You want to locate your friend using her mobile phone signals. Assume you have a map...
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You want to locate your friend using her mobile phone signals. Assume you have a map of Liverpool were the Ashton Building is located at the coordinates mo = (6, 3), whereas your friend's home is located at m₁ = (10, 8). You have access to the data that has been received by two cell towers, which are located at the coordinates xo (12, 4) and x1 = (5, 7) respectively. = = The distance between your friend's mobile phone and the two cell towers can be determined based on the strength of the mobile phone signals; both of which are affected by independent zero-mean Gaussian noise with the variances σ 26 = 1 for tower 0 and σ² 1.5 for tower 1. You discover that the signal strengths suggest a distance measurement of do = 3.9 and d₁ 4.5 from the two towers respectively. = = p(z\m)p(m) p(z) and assume a uniform 1. Determine whether your friend is more likely to be at home or at the Ashton Building. [Hint - use the Bayes rule; p(m/z) prior for p(m). Furthermore, as the towers are independent, you can assume that p(z\m) = p(do, d₁|m) = p(do|m) × p(d1\m)]. 2. Suppose you have prior knowledge about your friend's habits which suggests that she is at home with the probability P(home) = 0.7, and in the Ashton Building with the probability P(ashton) = 0.3. Assume that the probability of being at any other location is 0. Recalculate the likelihood of her location, that you did in the first part of the question. You want to locate your friend using her mobile phone signals. Assume you have a map of Liverpool were the Ashton Building is located at the coordinates mo = (6, 3), whereas your friend's home is located at m₁ = (10, 8). You have access to the data that has been received by two cell towers, which are located at the coordinates xo (12, 4) and x1 = (5, 7) respectively. = = The distance between your friend's mobile phone and the two cell towers can be determined based on the strength of the mobile phone signals; both of which are affected by independent zero-mean Gaussian noise with the variances σ 26 = 1 for tower 0 and σ² 1.5 for tower 1. You discover that the signal strengths suggest a distance measurement of do = 3.9 and d₁ 4.5 from the two towers respectively. = = p(z\m)p(m) p(z) and assume a uniform 1. Determine whether your friend is more likely to be at home or at the Ashton Building. [Hint - use the Bayes rule; p(m/z) prior for p(m). Furthermore, as the towers are independent, you can assume that p(z\m) = p(do, d₁|m) = p(do|m) × p(d1\m)]. 2. Suppose you have prior knowledge about your friend's habits which suggests that she is at home with the probability P(home) = 0.7, and in the Ashton Building with the probability P(ashton) = 0.3. Assume that the probability of being at any other location is 0. Recalculate the likelihood of her location, that you did in the first part of the question.
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Part 1 Determining the likelihood of your friends location Using Bayes rule we can calculate the posterior probability of your friend being at home or ... View the full answer
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
Posted Date:
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