Quasi-Tightly-Coupled GNSS-INS Integration with a GNSS Kalman Filter

Quasi-tightly-coupled (QTC) GNSS-INS integration is a method of loosely-coupled integration that has the salient characteristics of a tightly-coupled integration. This method is intended for the integration of an existing GNSS navigation engine into a GNSS-INS closed-loop configuration with little or no modification of the GNSS navigation engine. The method of integration uses the range measurement model matrix typically used to compute dilutions of precision (DOP) to identify the observable subspace in the time-space frame generated by the available satellites and project the loosely-coupled INS-GNSS Kalman filter position measurement into this subspace. INTRODUCTION Quasi-tightly-coupled (QTC) GNSS-INS integration was introduced in [1] as an enhanced method of looselycoupled integration that has the salient characteristic of continued aiding with fewer than four satellites that a tightly-coupled integration typically exhibits. This method of integration was introduced to meet the oft-times requirement to integrate an existing and possibly sophisticated GNSS navigation engine into a GNSS-INS configuration with little or no modifications to the engine. Such a requirement might arise if the GNSS navigation engine is an RTK engine that performs well as a consequence of a sophisticated algorithm implementation, is well-tested in its commercial field of use, and is subject to tight software configuration control so that major modifications are costly and time-consuming. Another reason for considering QTC integration is the requirement for the GNSS navigation engine to operate independently of a GNSS-INS integration in case inertial data is not available or is interrupted. The QTC integration method was presented in [1] using a simple epoch-by-epoch least squares adjustment (LSA) as the GNSS navigation engine to maintain a simple analysis while conveying the key concepts. QTC integration is however likely to be used with more sophisticated GNSS navigation engines such as a Kalman filter designed for RTK positioning. It was assumed but never shown in [1] that the same QTC integration method also applies to a Kalman filter based GNSS navigation engine. This paper removes this deficiency by presenting an analysis of the QTC integration method when the GNSS navigation engine is a Kalman filter and then by comparing the respective performances of a QTC integration and a tightly-coupled integration. In this sense this paper is a continuation of the development started in [1] . The common attribute of a least squares adjustment and a Kalman filter is the range measurement model matrix that contains the satellite geometry. A rank deficient measurement model due to an insufficient number of satellites defines an unobservable position-time subspace in which either estimator can’t produce a fully constrained position-time solution. In a tightly-coupled integration this subspace is automatically handled in the aided INS (AINS) Kalman filter. QTC integration is designed to handle such a satellite deficiency in a similar manner. A QTC integration achieves continued aiding with fewer than four satellites using a loosely coupled AINS Kalman filter via two functional additions to a loosely coupled integration. These are INS position seeding of the GNSS navigation engine and an observables subspace constraint (OSC) in the INS-GNSS position measurement in the AINS Kalman filter. INS position seeding sets the a priori position of the GNSS navigation engine to a predicted antenna position computed from the current INS position and attitude solution. The GNSS navigation engine then computes an updated position as a correction of the a priori antenna position using the estimated position error from its GNSS Kalman filter. An unobservable dimension in the GNSS Kalman filter solution due to insufficient satellites for full observability of position-time errors will contain uncorrected INS errors that appear in the antenna position solution sent to the AINS Kalman filter. The OCS blocks the uncorrected INS position errors from appearing in the loosely-coupled INS-GNSS position measurement constructed by the AINS Kalman filter. Figure 1: QTC GNSS-INS architecture Figure 1 shows the QTC integration architecture. The one visible difference from a loosely-coupled integration is the a priori position solution from the INS to the GNSS navigation engine for implementing the INS position seeding function. Not visible is the OSC that occurs in the AINS Kalman filter’s INS-GNSS position and velocity measurements. INS POSITION SEEDING The GNSS navigation engine in Figure 1 is a GNSS Kalman filter that processes rover receiver pseudorange observables from m satellites. Such a GNSS Kalman filter typically has a state vector dyn meas x x x   =     