Kalman Assumption
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From: Cagdas Ozgenc on 27 Apr 2010 10:11 On Apr 27, 4:29 pm, Rune Allnor <all...(a)tele.ntnu.no> wrote: > On 27 apr, 04:54, Tim Wescott <t...(a)seemywebsite.now> wrote: > > > Indeed, the first step in applying someone's "optimal" formulation is > > deciding if their "optimal" comes within the bounds of your "good enough". > > Ehh... I would rate that as the *second* step. The first item on > my list would be find out in what sense an 'optimal' filter is > optimal: > > - Error magnitude? > - Operational robustness? > - Computational efficency? > - Ease of implementation? > - Economy? > - Balancing all the above? > > Rune Of course you may discuss many aspects regarding optimality. But within the context of estimation theory it usually means unbiased estimate with the lowest variance among all other possible estimators.
From: Rune Allnor on 27 Apr 2010 10:21 On 27 apr, 16:11, Cagdas Ozgenc <cagdas.ozg...(a)gmail.com> wrote: > On Apr 27, 4:29 pm, Rune Allnor <all...(a)tele.ntnu.no> wrote: > > > > > > > On 27 apr, 04:54, Tim Wescott <t...(a)seemywebsite.now> wrote: > > > > Indeed, the first step in applying someone's "optimal" formulation is > > > deciding if their "optimal" comes within the bounds of your "good enough". > > > Ehh... I would rate that as the *second* step. The first item on > > my list would be find out in what sense an 'optimal' filter is > > optimal: > > > - Error magnitude? > > - Operational robustness? > > - Computational efficency? > > - Ease of implementation? > > - Economy? > > - Balancing all the above? > > > Rune > > Of course you may discuss many aspects regarding optimality. But > within the context of estimation theory it usually means unbiased > estimate with the lowest variance among all other possible estimators. Sure. Buth that's not the important question. The important questions are the second and third items in my list, robustness and computational efficiency. In that order. There is no need to use a very efficient estimator if it is so sensitive to model errors that any hint of model mis-match throws it off. Rune
From: Tim Wescott on 27 Apr 2010 11:19 Cagdas Ozgenc wrote: > On Apr 27, 6:54 am, Tim Wescott <t...(a)seemywebsite.now> wrote: >> Peter K. wrote: >>> On 26 Apr, 21:52, HardySpicer <gyansor...(a)gmail.com> wrote: >>>> Don't think so. You can design an H infinity linear Kalman filter >>>> which is only a slight modification and you don't even need to know >>>> what the covariance matrices are at all. >>>> H infinity will give you the minimum of the maximum error. >>> As Tim says, the Kalman filter is the optimal linear filter for >>> minimizing the average estimation error. Reformulations using H- >>> infinity techniques do not give an optimal linear filter in this >>> sense. >>> As you say, though, H-nifty (sic) give the optimal in terms of >>> minimizing the worst case estimation error... which may or may not >>> give "better" results than the Kalman approach. >>> Depending on the application, neither "optimal" approach may give >>> exactly what the user is after... their idea of "optimal' may be >>> different from what the mathematical formulations give. >> Indeed, the first step in applying someone's "optimal" formulation is >> deciding if their "optimal" comes within the bounds of your "good enough". >> >> -- >> Tim Wescott >> Control system and signal processing consultingwww.wescottdesign.com- Hide quoted text - >> >> - Show quoted text - > > Bottom line is without Gaussian distribution assumption only the > optimality condition doesn't hold. But it is still the best linear > estimator, but not the best overall estimator. Right? Right. -- Tim Wescott Control system and signal processing consulting www.wescottdesign.com
From: Tim Wescott on 27 Apr 2010 11:20 Frnak McKenney wrote: > On Mon, 26 Apr 2010 19:54:35 -0700, Tim Wescott <tim(a)seemywebsite.now> wrote: > >> Indeed, the first step in applying someone's "optimal" formulation is >> deciding if their "optimal" comes within the bounds of your "good enough". > > Tim, > > A phrase that deserves repeating in a variety of contexts. Mind if > I steal it? > > > Frank "TaglinesRUs" McKenney Attribute it to me, and otherwise it's all yours. -- Tim Wescott Control system and signal processing consulting www.wescottdesign.com
From: Tim Wescott on 27 Apr 2010 11:25
Rune Allnor wrote: > On 27 apr, 04:54, Tim Wescott <t...(a)seemywebsite.now> wrote: > >> Indeed, the first step in applying someone's "optimal" formulation is >> deciding if their "optimal" comes within the bounds of your "good enough". > > Ehh... I would rate that as the *second* step. The first item on > my list would be find out in what sense an 'optimal' filter is > optimal: > > - Error magnitude? > - Operational robustness? > - Computational efficency? > - Ease of implementation? > - Economy? > - Balancing all the above? That doesn't sound as nifty. Besides, evaluating all of those are (IMHO) an essential part of deciding of someone's "optimal" is within my bounds of "good enough". Sometimes the best _practical_ solution is really crappy _technically_, because sometimes the variable in most urgent need of optimization is engineering time, or weight, or power consumption, or some other parameter that just doesn't find its way into the usual elegant formulations of "optimal". -- Tim Wescott Control system and signal processing consulting www.wescottdesign.com |