Waldemar C. Leite Filho

Error analysis of analytical coarse alignment formulations for stationary SINS

This paper presents a comprehensive error analysis of coarse alignment formulations for stationary strapdown inertial navigation systems (SINS). Analytical expressions for the residual normality, orthogonality, alignment, and Euler angle errors are systematically derived, allowing us to establish comparisons in terms of rapidity, accuracy, and autonomy requirements. For the purpose of the error analysis, geographic latitude and local gravity acceleration uncertainties are considered, in addition to the inertial sensor uncertainties. As the main contribution of this paper, an improved coarse alignment method is proposed, which is based on orthonormality constraints existing between the Euler angles and the attitude matrix. In contrast to the traditional methods, the proposed formulation does not imply normality and orthogonality errors, besides producing time-independent alignment and Euler angle errors. The latter is seen to be particularly interesting for situations wherein, due to time constraints, posterior fine alignment and orthonormalization procedures cannot be implemented. The superiority of the proposed formulation is validated through simulated and experimental tests, regardless of the SINS initial orientation. The accuracy degradation produced by each alignment formulation in the navigation stage is used as the performance index.

On the Error State Selection for Stationary SINS Alignment and Calibration Kalman Filters—Part II: Observability/Estimability Analysis

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.

Influence of latitude in coarse self-alignment of strapdown inertial navigation systems

In this paper, a new approach for the coarse self-alignment of strapdown inertial navigation systems (SINS) is presented. This approach, here called indirect approach, consists on estimating the initial Euler angles of the SINS for a given rotation sequence, directly from the inertial sensors raw readings, to then proceed with the calculation of the corresponding direct cosine matrix (DCM), which represents the SINS initial orientation. It is demonstrated in this paper that the utilization of the proposed approach with rotation sequences 321, or 312, allows the SINS initial orientation to be accurately determined in terms of its DCM, even if the actual position of the SINS on the Earths surface is unknown. This approach is, therefore, particularly useful in situations where the SINS position is unknown, or for safety reasons, must not be informed.

On the Relation between NARX Clusters and Even/Odd Nonlinearities through Frequency-Domain Analysis

Although polynomial NARX models have been intensively used in nonlinear system identification, few papers discussed how to relate the inner nonlinearities to specific types of clusters and regressors. The objective of this paper is to discuss this relationship for a class of systems that contain even or odd nonlinearities. This class covers block-structured models (Hammerstein, Wiener, and others) and systems with dynamic nonlinearities. To achieve the paper’s aim, a deep frequency-domain analysis is performed. For each type of nonlinearity, all the NARX clusters are investigated and the results show that each regressor type provides specific nonlinear contribution. The investigation is based on an output power spectra analysis when a specific multisinusoidal excitation is applied. According to the spectral contributions in some of the frequency lines, the nonlinearity classification is possible. By applying the same procedure to the clusters, one interprets how these clusters can (or not) contribute to explain the system nonlinearity. The paper findings have two major impacts: (i) one gains deep knowledge on how the nonlinearities are coded by the clusters, and (ii) this information can be used, for instance, to aid a structure selection procedure (ERR, term clustering, etc.) during the discarding of the clusters which are not able to explain the system nonlinear behavior. Some practical and experimental aspects are discussed, while numerical examples are presented to show the validity of the theoretical analysis.

Discussão do sistema de controle de atitude de um veículo lançador

Neste trabalho sao discutidos os principais conceitos e requisitos utilizados durante o projeto da malha de controle de atitude de um veiculo lancador a partir da analise da dinâmica simplificada do veiculo. A analise e dividida em duas partes, primeiramente o veiculo e tratado como um corpo rigido e um controlador PID e apresentado. Em seguida o veiculo e considerado um corpo flexivel e dois metodos de estabilizacao dos modos flexao (ganho ou por fase) sao apresentados. Alem disso, um sistema de controle de atitude e projetado considerando os conceitos discutidos.

Sobre o procedimento de ortogonalização da dcm no auto-alinhamento grosseiro de sistemas de navegação inercial solidários

Neste artigo sao apresentadas duas metodologias de auto-alinhamento grosseiro para sistemas dexa0navegacao inercial solidarios, os quais conduzem a diferentes formulas de propagacao de erros para a matrizxa0de transformacao de coordenadas que relaciona o triedro do corpo ao de navegacao. Enquanto a primeiraxa0metodologia reduz os erros de normalidade atrelados a matriz, a segunda reduz os erros de alinhamento e eliminaxa0os de ortogonalidade, sendo considerada, portanto, superior. Um algoritmo iterativo de ortogonalizacao daxa0matriz obtida pela primeira metodologia e proposto, no intuito de se vericar se ele resultaria na obtencaoxa0da mesma matriz calculada pela segunda metodologia. Um ensaio experimental realizado em um sistema dexa0navegacao inercial solidario de alta precisao mostrou que, embora o procedimento de ortogonalizacao eliminexa0apropriadamente os erros de ortogonalidade da matriz, ele contribui para o aumento dos erros de alinhamento,xa0e portanto, sua implementacao nao e aconselhada.

Análise do tempo de alinhamento em sistemas de navegação Inercial solidários

Neste artigo e apresentada uma metodologia de auto-alinhamento usualmente empregada em sistemas de navegacao inercial solidarios (SINS) e sua correspondente analise de erros. E demonstrado que, com excecao do alinhamento em azimute, esta metodologia e influenciada basicamente pelas incertezas atreladas as leituras dos acelerometros. Uma analise estatistica utilizando o desvio padrao de Allan e realizada e permite se estimar analiticamente o tempo necessario para se obter uma determinada classe de precisao no alinhamento em azimute. Este resultado e comparado com resultados experimentais obtidos a partir de um SINS de alta precisao, demonstrando que as incertezas provenientes do giroscopio apontado para leste constituem o fator preponderante na determinacao do tempo de alinhamento em azimute, que por sua vez, determina o tempo e a precisao final do alinhamento em um SINS.

EXCITATION SIGNALS FOR STRUCTURE SELECTION OF NONLINEAR MODELS - RANDOM AND DETERMINISTIC CASES

Muitos estudos tem sido realizados sobre a escolha de estrutura de modelos nao-lineares autorregressivos e algumas tecnicas estao disponiveis para a definicao de modelos caixa-preta que ajustem os dados experimentais. Apesar da variedades de tecnicas, poucos trabalhos tratam claramente questoes envolvendo os sinais de excitacao. Tais textos apresentam comumente o uso de excitacoes aleatorias, mesmo se sabendo que esse tipo de sinal nao ´e usual em aplicacoes praticas. Neste artigo, alguns aspectos envolvendo tais sinais de excitacao sao discutidos, incluindo-se os casos deterministico e aleatorio. O objetivo ´e alertar o usuario a respeito dos resultados esperados do processo de escolha da estrutura com base no sinal de excitacao utilizado, bem como apresentar algumas caracteristicas importantes para que o procedimento de selecao produza resultados adequados.

Identification of a Hammerstein model for an aerospace electrohydraulic servovalve

Abstract This paper discusses the black-box identification of a real aerospace electrohydraulic actuator. A Hammerstein model structure is adopted due to its simplicity and capacity to represent a wide set of nonlinear phenomena. The identification strategy begins with a frequency-domain analysis so that a polynomial NARX model structure can be defined. Then, an extended least squares procedure is applied to obtain the coefficient values.