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rlabbe / Kalman-and-Bayesian-Filters-in-Python

Kalman Filter book using Jupyter Notebook. Focuses on building intuition and experience, not formal proofs. Includes Kalman filters,extended Kalman filters, unscented Kalman filters, particle filters, and more. All exercises include solutions.
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Problem in solution to "Exercise: The Effect of Acceleration" in Chapter 1 #381

Open axlan opened 3 years ago

axlan commented 3 years ago

For this exercise the solution is given as:


def gen_data(x0, dx, count, noise_factor, accel=0.):
    zs = []
    for i in range(count):
        zs.append(x0 + accel * (i**2) / 2 + dx*i + randn()*noise_factor)
        dx += accel
    return zs

If I'm understanding this correctly, this is basically sampling the closed form solution of integrating the acceleration to get the distance travelled with some random noise. The closed form solution is:

image

Which matches the expression in the solution, but I was confused by the incrementing of dx. My understanding is that dx is v0 so there's no need to increment it over time. The velocity is increasing, but dx in this expression shouldn't go up for each sample since that's already accounted for by the integration being used. Based on this I believe the solution should be:


def gen_data(x0, dx, count, noise_factor, accel=0.):
    zs = []
    for i in range(count):
        zs.append(x0 + accel * (i**2) / 2 + dx*i + randn()*noise_factor)
    return zs

Doesn't effect the actual lesson being communicated here, though.

LikeGiver commented 3 years ago

you're right!

PebetoUofC commented 2 years ago

See https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/issues/369