Kalman filter takes advantage of the fact that you don’t need to wait till the tennis hits the ground to know its positi

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ter in Frank Donoghue’s book The Fame Machine: Book Reviewing and 18th Century Literary Careers (1996), these conditions laid the groundwork for the development of literary criticism as a way of manufacturing fame for writers who sought to gain the attention of readers wading through a profusion of texts flying from the ever-expanding press. As the patronage system declined throughout the 18th century, the importance of a writer’s “fame,” as judged by other writers who crafted their own identity as expert readers, became central to their own ability to earn a living and crucial in the formation of “public taste” for literature. And if some writers had trouble earning a living by selling their work in an increasingly free and oversaturated market, they might do better if they could manage to set themselves up as tastemakers and critics to help readers navigate their way through an inundation of new works and new bylines.

I don’t mean to act like a dummy; I know why people react this way. All of us at some point in high school found ourselves writing a paper and wanting to get a better grade, so we started mining the thesaurus for fancier, more expensive words to substitute for the ones we had used. Often, we had no idea of what these fancier words meant, how misbegotten they were in our otherwise plain-spun paper. Our teachers sure noticed and slashed their mean red pencils through those wrongheaded words. Fear of the thesaurus thus begins. The idea that using a thesaurus is cheating can’t be shaken—but it’s ridiculous.

There is no question a thesaurus can lead you astray — it has the potential to be like shopping in a store with one of those pushy salespeople who insists you look great in everything. You have to resist that, and instead think of the thesaurus as a toolbox, full of interesting goodies. But you need to make sure you get the right one.

Do people expect that if you’re a writer you have a dictionary embedded in your brain? I mean, that would be nice, but it’s a lot nicer how much of my personal RAM is not devoted to variants of the word “agreed” — I can just look in the thesaurus and pick one. If that’s wrong, I don’t want to be right. Correct. Proper. Precise. Factual. Appropriate. Flawless. Free of error. On the button.

As you can see, the purpose of Kalman filter is to improve your predictions with periodic observations. If you have observations, great, let’s use them, if not, just continue the prediction process.

“Friday evening brings an opportunity for healing in the spiritual community as Mercury (in Sagittarius) harmonizes with Chiron (in Aries). This will be especially poignant for those wounded by religion and impacted by violence in defense of it. What have we learned as a collective about the masculine influence on religious bodies and doctrine? There may be discussions about self-identification via religion and where that can sometimes lead people astray.”

You start with your predicted state(position, velocity, acceleration) of the tennis ball and their predicted covariances (accuracy in prediction), the predicted covariance is updated during each step along with state proportional to how much random force is on the tennis ball.

It’s not going to give you a perfect observation (nothing can be perfect). But you can get a good estimate from it. Below is the mathematical representation of the observation:

H represents our camera, since from the picture taken by a camera you can only find position y at time t, it’s a horizontal unit vector. If, say, we have a radar that can actually observe the velocity as well, we can use [1, 1, 0] as observation model.

By going through this simple application of Kalman filter, I hope my readers have gained an intuitive understanding of the Kalman filter estimation improvement process. As we can see from the example, how accurate the prediction is ultimately depends on the model used to generate the prediction. Kalman filter can help improve the prediction with appropriately chosen error models for the prediction(sigma a) and the observation (sigma z). There are many improvements that can be made to the Kalman filter, we’ll talk about them in the future.

Do people expect that if you’re a writer you have a dictionary embedded in your brain? I mean, that would be nice, but it’s a lot nicer how much of my personal RAM is not devoted to variants of the word “agreed” — I can just look in the thesaurus and pick one. If that’s wrong, I don’t want to be right. Correct. Proper. Precise. Factual. Appropriate. Flawless. Free of error. On the button.

— if the variance of the position is high (the prediction is not very accurate), even if the observation is not that accurate, it’s a good idea to give a bit more weight to it since compared to the accuracy of the prediction it’s not so bad.

By going through this simple application of Kalman filter, I hope my readers have gained an intuitive understanding of the Kalman filter estimation improvement process. As we can see from the example, how accurate the prediction is ultimately depends on the model used to generate the prediction. Kalman filter can help improve the prediction with appropriately chosen error models for the prediction(sigma a) and the observation (sigma z). There are many improvements that can be made to the Kalman filter, we’ll talk about them in the future.

Have you ever pulled a stray thread on a sweater? Your effort to neaten it up sometimes leads to carefully stitched fibers coming undone. With enough pulling, the whole knit falls apart.

I have a decent vocabulary — not amazing, not dazzling, but good enough. It’s sturdy, probably better than average. When writing, I get tired of the words I use all the time and like getting goosed by the options the thesaurus suggests. I like to think I choose wisely, and I am careful not to slot in a word just because it’s obscure, and I definitely don’t use a word that I don’t thoroughly understand in all of its shaded meanings.