MAE 2: Introduction to Aerospace Engineering
Assignment 5
Study Problems Only. Do not hand in.
1. Suppose we are in a two-dimensional world. Two one-way range ob-
servations and an l.o.s. observation are made (at essentially the same
time) of a spacecraft. The one-way range observations are reported as
arrival times at two locations of a signal emitted by the spacecraft. The
one-way range observation station positions are (5000,0) and (0,5000)
in km. The l.o.s. observation station position is (0,5000) km (collo-
cated with the second one-way range observation station). The l.o.s.
observation is ~u = (0.8,โ0.6). The signal arrival times are 2446.1 and
2446.122808 seconds past midnight, respectively. Find the spacecraft
position. (Use cl= 2.9979 ร105km/sec as the speed of light.)
2. Use the derivative approach to estimate the sensitivity of this position
estimate to an error in the arrival time of the signal at the second
observation station.
3. We are in a one-dimensional world for this problem. Suppose a vehicle
is at x= 1 at time t= 0, and is traveling at constant speed. At
times t= 1,3,5,6,8, we measure its position, obtaining observations
y(1) = 0.5, y(3) = โ1, y(5) = โ2, y(6) = โ4 and y(8) = โ5. Using
the least-squares approach, estimate the vehicle speed. Estimate its
position at t= 8. Predict its position at t= 10.
4. In the above problem, suppose instead that we were given no informa-
tion on the vehicle position at t= 0. Using the least squares approach
(linear regression), estimate the initial position (at t= 0) and the ve-
hicle speed. Again also estimate its position at t= 8, and predict its
position at t= 10.
