Questions tagged [maximum-likelihood-estimation]
Use this tag for any question regarding or utilizing the Maximum Likelihood (MLE / ML) method.
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34 views
Equivalence of ML and FFT peak finding for Single-Tone estimation
My understanding is Maximum Likelihood and FFT peak finding for a single tone produce the same results assuming the ML is restricted to the same frequencies as the FFT.
I was wondering if there was ...
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1answer
483 views
Maximum Likelihood Detection of Signal Vectors in Gaussian Noise
Consider a binary-input additive white Gaussian noise channel.
Let $\mathbf{x}_0 = (\sqrt{Es},\sqrt{E_s},⋯,\sqrt{E_s})$ and $\mathbf{x}_1 = (-\sqrt{E_s},-\sqrt{E_s},⋯,-\sqrt{E_s})$, be two codewords ...
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1answer
50 views
Why Isn't the ML Estimator (MLE) in MIMO Spatial Multiplexing Obtained by the Least Squares Solution?
In the simplest scenario of MIMO spatial multiplexing: $$\mathbf{y} = H\mathbf{s} + \mathbf{n}$$
where: $\mathbf{s}=[s_0,s_1,...s_{M-1}] \\\mathbf{y}=[y_0,y_1,...y_{N-1}]$
$\mathbf{n}=[n_0,n_1,......
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0answers
17 views
Estimating a distribution of feature of sound based on a factor
I am currently working on creating a model of sound of inside of a car based on speed. To be specific, making a Gaussian distribution of MFCC(13 dim) for each speed, i.e. car running at 30 kmph, ...
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2answers
88 views
MLE parameter estimation — confusion regarding some terms in the pdf of complex normal r.v (Part 2)
This question is based on the application of the pdf which was an earlier question of mine asked here Confusion regarding pdf of circularly symmetric complex gaussian rv
If $v \sim CN(0,2\sigma^2_v)$ ...
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votes
2answers
60 views
MLE formulation — confusion regarding the terms in the equation (Part1)
If $v \sim CN(0,2\sigma^2_v)$ is a circularly complex Gaussian random variable which acts as the measurement noise in this model
$$y_n = x_n + v_n \tag{1} $$ where $x \sim CN(0,2\sigma^2)$, then is ...
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2answers
170 views
Optimum Filter Signal Detection for Non AWGN Channels
I have been reading this question and it confirms that the matched filter is the maximum-likelihood receiver in the presence of additive white Gaussian noise. So in the AWGN channel it maximizes the ...
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1answer
297 views
Cramer Rao Lower Bound for Cross Correlation (Time Shift Estimation)
UPDATE 2
Okay, I think I understand now why the defined CRLB is not applying to my use case.
In my use case, we have very high SNR, and the the first signal $x_1$ is always the same. So the classical ...
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1answer
99 views
Unable to understand what notations to use in formulating and example of Maximum likelihood estimation
The received
noisy signal $y_n \in \mathbb{R}$ is expressed as:
\begin{align}
y_n = \mathbf{h}^\mathsf{T}\mathbf{u}_n + w_n.
\tag{1}
\end{align}
$\mathbf{h} = [h_0,h_1,\ldots,h_{p-1}]^\mathsf{T} \in \...
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2answers
57 views
Why maximum likelihood estimation method is taken as the benchmark for comparing with other methods?
In many research articles the performance of an estimation method is compared to that of the ML estimation performance. If the performance of the method does not achieve the ML estimation performance, ...
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1answer
328 views
Maximum likelihood estimator of active time delay and passive time delay
A typical time delay estimation problem has the model:
$$
\begin{align}
x_1(t) &= s(t)+ n_1(t) \\
x_2(t) &= a s(t-D) + n_2(t)
\end{align}
$$
Where $n_1$ and $n_2$ are considered to be ...
0
votes
1answer
469 views
Matlab : How to implement the likelihood expression
I need to check if the estimation algorithm has converged or not. I am using the Maximum Likelihood estimation method. For convergence check, we see if the log-likelihood has reached its maximum value ...
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2answers
273 views
Maximum Likelihood for Colored Noise
I have the following question about the maximum likelihood (ML) in presence of inter-symbol interference and colored noise.
Assume the communication system is as follows. Information source, ...
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0answers
94 views
Maximum Likelihood in Communication
I have a basic question about maximum likelihood (ML) estimator and its implementation.
I am trying to simulate a communication system affected by ISI and noise, while using ML at the receiver side ...
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1answer
537 views
Matlab: Help in understanding if the example for Maximum Likelihood Equalizer is properly functioning
I am stuck in the part where I need to apply the MLSE Equalizer with Viterbi code. The equalizer is an optimal. I am using the Communication Toolbox http://www.mathworks.com/help/comm/ref/comm....
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1answer
624 views
What do we espect Likelihood function used for?
In my understanding, I let make a example.
For example, you can see in the following picture.
Consequently, We want to find ^sigma. and We have already known the observation data(which is random ...
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votes
1answer
203 views
Maximum Likelihood Through a Noisy Channel
I have random variables $X_1, X_2, \cdots, X_m $, which can take $n$ values and is distributed iid according to $\Theta=(\theta_1, \theta_2, \cdots, \theta_n)$. That is $X_k$ can take values $\{1,2,\...
6
votes
1answer
944 views
Maximum Likelihood Estimation in Presence of Colored Noise
I am trying to test system identification in presence of measurement noise (1) A white Gaussian noise (2) Colored noise - pink, violet. When we are estimating parameters we do so in presence of iid, ...
0
votes
1answer
107 views
Maximum Likelihood Derivation
as you can see on page 314 the derivation of the ln[f etc.] equation is done via the matched filter that i have also provided below. i would like to know how this equation is used to derive the ln[f ...
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2answers
292 views
Minimum SNR Requirements for Maximum Likelihood Frequency Estimation
In certain applications, you have enough SNR available to, for example, perform an FFT and identify peak location and hence the signal frequency. If my understanding is correct, parameter estimation ...
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2answers
2k views
Differences using Maximum Likelihood or Maximum a Posteriori for Deconvolution / Deblur?
Are there any differences if you use Maximum Likelihood or Maximum a Posteriori to estimate the Point Spread Function for image deconvolution?
