There is a function: $f(t,x,y,z)$, where $t$- time, $x,y,z$- some arguments.
The values of $f$ for $t\in [a,b]$ are known (100 samples). What is the most accurate way of predicting the value of $f$ for $t=b+1$, if the values of $x,y,z$ for $t\in [a,b+1]$ are known?
ADDITIONAL INFO
I'm propagating the satellite position using an analytical method. During the propagation, the errors accumulate. I endeavor to predict the future position errors. $f$ represents the error value and arguments $x,y,z$ are the affecting parameters, such as distance to the Moon, Sun, solar flux, atmospheric density, etc.
Without any a priori information about $f$, the problem seems ill-posed. Because you have data values only along a curve and you know little of $f$ . Extrapolation will be hazardous.
If you have a mathematical model with unknown parameters, you can estimate the parameters from the known values.
Otherwise, you can just relate $f$ to the curvilinear abscissa along the trajectory and perform univariate interpolation.