Filter Percentage Uniform Noise from a DC-signal?
The sample mean can be a choice for the estimator with the following pros and cons

Pros: 

it is unbiased

Cons:
1. The variance of the estimator increases with increase in absolute value of $x$ 


The estimator will converge to true value of $x$ only when number of observations over which the mean is taken is large.


A different approach is illustrated below, though estimation in uniform noise of this nature is not trivial and many a times the best that can be done is the sample mean over large data samples

Let $$y[n] = x + xw[n]$$ where w[n] is uniform between $[-0.5 \: 0.5]$. Let us denote the equivalent noise $z[n] = xw[n]$. The correlation between these equivalent noise samples accross time assuming that $w[n]$ are IID is $$E(z[n]z[n+1]^*) = E(xw[n]xw[n+1]^*)$$ since $x$ is deterministic and w[n] are IID hence $$E(z[n]z[n+1]^*) = 0$$ so $y[n]$ are uniform  RVs between $[0.5x \:   1.5x]$. The mean of each of this RVs is $x$. Therefore the sample mean is an unbiased estimator of $x$ $$ \hat{x} = \frac{\sum_n y[n]}{N}$$. The variance of the estimator is $$var(\hat{x}) = \frac{var(y[n] -x)}{N}$$ 
$$var(\hat{x}) = \frac{x^2}{12N}$$

However consider this $$p(y[n];x) = \frac{u(y[n] + 0.5x) - u(y[n] - 0.5x)}{x}$$

Since, the PDF above is nothing but $z[n]$ which are IID, hence combined off of $Y$ is $$p(Y;x) = \prod_{n=1}^{n=N}\,p(y[n];x)$$ the PDF will remain non zero as long as $-0.5x&lt;y[n]&lt;0.5x$, if this is the case the PDF is given by $$p(Y;x) = \frac{u(0.5x - max(y[n]))u(min(y[n] + 0.5x))}{x^N}$$

So $max(y[n])$ and $min(y[n])$ are joint sufficient statistics. The next step would be to find unbiased estimator of these statistics. For the case of IID uniform RVs this approach is illustrated in fundamentals of estimation theory by Stephen M Kay in the chapter on sufficient statistics to be $\frac{N+1}{2N +1}max(y[n])$, you can modify that a bit to this problem. It is shown to have less variance than the sample mean.

I have illustrated this method for the case where the sample mean doesn't make sense due to the cons mentioned above. In general estimation over uniform noise of this percentage nature is tricky.