Keywords

31.1 Introduction

As the electronic technology in air strikes and air defense against are extensive used in the field, electronic against becomes an important part of the modern war. As one of the important forces in ground to air defense, we air-defense unit of the ground will certainly put up drastic rivalry in electronic against conditions. So, how to evaluate the electronic against effectiveness is an important issue.

31.2 Methodology

31.2.1 Improving Evaluation Methods

Currently, there are many methods to evaluate the effectiveness. But in all of the methods the ADC is more comprehensive, precise and its index is more clear which can reflects weapon system’s physical advantages. There are also limitations in this method that every index must have a specific expression (AD A 109549 1981). As the ground to air defense electronic against system is complex and lack quantitative indexes, it is difficult to analyse its C matrix (Meng et al. 2003; Sang 2008; Li and Wang 2008).

So this article talks about how to ameliorate the ADC model, and its main part uses the improved ADC method to have a strict process and get an authentic outcome. In the premise of using as much analytical method as possible, calculate the weight by APH for some uncountable index and find out the point with Experts consult method to solve the calculation problem. Combining the quality and quantity can use the ADC to good advantage and can also make up its disadvantages, so that we can evaluate electronic against effectiveness effectively.

31.2.2 Building the Evaluation Index System of Ground to Air Defense Effect in Electronic Countermeasure Conditions

Combining with improved ADC model elements, the index system as follows: the evaluation of ground to air defense effect in electronic against conditions is decided by A, D, C three matrixes (AD A 109549 2010), A and D are decided by maintenance and reliability, C is decided by anti-jamming matrix C 1, the electronic reconnaissance capability matrix C 2, the anti-radiation missile resistance capability matrix C 3, the anti-stealth ability matrix C 4, the survival ability matrix C 5.

31.2.3 Building the Model of Effectiveness Valuation of Electronic Countermeasure

31.2.3.1 Analyzing the States of Electronic Countermeasure

Though ground to air defense electronic against systems are different in theory, function and structure, but the typical electronic against process is: Firstly, reconnaissance equipment such as satellite, radar and photoelectricity equipment reconnoitre the radiation source. Secondly, the Data-Processing-Center find out its position and radiation source recognition system identify and pick up features such as the working frequency. Thirdly, our ground to air defense electronic against systems takes soft killing or hard killing according to the obtained information. Soft against methods include radar jamming equipment and photoelectricity jamming equipment. Hard killing methods are launching missiles to against ARM.

According to its typical process, building elementary model can find out system’s reliable frame as Fig. 31.1, and it can also discover system’s original state as Table 31.1.

Fig. 31.1
figure 1

Reliability chart of electronic countermeasure system

Full size image
Table 31.1 Work state of electronic countermeasure system
Full size table

where:

1:

-Equipment of radar reconnaissance;

2:

-Equipment of photoelectricity reconnaissance;

3:

-Equipment of secondary plane reconnaissance;

4:

-Center of data processing;

5:

-System of radiation sources identifies;

6:

-Equipment of radar disturbing;

7:

-Equipment of photoelectricity disturbing;

8:

-Equipment of hard destroys.

Explanation: the number in the picture shows the serial number of each part.

31.2.3.2 Building Evaluation Model

The basic model of ADC mean is:

$$ E_{s} = A^{T} \left[ D \right]\left[ C \right] $$
(31.1)
E s :

—system’s effectiveness vector;

A T :

—availability vector;

C :

—competency matrix

D :

—dependability matrix

(1) the sub models of availability A

Electronic countermeasure system is made up of eight parts. The availability level of each part can be got by the formula (Yan et al. 2008):

$$ A_{i} = {\raise0.7ex\hbox{${MTBF_{i} }$} \!\mathord{\left/ {\vphantom {{MTBF_{i} } {MTBF_{i} + MTTR_{i} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${MTBF_{i} + MTTR_{i} }$}}\quad \left( {i = 1,2, \ldots ,8} \right) $$

where:

i-number in Fig. 31.1.

Combining eight states in Table 31.1, availability A of electronic countermeasure system can be got by the calculable models of combined system.

$$ \begin{aligned}&\quad\quad\quad\quad\quad A = \,\left( {a_{1} \,a_{2} \,a_{3} \,a_{4} \,a_{5} \,a_{6} \,a_{7} \,a_{8} } \right) \\& a_{1} \,=\, \prod\limits_{i = 1}^{8} {A_{i} } \quad a_{2} \,=\, \left( {1 - A_{1} } \right)\prod\limits_{i = 2}^{8} {A_{i} } \quad a_{3} \,=\, \left( {1 - A_{2} } \right)\prod\limits_{i = 1, \ne 2}^{8} {A_{i} } \quad a_{4} \,=\, \left( {1 - A_{3} } \right)\prod\limits_{i = 1, \ne 3}^{8} {A_{i} } \\ & a_{5}\,=\, \left( {1 - A_{6} } \right)\prod\limits_{i = 1, \ne 6}^{8} {A_{i} } \quad a_{6} \,=\, \left( {1 - A_{7} } \right)\prod\limits_{i = 1, \ne 7}^{8} {A_{i} } \quad a_{7} \,=\, \left( {1 - A_{8} } \right)\prod\limits_{i = 1}^{7} {A_{i} } \quad a_{8} \,=\, 1 - \sum\limits_{i = 1}^{7} {a_{i} } \\ \end{aligned} $$
(31.2)

(2) the sub models of dependability D

The factors of D are decided by dependability level. The dependability level’s expression of each parts in electronic against system is

$$ R_{i} = \exp \left( { - \lambda_{i} {\text{t}}} \right)\quad \left( {i = 1,2, \ldots ,8} \right) $$

where:

λ i is the parts’ invalidation possibility, and can be got by: λ i  = 1/MTBF i

State transfer probability d 11–d 88 can be got by system’s original state and every part’s dependability. The d 11 means the probability that system runs normally from beginning to the end. The d 12 means the probability that system runs normally at beginning but radar reconnaissance equipment conk out at last. It can be got by

$$ d_{12} = \left( {1 - R_{1} } \right)\prod\limits_{i = 2}^{8} {R_{i} } $$

In the same way dependability D can be found out by:

$$ D = D\left( t \right) = \left\{ {\begin{array}{*{20}c} {d_{ij} ,} & {i \le j} \\ 0 & {i > j} \\ \end{array} } \right.\quad \left( {i,j = 1,2, \ldots ,8} \right) $$
(31.3)

(3) the sub models of competency matrix C

Competency matrix C is determined by anti-jamming matrix C 1, the electronic reconnaissance capability matrix C 2, the anti-radiation missile resistance capability matrix C 3, the anti-stealth ability matrix C 4, the survival ability matrix C 5.

a.anti-jamming Capability C1

Anti-jamming capability can be expressed by the change of radar maximum detection distance in jamming conditions. If there is no jamming, the maximum detection distance of radar (Schrick 2008) that it can be denoted by Rmax is

$$ R_{\hbox{max} } = \left[ {\frac{{p_{t} G_{t}^{2} \lambda^{2} \sigma }}{{\left( {4\pi } \right)^{3} KT_{0} \Updelta f_{r} F_{n} L\left( {{S \mathord{\left/ {\vphantom {S {_{N} }}} \right. \kern-0pt} {_{N} }}} \right)_{\hbox{min} } }}} \right]^{\frac{1}{4}} $$
(31.4)

where:

P t :

—radio power;

G t :

—antenna gain;

λ :

—wavelength;

σ :

—RCS;

K :

—Boltzmann constant;

T 0 :

—receiver noise temperature, it can be denotation by 290 K;

∆f r :

—receiver bandwidth;

L :

—the loss factor of system;

F n :

—noise coefficient;

(S/N)min :

—minimum SNR

Radar maximum detection distance in jamming

conditions (Yan and Zhang 2009) is

$$ R_{\hbox{max} }^{'} = \frac{1}{3}\sqrt {\frac{{R_{j} }}{{\theta_{0.5} }}} \sqrt {\frac{{\pi P_{t} G_{t} \sigma K\Updelta f_{j} }}{{K\gamma_{j} P_{j} G_{j} \Updelta f_{r} }}} $$
(31.5)

where:

r j :

—polarization loss, r j  = 0.5;

P j :

—jamming power;

G j :

—interference machine lord disc plus;

∆f j :

—jamming signal bandwidth.

C1 can be got by it:

$$ C_{1} = 1 - \overline{{C_{1} }} = 1 - {\raise0.7ex\hbox{${\left( {R_{\hbox{max} } - R_{\hbox{max} }^{'} } \right)}$} \!\mathord{\left/ {\vphantom {{\left( {R_{\hbox{max} } - R_{\hbox{max} }^{'} } \right)} {R_{\hbox{max} } }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${R_{\hbox{max} } }$}} \times 100\% $$
(31.6)

b. The electronic reconnaissance capability matrix C 2

C2 is mainly decided by anti-signal intercepted capability N1 and anti-signal analysis capability N2,

where:

$$ N_{1} = 1 - K_{1} P_{1} \quad K_{1} = \frac{{\theta_{t} }}{{\theta_{t0} }}\frac{\Updelta f}{\Updelta F}\frac{{R_{t} }}{{R_{to} }} $$
(31.7)
K 1 :

—reconnaissance relative cover coefficient;

P 1 :

—intercept probability;

θ t :

—actual cover range in the detectable orientation of system;

θ t0 :

—expected or demanded by campaign mission cover range in the detectable orientation;

Δf t :

—actual cover range in the detectable frequency orientation of system (Ribeiro 2006);

ΔF t :

—expected or demanded by campaign mission cover range in the detectable frequency;

R t :

—actual reconnaissance distance of system;

R t0 :

—expected or demanded by campaign mission reconnaissance distance (Zhou and Tao 2007)

$$ N_{2} = P_{2} \rho $$
(31.8)

where:

P 2 :

—signal processing probability;

ρ :

—recognition confidence

we can get:

$$ C_{2} = \omega_{1} N_{1} + \omega_{2} N_{2} $$
(31.9)

where:

ω1ω2 are decided by experts, ω1 = 0.43, ω2 = 0.57.

c. The anti-radiation missile resistance capability matrix C3 (Liu 2010), the anti-stealth ability matrix C4

Because of the complexity and changefulness of the diverse random events deciding the competency matrix C 3, C 4, and the fact that some criterions lack quantified representation in ADC method, innovation of the method is proposed in the thesis. Through combination of qualitative and quantitative process with ADC method, hierarchical analytic process and Delphi method are used jointly to implement the effectiveness valuation of electronic countermeasure. And they can be broken up to index system in Table 31.2 (Ti 2005a).

Table 31.2 The standard of grade
Full size table

The weight of each index can be decided by hierarchical analytic process and every index’s relative importance can be shown by using ratio build judge matrix 1–9. Taking the anti-stealth ability matrix C 4 for an example: assuming that the sub model’s tactics measure and techniques ability constitute the matrix of remark collection:

$$ T = \left( {t_{mn} } \right)_{2 \times 2} \left[ {\begin{array}{*{20}c} 1 & {3.03} \\ {0.33} & 1 \\ \end{array} } \right] $$
(31.10)

The eigenvector of judge matrix can be calculated by “addition method” according to expression (31.10).

$$ \omega_{m} = \frac{1}{2}\sum\limits_{n = 1}^{2} {\frac{{t_{mn} }}{{\sum\limits_{k = 1}^{2} {t_{kn} } }}} $$

And the weight can be got as:

$$ \omega = \left( {\omega_{1} ,\omega_{2} } \right)^{\text{T}} = \left( {0.66,0.34} \right)^{\text{T}} . $$

Then ten experts mark basing on Table 31.2, and calculate the average figure. At last it can be got by linearity addition method:

$$ C_{4} = \sum\limits_{m = 1}^{2} {\omega_{m} } \left[ {\sum\limits_{k = 1}^{{m_{n} }} {\omega_{mk} \times F_{mk} } } \right] $$
(31.11)

where:

m n :

—the number of sub index;

ω m :

—the weight of the third layer index;

ω mk :

—the weight of sub index’s coefficient;

F mk :

—the sub index point given by experts.

d. the survival ability C 5

The survival ability can be showed by survival probability. In order to improve survival ability, we usually assume that there are m information centers which are redundancies of each other. So the survival probability is

$$ C_{5} = P_{cam} = 1 - \prod\limits_{k = 1}^{m} {p_{k} } = 1 - \prod\limits_{k = 1}^{m} {\left( {\prod\limits_{i = 0}^{Q} {p_{ik} } } \right)} $$
(31.12)

where:

K :

—the number of ruined center;

P 0k :

—the probability of raided on the center;

P1k , P2k ,…, P Qk :

—the probability of destroying the center after all effective against measures are taken.

(4) Calculating system’s effectiveness Es

As analyzed above, the formula can be got:

$$ C = \prod\limits_{k = 1}^{5} {C_{K} } $$
(31.13)

and formula (31.1)can be changed to

$$ E_{S} = AD\prod\limits_{k = 1}^{5} {C_{K} } $$
(31.14)

The improved ADC method which can evaluate the effectiveness of electronic countermeasure on ground air defense and anti-missile can be got by joining formulae (31.2)–(31.6), (31.9), (31.11), (31.12) to formula (31.14).

31.3 The Example

The effectiveness of two supposed typical ground air defense and anti-missile systems in electronic against conditions which can be evaluated by the model have been got. System 2 is partly advanced to system 1 by improving reliability level and radar’s anti-stealth ability of every part in System 2. The numerical value of each parameter of 2 systems above can be got from figure Tables 31.3 and 31.4.

Table 31.3 Reliability parameter
Full size table
Table 31.4 Points given by experts to the anti-stealth ability of radar
Full size table

Elucidation: in Table 31.4, the number which follows every index is its weight; other numbers in Table 31.4 are points.

From Table 31.3:

$$ {\text{A}}_{1} = \left[ {\begin{array}{*{20}c} {0.4279} & {0.0595} & {0.0214} & {0.0713} & {0.0371} & {0.0107} & {0.0951} & {0.277} \\ \end{array} } \right] $$
$$ {\text{D}}_{1} = \left[ {\begin{array}{*{20}c} {0.6392} & {0.0041} & {0.0720} & {0.0168} & {0.0002} & {0.0008} & {0.0001} & {0.2668} \\ 0 & {0.6943} & {0.0028} & {0.0513} & {0.0014} & {0.0003} & {0.0002} & {0.2497} \\ 0 & 0 & {0.7101} & {0.0082} & {0.0312} & {0.0051} & {0.0001} & {0.2453} \\ 0 & 0 & 0 & {0.7452} & {0.0362} & {0.0014} & {0.0006} & {0.2166} \\ 0 & 0 & 0 & 0 & {0.7642} & 0 & {0.0012} & {0.2346} \\ 0 & 0 & 0 & 0 & 0 & {0.8013} & {0.0004} & {0.1983} \\ 0 & 0 & 0 & 0 & 0 & 0 & {0.8537} & {0.1463} \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ \end{array} } \right] $$
$$ {\text{A}}_{2} = \left[ {\,\begin{array}{*{20}c} {0.7934} & {0.0012} & {0.0132} & {0.0162} & {0.0387} & {0.0118} & {0.0245} & {0.101} \\ \end{array} } \right] $$
$$ {\text{D}}_{2} = \left[ {\begin{array}{*{20}c} {0.7421} & {0.0052} & {0.0810} & {0.0170} & {0.0004} & {0.0009} & {0.0002} & {0.1532} \\ 0 & {0.7841} & {0.0032} & {0.0812} & {0.0040} & {0.0006} & {0.0001} & {0.1268} \\ 0 & 0 & {0.8021} & {0.0044} & {0.0923} & {0.0061} & {0.0004} & {0.0947} \\ 0 & 0 & 0 & {0.8428} & {0.0060} & {0.0998} & 0 & {0.0514} \\ 0 & 0 & 0 & 0 & {0.8690} & {0.0091} & {0.0760} & {0.0459} \\ 0 & 0 & 0 & 0 & 0 & {0.9215} & {0.0410} & {0.0375} \\ 0 & 0 & 0 & 0 & 0 & 0 & {0.9705} & {0.0295} \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ \end{array} } \right] $$

From Table 31.4: C 41 = 0.664; C 42 = 0.814.

To predigest the problem, these parameters of system1 and system 2 such as anti-jamming C 1, the electronic reconnaissance resistance capability C 2, anti-radiation missile resistance capability C 3, the survival ability C 5 can be supposed to equal to 1.

So it can be got that: E S1 = 0.426; E S2 = 0.603.

According to the analysis of result, the conclusion can be made that the effectiveness of electronic countermeasure can be strengthened obviously with radar’s anti-stealth ability and the reliability of system2’s improving. The result is accordant with practice (Yan et al. 2007; Chin 1998; Packer 2003; Whatmore 2005; Hall and Betts 1994; Rius et al. 1993). And it is fully proved that the improved ADC method is in validity to evaluate the effectiveness of electronic countermeasure on ground air defense and anti-missile.

31.4 Conclusion

In conclusion, the improved ADC model is used to evaluate the effectiveness of electronic countermeasure on ground air defense and anti-missile, and it is proved by example that the model is in validity (Volakis 1994; Zhang et al. 2000; Levison and Badler 1994; Badler et al. 2006). Currently, the model has been used to evaluate C4ISR air defense systems, and a synthetically effectiveness valuation software has been developed. So the improved ADC model is proved to be worthful.