Motivation behind writing the book. How to download and read the book. Requirements for IPython Notebook and Python. github links.
Intuitive introduction to the g-h filter, which is a family of filters that includes the Kalman filter. Not filler - once you understand this chapter you will understand the concepts behind the Kalman filter.
Introduces the Discrete Bayes Filter. From this you will learn the probabilistic reasoning that underpins the Kalman filter in an easy to digest form.
Introduces the least squares filter in batch and recursive forms. I've not made a start on authoring this yet.
Introduces using Gaussians to represent beliefs in the Bayesian sense. Gaussians allow us to implement the algorithms used in the Discrete Bayes Filter to work in continuous domains.
Implements a Kalman filter by modifying the Discrete Bayesian Filter to use Gaussians. This is a full featured Kalman filter, albeit only useful for 1D problems.
We extend the Kalman filter developed in the previous chapter to the full, generalized filter.
We gotten about as far as we can without forming a strong mathematical foundation. This chapter is optional, especially the first time, but if you intend to write robust, numerically stable filters, or to read the literature, you will need to know this.
This still needs a lot of work.
Building on material in Chapter 6, walks you through the design of several Kalman filters. Discusses, but does not solve issues like numerical stability.
Kalman filter as covered only work for linear problems. Here I introduce the problems that nonlinear systems pose to the filter, and briefly discuss the various algorithms that we will be learning in subsequent chapters which work with nonlinear systems.
Unscented Kalman filters (UKF) are a recent development in Kalman filter theory. They allow you to filter nonlinear problems without requiring a closed form solution like the Extended Kalman filter requires.
Kalman filter as covered only work for linear problems. Extended Kalman filters (EKF) are the most common approach to linearizing non-linear problems.
Still very early going on this chapter.
Works through some examples of the design of Kalman filters for nonlinear problems. This is still very much a work in progress.
Kalman filters are recursive, and thus very suitable for real time filtering. However, they work well for post-processing data. We discuss some common approaches.
Kalman filters assume a single process model, but manuevering targets typically need to be described by several different process models. Adaptive filtering uses several techniques to allow the Kalman filter to adapt to the changing behavior of the target.
Describes the $H_\infty$ filter.
I have code that implements the filter, but no supporting text yet.
Discusses the ensemble Kalman Filter, which uses a Monte Carlo approach to deal with very large Kalman filter states in nonlinear systems.
EKF and UKF are linear approximations of nonlinear problems. Unless programmed carefully, they are not numerically stable. We discuss some common approaches to this problem.
This chapter is not started. I'm likely to rearrange where this material goes - this is just a placeholder.
Particle filters uses a Monte Carlo technique to filter.
This is not implemented, and I have not decided if I want to make it part of this book or not.
Brief introduction of Python and how it is used in this book. Description of the companion library filterpy.
Symbols and notations used in this book. Comparison with notations used in the literature.
Still just a collection of notes at this point.