A correlational inference-based unscented total Kalman filter for integrated navigation

Abstract

An unscented total Kalman filter (UTKF) estimator with nonlinear dynamic errors-in-variables (DEIV) model is derived based on correlational inference. The proposed UTKF considers all random errors in both system and observation equations and is a Jacobian matrix free alternative to the existing TKF estimators. In particular, this estimator is applied to the inertial navigation system (INS)/ultra-wideband (UWB) integration, in which the marginalised unscented transformation (MUT) as well as the use of generalised Rodrigues parameter (GRP) for attitude updates are embedded into the UTKF to improve the computational efficiency and deal with the dimensional mismatching problems. Furthermore, a theoretical analysis to the effects of DEIV model on total Kalman filter is given. Simulation test has been conducted to compare the performance of UTKF and standard unscented Kalman filter (UKF) in terms of attitude, velocity and position errors. The results demonstrate the feasibility and effectiveness of the proposed estimator.

Keywords:

• Total Kalman filter
• nonlinear dynamic errors-in-variables model
• weighted total least squares
• integrated navigation

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Fundamental Research Funds for the Central Universities: [Grant Number 2018BSCXC23]; Postgraduate Research & Practice Innovation Program of Jiangsu Province: [Grant Number KYCX18_1955].

Notes on contributors

Hang Yu

Hang Yu is currently a PhD candidate at China University of Mining and Technology, China. He obtained his Master's degree in 2016, respectively. His current research focuses mainly involve GNSS/INS integrated high-precision positioning and geodetic dataprocessing.

Jian Wang

Jian Wang is a Professor in the School of Geomatics and Urban Spatial Information, Beijing University of Civil Engineering andArchitecture. He obtained his Bsc and PhD degrees in 2001 and 2006, respectively. He was granted as the New Century Excellent Talents in2013. His current research interests include precise GNSS positioning, GPS/Inertial and other sensors integration, indoor and personalnavigation, visual SLAM and mining disaster.

Bin Wang

Bin Wang is currently a Lecturer with the School of Geomatics Science and Technology, NanjingTech University, Nanjing, China. He obtained his PhD degree in 2017. His research interests include generalized total least-squares algorithmsand their applications in geoscience field.