CN111257824B - Distributed detection method based on diffusion Kalman filtering - Google Patents
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Abstract
The invention discloses a distributed detection method based on diffusion Kalman filtering, which is implemented according to the following steps: constructing a distributed sensing network; calculating to obtain node information by using a diffusion Kalman filtering method in a distributed sensor network; calculating a covariance matrix of the node innovation by using the node innovation, calculating an innovation variance according to the covariance matrix of the node innovation, and further obtaining a test statistic and a test threshold; and obtaining a judgment expression according to the test statistic and the test threshold, and making a decision by a binary hypothesis test theory. The detection performance of the invention is superior to the detection performance of a single node and a local node, and each node can dynamically obtain global information by virtue of a diffusion strategy, so that the invention can more quickly converge on the centralized detection performance.
Description
Technical Field
The invention belongs to the technical field of target detection methods, and particularly relates to a distributed detection method based on diffusion Kalman filtering.
Background
In recent years, the development and development of detection technology has promoted the progress of science and technology, and the detection technology cannot be separated from many professional fields. Although the active detection method can obtain a higher signal-to-noise ratio, it is difficult to implement long-time covert monitoring at the cost of high energy consumption. With the advancement of sensor technology, passive detection and location tracking of targets within a coverage area with distributed sensors is possible. The sensor performs object detection in a noisy background by receiving information from the object, and then processes the received information to determine whether the object is present. The target detection is realized under the wireless sensor network, each sensor node is used for judging after comparing the received signal with the corresponding threshold, the human factor error is reduced, the efficiency is high, and the reliability is strong. For the detection problem of the single-node signal, the detection performance is not good because the information of only one node of the single-node signal can be obtained. The detection technology using the sensor network (such as centralized type and local type) has good application prospect. In the centralized detection technology, all sensor data are sent to a fusion center when an overall decision is needed. Although this technique achieves the highest performance, it requires a very large bandwidth to obtain real-time results. In the distributed network, a fusion center is not needed, each node only depends on own observation information and shared data between adjacent nodes to obtain global information of the network, and binary decision of whether a target exists is made. The detection performance of the method is superior to that of single-node and local detection performance, and the method can be converged to centralized detection performance more quickly.
Disclosure of Invention
The invention aims to provide a distributed detection method based on diffusion Kalman filtering, which improves the processing gain and the detection probability of a target signal.
The technical scheme adopted by the invention is as follows: the distributed detection method based on the diffusion Kalman filtering is implemented according to the following steps:
and 4, obtaining a judgment expression according to the test statistic and the test threshold obtained in the step 3, making a decision by a binary hypothesis test theory, wherein the target signal is represented to exist when the test statistic is larger than the test threshold, and the target signal is represented to not exist when the test statistic is smaller than the test threshold.
The present invention is also characterized in that,
the step 1 specifically comprises the following steps: assume that a distributed sensor network of N sensor nodes is deployed in a region, i.e., undirected graph model G = (V, ζ), where the set of nodes V = {1,2,., N } and edge set ζ = { (i, l) | i, l ∈ V, i ≠ l } are unordered node pairs of nodes in a single-hop communication range, and an adjacent set N is set i Set of one-hop communication neighboring nodes with { l | (i, l) ∈ ζ }. U |, i as node i, and set N i Number of middle element N i For the degree of the node i, each node in the network independently observes the signal to be detected and shares information with the adjacent node of the single-hop communication.
The step 2 is implemented according to the following steps:
step 2.1: establishing a Gaussian-Markov model;
step 2.2: constructing a binary hypothesis testing theory;
step 2.3: and calculating the innovation of each node by using a diffusion Kalman filtering method.
The step 2.1 specifically comprises the following steps:
in a discrete time system, the gaussian-markov model of a M × 1 dimensional vector signal s (k) at time k is:
s(k)=Fs(k-1)+Gv(k-1)k≥0 (1)
the state transition matrix F and the control matrix G are respectively known matrixes with dimensions of M multiplied by M, M multiplied by r, and the eigenvalue amplitude of the matrix F is smaller than 1; the disturbance noise vectors v (k) to N (0,Q) are r × 1-dimensional white gaussian noise; the starting condition s (-1) is a random vector of dimension M × 1, following a Gaussian distribution s (-1) -N (. Mu.m) 0 ,Π 0 ) Which is independent of v (k).
The step 2.2 specifically comprises the following steps:
for node i, the discrete observation equation from 0 to K based on the theory of binary assumptions is:
H 1 :y i,0:K =Z i,0:K +w i,0:K (2)
H 0 :y i,0:K =w i,0:K (3)
in the formula, y i,0:K =[y i (0),y i (1),…,y i (K)] T Is an observation vector, Z i,0:K Is the signal to be detected, the observation noise w i,0:K =[w i (0),w i (1),…,w i (K)] T Is Gaussian whiteThe noise is generated by the noise-generating device,and Z is i,0:K And w i,0:K Independently of one another, Z i,0:K Is a partially observable markov process, expressed as:
Z i,0:K =H i,0:K s 0:K (4)
in the formula, Z i,0:K =[z i (0),z i (1),…,z i (N-1)] T ,s 0:K =[s T (0),s T (1),...,s T (K)] T ,And->h i (k)=[1 0 ... 0] T Is an observation vector of dimension mx 1; s (k) is a zero-mean Gaussian-Markov process in the dimension M1.
The step 2.3 specifically comprises the following steps:
let psi i (k) Represents the innovation, ψ, of node i calculated by the diffusion Kalman Filter method at time k i (k) And the linear relation is formed between the global observation information and the linear relation, and the linear relation is assumed as follows:
wherein, y 0:k =[y T (0),y T (1),...,y T (k)] T ,y(k)=[y 1 (k),...,y N (k)] T Vector b i,0:k Describe psi i (k) And y 0:k The linear relationship of (a); let psi i,0:K =[ψ i (0),ψ i (1),...,ψ i (K)] T Representing an innovation vector calculated by the diffusion Kalman filtering method from 0 to K moment of the ith node, and obtaining:
ψ i,0:K =B i,0:K y 0:K (6)
in the formula, B i,0:K Is (K + 1) × (K)+ 1) matrix of N, where the first j × N elements of the jth row consist of b i T ,0:K Given, the remaining elements are 0; since the innovation process is a linear combination of global observations i,0:K Is a zero mean gaussian variable.
The diffusion Kalman filtering method adopted in the step 2.3 is implemented according to the following steps: setting the initial state of each node asP i,0|-1 =Π 0 At time K =0,1,.., K, each node i =1,2,.., the information for N kalman filtering is of the form:
step 2.3.1, incremental updating:
step 2.3.2, diffusion updating:
P i,k+1|k =FP i,k|k F T +GQG T (13)
non-negative coefficient c in formula (11) l,i The weight representing that the node i receives the information of the adjacent node l; if it isThen c is l,i =0; otherwise, there is c l,i Not equal to 0 and ≠ X>
Step 2.3.3, by using the observation information from 0 to k, the incremental update and the diffusion update can know that the information is as follows:
converting the above equation into matrix dimension, innovation vector psi (k + 1) = [ psi 1 (k+1),...,ψ N (k+1)] T The calculation expression of (a) is:
The step 3 specifically comprises the following steps:
calculated from the equations (11), (12), (13) and (15)P l,k|k ,/>P l,k+1|k And psi i (k) (ii) a Assuming that the calculation formula of the innovation covariance matrix is:
after the innovation covariance matrix is calculated, the formula is followedAnd formulaCalculate variance of innovation +>And &>
The formula for deriving the test statistic based on the calculated innovation and innovation variance is:
because the innovation process is independent, the inspection threshold based on diffusion kalman filtering is:
the step 4 specifically comprises the following steps: after the test statistic and the test threshold are obtained in the step 3, by using a binary hypothesis test theory, and comparing values between the two, the binary judgment of the existence of the target can be obtained, wherein the judgment expression is as follows:
when T is i dif (k) Is greater thanWhen the target signal is present, T i dif (k) Is less than or equal to>When it is indicated that the target signal is not present.
The invention has the beneficial effects that: the distributed detection method based on the diffusion Kalman filtering solves the problems that the information of a network structure of a fusion center is collapsed, a single node can only obtain the information of one node, and the detection capability is limited. Due to the adoption of the distributed network structure and the DKF method, when the observation time is long enough, each node gradually senses the global information, the estimation precision of the information process can be effectively improved, and the detection performance of whether a target signal exists or not can be more quickly converged to a centralized mode.
Drawings
FIG. 1 is a flow chart of a distributed detection method based on diffusion Kalman filtering of the present invention;
FIG. 2 is a distributed sensing network of N nodes;
FIG. 3 (a) is a sensing network topology with a node count of 20; FIG. 3 (b) is an observed noise standard deviation of each node in a sensor network with a node number of 20;
FIG. 4 shows the false alarm probability P of each node in the sensor network f,i (k) Graph of network detection probability over time at = 0.001;
fig. 5 (a) is a graph comparing receiver operating characteristics curves for the present invention and the prior art detection method at time k = 2; fig. 5 (b) is a graph comparing receiver operating characteristics of the present invention and the prior art detection method at time k = 5.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention provides a distributed detection method based on diffusion Kalman filtering, which is implemented according to the following steps as shown in FIG. 1:
it is assumed that a distributed sensing network composed of N sensor nodes is deployed in one area. It can be described as an undirected graph model G = (V, ζ), where the set of nodes V = {1,2,... N }, the set of edges ζ = { (i, l) | i, l ∈ V, i ≠ l } are nodesUnordered node pairs, neighbor set N, in a single-hop communication range i Set of one-hop communication neighboring nodes with { l | (i, l) ∈ ζ }. U |, i as node i, and set N i Number of middle element N i Is the degree of node i. Each node in the network makes independent observation on the signal to be detected and shares information with the single-hop communication adjacent node.
And 2, calculating to obtain new information in the distributed sensor network by using a DKF method. The DKF method is to use the information of each node as a global cost function, and obtain innovation through kalman iterative estimation by using the information of adjacent nodes. With the increase of observation time, global information is gradually used when each node estimates innovation, so that the estimation precision is improved, specifically as follows:
step 2.1: establishing a Gaussian-Markov model;
in a discrete time system, a gaussian-markov model of a M × 1-dimensional vector signal s (k) at time k is:
s(k)=Fs(k-1)+Gv(k-1)k≥0 (1)
the state transition matrix F and the control matrix G are respectively known matrixes with dimensions of M multiplied by M, M multiplied by r, and the eigenvalue amplitude of the matrix F is smaller than 1; the disturbance noise vectors v (k) to N (0,Q) are r × 1-dimensional white gaussian noise. The starting condition s (-1) is a random vector of dimension M x 1, following a Gaussian distribution s (-1) to N (. Mu.m) 0 ,Π 0 ) Which is independent of v (k).
Step 2.2: constructing a binary hypothesis testing theory;
binary hypothesis detection makes a binary decision as to whether a target signal exists in observation data by using statistical characteristics of noise and signals. There are two possibilities to detect the input (i.e. observation data) y (K) of the system, K =0,1. By H 1 Suppose that it indicates the presence of a target signal in the input, H 0 Assuming that there is no target signal, i.e.
H 1 :y(k)=z(k)+w(k)
H 0 :y(k)=w(k)
In the formula, z (k) and w (k) represent additive noise of the target signal at time k, respectively. The test question is then concluded as test H 0 Hypothesis sum H 1 A hypothetical authenticity problem.
For node i, a discrete observation equation based on a binary hypothesis theory from 0 to K can be written by the above equation:
H 1 :y i,0:K =Z i,0:K +w i,0:K (2)
H 0 :y i,0:K =w i,0:K (3)
in the formula, y i,0:K =[y i (0),y i (1),...,y i (K)] T Is an observation vector, Z i,0:K Is the signal to be detected, the observation noise w i,0:K =[w i (0),w i (1),...,w i (K)] T Is white gaussian noise and is generated by the noise,and Z is i,0:K And w i,0:K Are independent of each other. Z i,0:K Is a partially observable markov process that can be expressed as:
Z i,0:K =H i,0:K s 0:K (4)
in the formula, Z i,0:K =[z i (0),z i (1),...,z i (N-1)] T ,s 0:K =[s T (0),s T (1),...,s T (K)] T ,And->h i (k)=[1 0 ... 0] T Is an observation vector of dimension mx 1; s (k) is a zero-mean Gaussian-Markov process in the dimension M1.
Step 2.3: calculating the innovation of each node by utilizing a DKF method;
let psi i (k) Representing the innovation calculated by the method DKF for node i at time k. With the benefit of the flooding strategy, each node can gradually acquire global information of the entire network to estimate ψ using the global information i (k) Thus phi i (k) In line with global observation informationA linear relationship, assuming that the linear relationship is:
wherein, y 0:k =[y T (0),y T (1),...,y T (k)] T ,y(k)=[y 1 (k),...,y N (k)] T Vector b i,0:k Describe psi i (k) And y 0:k The linear relationship of (c). Let psi i,0:K =[ψ i (0),ψ i (1),...,ψ i (K)] T Representing the information vector calculated by the method DKF from the time 0 to the time K of the ith node, the method can obtain:
ψ i,0:K =B i,0:K y 0:K (6)
in the formula, B i,0:K Is a matrix of (K + 1) × (K + 1) N, where the first j × N elements of the jth row consist ofGiven, the remaining elements are 0. Since the innovation process is a linear combination of global observations i,0:K Is a zero mean gaussian variable.
The DKF algorithm has the following specific steps:
setting the initial state of each node asP i,0|-1 =Π 0 At time K =0,1.., K, each node i =1,2.., the information for the N kalman filter is of the form:
step 2.3.1, incremental updating:
step 2.3.2, diffusion updating:
P i,k+1|k =FP i,k|k F T +GQG T (13)
non-negative coefficient c in formula (11) l,i Indicating the weight that node i accepts information from neighboring node l. If it isThen c is l,i =0; otherwise, there is c l,i Not equal to 0 and ≠ X>
Step 2.3.3, by using the observation information from 0 to k, the incremental update and the diffusion update are known as follows:
converting the above equation into matrix dimension, innovation vector psi (k + 1) = [ psi 1 (k+1),...,ψ N (k+1)] T The calculation expression of (a) is:
in order to derive the formula for calculating the variance of innovation, the covariance matrix of the innovation vector is used, and the formula (11), (12), (13) and the formula (15) can be used for calculatingP l,k|k ,/>P l,k+1|k And psi i (k) In that respect Assuming that the calculation formula of the innovation covariance matrix is:
after the innovation covariance matrix is calculated, the formula is followedAnd formulaThe variance of the innovation can be calculated->And &>
The test statistic is derived based on the above calculated innovation and innovation variance by the formula:
since the innovation process is independent, the inspection threshold based on DKF is:
according to the calculated test statistic and test threshold, the binary judgment of the existence of the target can be obtained by comparing the values of the two, and the judgment expression is as follows:
when T is i dif (k) Is greater thanWhen the target signal is present, T i dif (k) Less than or>When it is indicated that the target signal is not present.
Analysis of results
The detection algorithm based on DKF and the detection performance of a centralized type, a local type and a single node are simulated and compared. Assuming that the dimensions of s (k) and v (k) in the gaussian-markov process are 2 and 1, respectively, the state transition matrix F = [0.6,0.2;1,0]Control matrix G = [1,0 ]] T Covariance matrix of disturbance noise vector Q =0.1, initial states s (-1) to N ([ 0,0)] T Diag {0.5,0.5 }). Assume that the number of nodes in the sensing network is N =20. The network topology and the observed noise standard deviation for each node are given in turn in fig. 3 (a) and 3 (b). For all nodes i =1,2, N, at any time K =0,1 i (k)=[1,0] T hi(k)=[1;0]And T. Assume that in DKF algorithm, the non-zero weight in weight matrix C is set as C l,i =1/|N i L, where | N i And | is the number of single-hop communication neighbor nodes of the node i. Defining the detection probability of the network as max P d,1 (k),...,P d,N (k) Wherein max {. Represents the maximum value in the set {. -.
FIG. 4 simulates the false alarm probability P of each node f,i (k) Network detection probability at = 0.001. The threshold and detection probability were derived from 20,000 Monte Carlo simulations. As is apparent from the figure, the detection probability using a network (e.g., centralized, local, and based on DKF) is much higher than that of a single node. In the detection using the network, the best performance is shown in a centralized mode, and the detection performance of the method is superior to the local performance. With the increase of k, the detection probability of the method is faster than the improvement of local and single nodes, and the method can approach to the centralized mode more quickly.
Fig. 5 simulates Receiver Operating characteristic curves (ROC) of each detection method at times k =2 and k =5, sequentially referring to fig. 5 (a) and 5 (b). The number of monte carlo simulations was 20,000. It can be seen from the figure that when k =2, the centralized detection performance is better than that of other methods, but after 3 iterations, the ROC curve of the method of the present invention almost overlaps with that of the centralized one, and the single-node and local ROCs are still lower than that of the centralized one. This shows that as k increases, the method of the present invention can estimate the innovation process more accurately due to the diffusion strategy, and thus can approach the centralized detection performance more quickly.
Claims (3)
1. The distributed detection method based on the diffusion Kalman filtering is characterized by comprising the following steps:
step 1, constructing a distributed sensing network; the method specifically comprises the following steps: suppose a distributed sensing network composed of N sensor nodes is deployed in a region, i.e., undirected graph model G = (V, ζ), where a set of nodes V = {1,2.. The N } and a set of edges ζ = { (i, l) | i, l ∈ V, i ≠ l } are unordered nodes within a single-hop communication rangeNode pair, neighbor setCommunicating a set of adjacent nodes, set @, for a single hop of node i>Number of middle element->For the degree of a node i, each node in the network independently observes a signal to be detected and shares information with a single-hop communication adjacent node;
step 2, calculating to obtain node information by using a diffusion Kalman filtering method in the distributed sensor network obtained in the step 1; the method is implemented according to the following steps:
step 2.1: establishing a Gaussian-Markov model; the method specifically comprises the following steps:
in a discrete time system, a gaussian-markov model of a M × 1-dimensional vector signal s (k) at time k is:
s(k)=Fs(k-1)+Gv(k-1) k≥0 (1)
the state transition matrix F and the control matrix G are respectively known matrixes with dimensions of M multiplied by M, M multiplied by r, and the eigenvalue amplitude of the matrix F is smaller than 1; disturbance noise vectorWhite gaussian noise of dimension r × 1; the start condition s (-1) is a random vector of dimension M x 1, obeying a Gaussian distribution->It is independent of v (k);
step 2.2: constructing a binary hypothesis testing theory; the method specifically comprises the following steps:
for node i, the discrete observation equation from 0 to K based on the theory of binary assumptions is:
in the formula, y i,0:K =[y i (0),y i (1),…,y i (K)] T Is an observation vector, Z i,0:K Is the signal to be detected, the observation noise w i,0:K =[w i (0),w i (1),…,w i (K)] T Is white gaussian noise and is generated by the noise,and Z is i,0:K And w i,0:K Independently of one another, Z i,0:K Is a partially observable markov process, expressed as:
Z i,0:K =H i,0:K s 0:K (4)
in the formula, Z i,0:K =[z i (0),z i (1),…,z i (N-1)] T ,s 0:K =[s T (0),s T (1),…,s T (K)] T ,And->h i (k)=[10…0] T Is an observation vector of dimension mx 1; s (k) is a zero-mean Gaussian-Markov process in dimension M × 1;
step 2.3: calculating the innovation of each node by using a diffusion Kalman filtering method; the method comprises the following specific steps:
let psi i (k) Information, ψ, representing node i calculated by the diffusion kalman filter method at time k i (k) And the linear relation is formed between the global observation information and the linear relation, and the linear relation is assumed as follows:
wherein, y 0:k =[y T (0),y T (1),…,y T (k)] T ,y(k)=[y 1 (k),…,y N (k)] T Vector b i,0:k Describe psi i (k) And y 0:k The linear relationship of (c); let psi i,0:K =[ψ i (0),ψ i (1),…,ψ i (K)] T Representing an innovation vector calculated by the diffusion Kalman filtering method from 0 to K moment of the ith node, and obtaining:
ψ i,0:K =B i,0:K y 0:K (6)
in the formula, B i,0:K Is a matrix of (K + 1) × (K + 1) N, where the first j × N elements of the jth row consist ofGiven, the remaining elements are 0; since the innovation process is a linear combination of global observations i,0:K Is a zero mean gaussian variable; />
The adopted diffusion Kalman filtering method is implemented according to the following steps: setting the initial state of each node asP i,0|-1 =Π 0 At time K =0,1, …, K, each node i =1,2, …, the information form of N kalman filtering is as follows:
step 2.3.1, incremental updating:
step 2.3.2, diffusion updating:
P i,k+1|k =FP i,k|k F T +GQG T (13)
non-negative coefficient c in formula (11) l,i The weight representing that the node i receives the information of the adjacent node l; if it isThen c is l,i =0; otherwise, there is c l,i Not equal to 0 and ≠ X>
Step 2.3.3, by using the observation information from 0 to k, the incremental update and the diffusion update can know that the information is as follows:
converting the above formula into matrix dimension, and innovation vector psi (k + 1) = [ psi 1 (k+1),…,ψ N (k+1)] T The calculation expression of (a) is:
Step 3, calculating a covariance matrix of the node innovation obtained in the step 2, calculating an innovation variance according to the covariance matrix of the node innovation, and further obtaining test statistic and a test threshold;
and 4, obtaining a judgment expression according to the test statistic and the test threshold obtained in the step 3, making a decision by a binary hypothesis test theory, wherein the target signal is represented to exist when the test statistic is larger than the test threshold, and the target signal is represented to not exist when the test statistic is smaller than the test threshold.
2. The distributed detection method based on diffusion kalman filtering according to claim 1, wherein the step 3 specifically is:
calculated from the equations (11), (12), (13) and (15)P l,k|k ,/>P l,k+1|k And psi i (k) (ii) a Assuming that the calculation formula of the innovation covariance matrix is:
after the innovation covariance matrix is calculated, the formula is followedAnd formulasCalculate variance of innovation +>And &>
The formula for deriving the test statistic based on the calculated innovation and innovation variance is:
because the innovation process is independent, the inspection threshold based on diffusion kalman filtering is:
3. the distributed detection method based on diffusion kalman filtering according to claim 2, wherein the step 4 is specifically: after the test statistic and the test threshold are obtained in the step 3, by using a binary hypothesis test theory, and comparing values between the two, the binary judgment of the existence of the target can be obtained, wherein the judgment expression is as follows:
when T is i dif (k) Greater than gamma i dif (k) When the target signal is present, T i dif (k) Less than gamma i dif (k) When it is time toIndicating that the target signal is not present.
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