Came across this recently but didn't understand in plain language why it was needed. Does anybody know? Why is a Kalman filter not do the job?
Ensemble Kalman Filter
Started by ●June 11, 2013
Reply by ●June 12, 20132013-06-12
On Tue, 11 Jun 2013 14:25:34 -0700, gyansorova wrote:> Came across this recently but didn't understand in plain language why it > was needed. Does anybody know? Why is a Kalman filter not do the job?You have to define what the author means by "ensemble Kalman filter". That sounds like a term that the author has just invented, or that only has meaning to a small number of practitioners or researchers. -- Tim Wescott Control system and signal processing consulting www.wescottdesign.com
Reply by ●June 12, 20132013-06-12
On Thursday, June 13, 2013 3:49:15 AM UTC+12, Tim Wescott wrote:> On Tue, 11 Jun 2013 14:25:34 -0700, gyansorova wrote: > > > > > Came across this recently but didn't understand in plain language why it > > > was needed. Does anybody know? Why is a Kalman filter not do the job? > > > > You have to define what the author means by "ensemble Kalman filter". > > That sounds like a term that the author has just invented, or that only > > has meaning to a small number of practitioners or researchers. > > > > -- > > Tim Wescott > > Control system and signal processing consulting > > www.wescottdesign.comactually it is now reasonably well known in the literature as I have had time to have a good look. Seems like it is used for non-linear problems where an extended KF may have been used in the past. From what I can see they an average of the predicted state and substitute it as the real state (I think) and make a sample error covariance matrix to replace the "real one", In other words it is based more on sampled data than a mathematical model though it appears they need the A matrix (but not the C matrix). https://en.wikipedia.org/wiki/Ensemble_Kalman_filter http://www.mathworks.com/matlabcentral/fileexchange/31093-ensemble-kalman-filter all very confusing
Reply by ●June 12, 20132013-06-12
On Thursday, June 13, 2013 3:49:15 AM UTC+12, Tim Wescott wrote:> On Tue, 11 Jun 2013 14:25:34 -0700, gyansorova wrote: > > > > > Came across this recently but didn't understand in plain language why it > > > was needed. Does anybody know? Why is a Kalman filter not do the job? > > > > You have to define what the author means by "ensemble Kalman filter". > > That sounds like a term that the author has just invented, or that only > > has meaning to a small number of practitioners or researchers. > > > > -- > > Tim Wescott > > Control system and signal processing consulting > > www.wescottdesign.comThe idea behind the EnKF is to provide a filter that is suitable for large-scale nonlinear systems. The basic and extended Kalman filter have proven difficult to adapt to such systems due to computation time and handling of nonlinear dynamics. Often the difficulty lies in computing the error covariance matrix. In the EnKF the covariance matrix estimate ( P ) is predicted and analyzed using the ensemble statistics. The EnKF was introduced by G. Evensen in 1994 [ 18 ] for the purpose of handling large-scale nonlinear ocean models. The EnKF has been developed and examined further for various appli- cations in many papers. A good source for articles and developments of the EnKF can be found online [ 2 ]. This page is established as a reference page for users of the EnKF made by G. Evensen and Nansen Environmental and Remote Sensing Center (NERSC). At this page one can also find a Fortran 90 EnKF implementation and some examples. The method was originally used with oceanic forecasting models and, in addition to the work of Evensen, the ocean model described by K. Brusdal et. al. [ 9 ] has also showed good potential. An- other application where EnKF has showed promising results is the marine ecosystem case presented by both M. Eknes and G. Evensen [ 15 ] and J. I. Allen et. al. [ 4 ]. Lately the properties of the EnKFhas showed promising results in oil reservoir modelling. The latter application is the focus of this paper and will be discussed in Chapter 5 . The theoretical formulation of the EnKF will be described in this section. A more detailed exposition of the EnKF can be found in the book by Evensen [ 16 ] [1] The Mathworks, Inc. (http://www.mathworks.com/). [2] http://enkf.nersc.no/. [3] I. Aitokhuehi and L.J. Durlofsky. Optimizing the performance of smart wells in complex reser- voirs using continuously updated geological models. J. of Pet. Sci. and Eng. , 48:254�264, 2005. [4] J. I. Allen, M. Eknes, and G. Evensen. An ensemble kalman filter with a complex marine ecosystem model: hindcasting phytoplankton in the cretan sea. Annales Geophysicae , 20:1�13, 2002. [5] H. Berghuis and H. Nijmeier. A passivity approach to controller-observer design for robots. IEEE Transactions on Robotics and Automation , 9(6):740�754, December 1993. [6] D.R. Brouwer and J.-D. Jansen. Dynamic optimization of waterflooding with smart wells using optimal control theory. Proceedings of the 2004 SPE European Petroleum Conference, Aberdeen . (SPE 78278). [7] D.R. Brouwer, G. N�vdal, J.D. Jansen, E.H. Vefring, and C.P.J.W. van Kruijsdijk. Improved reservoir management through optimal control and continous model updating. Proceeding of the SPE Annual Techincal Conference and Exhibition held in Houston, Texas, U.S.A. , September 2004. (SPE 90149). [8] R.G. Brown and P.Y.C. Hwang. Introduction to random signals and applied Kalman filtering: with MATLAB exercises and solutions . Wiley New York, 1997. ISBN 0-471-12839-2. [9] K. Brusdal, J.M. Brankart, G. Halberstadt, G. Evensen, P. Brasseur, P.J. van Leeuwen, E. Dom- browsky, and J. Verron. A demonstration of ensemble-based assimilation methods with a layered ogcm from the perspective of operational ocean forecasting systems. Journal of Marine Systems , 40-41:253�289, 2003. [10] G. Burgers, P. J. van Leeuwen, and G. Evensen. Analysis scheme in the ensemble kalman filter. Mon. Weather Rev. , 126:1719�1724, 1998. [11] C.-T. Chen. Linear System Theory and Design . Saunders College Publishing, 1984. ISBN 0-03-071691-8 16] G. Evensen. Data Assimilation: The Ensemble Kalman Filter . Springer, 2007
Reply by ●June 12, 20132013-06-12
On Wed, 12 Jun 2013 13:09:33 -0700, gyansorova wrote:> On Thursday, June 13, 2013 3:49:15 AM UTC+12, Tim Wescott wrote: >> On Tue, 11 Jun 2013 14:25:34 -0700, gyansorova wrote: >> >> >> >> > Came across this recently but didn't understand in plain language why >> > it >> >> > was needed. Does anybody know? Why is a Kalman filter not do the job? >> >> >> >> You have to define what the author means by "ensemble Kalman filter". >> >> That sounds like a term that the author has just invented, or that only >> >> has meaning to a small number of practitioners or researchers. >> >> >> >> -- >> >> Tim Wescott >> >> Control system and signal processing consulting >> >> www.wescottdesign.com > > actually it is now reasonably well known in the literature as I have had > time to have a good look. Seems like it is used for non-linear problems > where an extended KF may have been used in the past. From what I can > see they an average of the predicted state and substitute it as the real > state (I think) and make a sample error covariance matrix to replace the > "real one", In other words it is based more on sampled data than a > mathematical model though it appears they need the A matrix (but not the > C matrix). > > https://en.wikipedia.org/wiki/Ensemble_Kalman_filter > > http://www.mathworks.com/matlabcentral/fileexchange/31093-ensemble-kalman-filter> > all very confusingIt sounds like they may be trying to solve the same problem as the unscented Kalman, only using different language. Basically, the Kalman filter is for linear systems, the extended Kalman is for mildly nonlinear systems, the unscented Kalman (and possibly the ensemble Kalman) are for moderately nonlinear systems, and when things get really bad you need to throw Kalman out the window and let Bayes in the front door. Alas, I don't have the time to figure out if the unscented and ensemble Kalmans are mathematically equivalent, sorta the same, or completely different animals. You may find it educational to look at what Wikipedia says about the unscented Kalman, however. -- Tim Wescott Control system and signal processing consulting www.wescottdesign.com
Reply by ●June 13, 20132013-06-13
On Thursday, June 13, 2013 10:44:15 AM UTC+12, Tim Wescott wrote:> On Wed, 12 Jun 2013 13:09:33 -0700, gyansorova wrote: > > > > > On Thursday, June 13, 2013 3:49:15 AM UTC+12, Tim Wescott wrote: > > >> On Tue, 11 Jun 2013 14:25:34 -0700, gyansorova wrote: > > >> > > >> > > >> > > >> > Came across this recently but didn't understand in plain language why > > >> > it > > >> > > >> > was needed. Does anybody know? Why is a Kalman filter not do the job? > > >> > > >> > > >> > > >> You have to define what the author means by "ensemble Kalman filter". > > >> > > >> That sounds like a term that the author has just invented, or that only > > >> > > >> has meaning to a small number of practitioners or researchers. > > >> > > >> > > >> > > >> -- > > >> > > >> Tim Wescott > > >> > > >> Control system and signal processing consulting > > >> > > >> www.wescottdesign.com > > > > > > actually it is now reasonably well known in the literature as I have had > > > time to have a good look. Seems like it is used for non-linear problems > > > where an extended KF may have been used in the past. From what I can > > > see they an average of the predicted state and substitute it as the real > > > state (I think) and make a sample error covariance matrix to replace the > > > "real one", In other words it is based more on sampled data than a > > > mathematical model though it appears they need the A matrix (but not the > > > C matrix). > > > > > > https://en.wikipedia.org/wiki/Ensemble_Kalman_filter > > > > > > http://www.mathworks.com/matlabcentral/fileexchange/31093-ensemble- > > kalman-filter > > > > > > all very confusing > > > > It sounds like they may be trying to solve the same problem as the > > unscented Kalman, only using different language. Basically, the Kalman > > filter is for linear systems, the extended Kalman is for mildly nonlinear > > systems, the unscented Kalman (and possibly the ensemble Kalman) are for > > moderately nonlinear systems, and when things get really bad you need to > > throw Kalman out the window and let Bayes in the front door. > > > > Alas, I don't have the time to figure out if the unscented and ensemble > > Kalmans are mathematically equivalent, sorta the same, or completely > > different animals. > > > > You may find it educational to look at what Wikipedia says about the > > unscented Kalman, however. > > > > -- > > Tim Wescott > > Control system and signal processing consulting > > www.wescottdesign.comYes I think you are right - thanks. I found this paper which compares the two http://arxiv.org/pdf/0901.0461.pdf
