CN112637807A - Sensor selection method based on disturbance and environment, distance and energy constraints - Google Patents

Abstract

The invention discloses a sensor selection method based on disturbance and environment, distance and energy constraints, which comprises the steps of initializing data and determining the lowest MSE of a sensor network; and constructing an objective function, selecting a number model for the sensor nodes with weights in the minimized moment, performing convex problem conversion on the sensor nodes after relaxation conversion, and performing update iteration until the distribution is finished. Aiming at the influence of environmental factors, node measurement disturbance and distance disturbance factors between nodes and a target on target monitoring precision, which are not considered in the existing sensor selection algorithm, the invention provides a sensor selection algorithm based on environment, energy and estimation precision constraints, and an iteration method for embedding penalty items in a target function is utilized to iteratively solve a minimum sensor selection number set on the premise of ensuring the estimation precision and balance the energy of a wireless sensor network.

Description

Translated fromChinese

基于扰动与环境、距离和能量约束的传感器选择方法Sensor selection method based on disturbance and environment, distance and energy constraints

技术领域technical field

本发明涉及无线传感器网络通信技术领域，尤其涉及一种基于扰动与环境、距离和能量约束的传感器选择方法。The invention relates to the technical field of wireless sensor network communication, in particular to a sensor selection method based on disturbance and environment, distance and energy constraints.

背景技术Background technique

目前，随着传感器小型化、智能化及计算能力提高，无线传感器网络(WSN)应用场景日益多元，使传感器选择逐渐成为无线传感器网络的研究热点。若利用无线传感器网络中的所有传感器节点对一个目标进行测量，可以获得与目标相关的最全面的信息，但这会增加无线传感器网络的能耗和处理负担。因此，根据无线传感器网络的精度要求，选择部分传感器节点对目标进行测量，可以节省能量，减少无线传感器网络的响应延迟，有利于延长无线传感器网络的使用寿命。At present, with the miniaturization, intelligence and improvement of computing power of sensors, the application scenarios of wireless sensor networks (WSN) are increasingly diversified, making sensor selection gradually become a research hotspot of wireless sensor networks. If all sensor nodes in the wireless sensor network are used to measure a target, the most comprehensive information about the target can be obtained, but this will increase the energy consumption and processing burden of the wireless sensor network. Therefore, according to the accuracy requirements of the wireless sensor network, selecting some sensor nodes to measure the target can save energy, reduce the response delay of the wireless sensor network, and prolong the service life of the wireless sensor network.

传感器对目标的估计性能和剩余能量是传感器选择中需要考虑的两个关键因素；Cristian Rusu等人提出了一种具有时间、能量和通信约束的传感器调度方法，在将问题建模为0-1问题，即不选择传感器节点或选择传感器节点问题的基础上，提出了一种基于凸松弛技术以及目标函数中嵌入惩罚项的迭代方法，直接优化均方误差，在保证估计精度的前提下，平衡无线传感器网络的能量和通信需求。但是，该方法仍然具有一些局限性。首先，此方法不涉及监测环境变化时对估计精度的影响；其次，未考虑传感器的量测信息和位置由于信号延迟等受到扰动时对传感器调度的影响。以上因素都会影响网络中的传感器节点调度，进而影响整个网络的估计精度和生命周期。The estimated performance of the sensor to the target and the remaining energy are two key factors to be considered in sensor selection; Cristian Rusu et al. proposed a sensor scheduling method with time, energy and communication constraints, in modeling the problem as 0-1 On the basis of the problem of not selecting sensor nodes or selecting sensor nodes, an iterative method based on convex relaxation technology and embedding penalty terms in the objective function is proposed to directly optimize the mean square error, and on the premise of ensuring the estimation accuracy, balance Energy and communication requirements for wireless sensor networks. However, this method still has some limitations. First, this method does not involve the impact of monitoring environmental changes on the estimation accuracy; secondly, it does not consider the impact on sensor scheduling when the sensor's measurement information and location are disturbed due to signal delays. The above factors will affect the scheduling of sensor nodes in the network, and then affect the estimation accuracy and life cycle of the entire network.

发明内容SUMMARY OF THE INVENTION

本发明的目的是提供一种基于扰动与环境、距离和能量约束的传感器选择方法，能够在传感器量测及位置存在有界扰动情况下，基于能量和估计精度约束，利用松弛技术，迭代求解最小数目传感器集，平衡能量和精度，实现最优选择。The purpose of the present invention is to provide a sensor selection method based on disturbance and environment, distance and energy constraints, which can iteratively solve the smallest Numerous sensor sets, balancing energy and precision for optimal selection.

本发明采用的技术方案为：The technical scheme adopted in the present invention is:

一种基于扰动与环境、距离和能量约束的传感器选择方法，依次包括以下步骤：A sensor selection method based on disturbance and environment, distance and energy constraints, including the following steps in sequence:

步骤一：在无线传感器监测区域内随机部署M个传感器构成集合Ω，测量目标x的N维参数，N∈N₊，N₊表示正整数；传感器节点i的量测为

i＝1,...,M；量测矩阵

[·]^T表示转置运算，设定传感器观测时刻T，T∈N₊；Step 1: Randomly deploy M sensors in the wireless sensor monitoring area to form a set Ω, measure the N-dimensional parameters of the target x, N∈N₊ , N₊ represents a positive integer; the measurement of sensor node i is

i=1,...,M; measurement matrix

[·]^T represents the transposition operation, set the sensor observation time T, T∈N₊ ;

步骤二：根据监测区域环境的温度、能见度和相对湿度，构造环境因子C；根据传感器节点i和目标x的位置，确定距离参数d_i，距离参数矩阵d_M＝[d₁,...,d_i,...,d_M]^T；由监测区域面积S和环境因子C以及传感器节点个数M确定相对区域面积S_M；Step 2: According to the temperature, visibility and relative humidity of the environment in the monitoring area, construct the environmental factor C; according to the position of the sensor node i and the target x, determine the distance parameter d_i , the distance parameter matrix d_M =[d₁ ,..., d_i ,...,d_M ]^T ; the relative area area S_M is determined by the monitoring area area S, the environmental factor C and the number M of sensor nodes;

由于距离目标较近的传感器节点具有较高的估计精度以及较少的能量消耗，因此由传感器节点i距离参数d_i和相对区域面积S_M，确定传感器节点i的选择距离权重H_i，所有传感器节点的距离权重矩阵H∈R^M；设定传感器节点i的量测扰动(Δ_Φ)_i，Δ_Φ∈R^M×N，量测扰动和传感器节点i与目标x的距离扰动(Δ_PL)_i,Δ_PL∈R^M的界分别为δ_Φ和δ_PL，传感器节点i的感测和处理成本s_i，

Since the sensor nodes closer to the target have higher estimation accuracy and less energy consumption, the selected distance weight H_i of sensor node i is determined by the sensor node i distance parameter d_i and the relative area S_M , and all sensors Node distance weight matrix H∈R^M ; set the measurement disturbance of sensor node i (Δ_Φ )_i , Δ_Φ ∈ R^M×N , the measurement disturbance and the distance disturbance between sensor node i and target x (Δ_PL )_i , Δ_PL ∈^RM are bounded by δ_Φ and δ_PL , respectively, the sensing and processing cost s_i of sensor node i,

步骤三：根据传感器量测矩阵Φ以及量测扰动矩阵Δ_Φ通过均方误差MSE公式确定传感器网络最低MSE，γ₀；Step 3: According to the sensor measurement matrix Φ and the measurement disturbance matrix_ΔΦ , determine the lowest MSE of the sensor network, γ₀ by the mean square error MSE formula;

步骤四：构造目标函数为最小化时刻T内带有权重(α_t)_i＝((ω_t)_i+∈)^-1,i＝1,...,M的传感器节点选择个数，即选择矩阵Θ中的非零个数，Θ＝[ω₁,ω₂,…,ω_T]，M维选择矢量ω_t∈{0,1}^M描述t时刻传感器集合Ω中传感器状态，传感器节点i被选中时，其序号对应的(ω_t)_i坐标为1，否则为0，其中(·)^-1表示逆运算，∈是防止迭代过程中权重矢量(α_t)_i分母为零无意义的参数；使用传感器节点i进行处理和感测的成本不高于可用参考能量

Step 4: Construct the objective function to minimize the number of sensor nodes with weight (α_t )_i =((ω_t )_i +∈)^-1 ,i=1,...,M in time T, that is Select the non-zero number in the matrix Θ, Θ=[ω₁ ,ω₂ ,...,ω_T ], the M-dimensional selection vector ω_t ∈{0,1}^M describes the sensor state in the sensor set Ω at time t, the sensor node When i is selected, the (ω_t )_i coordinate corresponding to its serial number is 1, otherwise it is 0, where ( )^-1 represents the inverse operation, ∈ is to prevent the weight vector (α_t )_i denominator from being zero in the iteration process is meaningless parameters; the cost of processing and sensing using sensor node i is no higher than the available reference energy

对额外使用能量E_i加以惩罚，E∈R^M；约束每个传感器节点i在观测时间T内最少选择一次；Penalize the extra use of energy E_i , E∈R^M ; constrain each sensor node i to be selected at least once within the observation time T;

步骤五：将步骤四中求解的时刻T内的非凸传感器选择矩阵Θ∈{0,1}^M×T采用0-1松弛技术，松弛为多面体约束Θ∈[0,1]^M×T，Θ中元素由只能为0或1，松弛为0和1之间的实数，从而将步骤四中问题转化为凸问题，利用凸优化工具包进行求解；Step 5: Use the 0-1 relaxation technique to relax the non-convex sensor selection matrix Θ∈{0,1}^M×T in the moment T solved in step 4 to the polyhedron constraint Θ∈[0,1]^M×T , The elements in Θ can only be 0 or 1, and the relaxation is a real number between 0 and 1, so that the problem in step 4 is transformed into a convex problem, and the convex optimization toolkit is used to solve it;

步骤六：设定初始传感器选择权重α_t＝1，初始全零解选择矩阵Θ₀＝0_M×T，未选择传感器节点集合

和选择传感器节点集合

是空集；Step 6: Set the initial sensor selection weight α_t =1, the initial all-zero solution selection matrix Θ₀ =0_M×T , no sensor node set is selected

and select sensor node set

is the empty set;

步骤七：根据步骤五转化后的凸问题中的目标函数与约束条件公式，求解出传感器节点选择矩阵Θ；Step 7: Solve the sensor node selection matrix Θ according to the objective function and constraint formula in the transformed convex problem in step 5;

步骤八：采用舍入方法更新集合：由N＝{n|Θ(n)≤∈}更新未选择传感器节点集合N，K＝{k|Θ(k)≥1-∈}更新选择传感器节点集合K，∈＝10e-5；Step 8: Use the rounding method to update the set: update the unselected sensor node set N by N={n|Θ(n)≤∈}, and update the selected sensor node set with K={k|Θ(k)≥1-∈} K, ∈ = 10e-5;

步骤九：如果迭代过程已经收敛，即

则更新集合

||·||_F表示F-范数；Step 9: If the iterative process has converged, i.e.

then update the collection

||·||_F represents the F-norm;

步骤十：当时刻T内M个传感器节点全部分配到集合N和K中，即|N|+|K|＝M×T时结束，否则令Θ₀＝Θ，由(α_t)_i＝((ω_t)_i+∈)^-1更新权重，重复步骤七至步骤十。Step 10: When all M sensor nodes are allocated to sets N and K at time T, that is, |N|+|K|=M×T, the process ends; otherwise, let Θ₀ =Θ, by (α_t )_i = ( (ω_t )_i +∈)^-1 to update the weights, and repeat steps seven to ten.

在步骤二中，所述由监测区域环境的温度、能见度和相对湿度确定的环境因子C、距离参数矩阵d_M和相对区域面积S_M、距离权重矩阵H，其表达式如下：In step 2, the environmental factor C, the distance parameter matrix d_M , the relative area area S_M , and the distance weight matrix H determined by the temperature, visibility and relative humidity of the monitoring area environment are expressed as follows:

C＝V/(pht₀)，C=V/(pht₀ ),

(d_M)_i＝1/||m_i-b||₂，i＝1,...,M,S_M＝SC/M,H_i＝(S_M(ω_t)_i)⊙(d_M)_i，(d_M )_i =1/||m_i -b||₂ , i=1,...,M,S_M =SC/M,H_i =(S_M (ω_t )_i )⊙(d_M )_i ,

其中V为能见度，p为环境调节参数,h为相对湿度，t₀为温度，(d_M)_i表示传感器节点i与目标x间距离的倒数，b＝[b_x,b_y]为目标x的坐标位置，m_i＝[m_ix,m_iy]为传感器节点i的坐标位置，S为监测区域面积，ω_t∈R^M为t时刻的传感器节点选择向量，||·||₂表示2-范数，⊙表示Hadamard积。where V is the visibility, p is the environmental adjustment parameter, h is the relative humidity, t₀ is the temperature, (d_M )_i is the reciprocal of the distance between the sensor node i and the target x, b₌ [b_x ,by ] is the target x The coordinate position of , m_i =[m_ix ,m_iy ] is the coordinate position of the sensor node i, S is the monitoring area area, ω_t ∈R^M is the sensor node selection vector at time t, ||·||₂ means 2 - norm, ⊙ denotes the Hadamard product.

在步骤三中，所述最低MSE如下：In step three, the minimum MSE is as follows:

γ₀＝tr((Φ^TΦ)^-1)，其中tr(·)表示求迹运算。γ₀ =tr((Φ^T Φ)^-1 ), where tr(·) represents a trace operation.

在步骤四中，所述目标函数和约束条件为：In step 4, the objective function and constraints are:

s.t.tr(((Φ+Δ_Φ)^Tdiag(H)(Φ+Δ_Φ))^-1)≤τγ₀-C (a)sttr(((Φ+Δ_Φ )^T diag(H)(Φ+Δ_Φ ))^-1 )≤τγ₀ -C (a)

C-γ₀(τ-1)≤0 (b)C-γ₀ (τ-1)≤0 (b)

(diag(s)Θ1)⊙(P_L+Δ_PL)≤e₀+E (c)(diag(s)Θ1)⊙(_PL +_ΔPL )≤e₀ +E (c)

其中α_t∈R^M，(α_t)_i＝((ω_t)_i+∈)^-1,i＝1,...,M为权重矢量，Θ＝[ω₁,ω₂,…,ω_T]为选择矩阵；Δ_Φ∈R^M×N为传感器节点量测扰动，diag(H)表示以距离权重矩阵H为对角线的对角矩阵；Δ_PL∈R^M×1为传感器节点与目标之间的距离扰动，δ_Φ、δ_PL分别为其扰动的界；

为处理和感测成本，diag(s)表示以成本矩阵s为对角线的对角矩阵；1^T×1为全1矩阵；P_L＝[(P_L)₁,...(P_L)_i,...(P_L)_M]^T，

表示传感器节点i与目标x距离相关的Rayleigh信道衰减，η为信道衰减因子；

为可用参考能量，E∈R^M为额外使用能量，惩罚函数

λ为正则化参数；||·||_∞表示∞-范数；where α_t ∈R^M , (α_t )_i =((ω_t )_i +∈)^-1 , i=1,...,M is the weight vector, Θ=[ω₁ ,ω₂ ,...,ω_T ] is the selection matrix; Δ_Φ ∈ R^M×N is the sensor node measurement disturbance, diag(H) represents the diagonal matrix with the distance weight matrix H as the diagonal; Δ_PL ∈ R^M×1 is the sensor node and the The distance disturbance between targets, δ_Φ and δ_PL are the bounds of the disturbance respectively;

For processing and sensing costs, diag(s) represents a diagonal matrix with cost matrix s as the diagonal; 1^T×1 is an all-one matrix; P_L =[(_PL )₁ ,...(_PL )_i ,...(_PL )_M ]^T ,

represents the Rayleigh channel attenuation related to the distance between sensor node i and target x, and η is the channel attenuation factor;

is the available reference energy, E∈R^M is the additional energy used, and the penalty function

λ is the regularization parameter; ||·||_∞ represents the ∞-norm;

1)通过矩阵变换，将约束条件||Δ_Φ||₂＜δ_Φ与(a)转化为线性矩阵不等式形式：1) Through matrix transformation, the constraints ||Δ_Φ ||₂ <δ_Φ and (a) are transformed into linear matrix inequality form:

tr(U^-1)≤τγ₀-C,tr(U^-1 )≤τγ₀ -C,

β≥0β≥0

U∈R^N×N是一个对称正定矩阵，且U≤(Φ+Δ_Φ)^Tdiag(H)(Φ+Δ_Φ)，I为N×N的单位阵，β≥0是转化过程中的辅助参数；U∈R^N×N is a symmetric positive definite matrix, and U≤(Φ+Δ_Φ )^T diag(H)(Φ+Δ_Φ ), I is an N×N identity matrix, β≥0 is the transformation process auxiliary parameters;

2)将约束条件(c)与||Δ_PL||_∞＜δ_PL，转化为矢量约束：2) Convert constraint (c) and ||_ΔPL ||_∞ <δ_PL into vector constraints:

其中，

in,

因此问题可表示为：So the problem can be expressed as:

在步骤五中，所述问题转化为凸问题表示为：In step five, the problem is transformed into a convex problem expressed as:

本发明针对现有传感器选择方法中未考虑环境因素以及节点量测扰动和节点与目标间距离扰动因素对目标监测精度的影响，提出一种基于环境、能量和估计精度约束的传感器选择方法，利用松弛技术以及目标函数中嵌入惩罚项的迭代方法，在保证估计精度的前提下，迭代求解最小传感器选择数目集，平衡无线传感器网络的能量。Aiming at the influence of environmental factors and node measurement disturbance and distance disturbance factors between nodes and targets on the target monitoring accuracy that are not considered in the existing sensor selection methods, the present invention proposes a sensor selection method based on the constraints of environment, energy and estimation accuracy. The relaxation technique and the iterative method of embedding the penalty term in the objective function, under the premise of ensuring the estimation accuracy, iteratively solve the minimum sensor selection number set to balance the energy of the wireless sensor network.

附图说明Description of drawings

为了更清楚地说明本发明实施例或现有技术中的技术方案，下面将对实施例或现有技术描述中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他的附图。In order to illustrate the embodiments of the present invention or the technical solutions in the prior art more clearly, the following briefly introduces the accompanying drawings that are used in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only These are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can also be obtained according to these drawings without creative efforts.

图1为本发明的流程图。FIG. 1 is a flow chart of the present invention.

具体实施方式Detailed ways

下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有付出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

如图1所示，本发明包括以下步骤：As shown in Figure 1, the present invention comprises the following steps:

(1)：在无线传感器监测区域内随机部署M个传感器构成集合Ω，测量目标x的N维参数，N∈N₊，N₊表示正整数。传感器节点i的量测为

量测矩阵

[·]^T表示转置运算，设定传感器观测时刻T，T∈N₊。(1): Randomly deploy M sensors in the wireless sensor monitoring area to form a set Ω, measure the N-dimensional parameters of the target x, N∈N₊ , N₊ represents a positive integer. The measurement of sensor node i is

Measurement matrix

[·]^T represents the transposition operation, and sets the sensor observation time T, T∈N₊ .

(2)：根据监测区域环境的温度、能见度和相对湿度，构造环境因子C＝V/(pht₀)，其中V为能见度，p为环境调节参数,h为相对湿度，t₀为温度；根据传感器节点i和目标x的位置，确定距离参数d_i＝1/||m_i-b||₂，i＝1,...,M，b＝[b_x,b_y]为目标x的坐标位置，m_i＝[m_ix,m_iy]为传感器节点i坐标位置，距离参数矩阵d_M＝[d₁,...,d_i,...,d_M]^T，||·||₂表示2-范数；由监测区域面积S和环境因子C以及传感器节点个数M确定相对区域面积S_M＝SC/M；显然距离目标较近的传感器节点具有较高的估计精度以及较少的能量消耗，因此由传感器节点i距离参数d_i和相对区域面积S_M确定传感器节点i的距离权重H_i＝(S_M(ω_t)_i)⊙(d_M)_i，所有节点的距离权重矩阵H∈R^M，ω_t∈R^M为t时刻的节点选择向量，⊙表示Hadamard积；设定传感器节点i的量测扰动(Δ_Φ)_i，Δ_Φ∈R^M×N和传感器节点i与目标x的距离扰动(Δ_PL)_i,Δ_PL∈R^M的界分别为δ_Φ和δ_PL，传感器节点i的感测和处理成本s_i，

(2): According to the temperature, visibility and relative humidity of the environment in the monitoring area, construct the environmental factor C=V/(pht₀ ), where V is the visibility, p is the environmental adjustment parameter, h is the relative humidity, and t₀ is the temperature; according to For the position of sensor node i and target x, determine the distance parameter d_i =1/||m_i -b||₂ , i=1,...,M, b₌ [b_x ,by ] as the target x Coordinate position, m_i =[m_ix ,m_iy ] is the coordinate position of sensor node i, distance parameter matrix d_M =[d₁ ,...,d_i ,...,d_M ]^T , || ·| |₂ represents the 2-norm; the relative area area S_M = SC/M is determined by the monitoring area area S, the environmental factor C and the number of sensor nodes M; it is obvious that the sensor nodes closer to the target have higher estimation accuracy and higher estimation accuracy. Therefore, the distance weight H_i =(S_M (ω_t )_i )⊙(d_M )_i of the sensor node i is determined by the distance parameter d_i of the sensor node i and the relative area_SM Weight matrix H∈R^M , ω_t ∈ R^M is the node selection vector at time t, ⊙ represents Hadamard product; set the measurement disturbance of sensor node i (Δ_Φ )_i , Δ_Φ ∈ R^M×N and sensor node The distance perturbation between i and target x (Δ_PL )_i , Δ_PL ∈^RM is bounded by δ_Φ and δ_PL , respectively, the sensing and processing cost si of sensor node_i ,

(3)：根据传感器量测矩阵Φ以及量测扰动矩阵Δ_Φ和均方误差MSE公式确定传感器网络最低MSE，γ₀＝tr((Φ^TΦ)^-1)，即选择所有的传感器节点，得到最好的估计精度。其中tr(·)表示求迹运算，(·)^-1表示逆运算。由于对传感器节点进行部分选择，估计精度下降，网络MSE增大，精度等级τ增加。设定估计精度等级τ≥1。均方误差MSE公式为现有的技术，在此不再赘述。(3): Determine the lowest MSE of the sensor network according to the sensor measurement matrix Φ, the measurement disturbance matrix Δ_Φ and the mean square error MSE formula, γ₀ =tr((Φ^T Φ)^-1 ), that is, select all sensor nodes, Get the best estimation accuracy. Where tr( ) represents the trace operation, and ( )^-1 represents the inverse operation. Due to the partial selection of sensor nodes, the estimation accuracy decreases, the network MSE increases, and the accuracy level τ increases. Set the estimation accuracy level τ≥1. The mean square error MSE formula is an existing technology and will not be repeated here.

(4)构造目标函数为最小化时刻T内带有权重矢量(α_t)_i＝((ω_t)_i+∈)^-1,i＝1,...,M的传感器节点选择个数，即选择矩阵Θ中的非零个数，Θ＝[ω₁,ω₂,…,ω_T]，M维选择矢量ω_t∈{0,1}^M描述t时刻传感器集合Ω中传感器状态，传感器节点i被选中时，其序号对应的(ω_t)_i坐标为1，否则为0；∈是防止迭代过程中权重矢量(α_t)_i分母为零无意义的参数；在监测环境因子C的条件下，若要提高传感器选择节点的估计精度，则需要更多节点满足环境要求，且距离目标较近的传感器节点具有较高的估计精度，因此约束在环境因子C和距离权重H影响下，由(3)中MSE公式，使选择节点的估计精度高于一定精度误差水平且低于最高误差水平；约束在Rayleigh信道衰减下，使用传感器节点i进行处理和感测的成本不高于可用参考能量

为了避免消耗传感器节点i的额外能量消耗，因此对额外使用能量E_i加以惩罚，E∈R^M；为平衡网络能量，避免多次使用同一个传感器节点，约束每个传感器节点i在观测时间T内最少选择一次。目标函数如下：(4) Construct the objective function to minimize the number of sensor nodes with weight vector (α_t )_i =((ω_t )_i +∈)^-1 ,i=1,...,M in time T, That is, select the non-zero number in the matrix Θ, Θ=[ω₁ ,ω₂ ,...,ω_T ], the M-dimensional selection vector ω_t ∈{0,1}^M describes the sensor state in the sensor set Ω at time t, the sensor When node i is selected, the (ω_t )_i coordinate corresponding to its serial number is 1, otherwise it is 0; ∈ is a parameter that prevents the denominator of the weight vector (α_t )_i from being zero in the iterative process; Under the conditions, to improve the estimation accuracy of sensor selection nodes, more nodes are required to meet the environmental requirements, and the sensor nodes closer to the target have higher estimation accuracy. Therefore, under the influence of the environmental factor C and the distance weight H, According to the MSE formula in (3), the estimation accuracy of the selected node is higher than a certain accuracy error level and lower than the highest error level; under the constraint of Rayleigh channel attenuation, the cost of processing and sensing using sensor node i is not higher than the available reference energy

In order to avoid consuming the extra energy consumption of sensor node i, the extra energy E_i is penalized, E∈R^M ; in order to balance the network energy, avoid using the same sensor node multiple times, and constrain each sensor node i in the observation time T Select at least once. The objective function is as follows:

s.t.tr(((Φ+Δ_Φ)^Tdiag(H)(Φ+Δ_Φ))^-1)≤τγ₀-C (a)sttr(((Φ+Δ_Φ )^T diag(H)(Φ+Δ_Φ ))^-1 )≤τγ₀ -C (a)

C-γ₀(τ-1)≤0 (b)C-γ₀ (τ-1)≤0 (b)

(diag(s)Θ1)⊙(P_L+Δ_PL)≤e₀+E (c)(diag(s)Θ1)⊙(_PL +_ΔPL )≤e₀ +E (c)

其中α_t∈R^M，(α_t)_i＝((ω_t)_i+∈)^-1,i＝1,...,M为权重矢量，Θ＝[ω₁,ω₂,…,ω_T]为选择矩阵；

表示传感器节点i与目标x距离相关的Rayleigh信道衰减，η为信道衰减因子；Δ_Φ∈R^M×N为节点量测扰动，Δ_PL∈R^M×1为节点与目标之间的距离扰动，δ_Φ、δ_PL分别为其扰动的界；

为处理和感测成本；

为可用参考能量，E∈R^M为额外使用能量，惩罚函数

λ为正则化参数；||·||_∞表示∞-范数。where α_t ∈R^M , (α_t )_i =((ω_t )_i +∈)^-1 , i=1,...,M is the weight vector, Θ=[ω₁ ,ω₂ ,...,ω_T ] is the selection matrix;

represents the Rayleigh channel attenuation related to the distance between sensor node i and target x, η is the channel attenuation factor; Δ_Φ ∈ R^M×N is the node measurement disturbance, Δ_PL ∈ R^M×1 is the distance disturbance between the node and the target, δ_Φ and δ_PL are the perturbation bounds respectively;

for processing and sensing costs;

is the available reference energy, E∈R^M is the additional energy used, and the penalty function

λ is the regularization parameter; ||·||_∞ represents the ∞-norm.

1)通过矩阵变换，将约束条件||Δ_Φ||₂＜δ_Φ与(a)转化为线性矩阵不等式形式：1) Through matrix transformation, the constraints ||Δ_Φ ||₂ <δ_Φ and (a) are transformed into linear matrix inequality form:

tr(U^-1)≤τγ₀-C,tr(U^-1 )≤τγ₀ -C,

β≥0β≥0

U∈R^N×N是一个对称正定矩阵，且U≤(Φ+Δ_Φ)^Tdiag(H)(Φ+Δ_Φ)，I为N×N的单位阵，β≥0是转化过程中的辅助参数；U∈R^N×N is a symmetric positive definite matrix, and U≤(Φ+Δ_Φ )^T diag(H)(Φ+Δ_Φ ), I is an N×N identity matrix, β≥0 is the transformation process auxiliary parameters;

2)将约束条件(c)与||Δ_PL||_∞＜δ_PL，转化为矢量约束：2) Convert constraint (c) and ||_ΔPL ||_∞ <δ_PL into vector constraints:

其中，

in,

因此问题可表示为：So the problem can be expressed as:

(5)将(4)中求解的时刻T内的非凸节点选择矩阵Θ∈{0,1}^M×T松弛为多面体约束Θ∈[0,1]^M×T，从而将(4)中问题转化为如下凸问题，利用凸优化工具包进行求解：(5) Relax the non-convex node selection matrix Θ∈{0,1}^M×T in the time T solved in (4) into a polyhedral constraint Θ∈[0,1]^M×T , so that in (4) The problem is transformed into the following convex problem, which is solved using the convex optimization toolkit:

(diag(s)Θ1)⊙(P_L+Π)≤e₀+E(diag(s)Θ1)⊙(P_L +Π)≤e₀ +E

tr(U^-1)≤τγ₀-Ctr(U^-1 )≤τγ₀ -C

β≥0β≥0

C-γ₀(τ-1)≤0C-γ₀ (τ-1)≤0

(6)：设定初始节点选择权重α_t＝1，初始全零解选择矩阵Θ₀＝0_M×T，未选择节点集合

和选择节点集合

(6): Set the initial node selection weight α_t =1, the initial all-zero solution selection matrix Θ₀ =0_M×T , no node set is selected

and select node collection

(7)：根据(5)确定的目标函数与约束条件公式，求解出节点选择矩阵Θ。(7): According to the objective function and constraint formula determined in (5), the node selection matrix Θ is solved.

(8)：由N＝{n|Θ(n)≤∈}更新未选择节点集合N，K＝{k|Θ(k)≥1-∈}更新选择节点集合K，∈＝10e-5。(8): Update the unselected node set N by N={n|Θ(n)≤∈}, and update the selected node set K with K={k|Θ(k)≥1-∈}, ∈=10e-5.

(9)：如果迭代过程已经收敛，即

则更新集合

||·||_F表示F-范数。(9): If the iterative process has converged, i.e.

then update the collection

||·||_F represents the F-norm.

(10)：当时刻T内M个传感器节点全部分配到集合N和K中，即|N|+|K|＝M×T时结束，否则令Θ₀＝Θ，由(α_t)_i＝((ω_t)_i+∈)^-1更新选择权重，重复(7)至(10)。(10): When all M sensor nodes are allocated to sets N and K at time T, that is, |N|+|K|=M×T, it ends, otherwise let Θ₀ =Θ, by (α_t )_i = ((ω_t )_i +∈)^-1 to update the selection weight, repeat (7) to (10).

以上结合附图详细说明了本发明的技术方案，本发明的技术方案提出了一种新的基于不确定性扰动的在环境、距离和能量约束下的传感器选择方法。The technical solution of the present invention is described in detail above with reference to the accompanying drawings, and the technical solution of the present invention proposes a new sensor selection method under the constraints of environment, distance and energy based on uncertainty disturbance.

注意，上述仅为本发明的较佳实施例及运用技术原理。本领域技术人员会理解，本发明不限于这里所述的特定实施例，对本领域技术人员来说能够进行各种明显的变化、重新调整和替代而不会脱离本发明的保护范围。因此，虽然通过以上实施例对本发明进行较详细的说明，但本发明不限于这里所述的特定实施例，在不脱离本发明构思的情况下，还可以包括更多其他等有效实施例，而本发明的范围由所附的权利要求范围决定。Note that the above is only the preferred embodiment of the present invention and the technical principle of its application. Those skilled in the art will understand that the present invention is not limited to the specific embodiments described herein, and various obvious changes, readjustments and substitutions can be made by those skilled in the art without departing from the protection scope of the present invention. Therefore, although the present invention is described in detail through the above embodiments, the present invention is not limited to the specific embodiments described herein, and can also include more other effective embodiments without departing from the concept of the present invention. The scope of the invention is determined by the scope of the appended claims.

Claims (5)

Translated fromChinese

1.基于扰动与环境、距离和能量约束的传感器选择方法，其特征在于：依次包括以下步骤：1. The sensor selection method based on disturbance and environment, distance and energy constraints, is characterized in that: comprise the following steps successively:步骤一：在无线传感器监测区域内随机部署M个传感器构成集合Ω，测量目标x的N维参数，N∈N₊，N₊表示正整数；传感器节点i的量测为

量测矩阵

[·]^T表示转置运算，设定传感器观测时刻T，T∈N₊；Step 1: Randomly deploy M sensors in the wireless sensor monitoring area to form a set Ω, measure the N-dimensional parameters of the target x, N∈N₊ , N₊ represents a positive integer; the measurement of sensor node i is

Measurement matrix

[·]^T represents the transposition operation, set the sensor observation time T, T∈N₊ ;步骤二：根据监测区域环境的温度、能见度和相对湿度，构造环境因子C；Step 2: According to the temperature, visibility and relative humidity of the monitoring area environment, construct the environmental factor C;根据传感器节点i和目标x的位置，确定距离参数d_i，距离参数矩阵d_M＝[d₁,...,d_i,...,d_M]^T；由监测区域面积S和环境因子C以及传感器节点个数M确定相对区域面积S_M；According to the positions of sensor node i and target x, determine distance parameter d_i , distance parameter matrix d_M =[d₁ ,...,d_i ,...,d_M ]^T ; C and the number of sensor nodes M determine the relative area area S_M ;由于距离目标较近的传感器节点具有较高的估计精度以及较少的能量消耗，因此由传感器节点i距离参数d_i和相对区域面积S_M，确定传感器节点i的选择距离权重H_i，所有传感器节点的距离权重矩阵H∈R^M；设定传感器节点i的量测扰动(Δ_Φ)_i，Δ_Φ∈R^M×N，量测扰动和传感器节点i与目标x的距离扰动(Δ_PL)_i,Δ_PL∈R^M的界分别为δ_Φ和δ_PL，传感器节点i的感测和处理成本s_i，

Since the sensor nodes closer to the target have higher estimation accuracy and less energy consumption, the selected distance weight H_i of sensor node i is determined by the sensor node i distance parameter d_i and the relative area S_M , and all sensors Node distance weight matrix H∈R^M ; set the measurement disturbance of sensor node i (Δ_Φ )_i , Δ_Φ ∈ R^M×N , the measurement disturbance and the distance disturbance between sensor node i and target x (Δ_PL )_i , Δ_PL ∈^RM are bounded by δ_Φ and δ_PL , respectively, the sensing and processing cost s_i of sensor node i,

步骤三：根据传感器量测矩阵Φ以及量测扰动矩阵Δ_Φ通过均方误差MSE公式确定传感器网络最低MSE，γ₀；Step 3: According to the sensor measurement matrix Φ and the measurement disturbance matrix_ΔΦ , determine the lowest MSE of the sensor network, γ₀ by the mean square error MSE formula;步骤四：构造目标函数为最小化时刻T内带有权重(α_t)_i＝((ω_t)_i+∈)^-1,i＝1,…,M的传感器节点选择个数，即选择矩阵Θ中的非零个数，Θ＝[ω₁,ω₂,…,ω_T]，M维选择矢量ω_t∈{0,1}^M描述t时刻传感器集合Ω中传感器状态，传感器节点i被选中时，其序号对应的(ω_t)_i坐标为1，否则为0，其中(·)^-1表示逆运算，∈是防止迭代过程中权重矢量(α_t)_i分母为零无意义的参数；使用传感器节点i进行处理和感测的成本不高于可用参考能量

Step 4: Construct the objective function to minimize the number of sensor nodes with weight (α_t )_i =((ω_t )_i +∈)^-1 ,i=1,...,M in time T, that is, the selection matrix The non-zero number in Θ, Θ=[ω₁ ,ω₂ ,...,ω_T ], the M-dimensional selection vector ω_t ∈{0,1}^M describes the sensor state in the sensor set Ω at time t, and the sensor node i is When selected, the (ω_t )_i coordinate corresponding to its serial number is 1, otherwise it is 0, where ( )^-1 represents the inverse operation, and ∈ is a parameter that prevents the denominator of the weight vector (α_t )_i from being zero in the iteration process. ; the cost of processing and sensing using sensor node i is no higher than the available reference energy

对额外使用能量E_i加以惩罚，E∈R^M；约束每个传感器节点i在观测时间T内最少选择一次；Penalize the extra use of energy E_i , E∈R^M ; constrain each sensor node i to be selected at least once within the observation time T;步骤五：将步骤四中求解的时刻T内的非凸传感器选择矩阵Θ∈{0,1}^M×T采用0-1松弛技术，松弛为多面体约束Θ∈[0,1]^M×T，Θ中元素由只能为0或1，松弛为0和1之间的实数，从而将步骤四中问题转化为凸问题，利用凸优化工具包进行求解；Step 5: Use the 0-1 relaxation technique to relax the non-convex sensor selection matrix Θ∈{0,1}^M×T in the moment T solved in step 4 to the polyhedron constraint Θ∈[0,1]^M×T , The elements in Θ can only be 0 or 1, and the relaxation is a real number between 0 and 1, so that the problem in step 4 is transformed into a convex problem, and the convex optimization toolkit is used to solve it;步骤六：设定初始传感器选择权重α_t＝1，初始全零解选择矩阵Θ₀＝0_M×T，未选择传感器节点集合

和选择传感器节点集合

是空集；Step 6: Set the initial sensor selection weight α_t =1, the initial all-zero solution selection matrix Θ₀ =0_M×T , no sensor node set is selected

and select sensor node set

is the empty set;步骤七：根据步骤五转化后的凸问题中的目标函数与约束条件公式，求解出传感器节点选择矩阵Θ；Step 7: Solve the sensor node selection matrix Θ according to the objective function and constraint formula in the transformed convex problem in step 5;步骤八：采用舍入方法更新集合：由N＝{n|Θ(n)≤∈}更新未选择传感器节点集合N，K＝{k|Θ(k)≥1-∈}更新选择传感器节点集合K，∈＝10e-5；Step 8: Use the rounding method to update the set: update the unselected sensor node set N by N={n|Θ(n)≤∈}, and update the selected sensor node set with K={k|Θ(k)≥1-∈} K, ∈ = 10e-5;步骤九：如果迭代过程已经收敛，即

则更新集合

||·||_F表示F-范数；Step 9: If the iterative process has converged, i.e.

then update the collection

||·||_F represents the F-norm;步骤十：当时刻T内M个传感器节点全部分配到集合N和K中，即|N|+|K|＝M×T时结束，否则令Θ₀＝Θ，由(α_t)_i＝((ω_t)_i+∈)^-1更新权重，重复步骤七至步骤十。Step 10: When all M sensor nodes are allocated to sets N and K at time T, that is, |N|+|K|=M×T, the process ends; otherwise, let Θ₀ =Θ, by (α_t )_i = ( (ω_t )_i +∈)^-1 to update the weights, and repeat steps seven to ten.2.根据权利要求1所述的基于扰动与环境、距离和能量约束的传感器选择方法，其特征在于，在步骤二中，所述由监测区域环境的温度、能见度和相对湿度确定的环境因子C、距离参数矩阵d_M和相对区域面积S_M、距离权重矩阵H，其表达式如下：2. The sensor selection method based on disturbance and environment, distance and energy constraints according to claim 1, wherein in step 2, the environmental factor C determined by the temperature, visibility and relative humidity of the monitoring area environment , distance parameter matrix d_M and relative area area S_M , distance weight matrix H, the expressions are as follows:C＝V/(pht₀)，C=V/(pht₀ ),(d_M)_i＝1/||m_i-b||₂，i＝1,...,M,S_M＝SC/M,H_i＝(S_M(ω_t)_i)⊙(d_M)_i，其中V为能见度，p为环境调节参数,h为相对湿度，t₀为温度，(d_M)_i表示传感器节点i与目标x间距离的倒数，b＝[b_x,b_y]为目标x的坐标位置，m_i＝[m_ix,m_iy]为传感器节点i的坐标位置，S为监测区域面积，ω_t∈R^M为t时刻的传感器节点选择向量，||·||₂表示2-范数，⊙表示Hadamard积。(d_M )_i =1/||m_i -b||₂ , i=1,...,M,S_M =SC/M,H_i =(S_M (ω_t )_i )⊙(d_M )_i , where V is the visibility, p is the environmental adjustment parameter, h is the relative humidity, t₀ is the temperature, (d_M )_i is the reciprocal of the distance between the sensor node i and the target x, b₌ [b_x ,by ] is the coordinate position of the target x, m_i =[m_ix ,m_iy ] is the coordinate position of the sensor node i, S is the area of the monitoring area, ω_t ∈R^M is the sensor node selection vector at time t, ||·| |₂ denotes the 2-norm, and ⊙ denotes the Hadamard product.3.根据权利要求1所述的基于扰动与环境、距离和能量约束的传感器选择方法，其特征在于，在步骤三中，所述最低MSE如下：3. The sensor selection method based on disturbance and environment, distance and energy constraints according to claim 1, wherein in step 3, the minimum MSE is as follows:γ₀＝tr((Φ^TΦ)^-1)，其中tr(·)表示求迹运算。γ₀ =tr((Φ^T Φ)^-1 ), where tr(·) represents a trace operation.4.根据权利要求1所述的基于扰动与环境、距离和能量约束的传感器选择方法，其特征在于，在步骤四中，所述目标函数和约束条件为：4. The sensor selection method based on disturbance and environment, distance and energy constraints according to claim 1, characterized in that, in step 4, the objective function and the constraints are:

s.t.tr(((Φ+Δ_Φ)^Tdiag(H)(Φ+Δ_Φ))^-1)≤τγ₀-C (a)sttr(((Φ+Δ_Φ )^T diag(H)(Φ+Δ_Φ ))^-1 )≤τγ₀ -C (a)C-γ₀(τ-1)≤0 (b)C-γ₀ (τ-1)≤0 (b)(diag(s)Θ1)⊙(P_L+Δ_PL)≤e₀+E (c)(diag(s)Θ1)⊙(_PL +_ΔPL )≤e₀ +E (c)

其中α_t∈R^M，(α_t)_i＝((ω_t)_i+∈)^-1,i＝1,...,M为权重矢量，Θ＝[ω₁,ω₂,…,ω_T]为选择矩阵；Δ_Φ∈R^M×N为传感器节点量测扰动，diag(H)表示以距离权重矩阵H为对角线的对角矩阵；Δ_PL∈R^M×1为传感器节点与目标之间的距离扰动，δ_Φ、δ_PL分别为其扰动的界；

为处理和感测成本，diag(s)表示以成本矩阵s为对角线的对角矩阵；1^T×1为全1矩阵；P_L＝[(P_L)₁,...(P_L)_i,...(P_L)_M]^T，

表示传感器节点i与目标x距离相关的Rayleigh信道衰减，η为信道衰减因子；

为可用参考能量，E∈R^M为额外使用能量，惩罚函数

λ为正则化参数；||·||_∞表示∞-范数；where α_t ∈R^M , (α_t )_i =((ω_t )_i +∈)^-1 , i=1,...,M is the weight vector, Θ=[ω₁ ,ω₂ ,...,ω_T ] is the selection matrix; Δ_Φ ∈ R^M×N is the sensor node measurement disturbance, diag(H) represents the diagonal matrix with the distance weight matrix H as the diagonal; Δ_PL ∈ R^M×1 is the sensor node and the The distance disturbance between targets, δ_Φ and δ_PL are the bounds of the disturbance respectively;

For processing and sensing costs, diag(s) represents a diagonal matrix with cost matrix s as the diagonal; 1^T×1 is an all-one matrix; P_L =[(_PL )₁ ,...(_PL )_i ,...(_PL )_M ]^T ,

represents the Rayleigh channel attenuation related to the distance between sensor node i and target x, and η is the channel attenuation factor;

is the available reference energy, E∈R^M is the additional energy used, and the penalty function

λ is the regularization parameter; ||·||_∞ represents the ∞-norm;1)通过矩阵变换，将约束条件||Δ_Φ||₂＜δ_Φ与(a)转化为线性矩阵不等式形式：1) Through matrix transformation, the constraints ||Δ_Φ ||₂ <δ_Φ and (a) are transformed into linear matrix inequality form:tr(U^-1)≤τγ₀-C,tr(U^-1 )≤τγ₀ -C,

β≥0β≥0U∈R^N×N是一个对称正定矩阵，且U≤(Φ+Δ_Φ)^Tdiag(H)(Φ+Δ_Φ)，I为N×N的单位阵，β≥0是转化过程中的辅助参数；U∈R^N×N is a symmetric positive definite matrix, and U≤(Φ+Δ_Φ )^T diag(H)(Φ+Δ_Φ ), I is an N×N identity matrix, β≥0 is the transformation process auxiliary parameters;2)将约束条件(c)与||Δ_PL||_∞＜δ_PL，转化为矢量约束：2) Convert constraint (c) and ||_ΔPL ||_∞ <δ_PL into vector constraints:

其中，

in,

因此问题可表示为：So the problem can be expressed as:

5.根据权利要求1所述的基于扰动与环境、距离和能量约束的传感器选择方法，其特征在于：在步骤五中，所述问题转化为凸问题表示为：5. The sensor selection method based on disturbance and environment, distance and energy constraints according to claim 1, wherein in step 5, the problem is transformed into a convex problem and expressed as:

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