International Journal of Antennas and Propagation

Volume 2015 (2015), Article ID 563726, 16 pages

http://dx.doi.org/10.1155/2015/563726

## Ship-Borne Phased Array Radar Using GA Based Adaptive *α*-*β*-*γ* Filter for Beamforming Compensation and Air Target Tracking

^{1}Department of Communications Engineering, Yuan-Ze University, 135 Yuan-Tung Road, Jungli, Taoyuan 320, Taiwan^{2}Communication Research Center, Yuan-Ze University, 135 Yuan-Tung Road, Jungli, Taoyuan 320, Taiwan

Received 7 March 2014; Revised 27 August 2014; Accepted 11 September 2014

Academic Editor: Hang Hu

Copyright © 2015 J. Mar et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Beam pointing error caused by ship motion over the ocean affects the tracking performance of the ship-borne phased array radar. Due to the dynamic nature of the sea environments, the ship-borne phased array radar must be able to compensate for the ship’s motion adaptively. In this paper, the adaptive *α*-*β*-*γ* filter is proposed for the ship-borne phased array radar to compensate for the beam pointing error and to track the air target. The genetic algorithm (GA) and the particle swarm optimization (PSO) methods are applied to estimate the gain parameters of adaptive *α*-*β*-*γ* filters, while achieving the optimum objective of minimum root mean square error (RMSE). The roll and pitch data measured from a gyroscope of the sea vehicle and generated from ship motion mathematical model are used in the experiments. The tracking accuracy of adaptive *α*-*β*-*γ* filter using the GA method is compared with PSO method under different ship motion conditions. The convergent time and tracking accuracy of ship-borne phased array radar using the proposed GA based adaptive *α*-*β*-*γ* filter are also compared with the adaptive extended Kalman filter (AEKF). Finally, it is proved that the proposed GA based adaptive *α*-*β*-*γ* filter is a real time applicable algorithm for ship-borne phased array radar.

#### 1. Introduction

Sea wave causes the effect of roll and pitch motions on ships. These ship rotational motions result in measurement error in phased array radar aboard the ship. The antenna stabilization to achieve the beam pointing accuracy over the long dwell time is an important issue for ship-borne phased array radar [1]. There are two ship motion compensations: compensation for rotational motion (i.e., pitch, roll, and heading angle) and compensation for translational motion (i.e., radial speed relative to the earth). Gyroscope provides pitch, roll, heading angles of the ship, speed, course, and vertical velocity of antenna installed on the ship at a data rate of 10 Hz. To compensate for the translational motion, the speed, course, and vertical velocity acquired from the gyroscope are averaged for the duration of radar-dwell time. Then the Doppler shift introduced by the translational motion is estimated in the digital signal processor (DSP) of the radar to compensate the radial velocity. The radar control computer (RCC) provides the target locations relative to earth, schedules beam directions, and predicts beam pointing error to the beam steering controller (BSC), which compensates for the beam pointing error and controls the phased array antenna to point the beam at the target direction relative to the ship coordinates.

The motion compensation method based on coordinate conversion has been described in [2, 3], which requires the measurement of a device’s coordinates, the ship’s coordinates, and the earth’s coordinates systems to compensate the device errors due to motion disturbances. In [1], Kalman filtering along with coordinates conversion is applied to reduce the beam pointing error and to stabilize a tracking beam. The * α*-

*-*

*β**filter, which is more easily implemented than a generalized Kalman filter, is used for motion compensation under different sea states in [1]. The sea environments are very dynamic; hence, there is need of an adaptive system for controlling and compensating devices regardless of ship motion. Most recent works have used Kalman filtering (KF) [4] and extended Kalman filtering (EKF) [5] to estimate the ship’s attitude. Estimation accuracy of KF and EKF depends on the values of different parameters, such as error covariance matrices; thus, the KF and EKF require knowledge of covariance. In [6], the automatic beam pointing error compensation mechanism employs the parallel fuzzy basis function network (FBFN) architecture to estimate the beam pointing error caused by roll and pitch of the ship. The effect of automatic beam pointing error compensation mechanism on the tracking performance of adaptive extended Kalman filter (AEKF) implemented in ship-borne phased array radar is investigated. It shows that the tracking error of AEKF converges to less than about 20 m at 550 iterations (sec/iteration) and the estimation error will remain within the range of about 20 m when beam pointing error is compensated by FBFN controller.*

*γ*The * α*-

*-*

*β**filter has a similar structure with the KF but depends on the gain value of*

*γ**,*

*α**, and*

*β**which are limited and interdependent [7–9]. The uses of various methods to adjust parameter values for Kalman filter, EKF, and*

*γ**-*

*α**-*

*β**filter have been proposed and implemented over the years. Fuzzy membership function is used in [10] to estimate and correct the target position for the signal being tracked. Genetic algorithm (GA) is used in [9] to search the suitable parameter values for the*

*γ**-*

*α**-*

*β**filter, which can provide the approximate position, velocity, and acceleration signal and simultaneously decrease the measurement noise. Particle swarm optimization (PSO) is used in [11] to tune the noise covariance of a Kalman filter. In [12], the PSO is used to find the optimal gain parameter values for an*

*γ**-*

*α**-*

*β**filter. PSO and GA methods are suitable for the real time application because they do not require differentiation and are less complicated than other methods.*

*γ*In this paper, GA based adaptive *α*-*β*-*γ* filter is proposed for automatic beam pointing error correction and air target tracking in three-dimensional space. Continuous monitoring of the environment and adapting filter gain parameter with less computational burden is needed for real time application. The adaptive * α*-

*-*

*β**filter requires knowledge of the coefficients for which GA algorithm is used only in certain time intervals. GA is used to find the gain values by minimizing the objective function, that is, root mean square error (RMSE). The proposed adaptive*

*γ**-*

*α**-*

*β**filter algorithm is implemented and compared with using PSO method. The roll and pitch data were recorded by a gyroscope of the sea vehicle to simulate the tracking performance of ship-borne phased array radar using the proposed adaptive*

*γ**-*

*α**-*

*β**filter. In addition, the roll and pitch data generated from ship motion mathematical model at sea states 2 and 3 are also applied for the proposed adaptive*

*γ**-*

*α**-*

*β**filter to verify the correctness of the test results.*

*γ*The rest of this paper is organized as follows: the model of ship rotational motion, coordinates transform, and planar array antenna of ship-borne phased array radar are described in detail in Section 2. The algorithm of the proposed adaptive * α*-

*-*

*β**filter based on the GA is presented in Section 3, where the*

*γ**-*

*α**-*

*β**filter, GA gain estimator, PSO gain estimator, and optimization problem formulation are described. In Section 4, six different experimental cases are performed; the variations of roll and pitch angles in sea states 2 and 3 are analyzed; the GA and PSO methods are used to determine the optimal filter gain of adaptive*

*γ**filter that minimizes RMSE; the tracking performance of ship-borne phased array radar using the proposed adaptive*

*α*-*β*-*γ**filter is simulated. Finally, conclusions are made in Section 5.*

*α*-*β*-*γ*#### 2. Ship Rotational Motion Compensation

The ship-borne phased array radar must be able to compensate the ship’s motion and track the maneuvering targets automatically. The adaptive * α*-

*-*

*β**filtering algorithm is designed to real time compensate the errors caused by the ship’s motion. The block diagram of rotational motion compensation system for ship-borne phased array radar is shown in Figure 1, which consists of adaptive*

*γ**-*

*α**-*

*β**filter for beam pointing error prediction, ship coordinates/earth coordinates conversion, earth coordinates/ship coordinates conversion, and adaptive*

*γ**filter for target tracking. The roll angle and the pitch angle of the ship angular motion are measured by the gyroscope. is the antenna beam pointing angle relative to the ship body, where is the angle off antenna boresight, and is the azimuth angle counterclockwise from the bow of the ship. Assume that the beam steering angle at a certain time instant is , the antenna point angle offset caused by the ship motion (pitch, roll) is , and then the current antenna pointing angle is with respect to the earth coordinates: If the beam pointing error is predicted as , then the beam pointing angle is corrected as The value of is approximate to .*

*α*-*β*-*γ*