MHB Kalman filter where does y_1 come from?

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The value \(y_1 = 0.9\) in the presentation is a hypothetical measurement derived from sensor data, reflecting noise in the system. It represents the first observation of the float level, denoted as \(y_i\) in the context of the Kalman filter. The discussion clarifies that this value is not based on empirical data but rather a conceptual example. The authors likely used this figure to illustrate the impact of noise on measurements. Understanding this context is crucial for interpreting the Kalman filter's application in the presentation.
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In this presentation, on page 7, they say due to noise \(y_1 = 0.9\). How or where did they get this value?

It isn't an article just a beamer presentation so going from page 1 - 7 is quick and easy.
 
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dwsmith said:
In this presentation, on page 7, they say due to noise \(y_1 = 0.9\). How or where did they get this value?

It isn't an article just a beamer presentation so going from page 1 - 7 is quick and easy.

It came out of the authors head, it is a hypothetical measurement that you might have gotten from the sensor. The $$y_i$$'s are the measurements (section 3 first sentence $${\bf{y}}=y$$ is the level of the float). So $$y_i$$ is the $$i$$ th observation (measurement) of the float level.

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Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...

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