We study the filtering problem over a Lie group that plays an important role in robotics and aerospace applications. present new particle algorithm based on stochastic control. In particular, our is duality between smoothing optimal Leveraging this duality, we reformulate into control problem, by approximately solving it (using, e.g., iLQR) establish superior proposal for smoothing. Combining w...

We establish the equivalence between the optimal least-squares state estimator for a linear time-invariant dynamic system with noise corrupted input and output, and an appropriately modified Kalman filter. The approach used is algebraic and the result shows that the noisy input/output filtering problem is not fundamentally different from the classical Kalman filtering problem. The result is ill...