Bayesian Estimation and Tracking: A Practical Guide

19.1 Introduction

Photogrammetry is the mathematical science of estimating an object's pose (three-dimensional position and orientation) and kinematic properties (translational and rotational velocities and accelerations) from a set of object features observed in a series of two-dimensional video image frame data from multiple cameras. Many approaches to this estimation problem have been applied, with the most common prior to the 1990s using a nonlinear least squares (NLLSQ) approach. These early NLLSQ methods were reviewed by Huang and Netravali [1]. In the NLLSQ method, at each time step, the residuals between the predicted video images and the actual current video images are used in an iterative NLLSQ procedure to arrive at a local residual error minimum producing an estimate of the rigid body state. Alternate, more modern, Bayesian estimation extended Kalman filter (EKF) methods were introduced by Iu and Wohn [2] and Gennery [3] with excellent results. These were followed by a single-constraint-at-a-time (SCAAT) EKF method introduced by Welch [4,5].

All of the above-mentioned methods had some drawbacks that affect the rigid body state estimation performance. The NLLSQ methods assumes a dynamic model without noise, is not recursive in time, and requires the computation of a Jacobian (matrix of partial derivatives) at each iteration. The observation set consists of video frame images and all image frames are reprocessed during each iteration, making the method very time consuming. ...