Particle filter demonstration using TrackSim program

-------------------- Movitation

Filter->Kalman
SysNoise->Gaussian
MeasNoise->Half Gaussian (pause here, look at distribution)
Display scale:  128:1 (default)
MeasNoise scale:  1.0 (default)
SysNoise scale:  0.015625 (press 'k' 6 times)
Run->continuous
      KF cannot handle non-Gaussian distribution

-------------------- The basics -- use 's' to run, so can pause
	note:  MeasNoise/SysNoise = actual MEAS_NOISE/DYN_NOISE = filter

Filter->Particle
SysNoise->Gaussian
MeasNoise->Half Gaussian
Plot->Display->matrix values (so can see ratio of Q to R)
Display scale:  128:1 (default)
MeasNoise scale:  1.0 (default)
SysNoise scale:  0.015625 (press 'k' 6 times)

Run pressing 's' one step at a time, look at particle distribution and weights

Pause and step through resampling iteration (ESS < 0.1)

Increase dynamic noise
SysNoise scale:  0.125 (press 'i' 3 times)
        look at effect of dynamic noise on distribution

Pause and look at output (using E[] = mean)

System->reset  (if particle weights all low, this crashes)
        think about iterative nature of process
        if p(y|x) for every particle ~= 0, what happens?
        solution-finding process is stuck

-------------------- Explain effect of #particles

System->reset
Variables->PF->#particles = 30
Run pressing 's' ....
        (look at ability of particles to accurately represent distribution)
Run->continuous  (notice speed - fast with few particles)

Run->stop
System->reset
Variables->PF->#particles = 9999 (max)
Run pressing 's' .... (now look at distribution - much more defined)
Run->continuous  (slow; this is the tradeoff)

-------------------- Demo magnets system

System->reset
Variables->PF->#particles = 1000
SysNoise->Gaussian
MeasNoise->Gaussian
System->Magnets  (automatically sets noise amounts)
Plot->Display->Filter output (turn off)
Run->continuous ... wait for bigger oscillations

Explain axes -- sensor ossilating past magnets,
        reading strength upside down (lower = closer to magnet)
        this is easiest to see with very low MeasNoise

Plot->Display->Filter output (turn on)
Run->continuous ... particle distribution is clearly non-Gaussian
        ** output may mirror due to symmetry of problem