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Velocity/Position Integration Formula (I): Application to In-flight Coarse Alignment 2 roughly known initial attitude, otherwise they cannot guarantee a rapid and accurate alignment result [1][2][3][4][5]. If the SINS is stationary or quasi-stationary, analytic methods are often used to derive a coarse attitude from gyroscope/accelerometer measurements [1,3,6]. The heading angle is more difficult to determine than the two level angles and for a consumer grade SINS, is usually aided by a magnetic compass. The in-motion or in-flight alignment is necessary for many military applications and commercial aviations [7]. In such cases, the SINS is in motion, e.g., onboard a ship or aircraft, the direction of velocity/trajectory from an aided source, such as GPS, can provide a rough pitch and heading angles during a straight course. This information is generally not good enough to perform a reliable fine alignment due to the water current and air speed [3], let alone the SINS misaligning angles relative to the carrier.It may be argued that the coarse alignment difficulty confronting the navigation field is largely owed to our "local eye" on the attitude representation in three-dimension space. Nowadays, we are used to the attitude approximation by three one-dimension error angles. For example, many works have been devoted to the nonlinear angle error models to account for large heading uncertainty [4,8,9]. By so doing, most inherent characteristics of the three-dimension attitude have been lost. Our group proposed a recursive alignment approach based on attitude optimization in [10], which, for the first time in the public literature, transforms the attitude alignment problem into a continuous attitude determination problem [11] using infinite vector observations. It was rigorously proven therein that the behavior of the estimated constant initial angles can be used to detect significant sensor biases. The optimization approach is related to the so-called inertial frame method [12,13], but more theoretically solid and more robust to disturbances and noise, because it makes full use of the special algebraic property of the attitude matrix (a three-dimension orthogonal matrix with unit determinant). If the nonzero velocity rate information was externally provided, the

Calibration of inertial measurement units (IMU) is carried out to estimate the coefficients which transform the raw outputs of inertial sensors to meaningful quantities of interest. Based on the fact that the norms of the measured outputs of the accelerometer and gyroscope cluster are equal to the magnitudes of specific force and rotational velocity inputs, respectively, an improved multi-position calibration approach is proposed. Specifically, two open but important issues are addressed for the multi-position calibration: (1) calibration of inter-triad misalignment between the gyroscope and accelerometer triads and (2) the optimal calibration scheme design. A new approach to calibrate the inter-triad misalignment is devised using the rotational axis direction measurements separately derived from the gyroscope and accelerometer triads. By maximizing the sensitivity of the norm of the IMU measurement with respect to the calibration parameters, we propose an approximately optimal calibration scheme. Simulations and real tests show that the improved multi-position approach outperforms the traditional laboratory calibration method, meanwhile relaxing the requirement of precise orientation control.

Abstract-Magnetometer has received wide applications in attitude determination and scientific measurements. Calibration is an important step for any practical magnetometer use. The most popular three-axis magnetometer calibration methods are attitude-independent and have been founded on an approximate maximum likelihood estimation (ML) with a quartic subjective function, derived from the fact that the magnitude of the calibrated measurements should be constant in a homogeneous magnetic field. This paper highlights the shortcomings of those popular methods and proposes to use the quadratic optimal ML estimation instead for magnetometer calibration. Simulation and test results show that the optimal ML calibration is superior to the approximate ML methods for magnetometer calibration in both accuracy and stability, especially for those situations without sufficient attitude excitation. The significant benefits deserve the moderately increased computation burden. The main conclusion obtained in the context of magnetometer in this paper is potentially applicable to various kinds of three-axis sensors.

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Abstract-Integration of inertial navigation system (INS) and global navigation satellite system (GNSS) is usually implemented in engineering applications by way of Kalman-like filtering. This form of INS/GNSS integration is prone to attitude initialization failure, especially when the host vehicle is moving freely. This paper proposes an online constrained-optimization method to simultaneously estimate the attitude and other related parameters including GNSS antenna's lever arm and inertial sensor biases. This new technique benefits from self-initialization in which no prior attitude or sensor measurement noise information is required. Numerical results are reported to validate its effectiveness and prospect in high accurate INS/GNSS applications.Index Terms-Inertial navigation, satellite navigation, velocity integration formula, lever arm, online Reference frame unification is a pre-condition for any accurate information blending of multiple sensors.This work was supported in part by the Fok Ying Tung Foundation (131061), National Natural Science Foundation of China (61174002), the Foundation for the Author of National Excellent Doctoral Dissertation of People's Republic of China (FANEDD 200897) and Program for New Century Excellent Talents in University (NCET-10-0900). A New Technique for INS/GNSS Attitude and Parameter Estimation Using Online Optimization 2For the case of INS/GNSS integration, there is an unavoidable displacement, usually called as the lever arm, between their respective sensing points of INS and GNSS [1]. The magnitude of the lever arm is significant for many applications. For example, when the GNSS antenna is mounted outside on the roof to better receive satellite signals, the INS is usually installed inside the carrier for reasons like easy maintenance. It is difficult or impossible, however, to precisely measure the lever arm vector in a designated frame, taking account of the virtual attributes of the sensing points and the frame axes [2,3]. Lever arm uncertainty acts as a major error source of INS/GNSS in accurate applications, e.g., pose determination in airborne direct georeferencing [4] and airborne gravity measuring [5].A good practice is to accommodate and estimate the lever arm within the extended Kalman filter (EKF) in INS/GNSS integration [2,6,7]. In addition to the knowledge of noise statistics, the Kalman filtering method relies heavily on a roughly known initial attitude that is only achievable under benign situations such as when the carrier is stationary or moving straight. If not properly initiated, however, INS/GNSS integration based on Kalman filtering would be subjected to failure [1,8,9]. These situations are not uncommon in practice, for example when the carrier is moving freely or the duration of benign situations is not long enough to reach a good initial attitude alignment. That is to say, the lever arm estimation is conditioned on a good initial attitude.On the other hand, to obtain a good initial attitude inversely requires a small INS/GNSS lever arm effect. ...