CN111257824B - Distributed detection method based on diffusion Kalman filtering - Google Patents

Distributed detection method based on diffusion Kalman filtering Download PDF

Info

Publication number
CN111257824B
CN111257824B CN202010067419.4A CN202010067419A CN111257824B CN 111257824 B CN111257824 B CN 111257824B CN 202010067419 A CN202010067419 A CN 202010067419A CN 111257824 B CN111257824 B CN 111257824B
Authority
CN
China
Prior art keywords
node
innovation
diffusion
kalman filtering
test
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202010067419.4A
Other languages
Chinese (zh)
Other versions
CN111257824A (en
Inventor
庞菲菲
李耀光
王晓华
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Xian Polytechnic University
Original Assignee
Xian Polytechnic University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Xian Polytechnic University filed Critical Xian Polytechnic University
Priority to CN202010067419.4A priority Critical patent/CN111257824B/en
Publication of CN111257824A publication Critical patent/CN111257824A/en
Application granted granted Critical
Publication of CN111257824B publication Critical patent/CN111257824B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/20—Instruments for performing navigational calculations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/20—Analysis of motion
    • G06T7/277—Analysis of motion involving stochastic approaches, e.g. using Kalman filters
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/30—Services specially adapted for particular environments, situations or purposes
    • H04W4/38—Services specially adapted for particular environments, situations or purposes for collecting sensor information
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Landscapes

  • Engineering & Computer Science (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Multimedia (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Theoretical Computer Science (AREA)
  • Automation & Control Theory (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Complex Calculations (AREA)

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

Distributed detection method based on diffusion Kalman filtering
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:
step 1, constructing a distributed sensing network;
step 2, calculating to obtain node information by using a Diffusion Kalman Filtering (DKF) method in the distributed sensor network obtained in the step 1;
step 3, calculating a covariance matrix of the node innovation obtained in the step 2 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 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,
Figure SMS_1
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 ，
Figure SMS_2
And->
Figure SMS_3
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:
Figure SMS_4
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 as
Figure SMS_5
P 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:
Figure SMS_6
Figure SMS_7
Figure SMS_8
Figure SMS_9
step 2.3.2, diffusion updating:
Figure SMS_10
Figure SMS_11
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 is
Figure SMS_12
Then c is l,i =0; otherwise, there is c l,i Not equal to 0 and ≠ X>
Figure SMS_13
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:
Figure SMS_14
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:
Figure SMS_15
in the above formula
Figure SMS_16
The step 3 specifically comprises the following steps:
calculated from the equations (11), (12), (13) and (15)
Figure SMS_17
P l,k|k ，/>
Figure SMS_18
P l,k+1|k And psi i (k) (ii) a Assuming that the calculation formula of the innovation covariance matrix is:
Figure SMS_19
Figure SMS_20
after the innovation covariance matrix is calculated, the formula is followed
Figure SMS_21
And formula
Figure SMS_22
Calculate variance of innovation +>
Figure SMS_23
And &>
Figure SMS_24
The formula for deriving the test statistic based on the calculated innovation and innovation variance is:
Figure SMS_25
/>
because the innovation process is independent, the inspection threshold based on diffusion kalman filtering is:
Figure SMS_26
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:
Figure SMS_27
when T is i dif (k) Is greater than
Figure SMS_28
When the target signal is present, T i dif (k) Is less than or equal to>
Figure SMS_29
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:
step 1, constructing a distributed sensing network, as shown in fig. 2, the network does not need a fusion center to acquire information of each node, so that the network can adapt to and track changes of data flow information in real time, and realize real-time signal detection of distributed network nodes, which specifically comprises the following steps:
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,
Figure SMS_30
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 ，
Figure SMS_31
And->
Figure SMS_32
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:
Figure SMS_33
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 of
Figure SMS_34
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 DKF algorithm has the following specific steps:
setting the initial state of each node as
Figure SMS_35
P 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:
Figure SMS_36
Figure SMS_37
Figure SMS_38
Figure SMS_39
step 2.3.2, diffusion updating:
Figure SMS_40
Figure SMS_41
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 is
Figure SMS_42
Then c is l,i =0; otherwise, there is c l,i Not equal to 0 and ≠ X>
Figure SMS_43
Step 2.3.3, by using the observation information from 0 to k, the incremental update and the diffusion update are known as follows:
Figure SMS_44
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:
Figure SMS_45
in the above formula
Figure SMS_46
Step 3, calculating the covariance matrix of the innovation by using the innovation obtained in the step 2, calculating the variance of the innovation by a formula according to the covariance matrix of the innovation, and further calculating the test statistic and the test threshold by the variance of the innovation and the variance of the innovation, wherein the method specifically comprises the following steps:
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 calculating
Figure SMS_47
P l,k|k ，/>
Figure SMS_48
P l,k+1|k And psi i (k) In that respect Assuming that the calculation formula of the innovation covariance matrix is:
Figure SMS_49
/>
Figure SMS_50
Figure SMS_51
after the innovation covariance matrix is calculated, the formula is followed
Figure SMS_52
And formula
Figure SMS_53
The variance of the innovation can be calculated->
Figure SMS_54
And &>
Figure SMS_55
The test statistic is derived based on the above calculated innovation and innovation variance by the formula:
Figure SMS_56
since the innovation process is independent, the inspection threshold based on DKF is:
Figure SMS_57
step 4, according to the test statistic and the test threshold obtained in the step 3, making a decision on the target signal by using a binary hypothesis test theory, which is specifically as follows:
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:
Figure SMS_58
when T is i dif (k) Is greater than
Figure SMS_59
When the target signal is present, T i dif (k) Less than or>
Figure SMS_60
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 set
Figure FDA0004076355980000011
Communicating a set of adjacent nodes, set @, for a single hop of node i>
Figure FDA0004076355980000012
Number of middle element->
Figure FDA0004076355980000013
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 vector
Figure FDA0004076355980000014
White gaussian noise of dimension r × 1; the start condition s (-1) is a random vector of dimension M x 1, obeying a Gaussian distribution->
Figure FDA0004076355980000015
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:
Figure FDA0004076355980000016
Figure FDA0004076355980000021
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,
Figure FDA0004076355980000022
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 ，
Figure FDA0004076355980000023
And->
Figure FDA0004076355980000024
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:
Figure FDA0004076355980000025
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 of
Figure FDA0004076355980000027
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 adopted diffusion Kalman filtering method is implemented according to the following steps: setting the initial state of each node as
Figure FDA0004076355980000026
P 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:
Figure FDA0004076355980000031
Figure FDA0004076355980000032
Figure FDA0004076355980000033
Figure FDA0004076355980000034
step 2.3.2, diffusion updating:
Figure FDA0004076355980000035
Figure FDA0004076355980000036
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 is
Figure FDA0004076355980000037
Then c is l,i =0; otherwise, there is c l,i Not equal to 0 and ≠ X>
Figure FDA0004076355980000038
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:
Figure FDA0004076355980000039
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:
Figure FDA00040763559800000310
in the above formula
Figure FDA00040763559800000311
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)
Figure FDA0004076355980000041
P l,k|k ，/>
Figure FDA0004076355980000042
P l,k+1|k And psi i (k) (ii) a Assuming that the calculation formula of the innovation covariance matrix is:
Figure FDA0004076355980000043
/>
Figure FDA0004076355980000044
after the innovation covariance matrix is calculated, the formula is followed
Figure FDA0004076355980000045
And formulas
Figure FDA0004076355980000046
Calculate variance of innovation +>
Figure FDA0004076355980000047
And &>
Figure FDA0004076355980000048
The formula for deriving the test statistic based on the calculated innovation and innovation variance is:
Figure FDA0004076355980000049
because the innovation process is independent, the inspection threshold based on diffusion kalman filtering is:
Figure FDA00040763559800000410
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:
Figure FDA00040763559800000411
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.
CN202010067419.4A 2020-01-20 2020-01-20 Distributed detection method based on diffusion Kalman filtering Active CN111257824B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010067419.4A CN111257824B (en) 2020-01-20 2020-01-20 Distributed detection method based on diffusion Kalman filtering

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010067419.4A CN111257824B (en) 2020-01-20 2020-01-20 Distributed detection method based on diffusion Kalman filtering

Publications (2)

Publication Number Publication Date
CN111257824A CN111257824A (en) 2020-06-09
CN111257824B true CN111257824B (en) 2023-03-28

Family

ID=70954684

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010067419.4A Active CN111257824B (en) 2020-01-20 2020-01-20 Distributed detection method based on diffusion Kalman filtering

Country Status (1)

Country Link
CN (1) CN111257824B (en)

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO1988001409A1 (en) * 1986-08-20 1988-02-25 Grumman Aerospace Corporation Distributed kalman filter
JPH1144754A (en) * 1997-07-29 1999-02-16 Mitsubishi Electric Corp Method and device for tracking target
CN105549049A (en) * 2015-12-04 2016-05-04 西北农林科技大学 Adaptive Kalman filtering algorithm applied to GPS navigation

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO1988001409A1 (en) * 1986-08-20 1988-02-25 Grumman Aerospace Corporation Distributed kalman filter
JPH1144754A (en) * 1997-07-29 1999-02-16 Mitsubishi Electric Corp Method and device for tracking target
CN105549049A (en) * 2015-12-04 2016-05-04 西北农林科技大学 Adaptive Kalman filtering algorithm applied to GPS navigation

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
张正本 ; 马同伟 ; .基于卡尔曼一致滤波和分布式协作网络控制的多目标跟踪.电子测量与仪器学报.2018,(03),全文. *
李忠良 ; 陈卫兵 ; 邹豪杰 ; 罗天资 ; 张洪波 ; 曾光华 ; .基于新息的神经网络自适应卡尔曼滤波.湖南工业大学学报.2011,(01),全文. *

Also Published As

Publication number Publication date
CN111257824A (en) 2020-06-09

Similar Documents

Publication Publication Date Title
CN112533149B (en) Moving target positioning algorithm based on UWB mobile node
CN107786959B (en) Compressed data collection method in wireless sensor network based on adaptive measuring
CN111294921B (en) RSSI wireless sensor network three-dimensional cooperative positioning method
CN109490826B (en) Ranging and position positioning method based on radio wave field intensity RSSI
CN103209478A (en) Indoor positioning method based on classified thresholds and signal strength weight
CN109710978B (en) Distributed heterogeneous adaptive particle filter direct tracking method
CN102752784B (en) Detection method of distribution type event domain based on graph theory in wireless sensor network
CN109688540B (en) Ad Hoc network physical topology non-cooperative inference system
Wu et al. Online dynamic event region detection using distributed sensor networks
CN111257824B (en) Distributed detection method based on diffusion Kalman filtering
Wang et al. Collaborative event-region and boundary-region detections in wireless sensor networks
CN109560972A (en) Non-cooperative inference method for Ad Hoc network physical topology
CN113543026A (en) Multi-floor indoor positioning method based on radial basis function network
Yu et al. Distributed single target tracking in underwater wireless sensor networks
Chen et al. Decentralized estimation of ocean current field using underwater acoustic sensor networks
CN108834043B (en) Priori knowledge-based compressed sensing multi-target passive positioning method
CN113078885B (en) Anti-pulse interference distributed adaptive estimation method
CN113038411B (en) Multi-sensor joint detection method based on decision-level and signal-level data fusion
Alasti An on-demand compressed sensing approach for spatial monitoring of correlated big data using multi-contours in dense wireless sensor network
CN105242238B (en) A kind of wireless network location technology based on particle auxiliary random search
Lu et al. Signal fusion-based detection with an intuitive weighting method
Speranzon et al. Adaptive distributed estimation over wireless sensor networks with packet losses
Ju et al. A joint jamming detection and link scheduling method based on deep neural networks in dense wireless networks
Wang et al. Moments based blind calibration in mobile sensor networks
Santos et al. Crowdsource-based signal strength field estimation by gaussian processes

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant