Automatic Outlier Detection: A Bayesian Approach

In order to achieve reliable autonomous control in advanced robotic systems like entertainment robots, assistive robots, humanoid robots and autonomous vehicles, sensory data needs to be absolutely reliable, or some measure of reliability must be available. Bayesian statistics can offer favorable ways of accomplishing such robust sensory data pre-processing. In this paper, we introduce a Bayesian way of dealing with outlier-infested sensory data and develop a "black box" approach to removing outliers in real-time and expressing confidence in the estimated data. We develop our approach in the framework of Bayesian linear regression with heteroscedastic noise. Essentially, every measured data point is assumed to have its individual variance, and the final estimate is achieved by a weighted regression over observed data. An expectation-maximization algorithm allows us to estimate the variance of each data point in an incremental algorithm. With the exception of a time horizon (window size) over which the estimation process is averaged, no open parameters need to be tuned, and no special assumption about the generative structure of the data is required. The algorithm works efficiently in realtime. We evaluate our method on synthetic data and on a pose estimation problem of a quadruped robot, demonstrating its ease of usability, competitive nature with well-tuned alternative algorithms and advantages in terms of robust outlier removal