Probability Archives | Wireless Pi

Theory of relativity and age of planet Earth

May 19, 2024 DSP / Localization

The Easiest Tutorial on Kalman Filter

Kalman filter is one of the most important but not so well explained filter in the field of statistical signal processing. As far as its importance is concerned, it has seen a phenomenal rise since its discovery in 1960. One of the major factors behind this is its role of fusing estimates in time and space in an information-rich world. For example, position awareness is not limited to radars and self driving vehicles anymore but instead has become an integral component in proper operation of industrial control, robotics, precision agriculture, drones and augmented reality. Kalman filter plays a major role

October 20, 2024 Machine Learning

AI – An Advanced Civilization or a One-Trick Pony

Oct 19, 2024 Author’s Note This article, unlike the others on this website, is not about how some AI algorithms work. Instead, it is a personal opinion on AI and the future of our world. My hope is to generate more discussions on AI from this perspective. In such an undertaking, it is likely that I have made mistakes and failed to consider some critical aspect of the whole picture. Please feel free to comment and help me learn more. After some false starts, we are witnessing the true dawn of Artificial Intelligence (AI) today. Many people, including high profile

Monty Hall at his show Let's Make a Deal

February 13, 2024 Miscellaneous

The Reason Why the Monty Hall Problem Continues to Perplex Everyone

The Monty Hall problem is an interesting puzzle loosely based on an American TV game show Let’s Make a Deal hosted by Monty Hall. While the puzzle looked simple, it perplexed some of the brightest mathematical minds in the United States, including the great Paul Erdös who was one of the most prolific mathematicians of the 20th century. This continues to be the case today. I looked upon a number of references to find the source of confusion in the Monty Hall problem but failed. All I found was different solutions. Therefore, I built one myself with the usual from

March 18, 2024 Miscellaneous

The Coin Toss Puzzle and the Simplest Possible Solution

Recently, I wrote an article on why the Monty Hall problem has perplexed so many brilliant minds where I showed that it was a corner case between 1 open and 1 closed door, while the intuitive but wrong answer is close to the probability curve of 1 open door. Now a coin toss puzzle has appeared on Twitter [1] that has gone viral as it goes against our common intuition of probability and random sequences (such as a series of coin tosses). The puzzle goes as follows. The Problem Flip a fair coin 100 times—it gives a sequence of heads

July 29, 2024 Wireless/SDR

The Extended Kalman Filter (EKF)

I have described in detail the story of the Kalman Filter (KF) in a previous article using intuitive arguments. The Kalman filter is applicable to linear models. Today we will learn about extending the Kalman filter to non-linear scenarios through an extended Kalman filter. Numerous applications today require estimating the range, velocity, and acceleration of objects moving along a straight path. It could be an airplane within the scope of a traditional radar or an autonomous vehicle cruising down a road in an ever-connected society. And who knows, perhaps the superhumans of the next century will engage in futuristic play