Kalman Filter Celebrates 60 Years — An Intro.
The Kalman filter is one of the most influential ideas used in Engineering, Economics, and Computer Science for real-time applications. This year we mention 60 years for the novel publication. This post is the first one in the series of “Kalman filter celebrates 60”.
I first came across the Kalman filter during my undergraduate studies when I took the navigation systems class. It was the last lecture, and the professor said it is out of the course syllabus, but if someone will deal with real-time applications, he is expected to meet it again. He was right, and I kept studying for a master’s degree in the field of Guidance, Control, and Navigation (GCN) at the Aerospace Engineering Faculty of the Technion. I came across the Kalman filter again, where I used it to filter noisy measurements from various sensors during real-time navigation problems. Later on, I used different Kalman filter extensions while exploring solutions for real-life problems, such as Extended Kalman Filter, Iterated EKF, etc. Today, I am pursuing my Ph.D. degree at the University of Haifa, and I use the Kalman filter aside from machine learning to solve challenging navigation problems.
I found the Kalman filter as one of the most interesting ideas and a viable solution to real-time engineering problems. I was fascinated by its relevance to the machine learning era, even 60 years after Rudolf Emil Kalman first published his paper, “A New Approach to Linear Filtering and Prediction Problems.” Actually, this paper was rejected many times before the final publication at ASME–Journal of Basic Engineering in 1960. The paper is available online (link) with over 34,000 citations.
Rudolf Emil Kalman was one of the great inventors of the last century who developed the Kalman filter algorithm. He graduated from MIT with B.Sc. and M.Sc. and completed his doctorate at Columbia University. For most of his career, he was part of the University of Florida. He was awarded The National Medal of Science from the US president Barak Obama, The Charles Stark Draper Prize, The Heritage Award, and many more awards for the Kalman filter algorithm. He died in July 2016 at the age of 86.
This unique algorithm is actually an efficient recursive filter that estimates the internal state of a dynamic system from a (time) series of noisy measurements. In control theory, it is also known as a Linear Quadratic Estimator (LQE) and is widely used. The algorithm contains two-steps: the prediction step, where a prediction of the current state, along with their uncertainties, is made, and the update step, where the next measurement is observed and noted using a weighted average. The algorithm is deemed to be optimal in the minimum mean square error sense, under several assumptions. Many extensions were developed during the last 60 years, trying to deal with nonlinear models, continuous/ discrete issues, challenging noisy measurements, and more.
We use the Kalman filter every day; almost all modern control systems use it, where the most famous use was in the Apollo 11 lunar module for the moon mission in July 1969.
The Kalman filter is used in data fusion schemes, automotive applications, navigation, image processing, finance, control, and estimation. As such, many modifications were suggested during the past 60 years.
The main breakthroughs during the past 60 years contain the extension to the continuous domain (was presented by the Kalman-Bucy filter), a continuous-discrete version, where the physical system is represented by the continuous-time model and the measurements are discrete-time (Hybrid Kalman filter), the Extended Kalman filter (EKF) for nonlinearity problems, Unscented Kalman Filter for dealing with bias issues, Iterated EKF, Invariant EKF, Particle filter, Ensemble Kalman filter and many more.
In the next post of this series, I’ll explore these breakthroughs with their current relevance to the machine learning edge. Meanwhile, I’d like to recommend a great website with various tutorials of the Kalman filter for beginners: https://www.kalmanfilter.net/default.aspx, created by Alex Becker.
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About the Author
Dr. Barak Or is a well-versed professional in the field of artificial intelligence and data fusion. He is a researcher, lecturer, and entrepreneur who has published numerous patents and articles in professional journals. Dr. Or is also the founder of ALMA Tech. LTD, an AI and advanced navigation company. He has worked with Qualcomm as DSP and machine learning algorithms expert. He completed his Ph.D. in machine learning for sensor fusion at the University of Haifa, Israel. He holds M.Sc. (2018) and B.Sc. (2016) degrees in Aerospace Engineering and B.A. in Economics and Management (2016, Cum Laude) from the Technion, Israel Institute of Technology. He has received several prizes and research grants from the Israel Innovation Authority, the Israeli Ministry of Defence, and the Israeli Ministry of Economic and Industrial. In 2021, he was nominated by the Technion for “graduate achievements” in the field of High-tech.
Website www.barakor.com Linkedin www.linkedin.com/in/barakor/ YouTube www.youtube.com/channel/UCYDidZ8GUzUy_tYtxvVjRiQ
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References
[1] Kalman, Rudolph Emil. “A new approach to linear filtering and prediction problems.” (1960): 35–45. ASME
