A Preliminary Study on Targets Association Algorithm of Radar and AIS Using BP Neural Network

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Procedia Engineering 15 (2011) 1441 – 1445

A Preliminary Study on Targets Association Algorithm of Radar and AIS Using BP Neural Network Hu Xiaoruia, Lin Changchuana a

Navigation Institute of Jimei University, Xiamen 361021, China

Abstract Targets association judgment is one of kernels in the processing of multi-targets information fusion. An association algorithm of the target information of the marine radar and AIS was proposed based on BP neural network theory. First, the design of the network structure was discussed in detail, then, the computer simulation based on Matlab was carried out. The results indicated that this method can achieve the association judgment effectively for different targets’ information. Keywords: Targets Association; BP Neural Network; Radar; AIS

0. Introduction AIS (Automatic Identification System) is a new kind of navigation aids system at sea, which can provide the dynamic and static information of ships. The dynamic information includes latitude, longitude, course, speed and UTC time etc., while the static comprising with MMSI, IMO number, ship types and the position of GPS antenna. AIS information obtains the advantages of rich content and high accuracy, but it is limited by a passive work manner and so on. Relatively, the radar can detect the targets actively and give the targets’ panoramic picture. But it’s susceptible to the outside circumstances and its data accuracy isn’t so high. So the information fusion of radar and AIS can complement each other to improve the accuracy and reliability of the targets. Therefore, research on the two’s fusion has a significant importance. Targets association judgment is an important part in multiple targets information processing. Many scholars have done something on this, for example, the membership method in fuzzy mathematics, the method based on gray theory and other methods based on Statistics. As the NN (Neural Network) is used and studied more and more widelyˈespecially for pattern recognition, targets association, prediction and data compression. So it’s meaningful to introduce this method in data fusion of radar and AIS. This paper discussed the targets association of the radar and AIS based on BP neural network. 1. A targets association algorithm based on BP network In the process of radar and AIS data association, to determine whether a radar target is associated with an AIS targets is to determine whether this two different information belongs to the same target. Under the condition of lots of radar and AIS targets, we can transform this problem into targets classification. The flowchart of this algorithm is presented as Fig.1. 1.1. Characteristic extraction As radar and AIS information are provided by different time and space, they need to be unified to the same time and space reference point and need to be measured by same features. Our study assumed that the above work has been carried out. To indicate a ship, the features we selected follow as this: target’s distance (with symbol of Dis), bearing (with symbol of ș), COG and SOG. Considering the practical use, the network’s structure is designed with single hidden layer, that is, there’s only one input layer, one hidden layer and one output layer. The detailed structure is shown as Fig.2 as following:

The project is supported by the major project of the university-industry-cooperation of the Fujian province (2010H6017) and by the Science Foundation of Jimei University (ZQ2010004). Corresponding author:Lin Changchuan. Tel:15880279546 ,E-mail address:[email protected].

1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.08.267

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Hu Xiaorui and Lin Changchuan / Procedia Engineering 15 (2011) 1441 – 1445

Start Set the association rules Data of radar

Data of AIS

Enter the well-trained network

Execute association judgment

Time and space unification

according

to the network’s

output Characteristic extraction Save the association pairs Data standardization End Fig.1. Procedure of targets association

Input layer

Hidden layer

Output layer

Zih (k)

'COGij (k )

Z hj ( k )

'SOGij (k )

yk 'Disij ( k )

'Tij (k) Fig.2. Network’s structure

The input vector is designed as P = (ǻCOGij(k),ǻSOGij(k),ǻDisij(k),ǻșij(k))ˈthat is the 4 input nodes is formed as formula (1) as following: ǻCOGij(k) =

| A_COGij(k ˉ R_COGij(k) |

ǻSOGij(k) =

| A_SOGij(k)ˉ R_SOGij(k) |

ǻDisij(k)= ǻșij(k) =

| A_Disij(k)ˉ R_Disij(k) | | A_șij(k)ˉ R_șij(k)|

Where symbols above denote respectively as following:

(1)

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ǻCOGij(k)—— the absolute difference between the ith AIS course and the jth radar course at moment k; ǻSOGij(k)—— the absolute difference between the ith AIS t course and the jth radar speed at moment k; ǻDisij(k)—— the absolute difference between the ith AIS course and the jth radar distance at moment k; ǻșij(k) —— the absolute difference between the ith AIS course and the jth radar bearing at moment k; ǻȦih(k)—— the weight between input layer and hidden layer at moment k; ǻȦhj(k)—— the weight between hidden layer and output layer at moment k; yk —— the network’s output at moment k. 1.1. Data standardization As there are differences among the dimensions and numeric range of the four features, some appropriate transformations should be carried out to the raw data before the network’s computing, which is known as data standardization or normalization. In this paper, we adopt the method of standard deviation. First, the input vector should be standardized as formula (2) as following: xi  x (2) xˆi s 1 n ¦ xi represents the average of the samples, s ni1

Where xi is the ith sample value, and x

1 n ¦ ( xi  x )2 n 1 i 1

is standard deviation of the sample, then according to formula (3) below, we can obtain the final input data. xˆi  min( x1 , …, xn )  x ' (3) i max( x1 ,…, xn )  min( x1 , …, xn ) 1.2. Network’s training First, we initialize the network’s structure, the input layer’s setting refers to section 2.2. As to the output layer, the binary output is enough for the association judgment, the node’s numbers are set as one. Number of the hidden layer’s node can be estimated using the following formula (4) and be automatically adjusted to the optimum in the simulation program. l m  n  a (4) Where, l is the hidden layer’s nodes number, m is the input layer’s nodes numberˈn is output layer’s nodes number, a is an integer among 1~10. 2. Description of BP algorithm BP algorithm is a kind of back propagation learning algorithm. In practice, it consists of two parts which are network training and network testing. Steps of this algorithm is described as follows[5]: Step 1 Initialize the parameters such as net structure, layer numbers, nodes number of each layer, the input vector ˄XˈD˅,the weight Ȧih between input layer and hidden layer, the weightȦhj between hidden layer and output layerˈthe learning rate Ș, the momentum coefficient Įˈthe MSE eps and so on. Step 2 Select a pattern and pass forward to calculate the hidden layer output p

nethk

Ohk

k k ih i

¦ (Z

x  aik )

(5)

f ( nethk )

i 1

Then calculate the output layer’s result:

net kj

q

¦ (Z

k hj

Ohk  bik )

O kj

M (net kj )

y kj

O kj

(6)

h 1

where f ( x) 1 (1  e  x )

M ( x ) 1 (1  e  x ) or M ( x )

x

Step 3 Pass backward to calculate the neuron error beginning from the output layer 

G jk

(d kj  O kj )(O kj )'

'Zhjk

KG jk Ohk

(7)

Then calculate the hidden layer’s error G hk

r

(¦ G jk Zhjk )(Ohk )' j 1

'Zihk

KG hk xik

(8)

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Hu Xiaorui and Lin Changchuan / Procedia Engineering 15 (2011) 1441 – 1445

Step 4 Update the weights

 Zhjk 1 Zhjk  'Zhjk  D'Zhjk -1 (9)  Zihk 1 Zihk  'Zihk  D'Zihk -1 10) Step 5 Calculate the network’s output error Hk

1

n

r¦ j 1

(11)

( y kj  d kj ) 2

If this value is greater than eps , then turn back to Step 2 , or come to the ends of the algorithm. After the above steps, the net will be trained to the pre-set accuracy, then tested and assessed by a pile of patterns, the network will be come to use. 3. Simulation and Results 3.1. Simulation parameters setting The simulation in this paper is based on Matlab neural network toolbox. To simplify this process, the own ship is selected as a reference with heading and speed both set as 0, the initial position of own ship is set as original point of axis. Lots of samples are required for training, that is targets’ AIS and Radar data. The radar’s antenna rotates one round every 2 or 4 seconds. So in [0,297s] we take a sample every 3s, 100 times for each target. The same target’s Radar and AIS data is viewed as association patterns while the different targets’ data seemed as not associated, then the input patterns are obtained. Shown as Table 1, data from target 1 to 4 will be taken as training patterns (the total number is 1300) after standardization and specific process. MSE of radar features on course, speed, distance and bearing error is 11.5°,1 kn,35 m and 1.2°while that of AIS is 5°,0.5 kn ,15.5 m and 0.8° repectively.Using the same way, target 5 and target 1,2,3,4 are treated as testing patterns (the total number is 900). Table 1. Original targets information

Initial speed

Initial course

Initial distance

Initial bearing

˄knot˅

˄degree˅

˄nm˅

˄degree˅

4

30

1.5

45

Target 2

8

315

2.0

60

Target 3

12

90

1.5

125

Target 4

18

200

2.0

225

Target 5

22

70

2.0

300

Target 1

3.2. Results and Analysis Performance is 9.78761e-005, Goal is 0.0001

1

10

0

Training-Blue Goal-Black

10

-1

10

-2

10

-3

10

-4

10

-5

10

0

1

Fig. 3.

2

3 4 7 Epochs

5

Error change in the net training stage

6

7

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Hu Xiaorui and Lin Changchuan / Procedia Engineering 15 (2011) 1441 – 1445

Comparison of actual output and desired output of training samples 1 Desired output Training output 0.5

0

200

400

600 800 1000 1200 1400 Samples sequence Difference analysis of training output and desired output

0.03

Output difference

O utput differenc e

0

0.02 0.01 0

A ss oc iation degree

output v alue

Figure 3 above shows the change of MSE during the process of net training, where there’re 9 hidden layer nodes. When eps is set as 0.0001, 7 iterations are needed to achieve the preset goal. Due to BP network’s own restrictions, at the initial stage, the curve comes to faster convergence, at the latter it becomes more gently. For the network training results, the desired output of association is set as 0.98 while the non-association set as 0.13. As can be seen from the graph, the two kinds of training samples are separated obviously. Both of he related samples and the unrelated samples are close to the desired output, and the absolute value of difference of training output and desired output remains below 0.03, i.e. |yk –D(k)|<0.03, which has reached preset effect.

0

200

Fig. 4.

400

600 800 1000 Samples sequence

1200

1400

Comparison of desired output and actual output of testing samples 1 Desired output Actual output 0.5

0

0

200

400 600 800 1000 Samples sequence Difference of desired output and actual output of testing samples 0.2

0

200

0

-0.2

(a)Comparison and Analysis of training and desired output;

400 600 Samples sequence

800

1000

(b)Comparison and Analysis of testing and desired output

The network testing results are shown as following, as can be seen from it, the related samples and the unrelated samples are separated obviously. The association output is close to 1 while the non-association close 0. Besides, difference between actual output and desired output also remains at the interval of [0, 0.15]. 4. Conclusion In this paper, a targets association algorithm of Radar and AIS is proposed based on BP network. Simulation based on Matlab demonstrates that the algorithm’s effectiveness. Under the condition of 9 hidden layer nodes and the MSE = 0.0001, difference between the net output and the desired output of the testing samples can remain within an acceptable range, which has separated the samples obviously. However, due to the slow convergence and easily falling into local minima, and the testing samples didn’t consider some special cases, so our next work is to improve the algorithm. References [1]Lin Changchuan. Algorithm and Simulation of Fuzzy Correlation of Tracks from Radar and AIS. Journal of System Simulation, 2006(8),p. 903-905. [2]Ou Yangping, Lin Changchuan. Arithmetic and Implementation of the Fusion Association of the Target Information from AIS with Radar. Journal of Jimei University, 2010(4),p.289-293. [3]Deng Shuzhang. Research and Implementation of Marine ARPA Radar and AIS Information Fusion. SHIP & OCEAN ENGINEERING, 2009(6):145-148. [4]Wang Chenxi. A Survey of Radar and AIS Information Fusion. Command Control & Simulation,2009(2),p.1-4. [5]Satish Kumar. Neural Networks. Beijing: Tsinghua University Press;2006. [6]Fecit Technology R&D Center. Theory of Neural Network and Realization with Matlab. Beijing: Electronic Industry Press; 2005. [7]MATLAB Chinese Forum. 30 EXAMPLES of MATLAB NEURAL NETWORK. Beijing: BUAA Press;2010.