When: Wednesday, April 6th at 15:00
Abstract: Classic state estimation tools (e.g., determining position/velocity of a robot from noisy sensor data) have been in use since the 1960s, perhaps the most famous technique being the Kalman filter. For difficult-to-model nonlinear systems with rich sensing (e.g., almost any real-world robot), clever adaptations are needed to the classic tools. In this talk, I will first briefly summarize an idea that has become standard practice in our group over the last several years: continuous-time trajectory estimation (and its connection to sparse Gaussian process regression). I will then discuss two new frameworks we have been pursuing lately: exactly sparse Gaussian variationally inference (ESGVI) and Koopman state estimation (KoopSE). ESGVI seeks to minimize the Kullback-Leibler divergence between a Gaussian state estimate and the full Bayesian posterior; however, the framework also easily allows for parameter learning through Expectation Maximization and we’ve used this to learn simple parameters such as constant system matrices and covariances, but also to model rich sensors using Deep Neural Networks and learn the weights from data. KoopSE takes a different approach by lifting a nonlinear system into a high-dimensional Reproducing Kernel Hilbert Space where we can treat it as linear and apply classic estimation tools; it also allows for the system to be learned from training data quite efficiently. I will give simple intuitive explanations of the mathematics and show some examples of things working in practice.