ps1 - Massachusetts Institute of Technology Department of...

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Unformatted text preview: Massachusetts Institute of Technology Department of Mechanical Engineering 2.160 Identification, Estimation, and Learning Spring 2006 Problem Set No. 1 Out: February 13, 2006 Due: February 22, 2006 Problem 1 Consider the following example of least squares estimation. Given 3 + 2 2 = 6 1 + 2 = 1 1 4 6 2 = 3 1 2 + 2 = 4 1 Obtain the least squares estimate of parameters 1 , . Suppose an additional 2 measurement: 2 + 2 2 = 3 1 is obtained. Find the revised estimate by two methods: Directly, by batch processing Indirectly, by the recursive algorithm. Problem 2 Shown below is a calibration range for determining the position of a ship. Three theodolite stations are placed at the three apexes of an equilateral triangle. Formulate the procedure for determining an optimal estimate of the ships location, coordinates x and y , based on three angular measurements, , , . First, obtain a model equation where 1 2 3 unknown parameters are linearly...
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This note was uploaded on 02/27/2012 for the course MECHANICAL 2.160 taught by Professor Harryasada during the Spring '06 term at MIT.

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ps1 - Massachusetts Institute of Technology Department of...

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