Exploitation of the Conditionally Linear Structure in Visual-Inertial Estimation

In this work, estimators for platform pose and landmark maps for visual-inertial data are analysed. It is shown that the full, non-linear, visual-inertial problem has a conditionally linear substructure in the 2D case which can be exploited for efficient solutions, e.g., Block Coordinate Descent (BCD). It is also shown that the measurement noise from the non-linear model becomes parameter dependent resulting in biased estimates if that fact is ignored. However, the bias can be accounted for using the Iteratively Reweighted Least Squares (IRLS) method. In the 3D case the conditionally linear substructure is not separable. However, it can be shown that the Jacobian of the non-linear substructure can be calculated recursively resulting in an efficient solution. A simulated 2D visual-inertial example is used to illustrate the theoretical results.