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

Abstract

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.

Análise De Erros Para Alinhamento Em Ahrs - Parte I: Algoritmo Triad

“…Apesar da existência dos erros de normalidade e ortogonalidade, os erros de alinhamento são de maior preocupação, uma vez que eles não são adequadamente estimados e compensados nem mesmo na etapa posterior de alinhamento fino. Como pode ser observado em (21) a (23), os erros de alinhamento são afetados pela maioria das fontes de erros investigadas neste trabalho (Silva et al, 2017). Nota-se, em (26), que estas fontes de erro também afetam o erro de guinada.…”

Quantifying Observability and Analysis in Integrated Navigation

“…In this sense, observability can be defined as a process for determining whether the initial state vector of navigation errors can be inferred, given the measurement information of the system. Estimability means that the state can be completely deduced from past observations and inputs. By applying the criteria of observability, we can only get a ‘yes‐no’ type answer that a system is observable or not but may not gain the information to what extent a state variable is observed .…”

“…Up until now, there are very few efforts employing the DoO for the sake of estimability analysis of navigation error‐states . Rothman et al investigate the observability and estimability of a navigation system; however, they do not study the individual estimability of each error state .…”

“…Rothman et al investigate the observability and estimability of a navigation system; however, they do not study the individual estimability of each error state . In addition, the eigenvalues and eigenvectors of the estimation error covariance matrix as well as the condition number do not enable us to properly evaluate how well estimated each navigation error‐state is during the whole navigation process . What is more, the existing methods mentioned earlier require calculating the eigenvalues and eigenvectors of the error covariance matrix or the maximum and minimum singular values of the observability matrix, which usually leads to a great amount of computation when the state transition matrix of the system has a high order.…”

A Damping Grid Strapdown Inertial Navigation System Based on a Kalman Filter for Ships in Polar Regions

“…Polar navigation technology is the basic condition for ships sailing in polar region safely and reliably [ 1 , 2 ]. Inertial navigation system has been the first choice for ships sailing in polar regions as a result of being autonomous, continuous, and comprehensive [ 3 , 4 , 5 , 6 , 7 ]. The working principle of the SINS is that the gyroscopes and accelerometers are strapped on the carrier.…”