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ISSN : 1229-3431(Print)
ISSN : 2287-3341(Online)

Journal of the Korean Society of Marine Environment and Safety Vol.20 No.2 pp.202-209
DOI : https://doi.org/10.7837/kosomes.2014.20.2.202

A Study on the Development of the Position Detection System of Small Vessels for Collision Avoidance

Dang-Khanh Le^*, Teak-Kun Nam^**†

^*Graudate school, Mokpo National Maritime University, 530-729, Korea010-4594-1025
^**Division of Marine Engineering, Mokpo National Maritime University, 530-729, Korea

Corresponding Author: tknam@mmu.ac.kr, 061-240-7225

Received October 1, 2013 Review February 6, 2014 Accepted April 25, 2014

Abstract

In this paper, a developed device for detecting target's location and avoiding collision is proposed. Velocity and acceleration model of target are derived to estimate target's information, i.e. position, velocity and acceleration considering process and measurement noise. Kalman filtering method applied to the estimation process and its results was confirmed by simulation. The distance measurements system using laser sensor for moving target system is also developed to confirm the effectiveness of the proposed scheme. Experiments to get information of moving target with velocity and acceleration model was executed. The data with filtering and without filtering was compared by experiments. Discontinuous measured data was changed to smooth and continuous data by Kalman filtering. It is confirmed that desired data was obtained by applying proposed scheme.. UI for measuring and monitoring the target data is developed and visual and auditory alarm function is attached on the system Finally, position estimation system of moving target with good performance is achieved by low price equipments.

Key Words : Marine accident , Small vessels , Data acquisition , Collision avoidance , Kalman filter

충돌 회피를 위한 소형 선박의 위치 검출 시스템 개발에 관한 연구

레 당카잉^*, 남 택근^**†

^*목포해양대학교 대학원010-4594-1025
^**목포해양대학교 기관시스템공학부

초록

본 연구에서는 단거리 영역 내에서 대상물표의 정확한 위치를 파악하여 물표와의 충돌을 방지하기 위한 시스템을 개발하 였다. 이를 위해 먼저 물표를 속도 모델과 가속도 모델로 표현하여 초기위치로부터의 움직임을 프로세스 잡음과 측정 잡음이 있는 상 태에서 위치, 속도 및 가속도를 추정하였다. 추정기법으로는 칼만필터를 적용하였고 시뮬레이션을 통해 제안기법의 유용성을 확인하였 다. 다음으로는 레이저센서를 적용하여 이동하는 물표와의 거리를 계측할 수 있는 시스템을 제작하여 물표의 이동 정보를 검출하였다. 이동 물표를 대상으로 속도 모델과 가속도 모델을 적용하여 실험을 수행하였고, 각각의 실험을 통해 불연속적인 측정데이터가 필터링 을 통해 매끄럽고 연속적인 측정값으로 얻어지는 것을 확인하였다. 또한 물표 데이터의 계측과 디스플레이를 위한 UI를 구축하였으며, 물표가 일정거리 영역이내에 접근했을 경우 시각, 청각적인 경보를 울릴 수 있는 기능을 부가하였다. 본 연구결과를 통해 저가의 장비 로 물표 위치의 추정 성능이 뛰어난 시스템을 구축할 수 있었다.

키워드 : 해상 사고 , 소형 선박 , 데이터 획득 , 충돌 회피 , 칼만필터

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Cited-By

Funding:

Honam Sea Grant

1.Introduction

Recently, the avoidance of ship collisions is becoming essential from the viewpoint of maneuvering ships safely in crowded or crossing areas. The information needed for safe navigation is currently obtained by combining radar data with visual information. Using radar, it is possible to determine the track of a target vessel by monitoring changes in its bearing and distance over the passage of time. However, because the short-term accuracy of radar is low then it is difficult to detect course changes immediately in case of using radar alone. For this reason, Sato and Ishii(1998) proposed a system for calculating the course of a target vessel, and evaluating the risk of collisions using images extracted by infrared image processing. That is an effective method to improve performance in terms of collision avoidance by using of radar and infrared images analysis. However, this system is sophisticated and cost to equip on ship. Sergiy et al.(2012) proposed the system to detect and track ships in open sea with rapidly moving buoy-mounted camera device. This system works with high accuracy and effective but it remains some disadvantages in rough sea conditions. It is also cost fairly much of money to equip on small-general ships. Automatic simulation for ship navigation considering relative motions of vessels is considered(Yanzhou, 2011) but it is not confirmed its effectiveness from experiments.

In this study, system to detect target's location and avoid collision by using laser sensors is proposed. This system works independent with radar equipment and suitable for almost ship, specially for small-general ships. In this work, the background and simulation of detecting target's location will be mentioned in section 2. Kalman filter technique to estimate distance, velocity and acceleration between reference vessel and target from measured distance is applied. Experiment results will be introduced to confirm the effectiveness of the proposed system.

2.Research Background

2.1.Detecting Target's Location

In this research, relative location between reference ship and target is determine by applying Kalman filter technique(Allan, 1996, Grewal, 2005, Fossen and Perez, 2009). Basing on measured distance from reference ship to target, corrected distance, velocity and acceleration of target will be estimated. Assuming that target is described as following discrete state space equation.

\begin{matrix} x \begin{matrix} (k + 1) = φ (k) x (k) + w_{k} : & φ (n \times n) \end{matrix} \\ \begin{matrix} y (k) = Cx (k) + v_{k} : & C (l \times n) \end{matrix} \end{matrix}

(1)

where, $x (k) \in R^{n}$ , $y (k) \in R^{l}$ are state variables and output vector, respectively. And Φ is state transition matrix,C is measurement matrix. w_k is zero mean white process noise with covariance matrix Q

w_{k} \sim N (0, Q)

(2)

v_k is zero mean white measurement noise with covariance matrix R and that is not correlated with the process noise.

v_{k} \sim N (0, R)

(3)

Assuming that initial value of the state variable $x_{0} = x (0)$ and initial estimated covariance P₀ are satisfied the condition.

\begin{matrix} E [x (0)] = x_{m} (0) \\ E [x (0) - x_{m} (0)] {[x (0) - x_{m} (0)]}^{T} = P_{0} \end{matrix}

(4)

We can consider the problem to minimize estimated covariance matrix P_k composed by estimation error e(k)

P_{k} = E [e (k) e {(k)}^{T}]; (n \times n)

(5)

where, error $e (k) = \hat{x} (k) - x (k) - x (k)$ is the difference between estimated state values $\hat{x} (k)$ and real state values x(k).

From Kalman filter theory(Grewal, 2005), the solution of the optimal estimation is achieved by

\hat{x} (k + 1) = φ (k) \hat{x} (k) + K_{k} (y (k) - C \hat{x} (k))

(6)

Kalman filter gain K_k obtained as,

K_{k} = P_{k}^{-} C^{T} {({CP}_{k}^{-} C^{T} + R)}^{- 1}

(7)

and estimated covariance matrix P_k can be obtained by Eq. (8).

P_{k} = (I - K_{k} C) P_{k}^{-}

(8)

where, P_k,P_k^-1 means P(k) and P(k-1), respectively.

2.2.Simulation results

Simulation to estimate target's distance and velocity is executed based on the above Kalman filter theory. In this research, velocity and acceleration model to represent target are proposed. The purpose of this simulation is to estimate target's information including its distance, velocity and acceleration under process noise and measurement noise.

Case 1: Appling Kalman filter for velocity case

In this case, the reference ship is assumed to move with constant velocity. For this case, target dynamics will be described as Eq. (9).

\begin{matrix} x (k + 1) = Φ (k) x (k) + w_{k} \\ y (k) = Cx (k) + v_{k} \end{matrix}

(9)

where,

\begin{matrix} \begin{matrix} \begin{matrix} x (k) = {[s (k) v (k)]}^{T} \\ Φ (k) = [\begin{matrix} 1 & - Δ T \\ 0 & 1 \end{matrix}] \end{matrix} \\ B_{k} = 0 \end{matrix} \\ C = [\begin{matrix} 1 & 0 \end{matrix}] \end{matrix}

s(k), v(k)means target distance and velocity, respectively.

Distance from target to reference ship and relative velocity of target in Fig. 1 can be estimated by above Kalman filter technique. Fig. 2 ~ Fig. 4 show simulation results by Matlab program in case of 1 km initial distance and 6 m/s velocity.

In the simulation, $\begin{matrix} Q = [\begin{matrix} 0 & 0 \\ 0 & 1.5 \end{matrix}], & R = [1] \end{matrix}$ and noise w_k,v_k are given by distributed random signal. And initial Kalman gain, K₀ and initial estimate covariance matrix, P₀ are

\begin{matrix} K_{0} = [\begin{matrix} 0.9009 \\ - 0.0892 \end{matrix}], & P_{0} = [\begin{matrix} 0.9009 & - 0.0892 \\ - 0.0892 & 10.4197 \end{matrix}] \end{matrix}

Final Kalman gain, K_if and final estimated covariance matrix, P_tf were

\begin{matrix} K_{tf} = [\begin{matrix} 0.3618 \\ 0.7989 \end{matrix}], & P_{tf} = [\begin{matrix} 0.3618 & - 0.7989 \\ - 0.7989 & 4.5284 \end{matrix}] \end{matrix}

Target's information with filtering is shown in Fig. 2 and Fig. 4. Fig. 2 shows distance data of moving target and dotted line means true position of target. Direct line and small dotted line shows distance without filtering and with Kalman filtering, respectively. Fig. 3 represents the distance error between true value and raw data. It is easy to understand that estimated data by applying Kalman filter is closer to real value than that without filtering.

Fig. 4 shows the estimated velocity of moving target. An estimated velocity of target converge to the true velocity. By the way, the velocity without filtering shows large variance from real velocity.

Case 2: Appling Kalman filter for acceleration case

Kalman filter to estimate the distance and velocity of target with acceleration is applied. The target dynamics will be described by Eq. (10).

\begin{matrix} x (k + 1) = Φ (k) x (k) + w_{k} \\ y (k) = Cx (k) + v_{k} \end{matrix}

(10)

where,

\begin{matrix} \begin{matrix} \begin{matrix} x (k) = {[\begin{matrix} a (k) & \begin{matrix} s (k) & v (k) \end{matrix} \end{matrix}]}^{T} \\ Φ (k) = [\begin{matrix} 1 & - Δ T & \frac{- Δ T^{2}}{2} \\ 0 & 1 & Δ T \\ 0 & 0 & 1 \end{matrix}] \end{matrix} \\ B_{k} = 0 \end{matrix} \\ C = [\begin{matrix} 1 & 0 & 0 \end{matrix}] \end{matrix}

s(k),v(k) and a(k) mean target distance, velocity and acceleration, respectively. In this case, ship moves with time variant velocity.

In the simulation, $\begin{matrix} Q = [\begin{matrix} 0 & 0 & 0 \\ 0 & 1.0 & 0 \\ 0 & 0 & 1.0 \end{matrix}], & R = [9] \end{matrix}$ and noise w_k,v_k are given by distributed random signal. Initial Kalman gain, K₀ and initial estimate covariance matrix, P₀ are

K_{0} = [\begin{matrix} 0.1009 \\ - 0.01 \\ - 0.0005 \end{matrix}], P_{0} = [\begin{matrix} 0.9081 & - 0.0904 & - 0.0045 \\ - 0.0904 & 2.009 & 0.0999 \\ - 0.0045 & 0.0999 & 2.0 \end{matrix}]

And, final Kalman gain, K_tf and final estimate covariance matrix, P_tf were

K_{tf} = [\begin{matrix} 0.2893 \\ - 0.4915 \\ - 0.2810 \end{matrix}], P_{tf} = [\begin{matrix} 2.6033 & - 4.4232 & - 0.2.5290 \\ - 4.4232 & 13.9723 & 9.4185 \\ - 2.5290 & 9.4185 & 17.4885 \end{matrix}]

Simulation results of this case are shown in Fig. 5 ~ Fig. 7. Estimated target distance is presented in Fig. 5. The variation of distance data with Kalman filtering is smaller than raw data without filtering. The distance error is shown in Fig. 6. It is easy to understand that distance error with Kalman filtering is smaller than that without filtering.

Velocity of simulation results is shown in Fig. 7. Similar to the distance case, estimated velocity with filtering shows small variances than raw data.

From results of 2 cases simulation above, we can conclude that location of target will be estimated at high accuracy by using Kalman filter technique.

3.Experiment

To check the effectiveness of the simulation results, experiments for two case of target's movements was executed. But experiments place was not sea but land. Movable board as moving target was applied instead of ship. It can be move linear direction by manually.

3.1.Experiment system composition

Fig. 8 shows experimental system composition. Laptop PC is used for running GUI. Laser sensor will measure distance from reference point to target and feed this signal to GUI through real time controller, NI cRIO 9022. Fig. 9 shows the photo of the real experiment system. In this scheme, NI cRIO 9022 is a converter that converts measurement signal for feeding to computer. GUI will display this measured signal and filtered signal based on Kalman technique.

In this system, laser sensor is OWTH 5130 AE S1 model. Table 1 below shows detail of laser sensor's specification.

3.2.User interface

Fig. 10 shows the development of the system's UI by using Labview program. This UI include system matrix input window, the disturbance input parameters, selecting switch of the model (speed model and acceleration model), data storage window, dangerous distance setting parameter, distance and speed graph from the sensor and filtering, and mixed distance and velocity graph.

For safety navigation, alarm region can be set from this GUI. When the ship pass to this region, developed device will send out alarm signal and commands for collision avoidance. Fig. 11 show the alarm region between reference ship and target.

3.3.Experimental results

Experiments were done on real set-up system in 2 cases for verifying research results. Case 1 and case 2 mean target movement with a constant velocity and time variant velocity, respectively.

Case 1: Velocity case

In this case velocity of target(movable board)l approximates to 1 m/s. In initial condition, target in stationary state. Around 5 second of measuring it moves with constant velocity until 15 second. Fig. 12 (a) illustrates measured and filtered distance from laser sensor to target. Fig. 12 (b) shows comparison of these data from 5 to 7 second of record. Dotted line with green color represents raw data without filtering. It shows discontinuous response like step shape Direct line with red color means estimation data by Kalman filtering. Smooth and continuous data was obtained by filtering scheme. In this results, filtered data shows more stable and continuous than measured raw data.

Fig. 13 shows measured and filtered velocity of target. Dotted line with green color represents raw data without filtering. We can see that the measured data shows fluctuation and big variance. Direct line with red color means estimation data by Kalman filtering. It is easy to recognize that filtered velocity is closer to real velocity than measured velocity.

Case 2: Acceleration case

In acceleration case, target's velocity is changed during experiment time. Initially, target in stationary and, at around second of 12 it moves forward to laser sensor. And then target moves backward, then forward and backward finally (Fig. 14(a)).

Fig. 14 (b) shows position data of moving target and detail result from second of 10 to 15 of experiment data. Dotted line with green color represents raw data without filtering. Direct line with red color means estimation data by Kalman filtering. Smooth and continuous data was obtained by Filtering method. Fig. 15 show out velocity data for this case. Similarly to previous analysis, filtered data shows more reliable results.

4.Conclusion

In this paper a proposed device for detecting target's location and avoiding collision were introduced. Velocity and acceleration model were derived to estimate moving target information considering process and measurements noise. Kalman filter technique for estimating target's location was also mentioned. Simulation on Matlab was accomplished for verifying mentioned estimation algorithm. The fluctuation and variance of error could be decreased by proposed filtering method and its results were confirmed by numerical simulation. It shows the effectiveness of proposed estimation scheme.

The distance measurements system using laser sensor for moving target system is also developed to confirm the usefulness of the proposed scheme. Measured data without filtering was discontinuous like step shape, whereas smooth and continuous data of moving target could be obtained by applying proposed estimation method.

UI for measuring and monitoring the target data is developed and visual and auditory alarm function is also attached on the system. Finally, position estimation system of moving target with good performance is achieved by low price equipments. From the experimental results we confirm that developed device is useful for real system because of its facilities and reliability.

Figure

Fig. 1..

Reference ship and target at sea.

Fig. 2..

Estimated distance of target

Fig. 3..

Distance error.

Fig. 4..

Target's velocity.

Fig. 5..

Target distance.

Fig. 6..

Distance error.

Fig. 7..

Target velocity.

Fig. 8..

Distance measurement system configuration.

Fig. 9..

System composition

Fig. 10..

User interface.

Fig. 11..

Danger zone.

Fig. 12..

Target distance data.

Fig. 13..

velocity data.

Fig. 14..

Target distance data.

Fig. 15..

Target velocity data.

Table

Table 1..

Laser sensor specification

Ordercode	OWTH 5130 AE S1
Measuring distance	0,2 ~ 13 m
Measuring distance (white 90 %)	0,2 ~ 13 m
Measuring distance (grey 18 %)	0,2 ~ 9 m
Measuring distance (black 6 %)	0,2 ~ 4 m
Resolution	5 mm
Accuracy (linearity)	± 5 ~ ± 20
Frequency	100 Hz
Repeatability	± 5 mm
Response time/ release time	< 10 ms
Voltage supply range	12 ~ 28 V DC
Output circuit	analog
Output signal	4 ~ 20 mA
Beam diameter	5 ~ 80 mm

Reference

Allan D. W (1996) “Statistics of atomic frequency standards” , IEEE Proceedings, Vol.54; pp.221-230
Fossen T. I , Perez T (2009) “Kalman filtering for positioning and heading control of ships and offshore rigs” , Journal of Control Systems IEEE, Vol.29 (6) ; pp.32-46
Grewal M. S (2005) Kalman filtering, Wiley, pp.15-45
Sato Yuji , Hiromitsu Ishii (1998) “Study of a collision avoidance system for ships” , Control Engineering Practice, Vol.6; pp.1141-1149
Sergiy F , Dmitry G , Matthew Sh , Chad L (2012) “Detection and tracking of ships in open sea with rapidly moving buoy-mounted camera system” , Journal of Ocean Engineering, Vol.54; pp.1-12
Yanzhuo Xue (2011) “Automatic simulation of ship navigation” , Ocean Engineering, Vol.38; pp.2290-2305