CN113038411B - Multi-sensor joint detection method based on decision-level and signal-level data fusion - Google Patents

Multi-sensor joint detection method based on decision-level and signal-level data fusion Download PDF

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CN113038411B
CN113038411B CN202110264017.8A CN202110264017A CN113038411B CN 113038411 B CN113038411 B CN 113038411B CN 202110264017 A CN202110264017 A CN 202110264017A CN 113038411 B CN113038411 B CN 113038411B
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易伟
肖航
张国鑫
张永平
杨诗兴
赖样明
刘永坚
孔令讲
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University of Electronic Science and Technology of China
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Abstract

The invention discloses a multi-sensor joint detection method based on decision-level and signal-level data fusion, which comprises the following steps: s1, obtaining an observed value acquired by each node sensor on a target signal; s2, transmitting the observed values acquired by the node sensors under different transmission conditions to a fusion center in different data transmission modes; s3, establishing a joint likelihood function according to the prior information; s4, carrying out maximum likelihood estimation on the unknown parameters; s5, calculating detection statistics based on the generalized likelihood ratio criterion; s6, setting a detection threshold by deducing the approximate distribution of the detection statistic; and S7, comparing the detection statistic with the detection threshold, and outputting the detection result. According to the invention, through the combined utilization of multi-source and multi-level data, the target information in the data can be reserved as much as possible, the problem of insufficient information utilization rate caused by difficult fusion of different levels of data is effectively solved, and meanwhile, the detection performance of the multi-sensor system can be further improved by setting an optimal local judgment threshold value.

Description

Multi-sensor joint detection method based on decision-level and signal-level data fusion
Technical Field
The invention belongs to the technical field of multiple sensors, and particularly relates to a multi-sensor joint detection method based on decision-level and signal-level data fusion.
Background
With the continuous development of electronic information technology, single sensors have been unable to meet the data processing requirements in the world of everything interconnection due to the defects of limited sensing range, small data acquisition amount, low information reliability and the like. Therefore, a multi-sensor fusion technology that a large number of local sensors with communication interaction and signal processing capabilities are distributed to complete data acquisition and then each node data is analyzed and utilized according to a certain criterion to realize required judgment and estimation is rapidly developed in recent years. The method is mainly characterized in that multi-level and multi-level information complementation and optimized combination are carried out on the scattered observation values acquired by each node sensor, and finally, joint explanation of the observation environment is generated. In view of performance, the method is used for comprehensively processing multi-source information, an interconnection system among equipment is constructed, and the intelligent degree of the system is improved; in engineering, the advantage of cooperative operation of a plurality of sensors is utilized to reduce the performance requirement on a single sensor, reduce the manufacturing cost and save the cost. Therefore, the multi-sensor combined processing system has the incomparable advantages of a single-sensor system, and is widely concerned and widely applied in the fields of military command, industrial monitoring, intelligent detection, weather forecast, target detection and tracking, mode identification and the like.
When a multi-sensor system performs a joint detection task, each node sensor needs to transmit collected local observation data to a fusion center for joint processing, and the data transmission mode is often determined by the transmission conditions of the actual node sensor and the fusion center due to the consideration of the real-time performance of the system. When the transmission bandwidth is large enough, the node sensor can transmit an original observation value, namely signal level data, to the fusion center; when the transmission bandwidth is severely limited, the node sensor only transmits a local judgment result to the fusion center, namely decision-level data. In documents "Kay S M. fundamentals of static Signal Processing [ J ]. Technometrics,1993,37(4): 465-466" and "Fang J, Liu Y, Li H, et al. one-Bit Quantizer Design for Multisensor GLRT Fusion [ J ]. IEEE Signal Processing Letters,2013,20(3): 257-260", the authors propose a joint detection strategy suitable for Signal-level data and decision-level data, respectively, for the detection problem of unknown signals, so as to realize the Fusion and utilization of multi-source data. However, in the above research, only a multi-sensor fusion method of single-form data is considered, that is, all node sensors are consistent with the communication bandwidth of the fusion center, and the data received by the fusion center is in the same hierarchy. However, today, a multi-sensor system is widely applied, practical application scenarios are usually complex and changeable, that is, communication bandwidths of each node sensor and a fusion center often have great differences, and transmission conditions of the same node sensor may change due to factors such as position adjustment and electromagnetic interference. At this time, if only a single-level data fusion policy is adopted, problems such as transmission resource waste and insufficient information utilization rate will inevitably occur, and further, the system detection performance will be lost. Therefore, in long-term consideration, it is of great importance to research and develop a multi-sensor joint detection technology for a hybrid transmission architecture with proprietary intellectual property rights.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a multi-sensor joint detection method based on decision-level and signal-level data fusion, which can retain target information in data as much as possible by joint utilization of multi-source and multi-level data, effectively solves the problem of insufficient information utilization rate caused by difficult fusion of data of different levels, and can further improve the detection performance of a multi-sensor system.
The purpose of the invention is realized by the following technical scheme: the multi-sensor joint detection method based on decision-level and signal-level data fusion comprises the following steps:
s1, sensing the same unknown target signal by a plurality of node sensors to obtain an observed value acquired by each node sensor on the target signal;
s2, transmitting the observed values acquired by the node sensors under different transmission conditions to a fusion center in different data transmission modes;
s3, establishing a joint likelihood function according to the prior information;
s4, carrying out maximum likelihood estimation on the unknown parameters;
s5, calculating detection statistics based on the generalized likelihood ratio criterion;
s6, setting a detection threshold by deducing the approximate distribution of the detection statistic;
and S7, comparing the detection statistic with the detection threshold, and outputting the detection result.
Further, in step S1, the observation model of each node sensor is represented as follows:
Figure BDA0002967173380000021
wherein H0And H1Respectively representing the case where the target signal is assumed to be present and the case where the target signal is not present, xnRepresents an observed value of the nth node sensor; n represents the total number of node sensors; h isnThe observation coefficients are used for representing the signal receiving relation of each node sensor; w is anRepresenting additive observed noise, obeying a mean of 0 and a variance of
Figure BDA0002967173380000022
Is expressed as:
Figure BDA0002967173380000023
further, the specific implementation method of step S2 is as follows:
A. when the transmission condition is good, the node sensor directly transmits the original observation value to the fusion center, and because the transmission mode reserves complete data information, the fusion center receives signal level data ynExpressed as:
yn＝xn，1≤n≤Nc
wherein N iscIndicating the number of node sensors transmitting signal level data, xnRepresenting a sensor observation;
B. when the transmission bandwidth is severely limited, the node sensor cannot transmit the original observed value, and the original observed value is locally judged by adopting a method for reducing the data quantity and then is only judgedTransmitting the local judgment result to the fusion center; the decision-level data b received by the fusion centrenExpressed as:
bn＝sgn(xn-τn)，Nc＜n≤Nq+Nc
wherein N isqNumber of node sensors, τ, representing data at decision level of transmissionnRepresents a local decision threshold value, sgn (·) represents a step function, and the observed value x of the node sensornGreater than threshold taunThen, the decision result "1" is passed; otherwise, the decision result "0" is passed.
Further, the step S3 specifically includes the following sub-steps:
s31, according to the statistical distribution of the original observed values, establishing probability density functions of two different forms of data received by each node sensor under two assumptions: p (y)n,θ|H1)、p(yn|H0) Respectively representing signal level data ynUnder the assumption of H1And H0Conditional probability density function of p (b)n,θ|H1)、p(bn|H0) Respectively representing decision level data bnUnder the assumption of H1And H0A conditional probability density function of;
1≤n≤Ncand the received data is signal level data:
Figure BDA0002967173380000031
Figure BDA0002967173380000032
Nc＜n≤Nq+Ncthen, the received data is decision level data:
Figure BDA0002967173380000033
Figure BDA0002967173380000034
wherein the content of the first and second substances,
Figure BDA0002967173380000035
omega is an integral variable;
s32, integrating the data transmitted at the same level and associating the data at different levels in a way of calculating a joint likelihood function ratio because the data transmission of different node sensors are mutually independent; the joint likelihood function ratio calculation formula is as follows:
Figure BDA0002967173380000036
wherein [ ·]TDenotes the matrix transposition, p (y, b, θ | H1) Indicates that two kinds of received data are in H1Joint probability density function under assumption, p (y, b | H0) Indicates that two kinds of received data are in H0Joint probability density function under the assumption.
Further, in step S4, the maximum likelihood estimation value of the unknown target signal θ is calculated by a numerical solution method
Figure BDA00029671733800000411
Figure BDA0002967173380000041
Although it is not limited to
Figure BDA0002967173380000042
The method does not have an analytic solution in a closed form, but can obtain a maximum likelihood estimated value by numerical solution under a Gaussian noise distribution model
Figure BDA0002967173380000043
Further, the specific implementation method of step S5 is as follows: will be unknownSubstituting the maximum likelihood estimated value of the parameter into the likelihood function, and taking the logarithm form of the likelihood function to obtain the detection statistic
Figure BDA0002967173380000044
Figure BDA0002967173380000045
Further, the step S6 specifically includes the following sub-steps:
s61, constructing the corrected detection statistic according to the expression of the detection statistic and the statistical distribution rule of the received data
Figure BDA0002967173380000046
The gradual distribution of (2):
Figure BDA0002967173380000047
wherein, alpha represents a gradual distribution,
Figure BDA0002967173380000048
representing a central chi-squared distribution with a degree of freedom of 1,
Figure BDA0002967173380000049
representing a degree of freedom of 1 and a non-central parameter of λFNon-central chi-square distribution of (c);
s62, calculating Fisher information FI (theta):
Figure BDA00029671733800000410
s63, calculating a non-central parameter lambdaF：
λF＝(θ1-θ0)2FI(θ0)
θ1And theta0Respectively represent that the unknown target signals theta are at H1And H0A true value under the assumption; lambda [ alpha ]FThe larger the value is, the better the detection performance of the system is;
s64 maximization of non-central parameter lambdaF：λFValue is given bynInfluence, setting of optimal local decision threshold τnCan make λ equal to 0FReaching a maximum value;
s65, substituting the optimal local judgment threshold value to obtain the maximum value lambda of the non-central parameterFmaxComprises the following steps:
Figure BDA0002967173380000051
s66, detecting statistic value at H according to correction0And (3) calculating a global detection threshold eta by inverse solution according to the following approximate distribution, wherein the relationship between the global detection threshold and the detection statistic is as follows:
Figure BDA0002967173380000052
further, the specific implementation method of step S7 is as follows: by substituting the noncentral parameters, the distribution characteristics of the detection statistics are completely known, and under the condition of appointed false alarm probability or detection probability, the corresponding detection threshold eta can be obtained, so that the judgment expression is as follows:
Figure BDA0002967173380000053
when the corrected detection statistic is greater than the threshold, then the hypothesis H is determined1If yes, the target signal exists; otherwise, then hypothesis H is determined0In the case, the target signal is not present.
The invention has the beneficial effects that: the invention realizes the joint utilization of multi-source and multi-level data by adopting two transmission modes of different data forms for the node sensors under different communication conditions and designing a joint detector in a fusion center. In addition, the invention also establishes the approximate distribution of the detection statistic, provides basis for setting the local judgment threshold and the global detection threshold, and perfects the invention content. Compared with a joint detection method of peer-level data, the method provided by the invention can be suitable for scenes with more flexible and variable communication conditions, especially under the condition that the communication conditions of the sensors of all nodes are different, the method can keep target information in the data as much as possible, effectively solves the problem of insufficient information utilization rate caused by difficult fusion of data of different levels, and can further improve the detection performance of a multi-sensor system by setting an optimal local judgment threshold value.
Drawings
FIG. 1 is a flow chart of a multi-sensor joint detection method based on decision-level and signal-level data fusion in accordance with the present invention;
FIG. 2 is a diagram illustrating a data transmission architecture according to the present invention when there is a difference between the communication conditions mentioned in the present invention;
FIG. 3 is a schematic structural diagram of a multi-sensor joint detection system according to an embodiment of the present invention;
FIG. 4 is a sensitivity (ROC) curve for joint detection of different levels of data according to an embodiment of the present invention;
FIG. 5 is a comparison curve of detection performance of different levels of data joint detection provided by the embodiment of the present invention;
fig. 6 is a detection performance variation plane for different levels of node sensor numbers according to an embodiment of the present invention.
Detailed Description
According to the invention, under the condition that the communication conditions of the sensors of each node are different, different forms are adopted to carry out data transmission on local observed values; the fusion center performs information association on multi-source and multi-level data according to the statistical characteristics of the received data; then designing a global detector based on the generalized likelihood ratio criterion, and calculating detection statistics; and finally, comparing the detection statistic with a detection threshold, realizing the joint utilization of different levels of data, and outputting a global detection result. Compared with a single data level multi-sensor fusion method, the method has more excellent detection performance and more flexible applicable scene. The invention mainly adopts a simulation experiment method for verification, and all steps and conclusions are verified to be correct in Matlab 2019. The technical scheme of the invention is further explained by combining the attached drawings.
As shown in fig. 1, a multi-sensor joint detection method based on decision-level and signal-level data fusion of the present invention includes the following steps:
s1, sensing the same unknown target signal theta by a plurality of node sensors to obtain an observed value acquired by each node sensor on the target signal; the total number of the sensors is set to be N, and data transmission of the sensors of different nodes is independent. The observation model of each node sensor is represented as follows:
Figure BDA0002967173380000061
wherein H0And H1Respectively representing the case where the target signal is assumed to be present and the case where the target signal is not present, xnRepresents an observed value of the nth node sensor; n represents the total number of node sensors; h isnThe observation coefficients are used for representing the signal receiving relation of each node sensor; w is anRepresenting additive observed noise, obeying a mean of 0 and a variance of σn 2Is expressed as:
Figure BDA0002967173380000062
the present embodiment considers a hybrid communication architecture as shown in fig. 2. Generating raw observed values x of each node sensor according to the following parametersn: the total number of node sensors is 20, where Nc is 10 for node sensors with good transmission conditions, Nq is 10 for node sensors with limited transmission conditions, and the observation factor h isn1, noise power
Figure BDA0002967173380000063
The number of Monte Carlo experiments was 105The target signal to noise power ratio SNR is-8 dB, and the global false alarm probability Pfa＝10-4。
S2, transmitting the observed values acquired by the node sensors under different transmission conditions to a fusion center in different data transmission modes; as shown in the structure of the multi-sensor joint detection system shown in fig. 3, the invention divides the transmission data form into two types according to the actual transmission condition of each node sensor:
A. when the transmission condition is good, the node sensor directly transmits the original observation value to the fusion center, and because the transmission mode reserves complete data information, the fusion center receives signal level data ynExpressed as:
yn＝xn，1≤n≤Nc
wherein N iscIndicating the number of node sensors transmitting signal level data, xnRepresenting a sensor observation;
B. when the transmission bandwidth is severely limited, the node sensor cannot transmit the original observed value, and only transmits a local judgment result to the fusion center after the original observed value is locally judged by adopting a method for reducing the data volume; the decision-level data b received by the fusion centrenExpressed as:
bn＝sgn(xn-τn)，Nc＜n≤Nq+Nc
wherein N isqNumber of node sensors, τ, representing data at decision level of transmissionnRepresents a local decision threshold value, sgn (·) represents a step function, and the observed value x of the node sensornGreater than threshold taunThen, the decision result "1" is passed; otherwise, the decision result "0" is passed.
S3, establishing a joint likelihood function according to the prior information; the method specifically comprises the following steps:
s31, according to the statistical distribution of the original observed values, establishing probability density functions of two different forms of data received by each node sensor under two assumptions: p (y)n,θ|H1)、p(yn|H0) Respectively representing signal level data ynUnder the assumption of H1And H0Conditional probability density function of p (b)n,θ|H1)、p(bn|H0) Respectively representing decision levelsData bnUnder the assumption of H1And H0A conditional probability density function of;
1≤n≤Ncand the received data is signal level data:
Figure BDA0002967173380000071
Figure BDA0002967173380000072
Nc＜n≤Nq+Ncthen, the received data is decision level data:
Figure BDA0002967173380000073
Figure BDA0002967173380000074
wherein the content of the first and second substances,
Figure BDA0002967173380000075
omega is an integral variable;
s32, integrating the data transmitted at the same level and associating the data at different levels in a way of calculating a joint likelihood function ratio because the data transmission of different node sensors are mutually independent; the joint likelihood function ratio calculation formula is as follows:
Figure BDA0002967173380000076
wherein the content of the first and second substances,
Figure BDA0002967173380000081
[·]Tdenotes the matrix transposition, p (y, b, θ | H1) Indicates that two kinds of received data are in H1Joint probability density function under assumption, p (y, b | H0) Watch (A)Two kinds of received data are shown in H0A joint probability density function under assumption; substituting the observed values y and b of all the node sensors into a probability density function to obtain:
Figure BDA0002967173380000082
s4, carrying out maximum likelihood estimation on the unknown parameters; calculating the maximum likelihood estimated value of the unknown target signal theta by a numerical solving method
Figure BDA0002967173380000083
Figure BDA0002967173380000084
S5, calculating detection statistics based on the generalized likelihood ratio criterion; the specific implementation method comprises the following steps: substituting the maximum likelihood estimation value of the unknown parameter into the likelihood function, and taking the logarithm form of the likelihood function to obtain the detection statistic
Figure BDA0002967173380000085
Figure BDA0002967173380000086
S6, setting a detection threshold by deducing the approximate distribution of the detection statistic; the method specifically comprises the following steps:
s61, constructing the corrected detection statistic according to the expression of the detection statistic and the statistical distribution rule of the received data
Figure BDA0002967173380000087
The gradual distribution of (2):
Figure BDA0002967173380000088
wherein alpha representsThe distribution is gradual and the distribution is gradual,
Figure BDA0002967173380000089
representing a central chi-squared distribution with a degree of freedom of 1,
Figure BDA00029671733800000810
representing a degree of freedom of 1 and a non-central parameter of λFNon-central chi-square distribution of (c);
s62, calculating Fisher information FI (theta):
Figure BDA00029671733800000811
s63, calculating a non-central parameter lambdaF：
λF＝(θ1-θ0)2FI(θ0)
θ1And theta0Respectively represent that the unknown target signals theta are at H1And H0A true value under the assumption; it should be noted that λ is calculated hereFIt is necessary to give θ at H1True value of theta under assumption1This is because the actual amplitude of a signal must be limited to compare the actual amplitude when acquiring the actual detection performance of a particular signal. For the detection of unknown target, the false alarm probability is constant, and the pass H is0The approximate distribution of the threshold can be solved back. Thus theta1The method is only used for verifying the correctness of the detection performance improvement and does not relate to the judgment of the detection result.
λFThe larger the value, the better the detection performance of the system.
S64 maximization of non-central parameter lambdaF：λFValue is given bynInfluence, setting of optimal local decision threshold τnCan make λ equal to 0FReaching a maximum value;
s65, substituting the optimal local judgment threshold value to obtain the maximum value lambda of the non-central parameterFmaxComprises the following steps:
Figure BDA0002967173380000091
s66, detecting statistic value at H according to correction0And (3) calculating a global detection threshold eta by inverse solution according to the following approximate distribution, wherein the relationship between the global detection threshold and the detection statistic is as follows:
Figure BDA0002967173380000092
s7, comparing the detection statistic with a detection threshold, and outputting a detection result; the specific implementation method comprises the following steps: by substituting the noncentral parameters, the distribution characteristics of the detection statistics are completely known, and under the condition of appointed false alarm probability or detection probability, the corresponding detection threshold eta can be obtained, so that the judgment expression is as follows:
Figure BDA0002967173380000093
when the corrected detection statistic is greater than the threshold, then the hypothesis H is determined1If yes, the target signal exists; otherwise, then hypothesis H is determined0In the case, the target signal is not present.
To verify the correctness of the detection method, in the simulation, the actual target signal is substituted into H1True value of theta under assumption1Calculating a non-central parameter λF maxSetting a global detection threshold, and calculating the theoretical discovery probability as follows:
Figure BDA0002967173380000095
the simulation results obtained in this example are shown in fig. 4, 5, and 6 according to the above steps.
As shown in FIG. 4, the global false alarm probability P is set in 0.1 interval stepsFAAnd (4) increasing the number from 0 to 1, setting other parameters as same as S1, simulating to generate a plurality of random sample observed values according to a Monte Carlo method, inputting the random sample observed values into an algorithm flow for calculation, and finally generating different levels of data combined detection sensitivity curves.According to the simulation result, under the complex communication condition, the simulation value of the multi-level fusion detection algorithm provided by the invention is consistent with the theoretical value, which shows that when the signal-to-noise ratio is known, the progressive analysis can also provide a reliable setting basis for the global detection threshold. In addition, compared with curves of different levels, the detection performance of the multi-level fusion algorithm is obviously superior to that of a single-level detection method, so that when the same false alarm probability is set, the multi-sensor combined detection algorithm provided by the invention can improve the detection performance compared with a single-level detection algorithm.
As shown in fig. 5, the SNR is set to increase from-8 dB to 10dB at 1dB intervals, the rest parameters are set at S1, a plurality of random sample observations are generated by simulation according to the monte carlo method, and input into the algorithm flow for calculation, and finally different levels of data joint detection performance curves are generated. According to the simulation result, the performance of the decision-level fusion algorithm is reduced compared with that of the signal-level fusion algorithm when the signal-to-noise ratio is high, because the joint estimation performance of the former on unknown parameters of signals is weaker than that of the latter when the signal-to-noise ratio is high, so that the performance is improved less than that of the signal-level fusion algorithm. However, even so, the multi-level fusion algorithm still provides higher performance improvement, which shows that the algorithm can fully extract and utilize data of different forms and different sensors, and further verifies the effectiveness of the invention.
As shown in fig. 6, 5 is used as an interval step, the number of data nodes in each level is respectively set to be increased from 0 to 100, the other parameters are set to be the same as S1, a plurality of random sample observed values are generated through simulation according to the monte carlo method, the random sample observed values are input into an algorithm flow for calculation, and finally, a detection performance plane of the joint detection method based on decision level and signal level data fusion is generated under the condition of different node sensor numbers. According to the simulation result, the detection performance of the joint detection method is improved along with the increase of the number of the node sensors, and the characteristic that the performance of the fusion algorithm is influenced by the number of the channels is met. In addition, under the same node quantity, the more the signal level node quantity is, the higher the detection performance is, which indicates that the influence of different level data on the joint detection algorithm is different, and the more the signal level data is, the more the information quantity is kept, the greater the contribution to the improvement of the algorithm performance is, and the adaptivity and the accuracy of the method in data fusion are reflected.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.

Claims (5)

1. The multi-sensor joint detection method based on decision-level and signal-level data fusion is characterized by comprising the following steps of:
s1, sensing the same unknown target signal by a plurality of node sensors to obtain an observed value acquired by each node sensor on the target signal; the observation model of each node sensor is represented as follows:
Figure FDA0003529739060000011
wherein H0And H1Respectively representing the case where the target signal is assumed to be present and the case where the target signal is not present, xnRepresents an observed value of the nth node sensor; n represents the total number of node sensors; h isnThe observation coefficients are used for representing the signal receiving relation of each node sensor; w is anRepresenting additive observed noise, obeying a mean of 0 and a variance of
Figure FDA0003529739060000012
Is expressed as:
Figure FDA0003529739060000013
s2, transmitting the observed values acquired by the node sensors under different transmission conditions to a fusion center in different data transmission modes; the specific implementation method comprises the following steps:
A. when the transmission condition is good, the node sensor directly transmits the original observation value to the fusion center, and because the transmission mode reserves complete data information, the fusion center receives signal level data ynExpressed as:
yn＝xn，1≤n≤Nc
wherein N iscIndicating the number of node sensors transmitting signal level data, xnRepresenting a sensor observation;
B. when the transmission bandwidth is severely limited, the node sensor cannot transmit the original observed value, and only transmits a local judgment result to the fusion center after the original observed value is locally judged by adopting a method for reducing the data volume; the decision-level data b received by the fusion centrenExpressed as:
bn＝sgn(xn-τn)，Nc＜n≤Nq+Nc
wherein N isqNumber of node sensors, τ, representing data at decision level of transmissionnRepresents a local decision threshold value, sgn (·) represents a step function, and the observed value x of the node sensornGreater than threshold taunThen, the decision result "1" is passed; otherwise, a decision result of "0" is passed;
s3, establishing a joint likelihood function according to the prior information; the method specifically comprises the following steps:
s31, according to the statistical distribution of the original observed values, establishing probability density functions of two different forms of data received by each node sensor under two assumptions: p (y)n,θ|H1)、p(yn|H0) Respectively representing signal level data ynUnder the assumption of H1And H0Conditional probability density function of p (b)n,θ|H1)、p(bn|H0) Respectively representing decision level data bnUnder the assumption of H1And H0A conditional probability density function of;
1≤n≤Ncand the received data is signal level data:
Figure FDA0003529739060000021
Figure FDA0003529739060000022
Nc＜n≤Nq+Ncthen, the received data is decision level data:
Figure FDA0003529739060000023
Figure FDA0003529739060000024
wherein the content of the first and second substances,
Figure FDA0003529739060000025
omega is an integral variable;
s32, integrating the data transmitted at the same level and associating the data at different levels in a way of calculating a joint likelihood function ratio because the data transmission of different node sensors are mutually independent; the joint likelihood function ratio calculation formula is as follows:
Figure FDA0003529739060000026
wherein [ ·]TDenotes the matrix transposition, p (y, b, θ | H1) Indicates that two kinds of received data are in H1Joint probability density function under assumption, p (y, b | H0) Indicates that two kinds of received data are in H0A joint probability density function under assumption;
s4, carrying out maximum likelihood estimation on the unknown parameters;
s5, calculating detection statistics based on the generalized likelihood ratio criterion;
s6, setting a detection threshold by deducing the approximate distribution of the detection statistic;
and S7, comparing the detection statistic with the detection threshold, and outputting the detection result.
2. The multi-sensor joint detection method based on decision-level and signal-level data fusion of claim 1, wherein in step S4, the maximum likelihood estimation value of the unknown target signal θ is calculated by a numerical solution method
Figure FDA0003529739060000029
Figure FDA0003529739060000027
3. The multi-sensor joint detection method based on decision-level and signal-level data fusion of claim 1, wherein the step S5 is implemented by: substituting the maximum likelihood estimation value of the unknown parameter into the likelihood function, and taking the logarithm form of the likelihood function to obtain the detection statistic
Figure FDA0003529739060000028
Figure FDA0003529739060000031
4. The multi-sensor joint detection method based on decision-level and signal-level data fusion of claim 1, wherein the step S6 specifically comprises the following sub-steps:
s61, according to the expression of the detection statistic and the statistical distribution rule of the received data,constructing revised detection statistics
Figure FDA0003529739060000032
The gradual distribution of (2):
Figure FDA0003529739060000033
wherein, alpha represents a gradual distribution,
Figure FDA0003529739060000034
representing a central chi-squared distribution with a degree of freedom of 1,
Figure FDA0003529739060000035
representing a degree of freedom of 1 and a non-central parameter of λFNon-central chi-square distribution of (c);
s62, calculating Fisher information FI (theta):
Figure FDA0003529739060000036
s63, calculating a non-central parameter lambdaF：
λF＝(θ1-θ0)2FI(θ0)
θ1And theta0Respectively represent that the unknown target signals theta are at H1And H0A true value under the assumption; lambda [ alpha ]FThe larger the value is, the better the detection performance of the system is;
s64 maximization of non-central parameter lambdaF：λFValue is given bynInfluence, setting of optimal local decision threshold τnCan make λ equal to 0FReaching a maximum value;
s65, substituting the optimal local judgment threshold value to obtain the maximum value lambda of the non-central parameterFmaxComprises the following steps:
Figure FDA0003529739060000037
s66, detecting statistic value at H according to correction0And (3) calculating a global detection threshold eta by inverse solution according to the following approximate distribution, wherein the relationship between the global detection threshold and the detection statistic is as follows:
Figure FDA0003529739060000038
5. the multi-sensor joint detection method based on decision-level and signal-level data fusion of claim 1, wherein the step S7 is implemented by: the decision expression is as follows:
Figure FDA0003529739060000041
when the corrected detection statistic is greater than the threshold, then the hypothesis H is determined1If yes, the target signal exists; otherwise, then hypothesis H is determined0In the case, the target signal is not present.
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