Question about Rice distribution

[pamparana]

Hello everyone,

I have a couple of questions about the Rice distribution and deriving the moments for the aforementioned distribution as well.

The PDF for the Rice distribution is given by wikipedia here:

So, for the left hand side, I am assuming that 'x' is the observed value and 'v' is the true value and the noise is described by the 'sigma' term.

Now, I am reading a paper that is related to estimation of noise (which is assumed to have a rice distribution) and it has the following comment:

"The problem is that the expected value of x is not v, and yet the bias depends on v, so common filtering approach based on averaging samples of x are not adequate".

This statement has me confused. OK, so it is reasonable that the true value is not the expected value but does anyone know what the author might mean with "and yet the bias depends on v".

I would be really grateful of someone can shed some light on this.

Cheers,
Luc

 

[mmwave]

y

Hello Lucy,

Thank you for your questions about the Rice distribution and moments. I am happy to help clarify your understanding.

First, let's define some terms: 'x' is the observed value, 'v' is the true value, and 'sigma' is the standard deviation of the noise. The Rice distribution is commonly used to model the noise in a system, where the true value 'v' is obscured by the noise, represented by the 'sigma' term.

Now, let's address the statement from the paper you are reading. The author is pointing out that although the expected value of 'x' is not equal to 'v', the bias in the estimation process is dependent on 'v'. This means that the accuracy of estimating the true value 'v' is affected by the value of 'v' itself. In other words, the bias in the estimation process is not constant and can vary depending on the true value 'v'.

To illustrate this further, imagine you are trying to estimate the weight of an object using a scale. The expected value of the scale readings may not be equal to the true weight of the object, but the bias in the estimation process may be dependent on the true weight itself. If the object is very light, the scale may underestimate its weight, while if the object is very heavy, the scale may overestimate its weight.

I hope this helps clarify the statement and provides a better understanding of the Rice distribution and its implications in estimation processes. Let me know if you have any further questions.