Books on Kalman Filter

Here is small note about the Kalman and Particle filters. The list and comment reflect only my humble point of view: I'm an engineer who does not particularly like terse theoretical-orientated volumes.

Optimal State Estimate by Dan Simon
A very comprehensive book and, which is more important, it uses a bottom-up approach that enables readers to master the material rather quickly. Dan Simon's book is the best and the most suitable for self-study. Explanations are concise and straightforward. This book relates control theory elegantly. The author uses well laid out algorithmic approaches, suitable for programming, and examples to explain the details and show the complexities in action.
You will find all estimation topics in one book: Kalman filter, Unscented Kalman (UKF), Extended Kalman (EKF) and a very good explanation of Particle filtering (PF).

Moreover, the author has a website with a lot of MATLAB code for the examples used in book. This is a great help in terms of understanding of the subject, as most of examples are very insightful.


Introduction to Random Signals and Applied Kalman Filtering by Brown and Hwang
The book is easy to read and easy to follow: it starts from the very detailed explanation of the background needed for the Kalman filter. Obviously, the authors had an extensive teaching experience. The explanation of the Discrete Kalman Filter is one of the best I ever found. The extended KF and some implementation issues (UDU filter, sequential estimation) are not covered as well as other topics.

One should admit, however, that starting from the Chapter 6, the authors evidently exhausted and the text started to be more and more terse. The chapter about Kalman smoothing I could hardly translate to human language - better to use Dan Simon book.



Advanced Kalman Filtering, Least Squares and Modelling: A practical Handbook by Bruce Gibbs
The book is very terse in terms of explanations, and one should read it only as a reference, with a good background in Kalman filtering. Advanced topics, such as Particle Filter and Unscented Kalman, are covered in a very short manner and not very insightful. This is a handbook after all and not the book for the self-study. However, the book provides a lot of in-depth information and insight into various areas not found elsewhere.
This will be most useful for somebody with a strong mathematical background, particularly in linear algebra, who is looking for a comprehensive understanding and the best solution for a particular application.
Overall: a good reference, but not very helpful in terms of explanation.

Notes on the structure of the scientific article

Here are some notes about the structure of the scientific papers and some helpfull tips. Basically, any scientific paper can be divided on:

• abstract
• introduction
• methods (mathematical formulation)
• results
• discussion
  
• conclusion
• acknowledgements
  

Title
The title should be short and unambiguous, yet be an adequate description of the work. A general rule-of-thumb is that the title should contain the key words describing the work presented. Remember that the title becomes the basis for most on-line computer searches - if your title is insufficient, few people will find or read your paper.


Abstract
Once you have the completed abstract, check to make sure that the information in the abstract completely agrees with what is written in the paper. Confirm that all the information appearing the abstract actually appears in the body of the paper.

A well-prepared abstract enables the reader to identify the basic content of a document quickly and accurately. The abstract concisely states the principal objectives and scope of the investigation where these are not obvious from the title. The abstract must be concise; most journals specify a length, typically not exceeding 250 words. If you can convey the essential details of the paper in 100 words, do not use 200.


Introduction
The introduction defines the subject and must: outline the scientific objectives for the research performed and give the reader sufficient background to understand the rest of the report.

A good introduction will answer several questions:

1. Why was this study performed? Answers to this question may be derived from observations of nature or from the literature.

2. What knowledge already exists about this subject? That is review of the literature, showing the historical development of an idea and including the confirmations, conflicts, and gaps in existing knowledge.

3. What is the specific purpose of the study? The specific hypotheses and experimental design pertinent to investigating the topic should be described.

4. What is the Novelty of this paper? An important function of the introduction is to establish the significance of your current work: Why was there a need to conduct the study? Having introduced the pertinent literature and demonstrated the need for the current study, you should state clearly the scope and objectives.

Fundamental questions to answer here include:

• Do your results provide answers to your testable hypotheses? If so, how do you interpret your findings?
• Do your findings agree with what others have shown? If not, do they suggest an alternative explanation or perhaps a unforseen design flaw in your experiment (or theirs?)
• Given your conclusions, what is our new understanding of the problem you investigated and outlined in the Introduction?
• If warranted, what would be the next step in your study, e.g., what experiments would you do next?

Methods
Materials and methods used in the experiments should be reported. What equipment was used, what is the mathematics that describes the process?
However, it is still necessary to describe special pieces of equipment and the general theory of the assays used. This can usually be done in a short paragraph, possibly along with a drawing of the experimental apparatus.


Results

1. All scientific names (genus and species) must be italicized. (Underlining indicates italics in a typed paper.)
2. Use the metric system of measurements. Abbreviations of units are used without a following period.
3. Be aware that the word data is plural while datum is singular. This affects the choice of a correct verb. The word species is used both as a singular and as a plural.
4. Numbers should be written as numerals when they are greater than ten or when they are associated with measurements; for example, 6 mm or 2 g but two explanations of six factors. When one list includes numbers over and under ten, all numbers in the list may be expressed as numerals; for example, 17 sunfish, 13 bass, and 2 trout. Never start a sentence with numerals. Spell all numbers beginning sentences.
5. Be sure to divide paragraphs correctly and to use starting and ending sentences that indicate the purpose of the paragraph. A report or a section of a report should not be one long paragraph.
6. Every sentence must have a subject and a verb.
7. Avoid using the first person, I or we, in writing. Keep your writing impersonal, in the third person. Instead of saying, "We weighed the frogs and put them in a glass jar," write, "The frogs were weighed and put in a glass jar."
8. Avoid the use of slang and the overuse of contractions.
9. Be consistent in the use of tense throughout a paragraph--do not switch between past and present. It is best to use past tense.
10. Be sure that pronouns refer to antecedents. For example, in the statement, "Sometimes cecropia caterpillars are in cherry trees but they are hard to find," does "they" refer to caterpillars or trees?

After writing a report, read it over, watching especially for lack of precision and for ambiguity. Each sentence should present a clear message.



Conclusion
Introductions and conclusions can be the most difficult parts of papers to write. While the body is often easier to write, it needs a frame around it. An introduction and conclusion frame your thoughts and bridge your ideas for the reader.

Your conclusion should make your readers glad they read your paper. Your conclusion gives your reader something to take away that will help them see things differently or appreciate your topic in personally relevant ways. It can suggest broader implications that will not only interest your reader, but also enrich your reader's life in some way.

Generally, three questions in the conclusion should be addressed:

1. What the problem was addressed?
2. What are results?
3. So what?

Play the "So What" Game. If you're stuck and feel like your conclusion isn't saying anything new or interesting, ask a friend to read it with you. Whenever you make a statement from your conclusion, ask the friend to say, "So what?" or "Why should anybody care?" Then ponder that question and answer it. Here's how it might go:

You: Basically, I'm just saying that education was important to Douglass.

Friend: So what?

You: Well, it was important because it was a key to him feeling like a free and equal citizen.

Friend: Why should anybody care?

You: That's important because plantation owners tried to keep slaves from being educated so that they could maintain control. When Douglass obtained an education, he undermined that control personally.

You can also use this strategy on your own, asking yourself "So What?" as you develop your ideas or your draft.

Synthesize, don't summarize. Include a brief summary of the paper's main points, but don't simply repeat things that were in your paper. Instead, show your reader how the points you made and the support and examples you used fit together.

Propose a course of action, a solution to an issue, or questions for further study. This can redirect your reader's thought process and help her to apply your info and ideas to her own life or to see the broader implications.

Looking to the future: Looking to the future can emphasize the importance of your paper or redirect the readers' thought process. It may help them apply the new information to their lives or see things more globally.

Books about Adaptive Optics

Here is a small list of books on Adaptive optics. There are not many of them since the subject is quite specific and requires wide and diverce background.

Adaptive Optics for Astronomical Telescopes (Oxford Series in Optical \& Imaging Sciences) by John Hardy
Hardy was a pioneer in adaptive optics and in the 1970s he built the first system capable of compensating the turbulence of a large astronomical telescope at visible wavelengths.

The book is very comprehensive, with an excellent bibliography and outstanding illustrations. The text is informative and consistent, with strong points in atmosphere turbulence and deformable mirrors. As a minor issues I must mention that the control part of adaptive optics is covered less deeply, but enough for the first-time reader. Despite of its age, the book gives all necessary background to enter to adaptive optics field.

The book by Hardy is by far The Best book in adaptive optics.

John W. Hardy, Adaptive optics for astronomical telescopes, Oxford University Press, USA, 1998.


Numerical Simulation of Optical Wave Propagation With Examples in MATLAB, by Jason Schmidt
The book presents the latest advances in numerical simulations of optical wave propagations in turbulent media. The book is clearly written and abundant of excellent examples in MATLAB giving to the reader a lot of step-by-step introductions as well as understanding of the waves propagation. The writing style is very engaging.

However, the Chapter 9 is slightly denser than others (I think it could be split on two different chapters). The operators notations used in Chapter 6 sometimes are more difficult to follow than conventional expressions. But those are minor issues that do not affect the material of the book.

Overall, the material of the book and the MATLAB code present a solid basis for the numerical simulations. Carefully selected bibliography of the book allows to use it as an excellent reference.


Jason D. Schmidt, Numerical Simulation of Optical Wave Propagation, With Examples in Matlab, Society of Photo-Optical Instrumentation Engineers, 2010.



Adaptive Optics in Astronomy by Francois Roddier
This is a very good example of how one should NOT write a book. This is not even a book but just a draft of several conference proceedings meshed together. There is no transition between chapters, the writing skills of different authors are very different and it is quite annoying.

For instance, in chapter about numerical simulations you will find NOTHING about how to really simulate the AO systems: no sinlge formula or plot. Chapter about ``theoretical'' background is written in a manner that there actually is a solid theory behind it - and most formulas are starting with numercial coefficient, which is improssible to get theoretically.

The second part of book is just a outdate garbage: stories of how the author built telescopes, with unnecessary detailed information that is useless now.

Don't waste your time on it.


Adaptive optics handbook by R.Tyson
The following books is by R. Tyson. Personally, I think that reading books from Tyson is mostly waste of time. He is like bakery that produces books as they are cakes. Very few useful information. More pity is that Tyson is a non-stop-backery than stamps and stamps books, one worse than other.