We also need to capture the robot's velocity in the state (pose) in case the robot has some momentum, so the three parameters may be not enough for a 2D robot.
assumes the Markov property
position and orientation
particles are uniformly distributed over the configuration space
Given a map
every time
every time
motion_update
sensor_update
sensor_update
some noise is applied
It now believes it is at one of two locations.
The robot has successfully localized itself.
actuation command
no actuator is perfect: they may overshoot or undershoot the desired amount of motion
the motion model must be designed to include noise as necessary
Particles which were consistent with sensor readings are more likely to be chosen
possibly more than once
a robot becomes increasingly sure of its position as it senses its environment
It is proportional with the factor \alpha.
\alpha = 1 / p(z_k|z_{1:k-1})
A way to compute the value of \alpha is shown below. It is common to all the updated states x_k at a given time k and measurement z_k.
We are typically interested in relative probabilities of the states. Equivalently [?], the p(x_k|z_{1:k}) across all the estimated states x_k is a probability distribution:
\Sum_{x_k}{p(x_k|z_{1:k})} = 1
simply normalized, since its integral must be unity