Kalman filter technique for defining solar regular geomagnetic variations

Motivated by recent attempts to derive geomagnetic activity from hourly mean data in long term studies, we test the recursive Kalman filter method to obtain the regular solar variation curve of the geomagnetic field. Using a simple algorithm, we are able to assign a quiet day curve to every day separately, without the need for additional input parameter(s) to define the geomagnetically quiet days. We derive a digital counterpart AhK of the analog range index Ak at the subauroral Sodankyl$\ddot{a}$ station and compare it to the earlier digital estimate Ah and the local Ak index. We find that the new method outperforms the former estimate in every aspect studied and provides a robust, straightforward manner of estimating and verifying the manually scaled Ak index, based on readily available hourly values. The model is independent of sampling; thus, for shorter term studies where high-sampling data are available, more accurate estimates can also be obtained when needed. Therefore, in contrast to other recent approaches, we do not provide a method to quantify irregular activity directly but derive the actual quiet day curves in the traditional manner. In future applications the same algorithm may be used to define a wide variety of geomagnetic indices (such as Ak, Dst, or AE).