A unified model for transfer alignment at random misalignment angles based on second-order EKF

Abstract

In the transfer alignment process of inertial navigation systems (INSs), the conventional linear error model based on the small misalignment angle assumption cannot be applied to large misalignment situations. Furthermore, the nonlinear model based on the large misalignment angle suffers from redundant computation with nonlinear filters. This paper presents a unified model for transfer alignment suitable for arbitrary misalignment angles. The alignment problem is transformed into an estimation of the relative attitude between the master INS (MINS) and the slave INS (SINS), by decomposing the attitude matrix of the latter. Based on the Rodriguez parameters, a unified alignment model in the inertial frame with the linear state-space equation and a second order nonlinear measurement equation are established, without making any assumptions about the misalignment angles. Furthermore, we employ the Taylor series expansions on the second-order nonlinear measurement equation to implement the second-order extended Kalman filter (EKF2). Monte-Carlo simulations demonstrate that the initial alignment can be fulfilled within 10 s, with higher accuracy and much smaller computational cost compared with the traditional unscented Kalman filter (UKF) at large misalignment angles.

A transfer alignment method for inertial attitude correction of spherical motor on moving base

“…Three different attitude estimation methods are discussed for mutual contrast. Method1 supposes the acceleration reference vector in (9) as fixed gravity acceleration g, measurement noise covariance Q ν,k is obtained by threshold for the error of innovation acceleration in (24) and Q ω,k = 0.25σ 2 ω . Method2…”

“…The alignment technology is based on the transfer model of carrier(high-precision master INS) to estimate the misalignment angle of load(lowprecision slave INS) under specific maneuver(acceleration or deceleration, s-maneuver, etc). The researches of alignment technology including matching methods [21,22] such as velocity or velocity-attitude matching, transfer errors suppression [23,24] for lever-arm effect and deformation vibration, observability of system state [25]. In curved electronic printing (figure 1), the base(stator) moves horizontally to ensure that the printing nozzle is consistent with the normal direction of substrate on rotor.…”

Applied singular value decomposition method in transfer alignment and bias calibration

“…An unscented Kalman filter is proposed to solve the problem of the large misalignment angle of transfer alignment in the polar region [12]. Also, a unified alignment model in the inertial frame with the linear state‐space equation and a second‐order non‐linear measurement equation based on the Rodriguez parameters are established for transfer alignment, which is suitable for arbitrary misalignment angles [13].…”

Neural network-aided variational Bayesian adaptive cubature Kalman filtering for nonlinear state estimation

“…Due to the inherent nonlinearities that exist in many practical problems, the nonlinear filter algorithm is a prominent and widely used technique. As an extension of the standard KF, the extended Kalman filter (EKF) has been widely used in many applications [18][19][20]. However, its performance may be poor if the dynamic systems are highly nonlinear.…”