# Estimation or detection?

Started by March 24, 2013
```Hi,
I read Steven Ray's book: Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory. It gives several type estimation problems in its first chapter, such as measurement of DC voltage in WGN, amplitude/frequency/phase of sine wave, and radar echo from a distant plane etc. Most of the examples are used repetitively in thereafter chapters except radar echo.

My project problem has some similarities to radar echo. Before we calculate the echo pulse, we have to make sure it is the beginning of the echo pulse. We may use threshold and/or other criteria, then we calculate the echo. Unfortunately, there is no further example on radar echo in the book. I do not see any beneficial from this book on my project.

I notice that there is a difference between radar echo example and DC voltage measurement, sine wave parameter estimation. The radar echo signal is not stationary while the DC voltage and sine wave parameter examples are stationary. Now my question is how to model my project (similar to radar echo) with the estimation theory? It is a little like a detection problem, but I do not study that theory yet.

Could you shed more light on my problem?

Thanks,

```
```fl <rxjwg98@gmail.com> writes:

> I read Steven Ray's book: Fundamentals of Statistical Signal
> Processing, Volume I: Estimation Theory. It gives several type
> estimation problems in its first chapter, such as measurement of DC
> voltage in WGN, amplitude/frequency/phase of sine wave, and radar echo
> from a distant plane etc. Most of the examples are used repetitively
> in thereafter chapters except radar echo.

> My project problem has some similarities to radar echo. Before we
> calculate the echo pulse, we have to make sure it is the beginning of
> the echo pulse.

That's the function of detection. How do decide you have a pulse in the
first place?

Further, I have no idea what you mean by "calculate the echo pulse." If
it's your own radar, you know what the echo pulse is and typically use a
matched filter to detect it.

Volume I of Kay's excellent texts is estimation theory; Volume II is
detection theory. The example on radar given in the first chapter of
Volume I is about _estimating_ the range of a radar pulse, NOT detecting
the pulse.

> We may use threshold and/or other criteria, then we calculate the
> echo. Unfortunately, there is no further example on radar echo in the
> book. I do not see any beneficial from this book on my project.

Again, I don't know what you mean by "calculate the echo." Do you mean
that you wish to estimate the range?

> I notice that there is a difference between radar echo example and DC
> voltage measurement, sine wave parameter estimation. The radar echo
> signal is not stationary while the DC voltage and sine wave parameter
> examples are stationary.

Not true. A sine wave in noise is not stationary.

> Now my question is how to model my project (similar to radar echo)
> with the estimation theory? It is a little like a detection problem,
> but I do not study that theory yet.

In any case, here are a few other references on detection, assuming
that's what you need to do:

@BOOK{kayII,
title = "{Fundamentals of Statistical Signal Processing, Volume II: Detection Theory}",
author = "Steven~M.~Kay",
publisher = "Prentice Hall",
year = "1998"}
@book{vantrees,
title = "Detection, Estimation, and Modulation Theory, Part I",
author = "Harry L. Van Trees",
publisher = "Wiley",
year = "2001"}
@book{poor,
title = "An Introduction to Signal Detection and Estimation",
author = "H. Vincent Poor",
publisher = "Springer",
edition = "second",
year = "1998"}
@book{mcdonough,
title = "Detection of Signals in Noise",
author = "{Robert~N.~McDonough and Anthony~D.~Whalen}",
year = "1995"}
@book{hayes,
title = "{Statistical Digital Signal Processing and Modeling}",
author = "Monson~H.~Hayes",
publisher = "Wiley",
year = "1996"}

These are all excellent, but I especially like Poor's text - I like the
way he thinks and writes.
--
Randy Yates
Digital Signal Labs
http://www.digitalsignallabs.com
```