Integrated navigation and self alignment using Square Root Unscented Kalman filtering

Abstract

GPS and INS integration is attracting researchers for decades. Advent of MEMS inertial sensors and low cost GPS receivers extended the use of this technology to airborne /ground vehicle navigation, mining, surveillance and robotics. Complementary characteristics of GPS and INS with Kalman filter can overcome the problem of huge INS drifts, GPS outages, dense urban multipath effects and other individual problems associated with these sensors. Extended Kalman filter (EKF) needs linearized system and measurement models, hence performs Jacobian or Hessian matrix evaluation on each time step. If small angle error assumption does not hold and system nonlinearity and large initial attitude errors are an issue Unscented Kalman Filter (UKF) is preferred over EKF. Although UKF does not evaluate Jacobian but it has a problem of Cholesky matrix factorization which is an unstable operation and leads towards divergence. Square Root Unscented Filters (SRUKF) solves this particular problem but still cannot work with non Gaussian noises A very few people have utilized Square Root Unscented Kalman filter in navigation application so far. This research explores use of different configuration of UKF like Central Difference UKF (CDUKF) along with SRUKF and SRCDUKF in the presence of large initial attitude errors, GPS outages and increased levels of noise. A Square Root Unscented Particle filter (SRUPF) is tested with ZUPT technique and in flight alignment to overcome non Gaussian noises. All the filters are tested on navigation grade sensors in loosely coupled mode. Trajectories of up to one hour duration are utilized to evaluate performance. CDUKF was found best in computation time and accuracy. This filter is found more stable towards increased level of noise.