Research of Moving Targets Tracking Algorithm

Based on Kalman Filtering

Huiying Dong1 ， Shengfu Chen1 School of Information Science and Engineering

Shenyang Ligong University Shenyang, China

huiyingdong@163.com

Jiayu Zhu2 Shenyang Normal University

Shenyang, China

Abstract—The purpose of moving targets tracking

is to determine the trajectories of moving targets,

the key of which is to establish the corresponding

relationships between the detected prospect targets

and the tracked moving targets. The established

corresponding relations are equivalent to the

matching problem of target features in consecutive

image frames. In the paper, Kalman filter is used

as the motion model of the targets. The recursive

filtering method is adopted to calculate and predict

the location of moving targets. Through the

experiment, the results show that the algorithm not

only track well the moving targets ,but also can

effectively overcome the obstacles in the process of

tracking and so on.

Keywords-target tracking; feature matching;

Kalman filter

I. INTRODUCTION

Moving targets tracking is to use the effective features of moving targets and adopt appropriate matching algorithm on the base of moving targets detection and recognition to find the candidate targets object’s position that is most similar to the targets template in the sequential images. It simply says to locate for targets in the sequence of each image. Filtering problem is to restore a time series interfered by the noise as much as possible and can also be regarded as a prediction problem. Mathematically speaking, the prediction is from past data of a time series to estimate the statistical parameters of the entire sequence. This estimate obtains the average value of the statistical parameters, which has certain

differences from objective reality. In general case, the best prediction should make these errors to least under the least mean-square error criterion.

II. KALMAN FILER PRINCIPLE

Kalman filter[1, 2] is an efficient recursive filter. It can estimate dynamic system state from a series of measurement of incomplete included noises. It can take any point as a starting point to begin to observe. Using recursive filtering method has the features of small amount of calculation and real-time computing. Kalman filter uses the state equation and observation equation to describe a dynamic system.

Kalman filter reduces the tracking of error

covariance matrix of each time point K to least, which consists of two steps to complete:

a) Prediction procedures: including state prediction and error covariance prediction.

b) Modification procedures: including Kalman gain calculation and behind state and error covariance modification.

Kalman filter estimates motion state by using the feedback control system, filter estimating the state of a certain time, and obtaining the prediction value of this state.

III. TARGET TRACKING BASED ON KALMAN

FILTER

Kalman filter, as the motion model of targets, predicts the location of moving targets. When matching the predicted moving targets and the current foreground targets, image centroid and

2010 Third International Conference on Intelligent Networks and Intelligent Systems

978-0-7695-4249-2/10 $26.00 © 2010 IEEE

DOI 10.1109/ICINIS.2010.104

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window size are used to locate precisely position of targets. First, calculating eigenvalues, then using the Kalman filter to build motion model ,at the same time, the next step movement is predicted through the moving targets that have been extracted on the current which will narrow the scope of target-matching and accelerate the speed of target matching. Second, target association is established by doing the target-matching in the next frame within the specified bound. Last, update motion model and form the target motion tracking chain to get moving target trajectory [3, 4].

A. Calculating Kalman filter tracking Eigen values

In the case of smaller interval, it can be considered the tracking window size and position of center of mass of a moving target in the adjacent two images change little, which means the movement of moving targets have continuity characteristics. Therefore, the Centroid tracking and tracking window size are chose as the characteristic value[4] to track targets. The tracking window size is slightly larger than the target image, and target image is trapped tightly by the tracking windows, thus, targets haven’t been affected by window background and noise. At the same time, due to the large amount of image data of the entire field of view, in order to shorten the time, tracking window can be used to reduce the size of the processing image and only process interesting partial image in real-time. For many emerging targets in the view field, it can also set up a few tracking windows to track moving targets respectively. After marking well in all tracking windows, the centroid of the targets in the window is sought respectively. Each window centroid coordinates can be calculated by the following formula:

∑∑∑∑

==

i j

i j

jif

jiif

mm

x),(

),(

00

10

（1）

∑∑∑∑

==

i j

i j

jif

jijf

mm

y),(

),(

00

01

（2）

In the formula, ),( jif is gray value of the target image in the tracking windows, ),( ji is the point of targets area in the tracking windows. Centroid coordinates of each tracking window is an important state parameter in moving targets tracking process, in the subsequent tracking process, the centroid coordinates is one of the key state variables.

B. Motion estimation model

Supposing the state vector 1+ks of time point 1+k in the model is composed of the transfer

function of vector ks at time point k and

noise. While the observation vector is determined

by the observation function of vector 1+ks at time point 1+k and noise.

Equation of state is as follows：

kkk wAss +=+1 （3）

Observation equation is as follows：

111 +++ += kkk vCsz （4）

Where: kw、 1+kv are noise. The

introduction of noise, first, rely on experience to determine, second, rely on studying statistics to obtain. Supposing dynamic noise and observation noise are normal white noise whose mean is zero.

ks is the state vector, and is composed of an

eight-dimensional vectors

] [ ykxkykxkkkkkT

k LLLLyxyxs = （5）

where: kx and ky are respectively target

cancroids coordinates； kx， ky are respectively

the unit displacement of the cancroids

coordinates in the x, y direction; xkL ， ykL are

respectively the width of tracking windows in the

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x, y direction; xkL ， ykL are respectively the unit

displacement of tracking windows width in the x, y direction.

1+kz is the observation vector, which is

composed of a four-dimensional vectors

] [ LLyx 1yk1xk1k1k +++++ =zTk

(6)

As the sampling time t =0.04 seconds, time is very short, so it can be approximately thought that the moving targets move at a constant speed, moreover tracking window size is changed little,

then the state transition matrix A is:

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

100000000100000004.00100000004.00100000000100000000100000004.00100000004.001

A

Observation matrix C is：

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

00001000000001000000001000000001

C

After defining the state equation and observation equation of motion model, Kalman filter is used to estimate the position of target cancroids and window size, and it can search cancroids within a small area in the next frame.

C. Target feature matching and model updating

For a group of motion image sequences,

{ }nfffF ,......,, 21= ，creating the same cartesian

coordinate system for each of these images, in

the k th frame image kf , m targets are

recorded as { }mrrrR ,......, 21= , centroid coordinates and window width of the i th targets are

recorded respectively as ikx ，

iky，

ixkL

，

iykL .

First defining the i th target’s centroid of

the k th frame and the centroid distance function

of the j th target of the 1+k th frame

*

1

1

max),(

+

+=k

ik

jk

ik

cc

ccjiD

(7)

Where:

( ) ( )21

211

jk

ik

jk

ik

jk

ik yyxxcc +++ −+−=

， 1),( ≤jiD

Subsequently defining area differences

function, that is comparing the i th target’s

windows area of the k th frame with the j th

target’s windows area of the 1+k th frame

*1

1

max),(

+

+

−

−=

kik

jk

ik

aa

aajiA

（8）

Where:

jyk

jxk

iyk

ixk

jk

ik LLLLaa 111 +++ ×−×=−

， 1),( ≤jiA

Defining similarity function

),(),(),( jiAjiDji ξγ +=Δ （9）

Where γ , ξ are weighting values, and

meeting the condition that ξγ > , 1=+ ξγ ,

1),( ≤Δ ji if the smaller the ),( jiD is, the closer

target it indicates, while the smaller the ),( jiA is, the more similar target shape it indicates,

while the smaller the ),( jiΔ is, the more probability of the two targets similar it indicates.

As a result, the threshold ΔT of similar function is setted to judge that the targets are the same goal or not. If all the goals on a frame and the smallest value of the results of estimating and matching on the fore frame are over a threshold, which shows that the frame has not the same follow-up targets; If it is below this threshold, which shows that the targets with the smallest value is the subsequentce of the fore frame

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targets. While the minimum value of similar function is found, the follow-up of the same

targets has been found, that is say, the j th

target of the 1+k th frame can be seen as the

follow-up of the i th target of the k th frame, it

shows that both of the two targets are the same target. At this time, the characteristic value of the

j th target of the 1+k th frame is used as the

input of motion model estimating the next frame, and so on, completing the model updates.

IV. ANALYSIS OF EXPERIMENTAL RESULTS

Target tracking algorithm based on Kalman filter is adopted to track the two moving cars on the road. In the experiment , the 320×240 pixels video image sequence have been processed, target moving along the x direction of the right

bottom of the road, taking γ =0.7，ξ = 0.3，

ΔT = 0.6. Figure 1 shows the eight images that have been extracted from the tracking experimental results respectively and Table 1 shows the centroid position of moving targets and tracking window size.

Figure 1 Target tracking results map based on Kalman filter

From Table 1, it can be shown that the algorithm can be better for moving targets tracking from the simulation results above. In the process of target motion, the tracking window size of each object can do the state transfer based on the actual state, adjusting itself in the process of the next frame tracking automatically.The exist of normal white noise of mean zero has been taken into account in the process of motion state transition. Because in the process of

tracking moving targets, the Eigen value’s centriod coordinates of the target and tracking window size can conduct the state transition in the process of the next frame tracking, such tracking algorithm can also effectively overcome the obstacles in the process of tracking and so on.

TABLE 1 THE CENTROID COORDINATES OF CONSECUTIVE FRAME MOVING TARGETS AND THE VALUES OF WINDOW SIZE

V. CONCLUSIONS

Kalman filter tracking model is divided into four sub-modules: Eigen value calculation, to calculate the Eigen value of moving targets, centroid, tracking windows. Motion model, use Kalman filter to establish the systematic motion model, define the state vector and predict possible position of moving targets in the next frame. Feature matching, define the similar function of targets, use the changes of targets in the relative frame targets, besides, apply the Eigen value to calculate similar function values, then, determine whether the targets are the same tracking targets. Model updating, update motion model, to take as the input of Kalman filter of the next motion model.

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prediction theory,T-ransactions of the ASME Journal of Basic Engineering,Vol.83,1961.95

[2] Meditch,J,S..Stochastic Optimal Linear Estimation and Control,McGraw-Hi-ll,1969.188-196

[3] S. Julier, J. Uhlmann, and H.F Durrant-Whyte. A new method for the nonl-inear transformation of means and covariances in filters and estimators. IEEE Transactions on Automatic Control, 2000. 43(3):477-482

[4] Ribaric S.G, Adrinek, Segvic S.. Real-time active visual tracking system. IEEE IEEE Proceedings Mediterranean Electrotechnical Conference. 2004, 5,vol.1:231-234

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