I'm assigned a task involving solving a problem that can be described as follows: Suppose I'm driving a car around a lake. In the lake there is an island of irregular shape. I have a GPS with me in the car so I know how far I've driven and every turns I've made. Now suppose I also have a camera that takes picture of the island 30 times a second, so I know how long sidewise the island appears to me all the time. Also assume I know the straight line distance between me and the island all the time. Given these conditions, if I drive around the lake for one full circle, will I be able to estimate the perimeter of the island? If yes, how? Thanks.
estimate the perimeter of the island
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estimation-theory
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1I suppose the shape of the island can not be too irregular. – 2011-11-23
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7You can probably derive a lower bound for the perimeter, but unless you know the island is convex, the coastline can have arbitrarily complex wiggles that don't influence your measurements. – 2011-11-23
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2How would we estimate the perimeter if we assume the island is a convex shape? Thanks for your help. – 2011-11-23
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2I presume you've seen [this paper](http://users.math.yale.edu/~bbm3/web_pdfs/howLongIsTheCoastOfBritain.pdf)? – 2011-11-23