function?[PAIABPQestlkh]=hsmm_new（PAIABPOIterationNo）
%?
%?Author:?Shun-Zheng?Yu
%?Available:?http://sist.sysu.edu.cn/~syu/Publications/hsmm_new_m.txt
%?
%?HSMM?solve?three?fundamental?problems?for?Hidden?Semi-Markov?Model?using?a?new?Forward-Backward?algorithm
%?Usage:?[PAIABPStateseqLoglikelihood]=hsmm_newScale_amm（PAIABPOMaxIterationNo）
%?MaxIterationNo=0:?estimate?StateSeq?and?calculate?Loglikelihood?only;?
%?MaxIterationNo>1:?re-estimate?parameters?estimate?StateSeq?and?Loglikelihood.
%?First?use?[ABPPAIVkOK]=hsmmInitialize（OMDK）?to?initialize
%?
%?Ref:?Practical?Implementation?of?an?Efficient?Forward-Backward?Algorithm?for?an?Explicit?Duration?Hidden?Markov?Model
%?by?Shun-Zheng?Yu?and?H.?Kobayashi
%?IEEE?Transactions?on?Signal?Processing?Vol.?54?No.?5?MAY?2006?pp.?1947-1951?
%?
%??This?program?is?free?software;?you?can?redistribute?it?and/or
%??modify?it?under?the?terms?of?the?GNU?General?Public?License
%??as?published?by?the?Free?Software?Foundation;?either?version
%??2?of?the?License?or?（at?your?option）?any?later?version.
%??http://www.gnu.org/licenses/gpl.txt
%
%++++++++?Markov?Model?+++++++++++
M=length（PAI）;???????????????%The?total?number?of?states
T=length（O）;?????????????????%The?total?time
D=size（P2）;?????????????????%The?maximum?duration?of?states
K=size（B2）;?????????????????%The?total?number?of?observation?values
%----------------------------------------------------
ALPHA=zeros（MD）;
bmx=zeros（MT）;
S=zeros（MT）;
E=zeros（MT）;
BETA=ones（MD）;
Ex=ones（MD）;
Sx=ones（MD）;
GAMMA=zeros（M1）;
Pest=zeros（MD）;
Aest=zeros（MM）;
Best=zeros（MK）;
Qest=zeros（T1）;

ir1=max（1IterationNo）;

for?ir=1:ir1

%????starttime=clock;
%++++++++++++++++++?????Forward?????+++++++++++++++++
%---------------????Initialization????---------------
ALPHA（:）=0;?ALPHA=repmat（PAI1D）.*P;		%Equation?（13）
r=（B（:O（1））‘*sum（ALPHA2））;			%Equation?（3）
bmx（:1）=B（:O（1））./r;				%Equation?（2）
E（:）=0