Implementation of Identification System for IMUs Based on Kalman Filtering Derya UNSAL Department of Guidance and Control Design Roketsan Missile Industries Inc. Ankara, Turkey dunsal@roketsan.com.tr Mustafa DOGAN Department of Control Engineering Dogus University Istanbul, Turkey mdogan@dogus.edu.tr Abstract— Modeling and simulation studies are used to measure the desired performance prior to the hardware implementation of inertial navigation systems. Inertial measurement units are the main components of the inertial navigation systems. Therefore, IMUs should be modeled within the scope of modeling and simulation studies of inertial navigation systems. Several time and frequency domain analysis are implemented in these simulation studies. In addition to deterministic and stochastic error parameters, frequency and delay characteristics of the sensors required for inertial sensor identification. Hence, transfer functions of accelerometer and gyroscope channels are required. Generally, transfer functions of COTS IMUs, accelerometers and gyroscopes are not provided to end-users. Therefore, identification of sensor transfer functions becomes a problem. In order to identify sensor transfer function several methods have been examined. This study explains the how the transfer functions of inertial sensors are defined by using system identification with Kalman Filter. System identification deals with the problem of building mathematical models of dynamical systems based on observed data from the system. System identification consists of data record, generating of model set and determining of the best model steps and lots of several methods can be used in these steps. In the scope of this study Kalman Filter is used to generate candidate transfer function set in the generating of model set step of the system identification. Transfer function identification process will be completed by selecting the best model from the model set. Thereby, effects of frequency and delay characteristics on the system performance can be observed. An IMU can be modeled in frequency domain with transfer function by using the methodology which is explained in this study. Keywords—accelerometer; gyroscope; transfer function; Kalman Filter; identification I. INTRODUCTION System identification is concerned with the topic of modeling of dynamic systems mathematically based on the data resulting from measurements and other observations and has a crucial place in engineering science; because providing a solution to the system and/or developing this system can be made possible only by constructing a suitable system model [1]. The process of system identification consists of three major steps, namely measuring data, constructing the set of models and choosing the optimal model, and certain methods can be used within these steps. The field of system modeling and identification has been developed sharply since 1795 and Gauss has become pioneer especially in estimating parameters of dynamic systems [2]. After 1960, starting with Kalman Filter Algorithm, artificial neural network algorithms and genetic algorithms has been applied widely. Kalman filter is a group of mathematical equations, which predicts the state of the system by reducing the errors recursively. Kalman filter supports the past, present end even future predictions of the states and realizes it without knowing the exact nature of the system [3]. Kalman filter is a tool used to predict the variables of the processes. Construction of the linear stable state model of the system based on the input-output data and the identification of the parameters of the control laws using Unscented Kalman Filter (UKF) can be counted as examples [4,5]. In this study, the determination of the transfer function of the inertial sensors is aimed. To achieve this, the prediction feature of the Kalman filter is used in the process of constructing the set of models Measurement data, which are necessary for system identification and used in Kalman filter algorithm, is obtained in simulated environment. II. SYSTEM IDENTIFICATION System identification is the process of construction of a mathematical model, based on the observation of the dynamical system output data. [1] Basically, system identification depends on 3 steps: 1. The Data Record 2. The Set of Models 3. Determining the best model in the set A. Data Record In this step, experiment/test procedure is designed according to the dynamical system properties. After the design phase, the experiment/test is performed and input-output data of the system is recorded. B. The Set of Models This stage is the most important and difficult phase of the system identification process. In this step, different candidate Roketsan Missile Industries Inc.     236