Bayesian Estimation and Tracking: A Practical Guide

20.5 Estimation Methods

The estimation methods used for comparative analysis of the sensor fusion models include methods using photogrammetric data alone, methods that use IMU data alone and our method that fuses the video data with the IMU data. In Chapter 19, we concluded that the second-order unscented Kalman filter (UKF(2)) achieves the best performance of all of the solvers tested and provides a marked improvement over the standard zeroth-order NLLSQ solver when only photogrammetric video data is used. For completeness, the comparative performance analysis of Section 20.6 will include performance results from both the UKF(2) and the NLLSQ when only photogrammetric observation data is used. When only IMU data is used as observations, a second-order Predictor–Corrector method and the UKF(2) are implemented as tracking filters. To do this, we set F_n = 1, for ∀n so that only IMU data is used as observations.

For a description of the NLLSQ and UKF(2) estimation processes when only photogrammetric video data is used, see Sections 19.4.1 and 19.4.2, respectively. A description of these methods will not be repeated here. In Section 20.5.1, we discuss the Predictor–Corrector estimation method used when only IMU data is being processed.

20.5.1 Initial Value Problem Solver for IMU Data

The accepted method for estimating the position and orientation of a rigid body using an IMU's translational acceleration and angular rate measurements is to numerically solve a system of ordinary differential ...