Research and Application of Radar Detection Error Model based on

Data Mining

Jun Song

Unit 92941 , Huludao liaoning 125000, China

Keywords: Radar Detection Error Model; Data Mining; Decision Tree.

Abstract: Aiming at the problem of establishing a radar detection error model, this paper proposes a method, which

uses SQL Server 2005 as a data mining implement and selects decision tree algorithm, based on lots of

detected data of the radar. This radar detection error model is used to forecast the detection error in a radar

simulation. The result of comparing with the traditional error simulation method shows that the method

based on the data mining is an efficient approach for analysis, modeling and forecast of the radar detection

error.

1 INTRODUCTION

In the military field, sensor simulation is an

important part of the battlefield situation awareness

system simulation, while the technology of sensor

error simulation plays a key role in sensor

simulation(Jianqing Cheng, 2007). At present, radar

is still the major information-source sensor in the

battlefield situation awareness and formation. To

build up an error model that goes with the detection

property of radar is the key to radar simulation.

The simulation modeling of radar detection error

is a complicated and systematic job, which can be

achieved by two fundamental methods. One method

is the theoretical analysis and deduction method.

That is, a model for radar detection error mechanism

is deduced according to the priori knowledge, which

is referred to as the “white box ” modeling. The

other method is to build up a mathematical model by

making data test for and making analysis on the

signals inputting into and outputting from the radar

system, which is referred to as the “black box”

modeling. Currently, the traditional mathematical

statistics method is commonly used to make “black

box” modeling for the simulation of radar detection

error. That is, radar’s systematic error and standard

deviation are obtained by making statistic analysis

on historical data, and then are simulated with a

white Gaussian noise model. However, this method

is only able to reflect the statistical law of error, but

is not able to reflect the true error characteristics,

thus influencing the fidelity of radar simulation.

Data mining is a process to extract hidden,

unknown but potentially useful information and

knowledge from a mass of incomplete, noisy,

ambiguous and random application data(Han J,2001).

In the real testing of target, abundant measured data

has been collected, including the distance of target

measured by radar, data of target orientation and the

true-value distance and orientation of target

(hereinafter referred to as target true track data).

However, these data has not been fully utilized. In

this paper, the data mining technology is used to find

out the relationship between the hidden radar

detection error and the target true track data from a

mass of test data, so as to improve the fidelity of

radar simulation.

2 MINING ALGORITHM FOR

RADAR DETECTION ERROR

Data mining has five functions, including concept

description, clustering analysis, correlation analysis,

trend analysis and forecast, and variance analysis. In

this paper, data mining is mainly used to analyze and

forecast the characteristics of radar detection error in

different distances and positions, thus the function of

trend analysis and forecast is adopted. Methods used

to make trend analysis and forecast mainly include

decision tree, artificial neural network and so on.

In this paper, the decision tree algorithm is

selected to make data mining. The decision tree has a

tree structure similar to the flow diagram. According

294

Song J.

Research and Application of Radar Detection Error Model based on Data Mining.

DOI: 10.5220/0006449302940298

In ISME 2016 - Information Science and Management Engineering IV (ISME 2016), pages 294-298

ISBN: 978-989-758-208-0

to the difference in hierarchy, the nodes can be

classified into root node, internal node and leaf node.

The root node indicates the data set of the whole

sample. Each internal node indicates the testing on a

property. Each branch represents a testing output.

Each leaf node represents class or class distribution.

The decision tree, after analyzing and studying the

sampled data, will make use of the tree structure to

classify the data in order to find out the valuable

and potential information, and then will acquire the

classification rule through training, and finally will

use the analyzed result to forecast more data. The

classification rule can be extracted from the decision

tree after it has taken shape. All the intermediate

nodes on the path from the root nodes to the leaf

nodes constitute the conditions of the rule. The

conclusion part of the rule can be obtained from the

leaf node(Jiawei Han,,2001).

The frequently-used decision tree algorithm is

based upon the information entropy, with its core

algorithms being ID3, C4.5, C5.0, CART, SLIQ,

SPRINT, Rain Forest and so on(Glover T W, 2005).

In the paper, the C4.5 algorithm is adopted because

in the sampled data, the data of distance, position

and error is the continuous attribute.

There are two steps to construct a decision tree,

including building decision tree and decision tree

pruning.

The first step is to build a decision tree. Generally,

the decision tree is built from top to bottom. To find

out the best extended attribute is the key to make the

decision tree grow. To achieve this, you shall firstly

determine the form of extended attribute, and then

find out and evaluate all the extended attributes in

this form, and finally select the most sensible ones as

the best extended attributes.

Definition 1: Information gain. Assuming that S is

the set of s data samples, the samples are classified

into c different classes ci (i=1,2, ..., c). Assuming

that si is the number of samples in class ci, S is

classified into c classes of information entropy (or

expected information) which can be expressed as

follows.

∑

−=

ppAI

)(log)(

(1)

In this formula,

SSP

Assuming that attribute A has V different values

{a1, a2, ..., av}, S is divided into v subsets {s1, s2, ...,

sv} by attribute A. According to attribute A, the

information entropy that dividing S can be defined as

follows.

)(),(

ASE

∑

−= (2)

Information gain Gain (S, A) is expressed as

),()(),( ASEAIASGain −

(3)

Definition 2: Information gain ratio. According to

the attribute A, the information gain ratio that divide

S can be defined as follows.

)(

),(

)(

ASplid

ASGain

AGainRatio = (4)

And

∑

−=

ppASplitI

)(log)(

C4.5 algorithm has selected the attribute that has

the maximum information grain ratio as the extended

attribute. It can process not only the discrete attribute

but also the continuous attribute. This algorithm

adopts the multi-section method for the discrete

attribute and the bi-section method for the

continuous attribute(An Chen,2006). For the reason

that the sampled data belongs to the continuous

attribute in this paper, it is regulated that the testing

of attribute A should produce two branches which

correspond to condition Av and A>V respectively.

v is referred to as the partial threshold. If A is the

best extended attribute, v is referred to as threshold.

To determine the partial threshold of A, you should

firstly sequence the attribute values of A which is in

the training sample rapidly, and then study the

median v of each pair of adjacent values and the

corresponding conditions Av and A>V. Assuming

A has m different values in the sample, then there are

m-1 medians v, which correspond to m-1 potential

GainRatio v. If the value of a certain information

gain ratio GainRatio v’ is the maximum, such v’ is

the partial threshold of A. Finally you will obtain the

best extended attribute after you have traversed all

the attributes(Guojun Mao, 2007).

Step two. Decision tree pruning. Many branches

of the decision tree may reflect noises and acnodes

of the training data. The purpose of pruning is to

detect and trim such branches, so as to solve the

problem of data overfitting. A subtree is replaced by

a leaf node in order to improve the accuracy in

forecast of unknown data. The frequently-used

pruning method is to set the maximum height

(number of levels) of the decision tree, so as to limit

the tree growth and to set the minimum number of

samples that must be contained in each leaf node to

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stop it from branching. The tree can be evaluated by

means of cross validation or by artificially selecting

partial data to make validation.

3 MINING SOLUTIONS FOR

RADAR DETECTION ERROR

In this paper, SQL Server 2005 is selected as the data

mining platform, and the decision tree algorithm is

used to mine the radar detection error. The SQL

Server 2005 provides the data mining functions

including SQL server integration services (SSIS) and

SQL server analysis services (SSAS)(Deli Zhu,

2007). The integration services are used in data

pre-processing while the analysis services provide

multiple data mining algorithms.

3.1 Data Pre-Processing

Data pre-processing is an important link in the data

mining. Usually the original data supplied for data

mining is lack of consistency, and has plenty of

redundancy and null values. Therefore, data

pre-processing is to process such original data as

well as the noisy data in it. the pre-processing mainly

includes the following procedures.

1) Data conversion, integration and matching. To

make data mining, you should firstly obtain the

difference value between the measured data and the

real tracking data of the target radar. It is necessary

to match the track and to reconcile the step length of

data mining by the method of three-point

interpolation, because the measured data and real

tracking data of radar are stored in different files and

the data mining is in different step lengths.

2) Data consistency processing. The data must be

made clean and consistent in order to improve the

accuracy of data mining. In the paper, the 3σrule is

used to distinguish the abnormal errors.

3.2 Error Data Mining

According to the above analysis, in the radar

detection error mining, the truth distance and truth

position are made as the input attributes, while the

distance errors and position errors are made as the

forecast attributes. The C4.5-based decision tree is

used to build an error model, and the reserved testing

method is used to evaluate the accuracy of decision

tree. The reserved testing method divides the entire

sampled data into the training data set and testing

data set which do not intersect. After the

pre-processing, the training data set contains 20

tracks and 5052 sampled data, and the testing data

set contains 1 track and 1092 sampled data. The

structure of sampled data is shown in Table 1, in

which Det_D and Det_B represent the distance and

position of target measured by radar respectively; D

and B represent the truth distance and truth position

of target; and ΔD and ΔB represent the distance error

and position error respectively. The unit for distance

is meter, and the unit for position is degree.

The modeling is done in SQL Server 2005. The

decision tree algorithm can be determined by

selecting parameters for the mining model. In this

paper, the entropy-based algorithm is used to

calculate and split the fractions, and the method of

bi-section is designated to split nodes. After

processing, the mining model has generated a

decision tree for distance error and one for position

error.

The pruning is to trim the decision tree according

to the minimum number of samples that must be

contained in each leaf node, and to evaluate the

trimmed tree with testing data set. When the

minimum number of samples contained in the leaf

node is equal to 140, the generated decision tree for

distance error present a good forecasting

performance. When the minimum number of

samples contained in the leaf node is equal to 280,

the generated decision tree for position error presents

a good forecasting performance.

The following is part of the decision tree model

for distance error:

B>=160.639

--B<162.453

-- -- D<93611.621:

ΔD=102. 212-5.585*(B-163.452) (439)

-- -- D>=93611.621:

ΔD=18.956+5.476*(B-166.170)-(D-98656.788)

(612)

-- B>=162.453

We can draw out a rule from the above. That is, if

B>=160.639, B<162.453 and D<93611.621, the

distance error model is expressed as ΔD=102.

212-5.585*(B-163.452), and the number of samples

contained is 439. Similarly, other rules can be drawn.

All these rules have covered the coverage of training

data set, and the aggregate of all these rules has

made up the radar detection error models for

distance and position.

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Table 1. Part of Sampled Data

Det_D Det_B D B

△D △B

…… …… …… …… …… ……

98704.87199 169.95026 98757.74688 169.70676 -52.87488 0.2435

98705.97614 169.92697 98735.94282 169.70448 -29.96668 0.22249

98708.16997 169.87285 98735.94282 169.70448 -27.77285 0.16837

98708.69452 169.84795 98735.94282 169.70448 -27.2483 0.14347

…… …… …… …… …… ……

4 VERIFICATION OF RESULT OF

RADAR SIMULATION

In order to verify the effect of the mined radar

detection error model, we have compared it with the

traditional radar error simulation, and have made use

of the test set data in the sample, with one track

containing 1092 track points. Both methods are to

superpose error on the target truth-value track data.

In one simulation method, the mined radar detection

error model (hereinafter referred to as error model

simulation) is used, with the simulated data detection

data equal to the sum of target truth-value track data

and model forecast error. While in the other method,

the traditional radar error simulation model

(hereinafter referred to as white-noise simulation),

with the simulated radar detection data equal to the

sum of target truth-value track data, system error and

Gaussian white noise, in which the the system error

and Gaussian white noise are obtained based on the

training data.

To compare the fidelity of the two simulation

methods, the author has made a comparison between

the measured data (distance and position) and the

results of the two simulation methods, with the

comparative results shown in Figure 1, Figure 2,

Table 2 and Table 3. In Figure 1 and Figure 2, “+”

represents the difference between the data measured

by radar and the result of white noise simulation, and

“O” represents the difference between the data

measured by radar and the result of error model

simulation. In Table 1 and Table 2, ΔD1 is the

difference between the data measured by radar and

the result of white noise simulation in distance,

while ΔB1 is that in position. From the two figures

and the two tables, it can be seen that the result of

error model simulation is more approximate to the

data measured by radar, showing that this model

achieves a higher fidelity.

Figure 1. Distance Difference

Table 2. Statistics on Distance Difference

Mean

Standard

deviatio

Min.

value

Max

.value

Points

ΔD

（m）

94.610 142.567 -622.407 -117.350 1092

ΔD

（m）

8.928 51.864 -117.350 136.330 1092

Table 3. Statistics on Position Difference

Mean

Standard

deviatio

Min.

value

Max

.value

Points

ΔB

（°）

0.083 0.333 -1.135 1.072 1092

ΔB

（°）

-0.045 0.066 -0.182 0.132 1092

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Research and Application of Radar Detection Error Model based on Data Mining

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Figure 2. Position Difference

5 CONCLUSIONS

The methods proposed in this paper can effectively

analyze, model and forecast the radar detection

errors, thus finding out a new thought for

radar

error

simulation. In the following researches, the

relationship between the factors such as radar

detection error, radar system, physical parameters,

environmental conditions and so on will be explored,

in order to acquire a radar detection error model with

higher fidelity.

REFERENCES

Jianqing Cheng, 2007.Development and Prospective of

Military Modeling and Simulation Technology.

Command Control & Simulation, (4): 1-8.

Han J, Kambr M, 2001.Data Mining: Concepts and

Techniques . Beijing Higher Education Press.

Jiawei Han,,2001.Data Mining: Concepts and Techniques

[M]. Beijing: China Machine Press.

Glover T W, Chang Dfaz, F R, Squire J P, 2005. Principal

VASIMR results and present objectives. Space

Technology and Applications International Forum.

An Chen, Ning Chen, 2006. Data Mining Technology and

Application . Beijing: Science Press.

Guojun Mao, Lijuan Duan, Shi Wang, 2007. Principle and

Algorithm of Data Mining. Beijing: Tsinghua

University Press .

Deli Zhu, 2007. SQL Server 2005 Total Solutions for Data

Mining and Business Intelligence [M]. Beijing:

Electronic Industry Press.

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