# HW5 - EML 6934 Fall 2009 Optimal Estimation University of...

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Unformatted text preview: EML 6934 Fall 2009 Optimal Estimation University of Florida Mechanical and Aerospace Engineering HW 5 Issued: September 25, 2009, Due: October 2, 2009 (in class) Problem 1. [30 pt] Consider the motion of a vehicle in a straight line that is equipped with a GPS receiver and an IMU (inertial measurement unit). The GPS unit provides noisy measurements of the absolute position with respect to a common origin, while the IMU unit provides noisy measurements of the relative position between two time instants. Specifically, if the vehicle gets a GPS measurement at time t second, the measurement is of the form x ( t )+ GPS ( t ), where x ( t ) is the position of the vehicle at time t and GPS ( t ) is a measurement noise. If the vehicle gets an IMU measurement at time t seconds and the last IMU measurement it received was at seconds, then the IMU measurement is of the form x ( t )- x ( ) + IMU ( t- ), where IMU is a measurement noise. Notice that all variables involved are scalars. Assume that the first GPS measurement is obtained at time 0 second, and the first IMU mea- surement at time 0 . 5 second, the latter being a noisy measurement of x (0 . 5)- x (0). The vehicle gets GPS measurements at 1 second intervals and IMU measurements at 0...
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## HW5 - EML 6934 Fall 2009 Optimal Estimation University of...

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