Quickstart

Import

using StaticArrays, LinearAlgebra, Plots
using SpatiotemporalGPs

Define the Problem Domain

# setup the spatial and temporal kernels
σt = 2.0   # m/s
σs = 1.0   # m/s
lt = 3*60.0  # minutes
ls = 3.0   # km

kt = Matern(3/2, σt, lt)
ks = Matern(1/2, σs, ls)

# determine the temporal step size
Δt = 5.0 # minutes
Δx = 0.25 # km

# create the spatial domain
xs = 0:Δx:7.0
ys = 0:Δx:10.0

grid_pts = vec([@SVector[x, y] for x in xs, y in ys]);

Initialize

problem = STGPKFProblem(grid_pts, ks, kt, Δt)
state_initial = stgpkf_initialize(problem) 

Assimilate a single point measurement

# for a single measurement
measured_pt = @SVector [ ... ] 
measured_value = ...
measured_σ = ...

state_corrected = stgpkf_correct(problem, state_initial, measured_pt, measured_y, measured_σ)

Assimilate a set of measurements

# define all the measurements
measured_pts = [ ... ] # should be a vector of positions that were measured
measured_ys = [ ... ] # should be a vector of measured values
measured_Σ = [ ... ]  # should be a pos def matrix


state_corrected = stgpkf_correct(problem, state_initial, measured_pts, measured_ys, measured_Σ)

Predict the next timestemp

state_predicted = stgpkf_predict(problem, state_corrected)

Generate Plots

plot(problem, state; plot_type=:estimate, kwargs...)

where plot_type can be :estimate, :std, :clarity, :percentile. If it is percentile use the percentile=0.95 kwarg to specify which percentile to visualize. Currently only supports visualization of 2D domains.

Extract Data

To get the estimate of the spatiotemporal field

get_estimate(problem, state)

or you can also call

get_estimate_covariance(problem, state)
get_estimate_std(problem, state)
get_estimate_clarity(problem, state)

See examples/synthetic_data.ipynb for a full demo.