[Zeng shuge's laser slam notes] gmapping filter based slam

One . What is filtering ？

Only estimating the current state is called filtering . If there is an error in the previous estimate , There is no way to correct .

Two . Mathematical concepts ：

All probability formula ： All probability formula _ Baidu Encyclopedia

Conditional Bayes formula ： stay P(x|y) Add and on the basis of y Independent variables z, obtain P(x|y,z), result P(y|z)=P(y), Other formulas only add conditions z.

Supplementary formula ： If x and y、z、k Independent , that P(x|y,z,k) =P(x);

for example ：Zt from Xt decision ,Ut from Xt decision ,

P(Zt|Xt,Ut)=P(Zt|Xt), among Zt Only by Xt decision , therefore P(Zt|Xt,Ut)=P(Zt|Xt).

P(Zt|Ut)=P(Zt|Ut), among Zt from Xt decision ,Ut from Xt decision , therefore P(Zt|Ut)=P(Zt|Ut).

3、 ... and . Bayesian filtering

If x Is a hope by y Extrapolated values , Then probability p(x) be called A priori probability distribution （prior prohability distribution）. among ,y It's called data （data）, That is, the measured value of the sensor . Distribution p(x) Summarized in the comprehensive data y There has been something about x Information about . probability p(x|y) Called in x Upper A posteriori probability distribution （posterior prohability distribution）.