Negative Indices: Explaining the "Super Minus

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SUMMARY

The discussion centers on the notation of the "super minus" in the context of the Kalman Filter, specifically addressing its use to differentiate between "a priori" and "a posteriori" measurements. The notation is confirmed not to be a typo, as it serves a specific purpose in the mathematical representation within the paper. Participants clarify that the superscript "-" is merely a choice of notation rather than a symbol with intrinsic meaning. This understanding is crucial for interpreting the Kalman Filter correctly.

PREREQUISITES
  • Understanding of Kalman Filter concepts
  • Familiarity with statistical notation
  • Basic knowledge of a priori and a posteriori measurements
  • Ability to read and interpret academic papers in mathematics or engineering
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  • Study the Kalman Filter and its applications in control systems
  • Learn about statistical notation and its significance in mathematical contexts
  • Explore the differences between a priori and a posteriori estimates in estimation theory
  • Review academic papers on filtering techniques for practical examples
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This discussion is beneficial for students studying control systems, engineers working with estimation algorithms, and anyone interested in the mathematical foundations of the Kalman Filter.

Gepard
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Hi,

Apologies if this is in the wrong place but I've no idea what *it* does...

I should just mention that I'm currently doing my A-levels (16) and so my maths skills aren't that advanced...

The problem:
I've found a paper on the Kalman Filter on the internet (source: http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf)

Now, I'm trying to get my head around it, but am struggling with what the "'super minus'" means at the bottom of page 2.

I've asked all the teachers at school and none of them have any idea and keep telling me it's a typo and we've only dealt with indices that have a number in them.

Could someone here please explain what it means?

Cheers,

Michael
 
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Well, firstly, I don't know anything about the topic, but it is clearly not a typo! My take on it is that it just a notation: he is using the superscript - to distinguish the "a priori" measurements from the "a posteriori" measurements (with no superscript). In this sense the superscript - doesn't itself "mean" anything-- he could have used a ' or anything else to distinguish this, but just chose the -

Hope that helps, but you may have to wait for someone who is familiar with the paper to confirm (or contradict) what I have just said!
 
Thanks Cristo, that makes a lot of sense.

Cheers,

Michael
 

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