<http://www2.informatik.uni-freiburg.de/~stachnis/pdf/grisetti07tro.pdf>

Section One

1. 大量的粒子滤波会使得计算过程相当复杂，主要挑战在减少粒子数量
2. 重采样的步骤可能会消灭正确的粒子（This effect is also known as the particle
depletion problem or as particle impoverishment）

which tends to eliminate particles with low weights

1、 proposal distribution

A proposal distribution that considers the accuracy of the
robot’s sensors and allows us to draw particles in a highly
accurate manner

An adaptive resampling technique which maintains a
reasonable variety of particles and in this way enables
the algorithm to learn an accurate map while reducing
the risk of particle depletion

the adaptive resampling strategy, allows us to perform a resampling step only
when needed and in this
way keeping a reasonable particle diversity

Section Two
Rao-Blackwellized particle是怎么去解决SLAM问题的

PS：SLAM问题有一个小小的分类，也就是分为在线SLAM问题，也就是根据过去时间的控制u和观测z得出地图和当前位置 p(Xt,m|Z1:t,U1:t)

z,u -> x
x,z-> m

model。m表示地图

The maps are built from the observations and the trajectory represented by
the corresponding particle

One of the most common particle filtering algorithms is the sampling
importance resampling (SIR) filter

1） Sampling
2） Importance Weighting

The weights account for the fact that the proposal distribution π is in
general not equal to the target distribution of successor states

3） Resampling
4） Map Estimation

For each particle, the corresponding map estimate p(m(i) | x( 1: i)t, z1:t)
is computed based on
the trajectory x( 1: i)t of that sample and the history of
observations z1:t.
（观测值observation来源于传感器）

A RaoBlackwellized SIR filter for mapping incrementally processes the sensor
observations and the odometry readings as they are available

Section Three

1、 On the Improved Proposal Distribution

Proposal Distribution就是预估下一代粒子的位姿，Proposal distribution越接近target distribution

For instance, if we were able to directly draw samples from the target
distribution, the
importance weights would become equal for all particles and the resampling
step would no longer be needed

distribution，这个方法的优点就是对于大多数机器人来说特别容易计算

During

PS:关于particles impoverishment的定义

Particularly, PF approaches show degraded performance for problems where the
state noise is very small or zero. This is because particles become identical
within a few iterations, which is so called particle impoverishment

Neff是粒子权重分布的一种测量，可以判断粒子集是否接近于目标值

a scan matcher algorithm is executed based on the map m starting from the
initial guess x.the search performed by the scan-matcher is bounded to a
limited region around x.if the scan-matching report a failure , the pose and
the weights are computed according to the motion model

Section 4 IMPLEMENTATION ISSUES