sol03 - CSCI 5512: Homework 3 Solutions Eric Theriault...

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Unformatted text preview: CSCI 5512: Homework 3 Solutions Eric Theriault Spring 2010 Problem 1 The Kalman filter assumes linear Gaussian transition and sensor models, a Gaussian prior, and a continuous state space. This would not be appropriate in the example of the bird flying at the tree, because a linear Gaussian could not estimate the evasive action of the bird. An extended Kalman filter would still have this problem, because this nonlinearity is local (close to the current mean, which would be at the tree trunk). Problem 2 Parts (a) and (b) are in the MATLAB files lwUmbrella.m and pfUmbrella.m . These can be tested by running the function in test.m . These are just sample solutions that are meant to be instructional. Other strategies can work as well. Example output is shown here: >> test ************************** * Likelihood Weighting ************************** For evidence set 1: P(R_10|u) for 100 samples: 0.0657 0.9343, variance: 0.0033 P(R_10|u) for 1000 samples: 0.0565 0.9435, variance: 0.0003 For evidence set 2: P(R_10|u) for 100 samples: 0.8045 0.1955, variance: 0.0250 P(R_10|u) for 1000 samples: 0.8520 0.1480, variance: 0.0015 For evidence set 3: P(R_10|u) for 100 samples: 0.1762 0.8238, variance: 0.0077 P(R_10|u) for 1000 samples: 0.1423 0.8577, variance: 0.0010 1 ************************** * Particle Filtering ************************** For evidence set 1: P(R_10|u) for 100 samples: 0.0645 0.9355, variance: 0.0008 P(R_10|u) for 1000 samples: 0.0568 0.9431, variance: 0.0001 For evidence set 2: P(R_10|u) for 100 samples: 0.8572 0.1428, variance: 0.0021 P(R_10|u) for 1000 samples: 0.8592 0.1408, variance: 0.0002 For evidence set 3: P(R_10|u) for 100 samples: 0.1582 0.8418, variance: 0.0022 P(R_10|u) for 1000 samples: 0.1519 0.8481, variance: 0.0002 The true probabilities are approximately P ( R 10 |...
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sol03 - CSCI 5512: Homework 3 Solutions Eric Theriault...

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