RIGHT-INVARIANT STEREO VISUAL-INERTIAL ODOMETRY: REJECTION THRESHOLDS AND NOISE SCALE

Abstract

A mathematical model is presented of a visual-inertial odometry filter built on a right-invariant error on the matrix Lie group  with appended inertial measurement unit biases, with landmarks eliminated by projecting the residual onto the left null space of the Jacobian and with measurements rejected by a normalised Mahalanobis distance. For every element of the model the transition matrices, Jacobians and retraction are given in both error conventions, the right-invariant and the classical additive one, which makes it possible to isolate the effect of the convention itself under otherwise identical conditions.

On five EuRoC MH sequences with four front ends arranged in a  design (two ways of tracking a point  two detectors: the learned XFeat and the classical ORB), the separate and joint contributions of two factors are measured: the error convention and the form of the rejection rule. The widely used constant threshold is shown to correspond to a  quantile for a two-component measurement and not to agree with the actual dimension of the projected residual. Replacing it by a quantile threshold reduces the mean position error by 21.1, 23.4 and 20.2 % on three front ends out of four: the best result of the grid is 0.136 m against 0.177 m with the constant threshold and 0.222 m with no rejection at all. The contribution of the error convention is smaller, 2.4–10.0 %, and on ORB with descriptor matching the ratio of the two factors reverses. At the same time the same replacement, with the noise scale left unchanged, causes a loss of solution in one configuration out of twenty (644.9 m), which is removed by matching  (0.436 m) rather than by relaxing the rule.

The scientific novelty consists in establishing that the form of the rejection threshold and the adopted measurement-noise scale are subject to joint rather than separate calibration: a threshold defined by a  quantile at the actual residual dimension needs no tuned constant, yet transferred without matching  it costs the solution. The practical value lies in assigning the threshold without manual tuning and in the quantitatively stated limits of transferability of settings between front ends.