# Tag Info

Accepted

### What would be the variance for complex number?

I will focus on the reason of the factor $1/2$ and leave aside the estimation things. The exact understanding should be : if a scalar Gaussian random variable (rv) is circular symmetric, its real and ...

### How to learn MUSIC algorithm?

Read the original paper: Schmidt, R. O. "Multiple Emitter Location and Signal Parameter Estimation." IEEE Transactions on Antennas and Propagation. Vol. AP-34, March, 1986, pp. 276–280 You may also ...
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### How Is the Formula for the Wiener Deconvolution Derived?

The Wiener Filter can also be derived by another (Easier) way. Let's assume the following model: $$y = h \ast x + n$$ Namely the data is a result of a linear combination (Convolution) of $x$ ...
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### Concept About Estimated Standard Deviation

Given data ${ \left\{ {x}_{i} \right\} }_{i = 1}^{N}$ the Empirical STD of the data is well defined: $$STD = \sqrt{ \frac{1}{N - 1} \sum_{i = 1}^{N} { \left( {x}_{i} - \bar{x} \right) }^{2} }$$ ...
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### 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 ...

### Estimators for improved spectral subtraction of noise

Maximum likelihood (ML) estimator Here will be derived a maximum-likelihood estimator of the power of the clean signal, but it doesn't seem to be improving things in terms of root mean square error, ...
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### Signal Estimation after detection Part 2

After signal detection, how to estimate the clean signal $s(t)$? Matched filtering is used to detect the presence of a known signal in noise. There is no estimation part when you are talking about a ...

### Kalman Filter on Sinusoidal Signal

This isn't quite what you're asking, because it neglects the amplitude, $A$, but it's a relatively straightforward example of application of an extended Kalman filter to the frequency tracking problem....
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### Kalman Filter on Sinusoidal Signal

I'm copying my answer to Estimate and Track the Amplitude, Frequency and Phase of a Sine Signal Using a Kalman Filter which solves a more general problem with example code: We can build a non linear ...
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### Kalman Filter State Covariance Matrix for Non Constant Process Noise Matrix in PyKalman

For classic Kalman Filter, where ${Q}_{k} = Q$ and ${R}_{k} = R$, namely the process noise covariance and the measurement noise covariance (I'm using Wikipedia - Kalman Filter notations) the ...
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### A Machine Learning Based Algorithm as an Alternative to the Matched Filter

The idea is to have a simple experiment to see if we can get, for a known signal, a better results than the Matched Filter for time delay estimation. Experiment Objective Generate, using ML (DL) a ...

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### Duration of unknown rectangular pulse with additive white Gaussian noise

You want a method that removes noise while preserving edges. This cannot be achieved well by linear filtering, as you noticed yourself. I know of two approaches that might work well for your problem. ...
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### Subsample Time Delay Estimation

Even though the signals are sampled you can get accuracy which is well above the accuracy offered by the samples as long as you sample using Nyquist. Actually, Using the Matched Filter you can achieve ...

### Kalman Filter for estimating position with nonconstant velocity & acceleration

So this is just the start of an answer. I'll have to keep updating it as I go. The first attempt is to say that the quantities you are interested in are the location of the center of the four LEDs, ...
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### Tracking a Sine Wave with Kalman Filter - How to Account for Offset (DC Signal)?

Well, in continuous time, a sinusoid with a bias can be seen as the output of the linear system \begin{align*} \begin{bmatrix}\dot x_1\\\dot x_2\\\dot x_3\end{bmatrix} &= \begin{bmatrix}0 & 1 ...