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in extended Kalman filter page 58, why it only expand variable
$x_{t-1}$ and do not expand variable$u_t$ .$g$ is function of$u_t$ and$x_{t-1}$ Answer:
It actually expands both. But we think that the motion
$u_t$ is accurate and we expand the function on point$u_t=u_t$ $$ g(x_{t-1},u_t)=g(\mu_{t-1},u_t)+\frac{\partial g}{\partial x_{t-1}}\Delta x+\frac{\partial g}{\partial u_t}\Delta u $$ and $$ \Delta u=u_t-u_t=0 $$ -
In beam models of range finder page 157, how to realize that the measurement distribution can be mixed by a weighted average such a linear combination. In real world, it should be that addition of the four errors. why the addition of the errors caused the addition of probability of errors.
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In likelihood fields for range finders, why the probability of sensor measurements is modeled by zero-centered Gaussian not
$z_t^k$ centered. -
In landmark measurement page 178, whom the i-th feature is belong to?? Is the j-th landmark a feature of the map??? why corresponding the i-th feature to the j-th landmark not the j-th landmark???
Answer:
It based on the assumption that the map is known.
For example, there 6 landmarks in the map and they are [rabbit, dog, cat, bird]. Rabbit is the
$1^{th}$ landmark. Dog is the$2^{th}$ landmark. Cat... Bird... At this time$t=t$ , we observe 2 feature$z_t = [z_t^1,z_t^2]$ . Which landmark does the feature belong to? If$z_t^1=bird$ , that means the$1^{th}$ feature corresponds to$4^{th}$ landmark. -
In line 16,17 of Algorithm EKF_localization_known_correspondences at page 204, ??? How to realize the accumulation of
$\bar{\mu}_t=\bar{\mu}_t+K_t^i(z_t^i-\hat{z}_t^i)$ ???? -
page 401
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problem 1: For $$ \Omega_t^0 = F_{x,m^+,m^0}F_{x,m^+,m^0}^T\Omega_t F_{x,m^+,m^0}F_{x,m^+,m^0}^T $$ Is not
$\Omega_t^0 = F_{x,m^+,m^0}^T\Omega_t F_{x,m^+,m^0}$ enough? Why do he multiply one more$F$ matrix -
problem 2: We note that
$\Omega_t^1,\Omega_t^2,\Omega_t^3$ could be obtained from$\Omega_t^0$ , which means that they are margined from$p(x_t,m^0,m^+,m^-=0|z_{1:t},u_{1:t},c_{1:t})$ . So, why they set$\Omega_t^0$ to be the information matrix of$p(x_t,m^0,m^+|m^-=0)$ in page 401?
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