Localization Posterior: Introduction

Formal Definition of Variables

z_{1:t} represents the observation vector from time 0 to t (range measurements, bearing, images, etc.).

u_{1:t} represents the control vector from time 0 to t (yaw/pitch/roll rates and velocities).

m represents the map (grid maps, feature maps, landmarks)

x_t represents the pose (position (x,y) + orientation \theta )

Given the map, the control elements of the car, and the observations, what is the definition of the posterior distribution for the state x at time t?

(A)

bel(x_t) = p(x_t|z_t, m, u_t)

(B)

bel(x_t) = p(x_t| z_{1:t}, u_{1:t})

(C)

bel(x_t) = p(x_t, m_t|z_{1:t}, u_{1:t})

(D)

bel(x_t) = p(x_t|z_{1:t}, u_{1:t}, m)

SOLUTION:

(D)