This paper presents the second part of a study aiming at the error state selection in Kalman filters applied to the stationary self-alignment and calibration (SSAC) problem of strapdown inertial navigation systems (SINS). The observability properties of the system are systematically investigated, and the number of unobservable modes is established. Through the analytical manipulation of the full SINS error model, the unobservable modes of the system are determined, and the SSAC error states (except the velocity errors) are proven to be individually unobservable. The estimability of the system is determined through the examination of the major diagonal terms of the covariance matrix and their eigenvalues/eigenvectors. Filter order reduction based on observability analysis is shown to be inadequate, and several misconceptions regarding SSAC observability and estimability deficiencies are removed. As the main contributions of this paper, we demonstrate that, except for the position errors, all error states can be minimally estimated in the SSAC problem and, hence, should not be removed from the filter. Corroborating the conclusions of the first part of this study, a 12-state Kalman filter is found to be the optimal error state selection for SSAC purposes. Results from simulated and experimental tests support the outlined conclusions.

The aim of this paper was to present a calibration procedure applied to an inertial measurement unit into account a technique based on least-square methods and wavelet denoising to perform the best estimateKeywords:

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-This paper describes the development of a method to quantify the control capability of the attitude control system of a launch vehicle under the action of external disturbances. The control capability is understood as the tracking capability of the commanded attitude, even in the presence of disturbances. Wind is considered the most significant external disturbance that acts on the launcher vehicle. Taking into account the aerodynamic and thrust conditions, the control forces and corresponding thrust deflection are computed, as required to counteract the action of wind gusts and wind shears. Thus, it is required that the control moment provided by thrust deflection can balance the maximum aerodynamic moment. Finally, data from a test case is presented, where a reference trajectory of a launch vehicle has been used.Keywords: Dynamic Pressure, Static Margin, Aerodynamic Effectiveness, Control Capability, Movable Nozzle System.Resumo -Este artigo descreve o desenvolvimento de um método para quantificar a capacidade de controle de sistema de controle de atitude de veículos lançadores quando submetidos a perturbações externas. Entende-se por capacidade de controle a propriedade de rastreamento a uma atitude comandada e, alem disso, de manter controlado na presença de perturbações. O vento é considerado o distúrbio mais relevante que atua externamente no veículo. Com base nas características das cargas aerodinâmicas (pressão dinâmica e margem estática) e do empuxo, determinam-se as forças de controle geradas a partir da deflexão do jato principal de empuxo necessárias para equilibrar os efeitos das rajadas e o gradiente do vento. Espera-se que o momento de controle deve ser maior que o momento máximo de aerodinâmica. Os valores dos ângulos de deflexão apresentados foram calculados pelo método proposto, a partir de uma trajetória de referência de um veículo lançador exemplo.

This communication presents a comparative analysis of tuning techniques for satellite launch vehicle attitude controllers. The investigated tuning techniques consist in the minimization of specific performance indexes, namely the Integral Absolute Error (IAE) index, the Integral of Time Multiplied Absolute Error (ITAE) index, the Integral Squared Error (ISE) index, and the Integral of Time Multiplied Squared Error (ITSE) index, being hence, termed optimal. By defining adequate figures of merit, relevant for evaluating the overall performance of satellite launch vehicles, and also taking into account requirements related to the physical limitations of the latter, the performance of attitude controllers tuned by the investigated techniques is compared to the one tuned by the methodology currently employed in the Brazilian Satellite Launch Vehicle (VLS), namely, the Linear Quadratic (LQ) methodology. Through simulation results, it is demonstrated that, despite sparse benefits produced by the alternative tuning techniques, in particular ​ITAE and ISE, the LQ methodology remains globally superior.