Dear Sir/Madam, Why the noise used in Kalman filter is assumed to be White noise? Any particular reason? Regards, Senthil Kumar S, Assistant Professor, Hindustan University, Chennai.
Kalman Filter
Started by ●November 17, 2010
Reply by ●November 17, 20102010-11-17
On 11/17/2010 04:29 AM, Senthil_Avionics wrote:> Dear Sir/Madam, > > Why the noise used in Kalman filter is assumed to be White noise? Any > particular reason?If you go over the math behind the Kalman filter you'll see that it assumes white Gaussian noise. The math isn't valid for noise that's not white (or at least for noise that isn't much broader band than the dynamics of the variables you're trying to estimate). If the real-world noise isn't white, then you must model a noise process with white noise as its input, and estimate the dynamics of that noise process along with the dynamics of the variables that you're 'really' interested in. My favorite Kalman filtering book that's specific to the subject (not that I have many) is "Optimal State Estimation" by Simon (Wiley, 2006): http://www.powells.com/partner/30696/biblio/9780471708582. I found it very useful, but if you want a firm foundation for Kalman filtering and all of it's offspring, you can't go wrong with "Detection, Estimation and Modulation Theory, Part I" by Van Trees (Wiley, 1968): http://www.powells.com/partner/30696/biblio/9780470542965. The Simon book teaches you a bit about estimation, then spends a chapter deriving a basic Kalman filter. The Van Trees book connects a fire hose directly to your brain and fills it with more estimation theory than you can shake a neuron at, then makes _you_ derive the Kalman filter in one of the homework problems in Chapter 5. The Simon book teaches you more about Kalman filters, but any time I've ever had to invent an algorithm to solve some new detection or estimation problem, it's the stuff I learned from Van Trees that always saves my behind. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" was written for you. See details at http://www.wescottdesign.com/actfes/actfes.html
Reply by ●November 18, 20102010-11-18
On Nov 17, 5:26=A0pm, Tim Wescott <t...@seemywebsite.com> wrote:> The Simon book teaches you a bit about estimation, then spends a chapter > deriving a basic Kalman filter. =A0The Van Trees book connects a fire hos=e> directly to your brain and fills it with more estimation theory than you > can shake a neuron at, then makes _you_ derive the Kalman filter in one > of the homework problems in Chapter 5.Well, van Trees wrote for the generation of engineers that at age 21 made a spacecraft that went to the moon and back, using little more than a slide rule and spares from a vacuum cleaner. Rune
Reply by ●November 18, 20102010-11-18
On 11/17/2010 09:36 PM, Rune Allnor wrote:> On Nov 17, 5:26 pm, Tim Wescott<t...@seemywebsite.com> wrote: > >> The Simon book teaches you a bit about estimation, then spends a chapter >> deriving a basic Kalman filter. The Van Trees book connects a fire hose >> directly to your brain and fills it with more estimation theory than you >> can shake a neuron at, then makes _you_ derive the Kalman filter in one >> of the homework problems in Chapter 5. > > Well, van Trees wrote for the generation of engineers that at age 21 > made a spacecraft that went to the moon and back, using little more > than a slide rule and spares from a vacuum cleaner.It's still in print. When I took the class where I got the book, the prof told us that it would be the hardest class we'd ever take. He was right. Other's complained because they were doing six credits worth of work and were only getting three credits. I was happy because I was getting six credits worth of information, and I was only paying for three. Different strokes for different folks... I'm not dissing the Simon book -- he goes into depths that Van Trees leaves completely unplumbed, in no small part because the advanced material in Simon's book hadn't been developed yet when Van Trees wrote his book. But having taken the detection & estimation course means that reading the Simon book is almost like having x-ray vision: I see what Simon is saying, and I can see blurry images of even more math behind it. Because I kind of know the shape of the math behind, what Simon is saying makes a lot more sense a lot more quickly. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" was written for you. See details at http://www.wescottdesign.com/actfes/actfes.html
