Nonlinear Filtering for Data Assimilation of Semi-Lagrangian Ocean Glider Data

Outline of Programs, Files, Data, and Results

1/13/11

Info

This version marks the start of Spring 2011 research. I have turned the particle filter script into a generic function that takes the system and filter parameters as arguments. It is restricted to just two vortices, but allows for different strengths. Also, the vortex strengths are unknown to the particle filter. I also have included the experiment_script.m script which runs numerous simulations of the particle filter. The resulting error time series are saved in errors.mat and all the variables are saved in workspace.mat .

Notes

• The variances for the initial distribution of particles is still hard-coded into two_point_vortex_particle_filter.m instead of being arguments.
• The variance (actually st. dev) of the stochastic part of the differential equation is hard-coded into g.m instead of being an argument to the particle filter. I'm not sure which is more appropriate, so I'm keeping it in g.m for now.

Files

Directory ~/research/1_13_11/

Filename	Description
experiment_script.m	Driver script for running numerous simulations of the particle filter. All variables saved in workspace.mat . Error timeseries for the weighted mean of the particle cloud are saved in errors.mat .
two_point_vortex_particle_filter.m	Generic function for performing a single simulation using the particle filter. Vortex strengths are unknown. Allows arbitrary number of observations, arbitrary time steps, arbitrary number of particles, arbitrary strengths for vortices. Can only handle two vortices.
SRK4.m	Numerical Runge-Kutta integration for stochastic differential equations. Function f.m is the deterministic part. Function g.m is the stochastic part.
f.m	Deterministic part of the stochastic differential equation describing the system used in two_point_vortex_particle_filter.m .
g.m	Stochastic part of the stochastic differential equation describing the system used in two_point_vortex_particle_filter.m .
H.m	Observation operator. Here, it maps the entire state vector to a two vector containing just the first two entries (the tracer location) of the state vector.
R.m	Fitness function for determining weights of particles after comparison with an observation.

Fall 2010

Info

This directory contains all files used in Fall 2010.

• It contains a script for a particle filter with resampling applied to the two point vortex system with equal and known vortex strengths.
• It contains a script for a particle filter with resampling applied to the two point vortex system with different, but known, vortex strengths.
• It contains a script for a particle filter with resampling applied to the two point vortex system with different and unknown vortex strengths.
• It contains a numerical Runge-Kutta integration routine for stochastic differential equations.

Files

Directory ~/research/Fall_2010