positions of the 3 beacon nodes are taken as the circle centers, and the corresponding distances are taken as the radius to make 3 circles. If the distance measurement is error-free, the 3 circles intersect at one point, namely the position coordinate of the mobile node;

(2) trilateration is a distance-based positioning algorithm. The algorithm is described as follows: assuming that the coordinates of the target position are (x, y), the coordinates of the three points a, B, and C are known as (xa, ya), (xb, yb), (xc, yc), respectively. Their distances to the target are da, db and dc, respectively. The following equation can be obtained;

(3) formula (1) minus formula (3), formula (2) minus formula (3), and simultaneous equations;

(4) when a filtering method is adopted for tracking and positioning of the wireless sensor network, nonlinear transformation is required. UT transforms are a new approach to the problem of nonlinear transforms. Trilateration and U-transform are combined to convert tracking from nonlinear filtering to linear filtering. Based on the former three-side positioning method model, the formula can be rewritten as follows;

(5) hypothetical distance observationsIs the true distance d_a,d_b,d_cWith observation noise epsilon_a,ε_b,ε_cThe superposition of (a) and (b) is as follows;

(6) if observing the noise ε_a,ε_b,ε_cIs independent 0 mean Gaussian distribution with variance ofThree actual distances d_a,d_b,d_cChanging into a Gaussian random vector;

wherein the content of the first and second substances,

and it is known that A, B, C are not collinear and are available;

(7) then, the mean value and the variance of the target position (x, y) can be obtained through UT transformation; the UT conversion method is as follows: assuming that the nonlinear function α is f (β), the input variable β is an n-dimensional random state vector, and the average value is known asVariance is P_β. The first and second moments of the function y can be calculated by UT transform techniques.

The specific steps of the UT transformation are as follows:

the random state vector is n-dimensional, so 2n +1 sample points s are calculated_iAnd corresponding weight w_i；

The upper typeIn the method, lambda is a fine tuning parameter, and the sample point can be closer to the state distribution of a true value by adjusting the size of the parameter. The parameter lambda can be used for adjusting the size of the high-order sample moment and the distance from the sample point to the mean value. Representing the ith column square root matrix. And the weight valueThe normalization requirement is met;

each sampling point is substituted into a nonlinear equation to obtain a transformed point set;

α_i＝f(s_i)(i＝1,2,...,2n)

the mean and variance of the transformed nonlinear function can be estimated by using the new sample points with weights. As shown in the following formula;

(8) and finally, taking the mean value and covariance of [ x, y ] as virtual observation of trilateral positioning of the sensor network, and further realizing positioning and tracking by combining Kalman filtering, wherein the calculation steps are as follows:

and (3) time updating:

pre-estimating state variables

Pre-estimation of state variance

And (3) observation updating:

computing kalman gain

Updating state variables

Updating state variance

Compared with the existing nonlinear filtering technology, the invention has the beneficial effects that:

(1) the invention effectively fuses the target state prior information obtained by means of the motion model and the target state likelihood information obtained by sensor data reverse estimation, and has the characteristics of higher precision and stronger robustness.

(2) The algorithm structure of the invention is more concise, the application range is wide, and the invention has very high practical value in the aspects of radar, multi-sensor, maneuvering and multi-target tracking.

Drawings

FIG. 1 is a general flow chart of the present invention;

FIG. 2 is a trace plot under two algorithms;

FIG. 3 is a graph comparing the mean square error of the present invention with that of the classical particle filter algorithm when different numbers of particles are selected;

Detailed Description

The invention is further explained below with reference to the drawings and simulations.

The motion state of the object is three-dimensional, being [ x; y; a ], each representing the abscissa, ordinate and orientation angle relative to a fixed coordinate system, denoted as a circle model in the present invention, whose motion model is as follows:

e_k+1＝F_kx_k+G_kw_k

wherein, w_kIs a mean value of0 covariance of Q_wThe process noise sequence of (1).

The simulation platform used herein is MATLAB R2016a, which simulates and verifies the improved algorithm, thereby analyzing the performance of the improved algorithm. The instantaneous rate of motion of the vehicle was fixed to 1m/s and then the yaw rate was fixed to 5 deg/s. Each time step adds gaussian white noise to the state, the noise is three-dimensional, the obedient mean is zero, and the covariance is diag ([0.01,0.01,1deg ^2 ]). When the observation noise is introduced, white gaussian noise with a mean value of 0 and a variance of 0.01 is introduced. The four node positions are (10,0) respectively; (10, 10); (0, 15); (-5,20), the maximum distance measurement discrimination threshold is 20, and three nodes closest to the target are selected for trilateral positioning each time. The numbers of the selected particles are 100, 500 and 1000 respectively, and simulation is carried out respectively. The number of monte carlo simulations per time was 40. The simulation results are shown in the graph.

Table 1 is the average run time for two algorithms:

Algorithm	Our method	100PF	500PF	900PF
					Time	7.043147	17.261485	68.499729	125.184469

TABLE 1

As can be seen from table 1, as the number of particles increases, the running time of the algorithm increases, which indicates that increasing the number of particles in a single step does not improve the overall performance of the algorithm. As can be seen from fig. 2 and 3, the closer the state estimation value of the improved algorithm is to the actual state value, and it can be found that the measurement error of the UT-based trilateration algorithm is smaller than PF regardless of the number of particles, which indicates that the estimation accuracy of the improved trilateration algorithm is better than PF.

In conclusion, the method has the advantages of low measurement error, low time complexity and good tracking effect. The method can provide reference for practical application of the wireless sensor network positioning and tracking technology.