ch3 ex_1.1 find a mistake about X_t

[howardchina]

https://github.com/pptacher/probabilistic_robotics/blob/d31a9f1a3f5e500bd85d98d7fb4fb5743d1222ad/ch3_gaussian_filters/ch3_gaussian_filters.pdf

Question 1.1, 1.2

formula of the kalman filter should be:

$$ x_t = At x{t-1} + B_t u_t + \epsilon_t $$

but not:

$$ x_t = At x{t-1} + Bt u{t-1} + \epsilon_t $$

which mean control variant $u_{t-1}$ on the last timestamp can't effect current state.

However, the distance (d), speed (v), acceleration (a) formula is:

$$ dt = d{t-1} + \Delta t \times v{t-1} + \frac{1}{2} \Delta t^2 \times a{t-1} $$

where acceleration ($a_{t-1}$) is from the last timestamp.

which means we need the acceleration from the last timestamp to update current distance and speed.

So we should make the acceleration into the consideration of state $X_t$.

And $X_t = [x_t, \dot{x}_t, \ddot{x}_t]^T$

[howardchina]

Sorry. I got the problem. The translated Chinese version mistakly expressed the problem from the original book.