Argonauts:Kalman Filters
From Wasteland
Contents |
Sun 27 November 2005
Spatio-temporal coordinates
WMVL, 11.00am to 1.00pm (exactly) + 15 min for conclusions.
Attendees (in alphabetical order)
- Ramón Casero Cañas.
- Rohan Loveland.
- Olivier Noterdaeme.
- WeiWei Zhang.
Minutes
Although we were aware of the seminal paper where Kalman filters were proposed
R.E. Kalman. A New Approach to Linear Filtering and Prediction Problems. Trans. of the ASME--Journal of Basic Engineering, 82(Series D), pp. 35--45, 1960.
we decided instead to look for a tutorial. We found a web page devoted to Kalman filters, that suggests
P. Maybeck. Stochastic Models, Estimation, and Control, Volume 1, Academic Press, Inc. Chapter 1.
as a gentle introduction. In fact so gentle that we now have more questions than answers. This time 120 min was way too short. Nonetheless we got some basic understanding of the issue:
- Kalman filters model linear systems.
- System and noise are supposed to be white and Gaussian, although these constraints can be relaxed.
- For each time t_k, the filter computes the pdf of a estimate x given the previous value x(k-1), and a set of measures z_1, z_2,... That is, the filter makes a prediction on a estimate given its previous value and some model, and then refines the prediction using new measures.
But we are a bit upset for not having got a good grasp of the subject, so we are meeting again next week. Instead of Sunday it will be Wednesday, to accommodate the needs of Olivier, a man with a tight agenda.
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Wed 30 November 2005
Spatio-temporal coordinates
LR7, 11.00am to 1.00pm (exactly) + 15 min for conclusions.
Attendees (in alphabetical order)
- Ramón Casero Cañas.
- Rohan Loveland.
- Olivier Noterdaeme.
Minutes
Why does technology hate us? It took us no less than 30 min before we could start working. First find a room where we could plug a computer. Learn that not all LAN sockets are good; find one that works (hint: red starts). The license server is not on speaking terms with the Matlab application installed on the common PC. The projector is a device with an uncanny resistance to project. The photocopier converted a heap of fine double-sided paper into 2 heaps of single-sided sheets, one with increasing odd page numbers, the other with decreasing even page numbers. Misery, misery.
But in the end we managed to read
G. Welch and G. Bishop. An Introduction to the Kalman Filter. University of North Carolina at Chapel Hill, Department of Computer Science. TR 95-041.
and we found it really interesting. What we saw the other day was a simple case of the Kalman filter. An image is worth a million words:
The filter has a prediction stage, that given the output x at time (k-1) can estimate the output at time k. Then it takes a measure related to x, and corrects the estimate. A key characteristic of the Kalman filter is that it also estimates how reliable is the prediction vs. the measure, and weights both inputs accordingly with K_k.
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Sun 22 January 2006
Spatio-temporal coordinates
Canceled.
Minutes
There's a time for everything. A time for the block diagram and a time for the Caipirinha. Last night was cocktail night at Oriel's MCR and the crew voted enthusiastically to drop the meeting and raise the glass. It must be sadly noted, though, that an Argonaut (I'm not pointing my finger at anyone here) dishonoured centuries worth of pirate tradition drinking cider. Yuk.
Mike Kadour has made some suggestions so the updated list of candidate topics is:
- Level sets (2 theory + 1 implementation).
- Splines.
- Wavelets.
- Support vector machines.
- Unsupervised clustering (self organizing maps).
- Atlases.
- Timor Kadir's thesis. Mutual information. Entropy. Information theory.
- PCA, LDA, ICA (blind source separation).
- Eq. (25) of Besl and McKay (1992).
- MAP.
- Viterbi algorithms.
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Sun 29 January 2006
Spatio-temporal coordinates
WMVL, 11.00am to 1.00pm + 15 min for conclusions.
Attendees (in alphabetical order)
- Ramón Casero Cañas.
- Niranjan Joshi.
- Mike Kadour.
- Rohan Loveland.
- Olivier Noterdaeme.
- Ingmar Posner.
Minutes
"Is sex dirty? Only if it's done right", Woody Allen dixit. And so with Science, it's not until you get your hands dirty that you truly understand something. And what you understand is that you should have taken something pleasing like English, Enviromental Science or Photography for your first degree.
But now it's too late for us (Young ones: Run, you fools!). Thus we had an implementation meeting. The goal? To make a simple example of the Kalman filter work. The tools? Our youth and beauty. The limit? The stars. The result? Ahem, we are almost getting there.
There's an impending change, and not one to be taken lightly, for it shakes the very foundations of the Argonauts till now: For the first time, we have homework. We have to read the chapter Kalman Filtering -Theory, Motivation and Application from Paul Newman's Lecture Notes on Mobile Robots and Estimation Resources. If needed we will use his Matlab sample code to guide us with our own Matlab implementation.
Finally, we welcome the first member from Engineering who is not in the WMVL, Ingmar, even though he didn't bring cookies (he's so selfish).
Sun 5 February 2006
Spatio-temporal coordinates
WMVL, 10.30am to 12.30pm + 15 min for conclusions.
Attendees (in alphabetical order)
- Ramón Casero Cañas.
- Douglas.
- Niranjan Joshi.
- Mike Kadour.
- Rohan Loveland.
- Ingmar Posner.
Minutes
There is something true about team work: It's a myth. Otherwise somebody would have come across it at least once. It's a bit like god: You cannot prove that it doesn't exist, but there is no evidence that such a thing has ever existed either. But I digress. We the Beagle Boys of registration and tracking had yet another (and the last) Kalman Filter meeting.
First we welcomed Douglas, who is friends with Mike, or at least he was until Mike made him spend Sunday morning in an Argonauts meeting.
Then we modified the notation in our diagram to match Paul Newman's and added more information. The control input can be e.g. the steering wheel angle; the prediction noise is called v instead of w, and viceversa with the measure noise; the gain factor is called W instead of K; A is called F and it is the plant model.
Then we made sure that everybody was reading on the same page. Ready, set, go... and then everything went terribly wrong.
Instead of setting clear objectives and try to get there together, we got obfuscated. Someone went autist and worked on the implementation alone. Some decided to write an essay on Meaning and history of the control input. Some took out crayons and pencils to paint a house, a happy family and butterflies on a sunny field. One started to play saxophone. Love poems were written. Others learnt to play piano. All but team work.
Some of us went to The Nosebag for lunch.
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