Sstep.Clutter function

Sequential Monte Carlo for A Moving Target under Clutter Environment

The function performs one step propagation using the sequential Monte Carlo method with partial state proposal for tracking in clutter problem.

Sstep.Clutter(mm, xx, logww, yyy, par, xdim, ydim)

Arguments

• mm: the Monte Carlo sample size m.
• xx: the sample in the last iteration.
• logww: the log weight in the last iteration.
• yyy: the observations.
• par: a list of parameter values (ssw,ssv,pd,nyy,yr), where ssw is the standard deviation in the state equation, ssv is the standard deviation for the observation noise, pd is the probability to observe the true signal, nyy the dimension of the data, and yr is the range of the data.
• xdim: the dimension of the state varible.
• ydim: the dimension of the observation.

Returns

The function returns a list with the following components: - xx: the new sample.

• logww: the log weights.

Examples

nobs <- 100; pd <- 0.95; ssw <- 0.1; ssv <- 0.5;
xx0 <- 0; ss0 <- 0.1; nyy <- 50;
yrange <- c(-80,80); xdim <- 2; ydim <- nyy;
simu <- simuTargetClutter(nobs,pd,ssw,ssv,xx0,ss0,nyy,yrange)
resample.sch <- rep(1,nobs)
mm <- 10000
yr <- yrange[2]-yrange[1]
par <- list(ssw=ssw,ssv=ssv,nyy=nyy,pd=pd,yr=yr)
yr<- yrange[2]-yrange[1]
xx.init <- matrix(nrow=2,ncol=mm)
xx.init[1,] <- yrange[1]+runif(mm)*yr
xx.init[2,] <- rep(0.1,mm)
out <- SMC(Sstep.Clutter,nobs,simu$yy,mm,par,xx.init,xdim,ydim,resample.sch)

References

Tsay, R. and Chen, R. (2018). Nonlinear Time Series Analysis. John Wiley & Sons, New Jersey.