Book Image

A Handbook of Mathematical Models with Python

By : Dr. Ranja Sarkar
Book Image

A Handbook of Mathematical Models with Python

By: Dr. Ranja Sarkar

Overview of this book

Mathematical modeling is the art of transforming a business problem into a well-defined mathematical formulation. Its emphasis on interpretability is particularly crucial when deploying a model to support high-stake decisions in sensitive sectors like pharmaceuticals and healthcare. Through this book, you’ll gain a firm grasp of the foundational mathematics underpinning various machine learning algorithms. Equipped with this knowledge, you can modify algorithms to suit your business problem. Starting with the basic theory and concepts of mathematical modeling, you’ll explore an array of mathematical tools that will empower you to extract insights and understand the data better, which in turn will aid in making optimal, data-driven decisions. The book allows you to explore mathematical optimization and its wide range of applications, and concludes by highlighting the synergetic value derived from blending mathematical models with machine learning. Ultimately, you’ll be able to apply everything you’ve learned to choose the most fitting methodologies for the business problems you encounter.
Table of Contents (16 chapters)
1
Part 1:Mathematical Modeling
4
Part 2:Mathematical Tools
11
Part 3:Mathematical Optimization

Kalman Filter

In a dynamic system, there is uncertain information. To capture the uncertainty, yet another mathematical tool, called the Kalman filter, comes into play. One can utilize the Kalman filter to optimally estimate the system’s next state, and it is ideal for continuously changing systems. It is especially useful for handling noisy sensor data by collating sensor data to best estimate the parameter of interest. In other words, the Kalman filter is an estimator of the system’s states in the presence of imprecise and uncertain measurements. It is mostly useful for the estimation of unobserved variables in real time.

The Kalman filter algorithm is widely used in signal processing, target tracking, navigation, and control applications. In tracking and control systems, an accurate and precise estimation of location and velocity, which are hidden (unknown) states, is a challenge. The uncertainty in the measurement of hidden states is attributed to external factors...