# pfLineartBS: Particle Filter Example In RcppSMC: Rcpp Bindings for Sequential Monte Carlo

## Description

The `pfLineartBS` function provides a simple example for RcppSMC. It is based on the first example in `SMCTC` and the discussion in Section 5.1 of Johansen (2009). A simple 'vehicle tracking' problem of 100 observations is solved with 1000 particles.

The `pfLineartBSOnlinePlot` function provides a simple default ‘online’ plotting function that is invoked during the estimation process.

The `simLineart` function simulates data from the model.

## Usage

 ```1 2 3``` ``` pfLineartBS(data, particles=1000, plot=FALSE, onlinePlot) pfLineartBSOnlinePlot(xm, ym) simLineart(len) ```

## Arguments

 `data` A two-column matrix or dataframe containing x and y values. The default data set from Johansen (2009) is used as the default if no data is supplied. `particles` An integer specifying the number of particles. `plot` A boolean variable describing whether plot should illustrate the estimated path along with the data. `onlinePlot` A user-supplied callback function which is called with the x and y position vectors during each iteration of the algorithm; see pfExOnlinePlot for a simple example. `xm` Vector with x position. `ym` Vector with y position. `len` Length of sequence to simulate

## Details

The `pfLineartBS` function provides a simple example for RcppSMC. The model is linear with t-distributed innovations. It is based on the `pf` example in the `SMCTC` library, and discussed in the Section 5.1 of his corresponding paper (Johansen, 2009). `simLineart` simulates from the model.

Using the simple `pfExOnlinePlot` function illustrates how callbacks into R, for example for plotting, can be made during the operation of SMC algorithm.

## Value

The `pfLineartBS` function returns a `data.frame` containing as many rows as in the input data, and four columns corresponding to the estimated x and y coordinates as well as the estimated velocity in these two directions.

The `simLineart` function returns a list containing the vector of states and the associated vector of observations.

## Author(s)

Adam M. Johansen and Dirk Eddelbuettel

## References

A. M. Johansen. SMCTC: Sequential Monte Carlo in C++. Journal of Statistical Software, 30(6):1-41, April 2009. https://www.jstatsoft.org/v30/i06/paper

The SMCTC paper and code at https://www.jstatsoft.org/v30/i06/paper.

## Examples

 ```1 2 3``` ``` res <- pfLineartBS(plot=TRUE) if (interactive()) ## if not running R CMD check etc res <- pfLineartBS(onlinePlot=pfLineartBSOnlinePlot) ```

### Example output ```
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RcppSMC documentation built on Aug. 30, 2020, 5:06 p.m.