Maximum Likelihood Estimate of Angle Measurements
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Find the maximum likelihood estimate of the angle $theta$, given that you have two independent noisy measurements, $c$ and $s$, where $c$ is a measure of the cosine, and $s$ is a measure of the sine, of the angle $theta$. Assume each measurement has a known Gaussian standard deviation $sigma$ (same in both cases).
I know that the maximum likelihood for a Gaussian is given by:
$$mu_{text{ML}} = frac{1}{N} sum limits_{i=1}^N x_i$$
But surely you cannot simply enter $c$ and $s$ for the $x_i$. So I think that
$$ theta_{text{ML}} neq frac{1}{2}(c + s) $$
But then I don't know how to answer this question.
maximum-likelihood
asked Nov 14 at 21:35
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up vote
0
down vote
favorite
Find the maximum likelihood estimate of the angle $theta$, given that you have two independent noisy measurements, $c$ and $s$, where $c$ is a measure of the cosine, and $s$ is a measure of the sine, of the angle $theta$. Assume each measurement has a known Gaussian standard deviation $sigma$ (same in both cases).
I know that the maximum likelihood for a Gaussian is given by:
$$mu_{text{ML}} = frac{1}{N} sum limits_{i=1}^N x_i$$
But surely you cannot simply enter $c$ and $s$ for the $x_i$. So I think that
$$ theta_{text{ML}} neq frac{1}{2}(c + s) $$
But then I don't know how to answer this question.
maximum-likelihood
asked Nov 14 at 21:35
Wavy
235
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Find the maximum likelihood estimate of the angle $theta$, given that you have two independent noisy measurements, $c$ and $s$, where $c$ is a measure of the cosine, and $s$ is a measure of the sine, of the angle $theta$. Assume each measurement has a known Gaussian standard deviation $sigma$ (same in both cases).
I know that the maximum likelihood for a Gaussian is given by:
$$mu_{text{ML}} = frac{1}{N} sum limits_{i=1}^N x_i$$
But surely you cannot simply enter $c$ and $s$ for the $x_i$. So I think that
$$ theta_{text{ML}} neq frac{1}{2}(c + s) $$
But then I don't know how to answer this question.
maximum-likelihood
asked Nov 14 at 21:35
Wavy
235
Find the maximum likelihood estimate of the angle $theta$, given that you have two independent noisy measurements, $c$ and $s$, where $c$ is a measure of the cosine, and $s$ is a measure of the sine, of the angle $theta$. Assume each measurement has a known Gaussian standard deviation $sigma$ (same in both cases).
I know that the maximum likelihood for a Gaussian is given by:
$$mu_{text{ML}} = frac{1}{N} sum limits_{i=1}^N x_i$$
But surely you cannot simply enter $c$ and $s$ for the $x_i$. So I think that
$$ theta_{text{ML}} neq frac{1}{2}(c + s) $$
But then I don't know how to answer this question.
maximum-likelihood
maximum-likelihood
asked Nov 14 at 21:35
Wavy
235
asked Nov 14 at 21:35
Wavy
235
asked Nov 14 at 21:35
Wavy
235
asked Nov 14 at 21:35
Wavy
235
asked Nov 14 at 21:35
Wavy
235
235
add a comment |
add a comment |
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