The longitude, z, of an air plane is affected by a random component , due to the wind effect and its speed ut. It = It-1+20₁-1+ €₂. The speed of the plane is affected by a constant global linear trend, ß₁ = 3₁-1 = 3, and varies randomly due to weather conditions, v₁ = V₁-1 + B₁-1+ we. In the above equations, is assumed to be white Gaussian noise with zero mean and o = 3. Similarly we is assumed to be white Gaussian noise with zero mean and o2, = 0.5. A GPS transmitter mounted on the plane sends a noisy measurement to a receiver about its position, X₁ = 0.5x + nt, where n, is assumed to be white Gaussian noise with zero mean and o2 = 2. (a) Using the following definition for the state vector, 8. It + ve [***] Vt 0₁ = write the motion of the plane in state space form. Note: You need to provide the exact form of the h, G and W matrices. (b) Evaluate the initial estimate for the state vector 03.
The longitude, z, of an air plane is affected by a random component , due to the wind effect and its speed ut. It = It-1+20₁-1+ €₂. The speed of the plane is affected by a constant global linear trend, ß₁ = 3₁-1 = 3, and varies randomly due to weather conditions, v₁ = V₁-1 + B₁-1+ we. In the above equations, is assumed to be white Gaussian noise with zero mean and o = 3. Similarly we is assumed to be white Gaussian noise with zero mean and o2, = 0.5. A GPS transmitter mounted on the plane sends a noisy measurement to a receiver about its position, X₁ = 0.5x + nt, where n, is assumed to be white Gaussian noise with zero mean and o2 = 2. (a) Using the following definition for the state vector, 8. It + ve [***] Vt 0₁ = write the motion of the plane in state space form. Note: You need to provide the exact form of the h, G and W matrices. (b) Evaluate the initial estimate for the state vector 03.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The longitude, rt of an air plane is affected by a random component e, due to the
wind effect and its speed t
It = -1 + 20t-1 + 6t.
The speed of the plane is affected by a constant global linear trend, ß = B₁-1 = 3, and varies
randomly due to weather conditions,
v₁ = V₁-1 + B₁-1+w₂.
In the above equations, is assumed to be white Gaussian noise with zero mean and o = 3.
Similarly w is assumed to be white Gaussian noise with zero mean and 2,=0.5. A GPS transmitter
mounted on the plane sends a noisy measurement to a receiver about its position,
X₁ = 0.5xt + nt,
where n, is assumed to be white Gaussian noise with zero mean and o2 = 2.
(a) Using the following definition for the state vector, 0t.
0₁
It + ve
B₂
write the motion of the plane in state space form. Note: You need to provide the exact form
of the h, G and W matrices.
(b) Evaluate the initial estimate for the state vector 03-
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