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What is a covariance matrix? A covariance matrix is an essential part of the Kalman Filter output. If you have tried to learn about it by working through the expected value proof, you probably are still having a hard time understanding it. Why? Because the covariance matrix is best understood by visualizing it as an… Continue reading Covariance Matrix Explained With Pictures

What is the Extended Kalman Filter? The Extended Kalman Filter is a special Kalman Filter used when working with nonlinear systems. Since the Kalman Filter can not be applied to nonlinear systems, the Extended Kalman Filter was created to solve that problem. Specifically, it was used in the development of navigation control systems aboard Apollo… Continue reading Extended Kalman Filter Python Example

This post demonstrates how to implement a Kalman Filter in Python that estimates velocity from position measurements. If you do not understand how a Kalman Filter works, I recommend you read my Kalman Filter Explained Simply post. This example will use two Python libraries. I will use the NumPy Python library for arrays, matrices, and… Continue reading Kalman Filter Python Example – Estimate Velocity From Position

Most tutorials for the Kalman Filter are difficult to understand because they require advanced math skills to understand how the Kalman Filter is derived. If you have tried to read Rudolf E Kalman’s 1960 Kalman Filter paper, you know how confusing this concept can be. But do you need to understand how to derive the… Continue reading Kalman Filter Explained Simply