Driverless learning (4): Bayesian filtering

notes ： Learning notes , Refer to others more , Accumulate gradually

One 、 Occupy the grid map -- Binary Bayesian filtering

1.1 Binary Bayesian filtering background

        Each small grid has three possible states at a certain time -- occupy occupied、 Free free, Among them, the small grid scanned by lidar points is the occupied grid 、 What is not swept is the idle grid . Suppose a single lidar scan , Sweep to a small space , The occupancy probability of this small cell is 0.9, The probability of being idle is 0.1; When you don't scan a small space , The probability of occupation is 0.2, The probability of being idle is 0.8.（ These figures are assumed values ）

        Next, a small cell is scanned several times in succession / No scanned problems , That is, some of the several scans have scanned the small cell , After these times , What is the probability of the small cell being occupied . Let's change the expression of the occupancy probability of the lattice , The box “ Degree of confidence ” Express .

        p(x)/p(-x)=p(x)/(1-p(x)) among x Indicates that the small cell is occupied ,p(x) Indicates the probability of being occupied

Take the natural logarithm on both sides at the same time ：

        l(x)=ln(p(x)/(1-p(x)))  among l(x) Indicates the confidence that the small cell is occupied

In turn, , The probability that the small cell is occupied can be expressed as ：

        p(x)=1-1/(1+e^(l(x)))

1.2 Bayesian filtering

        Bayesian filtering calculation routine ：

        l(t)=l(t-1)+ln(p(x|zt)/(1-p(x|zt)))-ln(p(x)/(1-p(x)))

among ：

        l(t) by t The confidence that time is occupied ,

        l(t-1) by t-1 The confidence that time is occupied ,

        zt by t Observations at the moment ,

        p(x|zt) For in t moment , At the observed value （ Occupied or idle ） The probability of occupation in the case of

        p(x) In order not to consider the actual situation , The probability of any small lattice being occupied , In this case 0.5

        

        hypothesis 1.1 When a small cell is occupied, it is scanned three times in succession , Then it was not scanned , The confidence is calculated as follows ：

        initial value ：L0=ln(0.5/0.5)=0

        It was scanned for the first time ：L1=L0+ln(0.9/0.1)-L0=ln9

        It was scanned for the second time ：L2=L1+ln(0.9/0.1)-L0=ln9+ln9

         It was scanned for the third time ：L3=L2+ln(0.9/0.1)-L0=ln9+ln9+ln9

         It was scanned for the fourth time ：L4=L3+ln(0.2/0.8)-L0=ln9+ln9+ln9-log4≈5.2

        Then the probability of being occupied after four scans p(4)=1-1/(1+e^5.2)≈0.9945

1.3 Reference link ：

Occupy the grid map （occupancy grid maps） -- Application of binary Bayesian filtering https://blog.csdn.net/haishaoli/article/details/79647594