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CN112417377A - Military reconnaissance system efficiency evaluation method - Google Patents

Military reconnaissance system efficiency evaluation method Download PDF

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CN112417377A
CN112417377A CN202011298467.0A CN202011298467A CN112417377A CN 112417377 A CN112417377 A CN 112417377A CN 202011298467 A CN202011298467 A CN 202011298467A CN 112417377 A CN112417377 A CN 112417377A
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李俊
范斌
胡磊
戴文瑞
孙吉红
武昕伟
王锐
吴坤
陆珊珊
秦鹏程
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PLA Army Academy of Artillery and Air Defense
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Abstract

本发明提供一种军事侦察系统效能评估方法，包括建立基于信息论的效能评估模型，建立效能评估模型包括建立信息完整度模型、信息准确度模型、信息时效度模型，所述效能评估模型由由准确度QSacc、完整度QScomp和时效度QScurr组成，综合效能E可表示为：E＝WSaccQSacc+WScompQScomp+WScurrQScurr，其中，WSacc、WScomp和WScurr分别是准确度QSacc、完整度QScomp和时效度QScurr的权值。本发明建立了军事侦察系统信息完整度模型、信息准确度模型和信息时效度模型，达到了对军事侦察系统综合作战效能评价的目标，该评估方法理论完备、技术先进，具有很强的可操作性，适用于对各类军事侦察系统进行作战效能评估，可为装备研制、作战筹划等工作提供技术支撑。

Figure 202011298467

The invention provides a method for evaluating the effectiveness of a military reconnaissance system, which includes establishing an effectiveness evaluation model based on information theory, and establishing an effectiveness evaluation model includes establishing an information integrity model, an information accuracy model, and an information timeliness model. The comprehensive efficiency E can be expressed as: E=W Sacc Q Sacc + W Scomp Q Scomp + W Scurr Q Scurr , where W Sacc , W Scomp and W Scurr are respectively is the weight of accuracy Q Sacc , completeness Q Scomp and timeliness Q Scurr . The invention establishes an information integrity model, an information accuracy model and an information timeliness model of the military reconnaissance system, and achieves the goal of evaluating the comprehensive combat effectiveness of the military reconnaissance system. The evaluation method is complete in theory, advanced in technology, and has strong operational It is suitable for evaluating the combat effectiveness of various military reconnaissance systems, and can provide technical support for equipment development and combat planning.

Figure 202011298467

Description

Military reconnaissance system efficiency evaluation method
Technical Field
The invention relates to the field of military reconnaissance, in particular to a military reconnaissance system efficiency evaluation method.
Background
The military reconnaissance system mainly reconnaissance key areas on a battlefield, then processes and synthesizes reconnaissance data to generate corresponding information, provides information support for a command decision system or a combat unit, measures the size of the information support effect, and mainly judges whether the reconnaissance system can provide support information timely, accurately and reliably.
Disclosure of Invention
The present invention is directed to a military reconnaissance system performance evaluation method to solve the above-mentioned technical problems.
In order to solve the technical problems, the invention adopts the following technical scheme: the military reconnaissance system efficiency evaluation method comprises the steps of establishing an efficiency evaluation model based on information theory, wherein the establishment of the efficiency evaluation model comprises the establishment of an information integrity model, an information accuracy model and an information timeliness model, and the efficiency evaluation model consists of an accuracy QSaccIntegrity QScompAnd aging degree QScurrComposition, the overall efficacy E can be expressed as: e ═ WSaccQSacc+WScompQScomp+WScurrQScurrWherein W isSacc、WScompAnd WScurrAre respectively the accuracy QSaccIntegrity QScompAnd aging degree QScurrThe weight of (2).
Preferably, the information theory is a state description of a system or event or a message about the state, and let M ═ x1,x2,…,xnIs the set of all possible states of system X, P ═ P1,p2,…,pnThe probability of occurrence of each state is set, and according to the shannon entropy concept, if the probability of occurrence of a state of a system or an event can be represented mathematically, the entropy of the information describing the system is:
H(x)＝-∑xlog[p(x)]
if the system state set is a continuous interval [ a, b ] and there is a probability distribution density function f (x), then the information entropy is:
Figure BDA0002786100140000021
preferably, the information integrity model establishment comprises a target detection process, wherein n signals to be detected are set, and H is enabled0Indicating "no target signal present", H1Indicating "there is a target signal present", D0Meaning "decision is targeted", D1Meaning "decide not to target", i.e. for H0:z(t)、H1Z (t) performing a statistical test to determine which hypothesis is true, z (t) being an observation signal, and comparing H0And H1Magnitude of probability of occurrence, i.e. comparative posterior probability P (H)0| z) and P (H)1I z), which probability is large and which is true, is expressed as P (H) by the decision formula1|z)＞P(H0I z) is satisfied, it is judged as H1，P(H1|z)＜P(H0I z) is satisfied, it is judged as H0According to the Bayesian formula, the posterior probability can be expressed as:
Figure BDA0002786100140000022
wherein P (z) is the probability density of z, P (zH)0)、P(zH1) Is a conditional probability density when
Figure BDA0002786100140000023
When it is established, it is judged as H1(ii) a When in use
Figure BDA0002786100140000024
When it is established, it is judged as H0；P(H0)、P(H1) Are respectively H0Hypothesis sum H1The assumed prior probabilities, generally known as a priori knowledge,
Figure BDA0002786100140000025
is a decision threshold value;
four cases occur in the decision making of the binary detection problem, which describe the performance of the binary detection device, and they can be expressed by conditional probabilities as follows:
(1) let H0If true, the decision is D0Denotes selection H0For true correct decision, use conditional probability P (D)0|H0) It is shown that,
Figure BDA0002786100140000026
(2) let H1If true, the decision is D1Denotes selection H1For true correct decision, use conditional probability P (D)1|H1) It is shown that,
Figure BDA0002786100140000027
in signal detection, there is a target signal and the decision is made that there is a target, also called the probability of detection, with PdIt is shown that,
(3) let H0If true, the decision is D1Denotes selection H0For false first type of erroneous decision, using conditional probability P (D)1|H1) It is shown that,
Figure BDA0002786100140000028
in signal detection, if there is no target signal and the target is determined to be present, also called false alarm probability, P is usedfIt is shown that,
(4) let H1If true, the decision is D0Denotes selection H1For false second type of erroneous decision, use is made of the conditional probability P (D)0|H1) It is shown that,
Figure BDA0002786100140000031
in signal detection, if there is a target signal and the decision is no target, also called false alarm probability, P is usedmRepresents;
according to a Bayes formula and a total probability formula, a corresponding posterior probability can be obtained:
Figure BDA0002786100140000032
Figure BDA0002786100140000033
Figure BDA0002786100140000034
Figure BDA0002786100140000035
Figure BDA0002786100140000036
as can be seen from the basic principle of information theory, h (x) represents the degree of loss of information amount caused by false alarm and false alarm, and the greater the false alarm and false alarm probability, the greater the loss of information,
the information acquisition integrity model is
Figure BDA0002786100140000037
In the formula
Hmax(X) -entropy at maximum uncertainty, reached when both false alarm probability and false alarm probability are 0.5;
Hmin(X) -entropy at minimum uncertainty, reached when both false alarm probability and false alarm probability are 0;
the result of enemy interference reduces my correct decision P (D)0|H0) And P (D)1|H1) (probability of detection) so that H (X) is increased, QScomp(X) is decreased.
Preferably, the information accuracy model establishing step is as follows:
let the one-dimensional random variable be [ - Δ, Δ [ - Δ [ ]]The interval obeys the uniform distribution of equal probability, delta is the maximum range of uncertainty of random variables, is generally priori knowledge, and the probability density function of the interval is
Figure BDA0002786100140000038
Its information entropy is
Figure BDA0002786100140000041
If the one-dimensional continuous random variable obeys normal distribution, the probability density function is
Figure BDA0002786100140000042
Its information entropy is
Figure BDA0002786100140000043
The difference between the two information entropies is the reduction degree of the uncertain range
Figure BDA0002786100140000044
Generalizing this conclusion to the case of N dimensions, where the N-dimensional continuous random vector X is (X)1,x2,…,xn)TIs defined as a joint entropy of
Figure BDA0002786100140000045
If the N-dimensional continuous random vector X follows a normal distribution, its probability density function is
Figure BDA0002786100140000046
Wherein [ mu ] is1,μ2,…,μN]Is a mean value and has a covariance matrix
Figure BDA0002786100140000047
The non-diagonal elements being random variables xiAnd xjCovariance value of (a) ofi,j＝(xi-μi)(xj-μj) Get, a random variable xiAnd xjIs expressed as
Figure BDA0002786100140000048
When i is j then ∑i,jIs the variance of the covariance matrix;
the joint entropy of the N-dimensional continuous random vector X is
Figure BDA0002786100140000051
Wherein | Σ | is a modulus of a determinant of the covariance matrix Σ, and since n is a constant, H (x) is simplified to obtain a relative entropy Hr(X) log | ∑ i, i.e. related to covariance only,
for multivariate normal distribution, it is first assumed that the maximum joint entropy exists, i.e. it is reached when the distribution is uniform
Hmax(X)＝log|∑|max
Definition of QSacc(X) is the interval [0, 1 ]]A value in between, and
Figure BDA0002786100140000052
the information entropy can obtain the representation Q of the information acquisition accuracySacc(X)，0≤QSacc(X) is less than or equal to 1, namely the information element { a ≦ is reflected1,a2,…,aCValue and degree of mastery of relationship between them, when QSacc(X) → 1, indicating the highest accuracy and QSacc(X) → 0 indicates the lowest accuracy.
Preferably, the information aging model is established by the following steps: the degree of recency of the obtained information described by the time effectiveness of the information can be expressed as
Figure BDA0002786100140000053
tiIndicating the current time, i.e. the time at which the combat unit has requested the information, tlIndicates the latest update time t of the information0Which is the time when the information actually begins to exist, and eta is a coefficient related to the importance of the information. .
The invention has the beneficial effects that:
the method adopts an information theory method, establishes an information integrity model, an information accuracy model and an information timeliness model of the military reconnaissance system, achieves the aim of evaluating the comprehensive combat effectiveness of the military reconnaissance system, is complete in theory, advanced in technology and strong in operability, is suitable for carrying out combat effectiveness evaluation on various military reconnaissance systems, and can provide technical support for equipment development, combat planning and other work.
Drawings
FIG. 1 is a schematic diagram of a target detection process according to the present invention;
FIG. 2 is a graph of the transition probability of target detection according to the present invention;
fig. 3 is a schematic diagram of the information acquisition timeliness of the present invention.
Detailed Description
In order to make the technical means, the original characteristics, the achieved purposes and the effects of the invention easily understood, the invention is further described below with reference to the specific embodiments and the attached drawings, but the following embodiments are only the preferred embodiments of the invention, and not all embodiments. Based on the embodiments in the implementation, other embodiments obtained by those skilled in the art without any creative efforts belong to the protection scope of the present invention.
Specific embodiments of the present invention are described below with reference to the accompanying drawings.
Example 1
As shown in figure 1, the military reconnaissance system efficiency evaluation method comprises the steps of establishing an efficiency evaluation model based on information theory, establishing the efficiency evaluation model, and establishing an information integrity model, an information accuracy model and an information timeliness model, wherein the efficiency evaluation model is composed of an accuracy QSaccIntegrity QScompAnd aging degree QScurrComposition, the overall efficacy E can be expressed as: e ═ WSaccQSacc+WScompQScomp+WScurrQScurrWherein W isSacc、WScompAnd WScurrAre respectively the accuracy QSaccIntegrity QScompAnd aging degree QScurrThe weight of (2).
Information theory is a description of the state of a system or event or a message about that state, let M ═ x1,x2,…,xnIs the set of all possible states of system X, P ═ P1,p2,…,pnThe probability of occurrence of each state is set, and according to the shannon entropy concept, if the probability of occurrence of a state of a system or an event can be represented mathematically, the entropy of the information describing the system is:
H(x)＝-∑xlog[p(x)]
if the system state set is a continuous interval [ a, b ] and there is a probability distribution density function f (x), then the information entropy is:
Figure BDA0002786100140000061
the information integrity model establishment comprises a target detection process and n to-be-detected modelsDetecting a signal, let H0Indicating "no target signal present", H1Indicating "there is a target signal present", D0Meaning "decision is targeted", D1Meaning "decide not to target", i.e. for H0:z(t)、H1Z (t) performing a statistical test to determine which hypothesis is true, z (t) being an observation signal, and comparing H0And H1Magnitude of probability of occurrence, i.e. comparative posterior probability P (H)0| z) and P (H)1I z), which probability is large and which is true, is expressed as P (H) by the decision formula1|z)＞P(H0I z) is satisfied, it is judged as H1，P(H1|z)＜P(H0I z) is satisfied, it is judged as H0According to the Bayesian formula, the posterior probability can be expressed as:
Figure BDA0002786100140000071
wherein P (z) is the probability density of z, P (zH)0)、P(zH1) Is a conditional probability density when
Figure BDA0002786100140000072
When it is established, it is judged as H1(ii) a When in use
Figure BDA0002786100140000073
When it is established, it is judged as H0；P(H0)、P(H1) Are respectively H0Hypothesis sum H1The assumed prior probabilities, generally known as a priori knowledge,
Figure BDA0002786100140000074
is a decision threshold value;
four cases occur in the decision making of the binary detection problem, which describe the performance of the binary detection device, and they can be expressed by conditional probabilities as follows:
(1) let H0If true, the decision is D0Denotes selection H0For true correct decision, use conditional probability P (D)0|H0) It is shown that,
Figure BDA0002786100140000075
(2) let H1If true, the decision is D1Denotes selection H1For true correct decision, use conditional probability P (D)1|H1) It is shown that,
Figure BDA0002786100140000076
in signal detection, there is a target signal and the decision is made that there is a target, also called the probability of detection, with PdIt is shown that,
(3) let H0If true, the decision is D1Denotes selection H0For false first type of erroneous decision, using conditional probability P (D)1|H1) It is shown that,
Figure BDA0002786100140000077
in signal detection, if there is no target signal and the target is determined to be present, also called false alarm probability, P is usedfIt is shown that,
(4) let H1If true, the decision is D0Denotes selection H1For false second type of erroneous decision, use is made of the conditional probability P (D)0|H1) It is shown that,
Figure BDA0002786100140000078
in signal detection, if there is a target signal and the decision is no target, also called false alarm probability, P is usedmRepresents;
according to a Bayes formula and a total probability formula, a corresponding posterior probability can be obtained:
Figure BDA0002786100140000079
Figure BDA0002786100140000081
Figure BDA0002786100140000082
Figure BDA0002786100140000083
Figure BDA0002786100140000084
as can be seen from the basic principle of information theory, h (x) represents the degree of loss of information amount caused by false alarm and false alarm, and the greater the false alarm and false alarm probability, the greater the loss of information,
the information acquisition integrity model is
Figure BDA0002786100140000085
In the formula
Hmax(X) -entropy at maximum uncertainty, reached when both false alarm probability and false alarm probability are 0.5;
Hmin(X) -entropy at minimum uncertainty, reached when both false alarm probability and false alarm probability are 0;
the result of enemy interference reduces my correct decision P (D)0|H0) And P (D)1|H1) (probability of detection) so that H (X) is increased, QScomp(X) is decreased.
The information accuracy model establishment steps are as follows:
let the one-dimensional random variable be [ - Δ, Δ [ - Δ [ ]]The interval obeys the uniform distribution of equal probability, delta is the maximum range of uncertainty of random variables, is generally priori knowledge, and the probability density function of the interval is
Figure BDA0002786100140000086
Its information entropy is
Figure BDA0002786100140000087
If the one-dimensional continuous random variable obeys normal distribution, the probability density function is
Figure BDA0002786100140000088
Its information entropy is
Figure BDA0002786100140000091
The difference between the two information entropies is the reduction degree of the uncertain range
Figure BDA0002786100140000092
Generalizing this conclusion to the case of N dimensions, where the N-dimensional continuous random vector X is (X)1,x2,…,xn)TIs defined as a joint entropy of
Figure BDA0002786100140000093
If the N-dimensional continuous random vector X follows a normal distribution, its probability density function is
Figure BDA0002786100140000094
Wherein [ mu ] is1,μ2,…,μN]Is a mean value and has a covariance matrix
Figure BDA0002786100140000095
The non-diagonal elements being random variables xiAnd xjCovariance value of (a) ofi,j＝(xi-μi)(xj-μj) Get, a random variable xiAnd xjIs expressed as
Figure BDA0002786100140000096
When i is j then ∑i,jIs the variance of the covariance matrix;
the joint entropy of the N-dimensional continuous random vector X is
Figure BDA0002786100140000097
Wherein | Σ | is a modulus of a determinant of the covariance matrix Σ, and since n is a constant, H (x) is simplified to obtain a relative entropy Hr(X) log | ∑ i, i.e. related to covariance only,
for multivariate normal distribution, it is first assumed that the maximum joint entropy exists, i.e. it is reached when the distribution is uniform
Hmax(X)＝log|∑|max
Definition of QSacc(X) is the interval [0, 1 ]]A value in between, and
Figure BDA0002786100140000101
the information entropy can obtain the representation Q of the information acquisition accuracySacc(X)，0≤QSacc(X) is less than or equal to 1, namely the information element { a ≦ is reflected1,a2,…,aCValue and degree of mastery of relationship between them, when QSacc(X) → 1, indicating the highest accuracy and QSacc(X) → 0 indicates the lowest accuracy.
The information aging model establishing steps are as follows: the degree of recency of the obtained information described by the time effectiveness of the information can be expressed as
Figure BDA0002786100140000102
tiIndicating the current time, i.e. the time at which the combat unit has requested the information, tlIndicates the latest update time t of the information0Which is the time when the information actually begins to exist, and eta is a coefficient related to the importance of the information.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and the preferred embodiments of the present invention are described in the above embodiments and the description, and are not intended to limit the present invention. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (5)

1.一种军事侦察系统效能评估方法，其特征在于，包括建立基于信息论的效能评估模型，建立效能评估模型包括建立信息完整度模型、信息准确度模型、信息时效度模型，所述效能评估模型由由准确度QSacc、完整度QScomp和时效度QScurr组成，综合效能E可表示为：E＝WSaccQSacc+WScompQScomp+WScurrQScurr，其中，WSacc、WScomp和WScurr分别是准确度QSacc、完整度QScomp和时效度QScurr的权值。1. a military reconnaissance system effectiveness assessment method, is characterized in that, comprises establishing the effectiveness assessment model based on information theory, and establishing the effectiveness assessment model comprises establishing information integrity model, information accuracy model, information timeliness model, and described effectiveness assessment model. Composed of accuracy Q Sacc , completeness Q Scomp and timeliness Q Scurr , the comprehensive efficiency E can be expressed as: E=W Sacc Q Sacc + W Scomp Q Scomp + W Scurr Q Scurr , where W Sacc , W Scomp and W Scurr is the weight of accuracy Q Sacc , completeness Q Scomp and timeliness Q Scurr respectively. 2.根据权利要求1所述的一种军事侦察系统效能评估方法，其特征在于：所述信息论为对系统或事件的状态描述或是有关该状态的消息，令M＝{x1,x2,…,xn}是系统X所有可能状态集，P＝{p1,p2,…,pn}是各状态的出现概率集，根据香农熵的概念，如果系统或事件的状态出现概率能够数学表示的话，则描述该系统的信息的熵为：2. The method for evaluating the effectiveness of a military reconnaissance system according to claim 1, wherein the information theory is a state description of a system or an event or a message about the state, let M={x 1 , x 2 ,...,x n } is the set of all possible states of the system X, P={p 1 ,p 2 ,...,p n } is the set of occurrence probability of each state. According to the concept of Shannon entropy, if the state of the system or event has the probability of occurrence If it can be represented mathematically, the entropy of the information describing the system is: H(x)＝-∑xlog[p(x)]H(x)=-∑xlog[p(x)] 如果系统状态集是连续区间[a,b]，且存在着概率分布密度函数f(x)，那么信息熵为：If the system state set is a continuous interval [a, b], and there is a probability distribution density function f(x), then the information entropy is:
Figure FDA0002786100130000011
Figure FDA0002786100130000011
 3.根据权利要求1所述的一种军事侦察系统效能评估方法，其特征在于：所述信息完整度模型建立包括目标检测过程，设有n个待检测信号，令H0表示“无目标信号存在”，H1表示“有目标信号存在”，D0表示“判决为有目标”，D1表示“判决为无目标”，即对H0:z(t)、H1:z(t)进行统计检验，判决哪一个假设成立，z(t)为观测信号,比较H0和H1出现概率的大小，即比较后验概率P(H0|z)和P(H1|z)，哪一个概率大就判决哪个成立，用判决式表示为P(H1|z)＞P(H0|z)成立时，判为H1，P(H1|z)＜P(H0|z)成立时，判为H0,根据叶贝丝公式，后验概率可表示为：
Figure FDA0002786100130000012
其中，为p(z)为z的概率密度，P(z|H0)、P(z|H1)为条件概率密度，当
Figure FDA0002786100130000013
成立时，判为H1；当
Figure FDA0002786100130000014
成立时，判为H0；P(H0)、P(H1)分别为H0假设和H1假设的先验概率，一般作为先验知识是已知的，
Figure FDA0002786100130000021
为判决门限值；3. a kind of military reconnaissance system effectiveness evaluation method according to claim 1 is characterized in that: described information integrity model establishment comprises target detection process, is provided with n signals to be detected, let H 0 represent "no target signal". "exist", H 1 means "there is a target signal", D 0 means "the decision is to have a target", D 1 means "the decision is to have no target", that is, for H 0 :z(t), H 1 :z(t) Statistical test is performed to determine which hypothesis holds, z(t) is the observed signal, and the probability of occurrence of H 0 and H 1 is compared, that is, the posterior probability P(H 0 |z) and P(H 1 |z) are compared, Whichever probability is higher will be judged to be true. The decision formula is expressed as P(H 1 |z)>P(H 0 |z) when it is true, it will be judged as H 1 , P(H 1 |z)<P(H 0 | When z) is established, it is judged as H 0 . According to the Yebes formula, the posterior probability can be expressed as:
Figure FDA0002786100130000012
Among them, p(z) is the probability density of z, P(z|H 0 ), P(z|H 1 ) are the conditional probability densities, when
Figure FDA0002786100130000013
When established, it is judged as H 1 ; when
Figure FDA0002786100130000014
When established, it is judged as H 0 ; P(H 0 ) and P(H 1 ) are the prior probabilities of H 0 hypothesis and H 1 hypothesis respectively, which are generally known as prior knowledge,
Figure FDA0002786100130000021
is the decision threshold; 二元检测问题作出判决出现四种情况，这四种情况描述了二元检测设备的性能，它们可以用条件概率分别表示如下：There are four situations in the decision of the binary detection problem. These four situations describe the performance of the binary detection device. They can be expressed as follows by conditional probabilities: (1)设H0假设为真，判决为D0,表示选择H0为真是正确判决，用条件概率P(D0|H0)表示，
Figure FDA0002786100130000022
(1) Let the hypothesis H 0 be true, and the decision is D 0 , which means choosing H 0 to be the true and correct decision, expressed by the conditional probability P(D 0 |H 0 ),
Figure FDA0002786100130000022
 (2)设H1假设为真，判决为D1,表示选择H1为真是正确判决，用条件概率P(D1|H1)表示，
Figure FDA0002786100130000023
在信号检测中，是有目标信号而判决为有目标，又称作探测概率，用Pd表示，(2) Let the hypothesis of H 1 be true and the decision as D 1 , which means choosing H 1 to be the true and correct decision, expressed by the conditional probability P(D 1 |H 1 ),
Figure FDA0002786100130000023
In signal detection, there is a target signal and it is judged to have a target, also known as detection probability, which is represented by P d , (3)设H0假设为真，判决为D1，表示选择H0为假是第一类错误判决，用条件概率P(D1|H1)表示，
Figure FDA0002786100130000024
在信号检测中，是没有目标信号而判决为有目标，又称作虚警概率，用Pf表示，(3) Let the hypothesis H 0 be true and the decision as D 1 , indicating that choosing H 0 to be false is the first type of wrong decision, which is represented by the conditional probability P(D 1 |H 1 ),
Figure FDA0002786100130000024
In signal detection, there is no target signal and it is judged to have a target, also known as false alarm probability, which is represented by P f , (4)设H1假设为真，判决为D0，表示选择H1为假是第二类错误判决，用条件概率P(D0|H1)表示，
Figure FDA0002786100130000025
在信号检测中，是有目标信号而判决为没有目标，又称作漏警概率，用Pm表示；(4) Suppose H 1 hypothesis is true and the decision is D 0 , indicating that choosing H 1 to be false is the second type of wrong decision, which is represented by the conditional probability P(D 0 |H 1 ),
Figure FDA0002786100130000025
In signal detection, there is a target signal and it is judged that there is no target, which is also called the probability of missing alarm, which is represented by P m ; 根据贝叶斯公式和全概率公式，可以得到相应的后验概率：According to the Bayesian formula and the full probability formula, the corresponding posterior probability can be obtained:
Figure FDA0002786100130000026
Figure FDA0002786100130000026
Figure FDA0002786100130000027
Figure FDA0002786100130000027
Figure FDA0002786100130000028
Figure FDA0002786100130000028
Figure FDA0002786100130000029
Figure FDA0002786100130000029
Figure FDA00027861001300000210
Figure FDA00027861001300000210
 由信息论的基本原理可知，H(X)表示由虚警和漏警带来的信息量的损失程度，虚警和漏警概率越大，则信息的损失越大，According to the basic principles of information theory, H(X) represents the degree of information loss caused by false alarms and missed alarms. The greater the probability of false alarms and missed alarms, the greater the loss of information. 信息获取完整度模型为The information acquisition integrity model is
Figure FDA0002786100130000031
Figure FDA0002786100130000031
 式中in the formula Hmax(X)——最大不确定时的熵，当虚警概率和漏警概率都为0.5时达到；H max (X) - the entropy at the maximum uncertainty, when both the false alarm probability and the missed alarm probability are 0.5; Hmin(X)——最小不确定时的熵，当虚警概率和漏警概率都为0时达到；H min (X)——the entropy at the minimum uncertainty, when both the false alarm probability and the missed alarm probability are 0; 敌方干扰的结果降低了我方的正确判决P(D0|H0)和P(D1|H1)(探测概率)，从而使H(X)增大，QScomp(X)减小。The result of enemy interference reduces our correct decisions P(D 0 |H 0 ) and P(D 1 |H 1 ) (probability of detection), so that H(X) increases and Q Scomp (X) decreases . 4.根据权利要求1所述的一种军事侦察系统效能评估方法，其特征在于：所述信息准确度模型建立步骤如下：4. a kind of military reconnaissance system effectiveness evaluation method according to claim 1, is characterized in that: described information accuracy model establishment step is as follows: 设一维随机变量在[-Δ,Δ]区间服从等概率的均匀分布，Δ是随机变量不确定的最大范围，一般为先验知识，其概率密度函数为
Figure FDA0002786100130000032
则它的信息熵为
Figure FDA0002786100130000033
如果一维连续随机变量服从正态分布，其概率密度函数为
Figure FDA0002786100130000034
则它的信息熵为Suppose a one-dimensional random variable obeys a uniform distribution with equal probability in the interval [-Δ,Δ], Δ is the maximum range of uncertainty of the random variable, which is generally a priori knowledge, and its probability density function is
Figure FDA0002786100130000032
Then its information entropy is
Figure FDA0002786100130000033
If a one-dimensional continuous random variable follows a normal distribution, its probability density function is
Figure FDA0002786100130000034
Then its information entropy is
Figure FDA0002786100130000035
Figure FDA0002786100130000035
 那么两者信息熵的差就是不确定范围的减少程度
Figure FDA0002786100130000036
将此结论推广到N维的情况，N维连续随机矢量X＝(x1,x2,…,xn)T的联合熵定义为
Figure FDA0002786100130000037
假如N维连续随机矢量X服从正态分布，那么它的概率密度函数为Then the difference between the two information entropy is the reduction of the uncertainty range
Figure FDA0002786100130000036
Extending this conclusion to the N-dimensional case, the joint entropy of N-dimensional continuous random vector X=(x 1 ,x 2 ,...,x n ) T is defined as
Figure FDA0002786100130000037
If the N-dimensional continuous random vector X obeys the normal distribution, then its probability density function is
Figure FDA0002786100130000041
Figure FDA0002786100130000041
 其中，μ＝[μ1,μ2,…,μN]是均值，并且有协方差矩阵where μ=[μ 1 , μ 2 ,...,μ N ] is the mean, and there is a covariance matrix
Figure FDA0002786100130000042
Figure FDA0002786100130000042
 非对角线元素是随机变量xi和xj的协方差值，由∑i,j＝(xi-μi)(xj-μj)得到，随机变量xi和xj的相关性表示为
Figure FDA0002786100130000043
当i＝j时∑i,j就是协方差矩阵的方差；The off-diagonal elements are the covariance values of the random variables x i and x j , obtained by ∑ i,j =(x i -μ i )(x j -μ j ), the correlation between the random variables x i and x j sex is expressed as
Figure FDA0002786100130000043
When i=j, ∑ i,j is the variance of the covariance matrix; N维连续随机矢量X的联合熵为The joint entropy of an N-dimensional continuous random vector X is
Figure FDA0002786100130000044
Figure FDA0002786100130000044
 其中，|∑|是协方差矩阵∑的行列式的模，由于n是常量，对H(X)进行简化，得到相对熵Hr(X)＝log|∑|，即只与协方差有关，Among them, |∑| is the modulus of the determinant of the covariance matrix ∑. Since n is a constant, H(X) is simplified to obtain the relative entropy H r (X)=log|∑|, which is only related to the covariance, 对多变量的正态分布，首先设存在最大联合熵，即均匀分布时达到For the multivariate normal distribution, first set the maximum joint entropy, that is, when the uniform distribution reaches Hmax(X)＝log|∑|max H max (X)=log|∑| max 定义QSacc(X)为区间[0，1]之间的值，并且有Define Q Sacc (X) as a value in the interval [0, 1], and have
Figure FDA0002786100130000045
Figure FDA0002786100130000045
 通过信息熵可以得到信息获取准确度的表示QSacc(X)，0≤QSacc(X)≤1反映了信息获取准确程度，即对信息元素{a1,a2,…,aC}值以及之间关系的掌握程度，当QSacc(X)→1，表示准确度最高，而QSacc(X)→0表示准确度最低。The representation of information acquisition accuracy Q Sacc (X) can be obtained through information entropy, 0≤Q Sacc (X)≤1 reflects the accuracy of information acquisition, that is, the value of information elements {a 1 ,a 2 ,...,a C } As well as the mastery of the relationship, when Q Sacc (X)→1, it means the highest accuracy, and Q Sacc (X)→0 means the lowest accuracy. 5.根据权利要求1所述的一种军事侦察系统效能评估方法，其特征在于：所述信息时效模型建立步骤如下：信息的时效度描述的所获得信息的新旧程度，可表示为5. a kind of military reconnaissance system effectiveness evaluation method according to claim 1, is characterized in that: described information aging model establishment step is as follows: the degree of freshness of the obtained information described by the timeliness of information, can be expressed as
Figure FDA0002786100130000051
Figure FDA0002786100130000051
 ti表示当前时刻，即作战单元提出情报需求的时刻，tl指该信息最新的更新时刻，t0是指信息真实开始存在的时刻，η是和信息重要程度相关的系数。t i represents the current moment, that is, the moment when the combat unit puts forward information requirements, t l refers to the latest update moment of the information, t 0 refers to the moment when the information actually begins to exist, and η is a coefficient related to the importance of the information.
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