DIRECTION OF ARRIVAL CALIBRATION USING ITERATIVE LEARNING CONTROL

IJST, Transactions of Electrical Engineering, Vol. 38, No. E2, pp 165-175 Printed in The Islamic Republic of Iran, 2014

© Shiraz University

DIRECTION OF ARRIVAL CALIBRATION USING

ITERATIVE LEARNING CONTROL*

S. SOLTANI** AND P. KARIMAGHAEE

School of Electrical and Computer Engineering. Shiraz University. I. R. of Iran Email: sinasoltani@shirazu.ac.ir

Abstract– In this paper, an array calibration method focusing on Direction of Arrival (DOA) on narrowband signals is presented. An array calibration procedure expresses adaptive beam forming and direction finding, which includes unknown phase and gain perturbation of the active sensor. The main purpose of this study is estimation of DOA on two or more known signal sources using Iterative Learning Control (ILC) method. Due to ILC learning ability, the amount of required calculations decreases. Furthermore, ILC method has a simple structure for working on-line. As ILC is a model-free method, it requires little modeling knowledge, making it suitable for use in DOA. In this paper, a new method is proposed for finding DOA of long distance targets in sonar systems. Moreover, in the last section the simulation results approves improvement in performance of the proposed method and helps show the capabilities of the method presented.

Keywords– DOA estimation, iterative learning control, active sonar and radar

1. INTRODUCTION

Increase of the accuracy and speed of target detection is an important goal in sonar and radar systems. Currently, a high-resolution frequency method that is being used for detection, is mainly based on the structure of the distribution function of the Cohen family [1]. This article introduces a new method for finding DOA in multi-input, multi-output sonar systems and array signals in active sensor devices.

In active sonars and radars, estimation of DOA in presence of noise requires a high resolution and a robust method. Since ILC is a robust optimal method in various control fields [2], it is appropriate for solving DOA problem in active sonar and radar system.

Uncertainty in array manifold sensors can be expressed in one or any combination of parameters such as location, frequency, gain & phase and mutual coupling with sensor. These errors are inevitable in practical systems. Since the uncertainty is in the actual array system, the array manifold is only nominal and not true. Therefore, estimation of the true one is required before processing array data [3]. Furthermore, in most of the published papers, it was supposed that the array manifolds in the field of array processing systems are known [3].

In this paper, we focus on the narrow-band signals. Of course, we know that in order to find DOA on wide-band signals the output of each sensor can be converted into a narrow-band signal with the aid of Fast Fourier Transform (FFT) and filter banks [4]. Therefore, wide-band signal and its applications will be discussed.

Since the new method that is presented in this paper has not been used for sensor calibration on sonar or other applications, we will look at the history of this method, which has been employed in control systems.

S. Soltani and P. Karimaghaee

IJST, Transactions of Electrical Engineering, Volume 38, Number E2 December 2014 166

Today, in modern technology smart control systems play an effective role in the development and improvement of industries. Therefore, by developing science and technology, industries are built with intelligent control algorithms which are aimed to improve the safety and operation of machines. In control engineering, studies on learning control are inspired by human capabilities and behavior. The main feature being employed in control engineering is the use of control signals to improve system performance. Iterative Learning Control (ILC) is a new field and yet stabilized in the control. In 1978 in Japan, Uchyama published the basic idea of iterative learning control in Japanese language. Later, in 1984 and 1989, Arimoto, Kawamura, et al and Goodwin, et al presented the exact definition of ILC in English [5-6]. ILC has a large number of control applications, such as robotics, control task, etc [7].

The main idea behind ILC is derived from the ability of human learning. Human beings learn by rehearsing until the end of practice. The basic idea of ILC is that when the earliest trial is completed, the algorithm uses earliest trial outputs, inputs and errors to improve performance from trial to trial.

Although all previous references for application of ILC are in control field, in this paper, control aspects are not considered and the proposed method focuses on calibration.

By storing the error signal and control input in previous iterations, ILC method calculates a new command. Thus, learning process in ILC method, is similar to human memory. There is a difference between ILC and other methods, using the idea of learning such as adaptive control and neural networks. The idea of adaptive control and neural networks is to modify the controller that is a system itself. On the other hand, in ILC the input control signal is modified at each iteration.

Note that in this article we talk about calibration process. Therefore, we try to perform a repetitive process of the calibration method, which is used with ILC. The adjustable complex vector weights in each dimension can be improved.

In this paper, ILC method is introduced and is employed along with Weighted Iterative Learning Control (WILC) to solve DOA problem. Afterwards, WILC is compared with the Weighted Least Means Square (WLMS) and Weighted Recursive Least squares (WRLS) methods. Finally, the effect of WILC method on Signal to Noise Ratio (SNR) is evaluated.

2. DOA CALIBRATION METHODS

a) DOA signal model

To define an array reference in a sonar system coordinate in Fig. 1 consider a narrow-band sonar system with arbitrarily N radiation transmitting sources and M receiving sensors for the sonar identical system. In addition, we can assume a wide-band sonar system with N transmitting orthogonal sources and decompose output of the sonar identical system by using an N point FFT in each segment into the L segment. Targets of DOA are assumed to be in the far field of the array.

In Fig. 2, the structure of the L segment narrow-band array is shown. The array response into the plant waveform in direction of (φ, ɸ) is defined as:

, , ∗ , , (1)

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December 2014 IJST, Transactions of Electrical Engineering, Volume 38, Number E2 169

Let us introduce the Laplace transform of the ILC law as follows:

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Equation (16) provides an estimation of the present value of input from data provided by the previous sample. Where γ and ψ s are the learning gain and the compensator in the Laplace domain, respectively. In Eq. (15), e is the error at k-1th iteration. The frequency characteristic of learning compensator is.

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December 2014 IJST, Transactions of Electrical Engineering, Volume 38, Number E2 175

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