The AstroStat Slog

I decide to discuss Kalman Filter a while ago for the slog after finding out that this popular methodology is rather underrepresented in astronomy. However, it is not completely missing from ADS. I see that the fulltext search and all bibliographic source search shows more results. Their use of Kalman filter, though, looked similar to the usage of “genetic algorithms” or “Bayes theorem.” Probably, the broad notion of Kalman filter makes it difficult my finding Kalman Filter applications by its name in astronomy since often wheels are reinvented (algorithms under different names have the same objective).

When I learned “Kalman filter” for the first time, I was not sure how to distinguish it from “Yule-Walker equation” (time series), “Pade approximant, (unfortunately, the wiki page does not have its matrix form). Wiener Filter” (signal processing), etc. Here are those publications, specifically mentioned the name Kalman filter in their abstracts found from ADS.

• Application of Data Assimilation Method for Predicting Solar Cycles (2008) in ApJ
• Time series analysis in astronomy: Limits and potentialities (2005) in A&A
  From the abstract: Only techniques of data aalysis developed in a specific physical context can be expected to provide useful results. The filed of stochastic dynamics appears to be an interesting framework for such an approach.
• Determination of the Mass of Jupiter Using the Motion of Its Ninth Satellite and a Kaiman-Bucy Filter (1972) in A&A

The motivation of introducing Kalman filter although it is a very well known term is the recent Fisher Lecture given by Noel Cressie at the JSM 2009. He is the leading expert in spatial statistics. He is the author of a very famous book in Spatial Statistics. During his presentation, he described challenges from satellite data and how Kalman filter accelerated computing a gigantic covariance matrix in kriging. Satellite data of meteorology and geosciences may not exactly match with astronomical satellite data but from statistical modeling perspective, the challenges are similar. Namely, massive data, streaming data, multi dimensional, temporal, missing observations in certain areas, different exposure time, estimation and prediction, interpolation and extrapoloation, large image size, and so on. It’s not just focusing denoising/cleaning images. Statisticians want to find the driving force of certain features by modeling and to perform statistical inference. (They do not mind parametrization of interesting metric/measure/quantity for modeling or they approach the problem in a nonparametric fashion). I understood the use of Kalman filter for a fast solution to inverse problems for inference.