I'm merging 2 data streams together. One of them is precise, the other accurate. Excuse if this is obvious, but let me be sure I'm clear:
- Accurate: Long term average is correct, but otherwise a noisy signal
- Precise: short term changes are indeed the desired signal, but an overall unknown DC bias exists, and may also drift (i.e, the result of an integration)
In essence, these two signals compliment each other (correct me if there's a better word than "complement"). I can think of a number of ways to merge these mathematically, but not quite the question. What I'd like to know is the terminology around this.
- Is there a term that encapsulates the functionality of merging these signals, and in this case to obtain both precision and accuracy in an output stream? Linear or non-linear.
The specific calculation I'm looking at is below. It is non-linear if the $K$ term is used:
$Output_n = Output_{n-1} + \Delta Precise_n \\ \qquad\qquad + f(Accurate_n -Output_{n-1}-\Delta Precise_n)$
Where $f(\varepsilon) $ is an error transfer function, and can be something like
$\qquad\qquad f(\varepsilon) = P*\varepsilon + K *sign(\varepsilon)$
P as a proportional error correction, and/or K as a fixed error correction. K should be smaller than the noise in the Precise signal, but can be augmented if $sign(\varepsilon)$ is consistent (geometrically augmented with $G$, and/or cumulatively augmented with $C$
$K_n = K_{n-1} * G^{sign(\varepsilon_n)*sign(\varepsilon_{n-1})} \\ \qquad\qquad\space\space\space + C*sign(\varepsilon_n)*sign(\varepsilon_{n-1})\\ $
- C if used is much smaller than the noise in the precise signal
- G if used is slightly greater than 1, on the order of $\frac{K+C}K$
And bounded to reasonable, positive limits: $Lower <= K_n <= Upper$.
Thanks to all for terminology correction suggestions