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Description
Background
Current sensor measurements are in polar coordinates. However, state estimation uses 2 different
- ILSE uses uniform random variables (1 variance for the entire complex random variable)
- NRSE uses decomposed complex random variables (2 separate variances for the real and imaginary part)
There is a cadence where polar complex random variables are first transformed into decomposed random variables. NRSE uses the result directly, while ILSE consecutively transforms those decomposed random variables into uniform random variables, i.e.:
[(I, Var{I}) ] [(Re{I}, Var{Re{I}})]
[(theta, Var{theta})] [(Im{I}, Var{Im{I}})] [(Ie^i theta, Var{Ie^(i theta)})]
polar -------------- decomposed ----(calc_params)--------------- uniform
| | |
measurement NRSE ILSE
After #1150 , the NRSE current statistics has improved. However, at the same time, there is a small additional variance introduced by the 2nd order approximation from polar to decomposed which is then propagated into the uniform random variable. Going directly from polar to uniform random variables makes the change more precise.
Scope
This issue is about using polar coordinates in the calculation parameters, instead of decomposed random variables, so that NRSE and ILSE can both determine their optimal coordinate system with optimal variances:
[(Re{I}, Var{Re{I}})]
[(Im{I}, Var{Im{I}})]
/--------- decomposed
[(I, Var{I}) ] / |
[(theta, Var{theta})] / NRSE
polar ---------(calc_params)
| \
measurement \ [(Ie^i theta, Var{Ie^(i theta)})]
\---------- uniform
|
ILSE
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