Tag Info

Understanding the Difference Between MAP Estimation and ML Estimation

Maximium A Posteriori (MAP) and Maximum Likelihood (ML) are both approaches for making decisions from some observation or evidence. MAP takes into account the prior probability of the considered ...
• 3,020

Estimate Sine Frequency under White Noise — simple and effective method

I assume the model to be: $$x \left[ n \right] = \sin \left[ 2 \pi \frac{f}{ {f}_{s} } n + \phi \right] + w \left[ n \right]$$ Where $w \left[ n \right]$ is white noise uncorrelated with the ...
• 19.6k

A Machine Learning Based Algorithm as an Alternative to the Matched Filter

Sure, you can learn the matched filter, as convolution with a filter is just a function applied to a signal, and e.g. Neural Networks (through the universal approximation theorem) are good function ...
• 30.7k

Understanding the Difference Between MAP Estimation and ML Estimation

You have a set of message set $m_i$, $0 \le i \le N-1$. (For example, QPSK will be $N=4$). For the transmitted message $m_i$, the corresponding symbol vector is $\textbf{x}_i$, and the received symbol ...
• 2,263
Accepted

Sequential Form of the Least Squares Estimator for Linear Least Squares Model

Slope from all samples obtained To summarize the question's problem, you want to calculate the slope based on all samples obtained thus far, and as new samples are obtained, update the slope without ...
• 13.5k

Estimate Sine Frequency under White Noise — simple and effective method

A common way to do this is to take the FFT of the input signal. Since the frequency might not be right at a FFT bin, usually a second step of interpolation is done after choosing the initial peak. A ...
• 3,032

• 19.6k
Accepted

Relationship between information retrieval and source separation in signal processing

There are, a few discrepancies that might be making a difference here. My suggestion would be to edit the question for clarity. There are quite a few assumptions that lead to non-straightforward ...
• 10.7k
Accepted

Extract Sine Phase and Amplitude - accurate and robust method

Regarding your Edit #2: It is not true that phase estimation requires that frequency be at a bin center. However if a frequency estimate requires interpolation between FFT result bins, so does any ...
• 35.3k

Estimate Sine Frequency under White Noise — simple and effective method

I wasn't going to answer this, since the question is stale. But I'm a little bit dissatisfied with Royi's answer and with the Kay algorithm as presented. The Kay method is, at first glance, simply ...

Extract Sine Phase and Amplitude - accurate and robust method

This is the problem we have in sinusoidal modeling. There are lots of issues, and your window function might be one of them. This paper by me is a little more general in that it not only are the ...
Accepted

What is meant by optimal estimator and how to determine optimality?

So Least squares estimator is as it literally - the estimator which brings the mean square error to minimum. In the case of Gaussian white noise it has a simple and analytic solution. I recommend you ...
• 471

MMSE Estimation - Fusion of 2 Measurements

*STOP! If you only want a hint and not the complete solution please see Stanley P.'s or Peter K.'s answers. * Since you do not specify if there is model for the temperature evolving over time $n$, I ...
• 4,134

Understanding the Difference Between MAP Estimation and ML Estimation

A brief, non-mathy explanation: ML assumes that all hypothesis are equally likely. MAP does not make this assumption. MAP is the optimum criterion, but under some conditions ML is optimum too. When ...
• 15.3k
Accepted

Why Is The Maximum Likelihood Estimation (MLE) Method Taken as the Benchmark for Comparing with Other Methods?

Coming up with a "good" estimator for a parameter of interest is not an easy task because it is important to define what good means. There are many ways of defining it, depending on your application. "...
• 4,134
Accepted

How to apply least-squares estimation for sparse coefficient estimation?

I am not entirely sure what Matlab's LASSO routine does so I started with Ordinary Least Squares (OLS) and worked backwards. From an OLS perspective X1 as you have it won't work. You've got a ...

Maximum Likelihood for Colored Noise

Let's have a look on the following model: $$y \left[ n \right] = \left( h \ast x \right) \left[ n \right] + \left( g \ast w \right) \left[ n \right]$$ Where $x \left[ n \right]$ is the signal of ...
• 19.6k

Is there an algorithm to compute the phase for a single frequecy?

You could also do this (in numpy notation): np.arctan( (signal*cos).sum() / (signal*sin).sum() )) where signal is your phase-shifted signal, cos and sin are the ...
• 1,736