# Help: Learning Probability of Detection and False Alarm

1. Jun 7, 2006

### chingkui

I am reading a radar book about probability of detection and false alarm. The book present the basic idea of the two concepts, but did not go deep into the details of mathematical derivations, which I would like to see. Can anyone suggest some books or online resources (not necessarily has to be radar related) that I could look up the mathematical theory behind? The book I am reading now is "Introduction to Radar Systems" by Skolnik. Thank you.

2. May 16, 2008

### Bachir

I suggest Steven Key book Fundamentals of Statistical Signal Processing Volume II: detection theory.

3. Apr 5, 2011

### AnnapolisStar

I have had the same problem for many years when I worked for Northrop Grumman i.e. the radar book authors do not indicate how to compute the Pd. Skolnick and many others contain curves for isolated situations but specifically exclude the essential pd calculations for M of N detectors , and alert confirm waveforms and other situations that are important for computing the PD for actual radars. They spend a great deal of time on approximations that are usually not applicable in real cases and which are dangerous to use (as you get the wrong answer because of some obscure assumption that may not be correct). Usually the presented curves are hard to read as they have been either reproduced many times or have crazy scales that cannot be interpolated, or have terms that are undefined like false alarm number or radar peak power as opposed to average power, or the R0 number. Furthermore the authors like to impress you with terms like the Incomplete Toronto Function and Bessel Functions of order N etc, and incomplete Gamma functions.

I have developed a 50 page MathCad sheet that explains in detail how to compute the PD which includes the work of both Marcum and Swerling. I also developed a much much simplier excel spread sheet (with visual basic programs) that does the calculations for all the cases of Swerling 1,2,3,4 as well as the General Chi-Squared targets, Meyer and Meyer, Weinstock, Log Normal targets and PDI and m of N detectors. The spread sheet is very fast and surprizingly the computations are quite simple once you understand the general principles of 1) Target probability distribution functions, 2) probability distribution functions for a steady target in noise, 3) probability distribution functions for noise, 4) the probability distribution function for the sums of random numbers (convolution theorm) and the 5) the binomial theorem all of which can be obtained from the WikiPedia.
You can get a lot of information on how to perform the computations from a great book called "Radar Calculations for the TI-59 Calculator" by Skillman. Although he does the computations for an archaric device he has all the equations layed out. The only problem with the book is that the descriptions and writeups are succint and do not include all the details as his main objective was programming for the TI calculator. Matlab also has a library of functions for computing the PD but MatLab uses its own Non standard language (not C++)that is usually not worth learning. Furthermore, they are short on explanations for how to actually compute the PD as they are selling their own product and do not want to reveal how simple the computation actually is.

If you have further questions send me an email at AnnapolisStar@gmail.com