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.
where, x(k)∈Rn, y(k)∈Rl are state variables and output vector, respectively. And Φ is state transition matrix,C is measurement matrix. wk is zero mean white process noise with covariance matrix Q
vk is zero mean white measurement noise with covariance matrix R and that is not correlated with the process noise.
Assuming that initial value of the state variable x0=x(0) and initial estimated covariance P0 are satisfied the condition.
We can consider the problem to minimize estimated covariance matrix Pk composed by estimation error e(k)
where, error e(k)=ˆx(k)−x(k)−x(k) is the difference between estimated state values ˆx(k) and real state values x(k).
From Kalman filter theory(Grewal, 2005), the solution of the optimal estimation is achieved by
Kalman filter gain Kk obtained as,
and estimated covariance matrix Pk can be obtained by Eq. (8).
where, Pk,Pk-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).
where,
x(k)=[s(k) v(k)]TΦ(k)=[1−ΔT01]Bk=0C=[10]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, Q=[0001.5],R=[1] and noise wk,vk are given by distributed random signal. And initial Kalman gain, K0 and initial estimate covariance matrix, P0 are
K0=[0.9009−0.0892],P0=[0.9009−0.0892−0.089210.4197]Final Kalman gain, Kif and final estimated covariance matrix, Ptf were
Ktf=[0.36180.7989],Ptf=[0.3618−0.7989−0.79894.5284]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).
where,
x(k)=[a(k)s(k)v(k)]TΦ(k)=[1−ΔT−ΔT2201ΔT001]Bk=0C=[100]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, Q=[00001.00001.0],R=[9] and noise wk,vk are given by distributed random signal. Initial Kalman gain, K0 and initial estimate covariance matrix, P0 are
K0=[0.1009−0.01−0.0005],P0=[0.9081−0.0904−0.0045−0.09042.0090.0999−0.00450.09992.0]And, final Kalman gain, Ktf and final estimate covariance matrix, Ptf were
Ktf=[0.2893−0.4915−0.2810],Ptf=[2.6033−4.4232−0.2.5290−4.423213.97239.4185−2.52909.418517.4885]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.
