Inference for Robotic State Estimation

Tools to infer the state of a robot from measurements are commonplace in robotics today, enabling core capabilities such as localization and mapping. The mathematical bedrock underpinning most of these methods is Bayesian inference, which allows us to update a prior belief about the world based on some measurements in order to produce a posterior belief. Both filtering (e.g., Kalman filter) and batch methods (e.g., Gauss-Newton) can be viewed as examples of inference. This manuscript has two goals. First, to serve as a tutorial by showing how many common estimators (e.g., EKF, IEKF, SPKF, ISPKF, PF, GN) approximate different aspects of the full Bayesian posterior; for example, many of these seek only a local maximum and are hence referred to as maximum a posteriori estimators. Second, we explore some other ideas including seeking the mean of the full Bayesian posterior, a bias-correction technique, and what to do when a prior is not available. Throughout the manuscript we ground our discussions in the context of a simple-yet-tangible nonlinear robotic state estimation example: landmark position estimation through a stereo camera.