Thanks, Bo and Ric. Yes, I'd tried searching jwiki on "Kalman" and Pieter's page was the only instance.
I neglected to mention that in the most general case I can't really be confident that X1 and X2 have the same distribution function, let alone the same variance. But looking at it again, I see that under the restrictions I've placed the problem simplifies immensely to fitting a step-function H to: X=: K+G+H. If I can just do that, I'll be happy for now. Repeated application of FFT should allow me to subtract the noise spectrum F(G), or at least see a significant change in the overall spectrum emerge after point T, and that might handle the more general cases as well. Anyway it's simple-minded enough for me, and worth a try. FFT is, after all, "fast" :-) But won't an even faster transform do the trick, such as (+/X)? On the above model, X performs a drunkard's walk around a value M1 until some point T, after which it walks around M2. Solution: simply estimate M1 and M2 on an ongoing basis. I get the feeling I ought to be searching on terms like "edge detection", "step detection" and CUSUM. Anyway, there's enough here to try. On Thu, Jun 21, 2012 at 10:28 AM, Ric Sherlock <tikk...@gmail.com> wrote: > Hi Ian, > > A quick search of the J wiki finds this: > http://www.jsoftware.com/jwiki/Stories/PietdeJong > Sounds like he might have what you're after? > > Cheers, > Ric > > On Thu, Jun 21, 2012 at 4:33 PM, Ian Clark <earthspo...@gmail.com> wrote: >> Can anyone help? Has anyone written a Kalman filter in J? >> >> I'm not a specialist in either statistics or control theory, so I'm >> only guessing a Kalman filter is what I need. Though I do have a >> passing acquaintance with the terms: stochastic control and linear >> quadratic Gaussian (LQG) control. I am aware that a "Kalman filter" >> (like ANOVA) is more a topic than a black-box. >> >> So let me explain what I want it for. >> >> I have a time series X which I am assuming can be modelled like this: >> >> X=: K + G + (X1,X2) >> >> where >> >> K is constant >> G is Gaussian noise >> X1 is a random variable with mean: M1 and variance: V1 >> X2 is a random variable with mean: M2 and variance: V2 >> >> Typically X is a sequence of sensor readings, but may also be >> measurements from a series of user trials conducted on a working >> prototype, which suffers a design-change at a given point T. >> >> Simplifying assumptions (which unfortunately I may need to relax in due >> course): >> >> (a) X is not multivariate >> (b) X1 and X2 are Gaussian >> (c) V1=V2 (only the mean value changes, not the variance). >> >> The problem: >> >> 1. Estimate T=: 1+#X1 -- the point at which X1 gives way to X2. >> >> 2. Given T, estimate (M2-M1) -- the "underlying improvement", if any, >> of the change to the prototype. >> >> 3. (subcase of 2.) Given T, test the null hypothesis: M1=M2, viz that >> there has been no underlying improvement. >> >> 4. Estimate U=: #X2 -- the minimum number of samples needed after T in >> order to achieve 1-3 above with 95% confidence. >> >> In other words, detect the signal-in-noise: M1-->M2, and do so in real-time. >> >> Because of 4, the need to estimate T and (M2-M1) on an ongoing basis, >> I can't do a randomised block design. I gather that a Kalman filter, >> or some sort of adaptive filter, will handle this problem. >> >> But maybe something simpler will turn out good enough? >> >> Supposing I can get hold of a "black box" Kalman filter, I propose to >> test it out on generated data and compare its performance to some >> simple-minded approach, like estimating M1 / M2 from a simple moving >> average of the last U samples, or applying the F-test to 2 sets of U >> samples taken either side of T. >> >> But since the technique aims to be published, or at least critically >> scrutinised (and maybe incorporated in a software product), I'd rather >> depend on a state-of-art packaged solution than reinvent the wheel: a >> large and very well-turned wheel it appears to me. >> >> Ian Clark >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
