What does Temporal and Spatial resolution mean in the context of a NDIR CO2 sensor?
I'm reading a paper called "Sensing by Proxy" where an algorithm to estimate occupancy is presented. They define two variables, Spatial resolution and Temporal resolution but don't explain what they are. AFAIK these terms are generally used in the context of Visual sensors such as cameras. What would they mean for a CO2 sensor?
edit: typo
Posted Oct 25, 2019, 3:08 PM UTC · edited
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venturing a guess: CO2 is a concentration which naturally is interpreted existing in a continuum space (a room for example, has a 3D continuous coordinate space, not a discrete one)
As infinite-dimensional analysis is quite difficult especially in high dimensions, people turn to finite element methods to discretize evolution equations on infinite-dimensional function spaces (partial differential equations) into discrete difference equations. Doing this necessitates defining a mesh, i.e. defining spatial (3D space) and temporal (time) resolutions.
How would you go about defining temporal and spatial resolutions?
its very dependent on your equation. Some people get entire PhDs for studying how to generate numerical methods for solving these things in a specific context, much less how to do estimation for it...
if this is Bayen’s paper like i’m guessing it is, they probably just used first-order finite difference method. i remember the equation is a 1 spatial dimension equation of a hyperbolic class (convection), so you have to fulfill something called the Courant-Friedrichs-Lewy (CFL) condition. but defining a finite difference for 1 spatial dimension should not be difficult