Well, unfortunately the real world is not that simple. If you are dropping a lead ball I suppose the equations of motion

Before we start, if you are reading this article, I am sure that we share similar interests and are/will be in similar industries. So let’s connect via Linkedin! Please do not hesitate to send a contact request! Orhan G. Yalçın — Linkedin,Kalman filter takes advantage of the fact that you don’t need to wait till the tennis hits the ground to know its position. If you have a camera with you, for example, you can take a picture of the tennis ball every 10 seconds and estimate its position from it so that you can update your prediction from the observation. (So don’t ever forget to bring your phone!),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.,Last night I was scrolling mindlessly through TikTok, as one does, and came across this attractive British man spewing truth bombs and relationship zingers. The weight of his words smacked me in the face. It was a wake-up call like I hadn’t had in years.,Where F is the equations of motion we just discussed. G and N are the random forces affecting the ball in real life (wind and alligators). N is basically a random variable of normal distribution, with mean 0 and standard deviation sigma(a).,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.,Saturday could be “dreamy” and intoxicating, but Day warns us to hold our horses and sleep on it. And Sunday? Well, Sunday brings a classic battle between Venus and Mars and Mars will win. Adjust your expectations and angst accordingly.,Saturday could be “dreamy” and intoxicating, but Day warns us to hold our horses and sleep on it. And Sunday? Well, Sunday brings a classic battle between Venus and Mars and Mars will win. Adjust your expectations and angst accordingly.,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.,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.,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.,Suppose we drop a ball 20,000 meters above ground, it will mostly follow the the equations of motion, with random forces such as wind and alligators affecting it’s trajectory:,— 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.,“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.”,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: