Foundations of state Estimation Topics: Bayes Filters Kalman filters Hidden markov models 。 Additional readins G. Welch and G. Bishop. An Introduction to the Kalman Filter ". University of North Carolina at Chapel Hill, DepartmentofComputersCience.Tr95-041.http://www.cs.unc.edu/-welch/kalman/kalmanintro.html JJ. Leonard and H. F. Durrant-Whyte. " Mobile robot localization by tracking geometric beacons. "IEEE Trans Robotics and Automation, 7(3): 376-382, June 1991 L.R. Rabiner, "A tutorial on hidden Markov models, " Proceedings of the IEEE, vol. 77, pp. 257-286, 1989 Issues Statement Given a set of observations of the world. what is the current state of the world? Alternatives Given a set of observations of the world what is the state of the world at time t? Inputs Sequence of observations, or perhaps actions and observations Outputs from different algorithms Most likely current state x Probability distribution over possible current states p(xi) Most likely sequence of states over time: X,, 2, X3, x4, .X, Sequence of probability distributions over time p(,), p(x2), p(x3).p(x,) Choices compute the estimate x, or p(xi) present p(x)Foundations of State Estimation Topics: Hidden Markov Models Ɣ Additional reading: Ɣ Ɣ J. J. Leonard and H. F. Durrant-Whyte. “ IEEE Trans. Ɣ Issues Ɣ Statement: – world? Ɣ – time t? Ɣ Inputs: – Model – Ɣ Outputs from different algorithms: – Most likely current state xi – i ) – Most likely sequence of states over time: x1, x2, x3, x4, ... xt – 1), p(x2), p(x3) ... p(xt ) Ɣ Choices: – How to compute the estimate xi or p(xi ) – i ) Bayes Filters Kalman Filters G. Welch and G. Bishop. “An Introduction to the Kalman Filter”. University of North Carolina at Chapel Hill, Department of Computer Science. TR 95-041. http://www.cs.unc.edu/~welch/kalman/kalmanIntro.html Mobile robot localization by tracking geometric beacons.” Robotics and Automation, 7(3):376-382, June 1991 L.R. Rabiner, “A tutorial on hidden Markov models," Proceedings of the IEEE, vol. 77, pp. 257-286, 1989. Given a set of observations of the world, what is the current state of the Alternatives: Given a set of observations of the world, what is the state of the world at Sequence of observations, or perhaps actions and observations Probability distribution over possible current states p(x Sequence of probability distributions over time p(x How to represent p(x