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Questions tagged [parameter-estimation]

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Complex Spectral Phase Evolution (CSPE) Performance depending on signal windowing?

I am look into CSPE. "Signal Analysis Using the Complex Spectral Phase Evolution (CSPE) Method" The method is simple. It compares the original signal's FFT and shifted signal FFT in phase domain so ...
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1answer
42 views

Cramer-Rao Lower Bound

In estimation problems, we may use Cramer-Rao Lower Bound (CRLB) to evaluate the best performance. But if there is no unbiased estimator can attain CRLB, what is the meaning of CRLB? To clarify the ...
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1answer
33 views

Demonstrate the mean of the sample variance

Let's suposse I have a vector of elements $x(n) = \{x(0), x(2), \cdots ,x(N-1)\}$ from a random process X of mean $\mu_x$ and variance $\sigma_x^2$. I want to see if I can estimate the mean and ...
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4answers
250 views

Sequential Form of the Least Squares for Linear Least Squares Model

I'm currently working on a project in which I need to find the tilt of a surface. Let's assume I'm only concerned with a single dimension tilt (i.e. slope) to begin. I currently have the ability to ...
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0answers
58 views

How to calculate the Fourier Transform of a solvable chaos waveform?

Recently I am stucking in frequency estimation of a solvable chaos waveform. Its local analytic expression in time domain is $$ z(t)=s_m(u_m-s_m)e^{\beta(t-mT)}\cos(\omega_0 t+\varphi),mT\leq t<(m+...
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1answer
96 views

Sequential Non Linear Least Squares Problem

I have the the following non-linear function, $$s(x;A_k,\mu_k,\sigma_k)=\sum_{k=1}^2 A_k \exp\left(\frac{-(x-\mu_k)^2}{\sigma_k^2}\right)$$ with unknown (but deterministic) parameters $A_k,\mu_k,\...
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2answers
270 views

Least Squares Fitting to Inverse Exponential Function

I have a time series of measurements that resembles the shape of an exponential function. The samples are a bit noisy and sometimes there is a weak sine like ripple signal ontop of it. Simplified the ...
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0answers
113 views

Parseval's Theorm and Effective Bandwidth

This question says that RMS bandwidth (effective bandwidth) is defined based on the carrier frequency of a signal. This makes intuitive sense to me that the carrier frequency shouldn't determine the ...
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2answers
74 views

Is it possible to estimate variance of noise for a step answer signal?

I know there is not possible to find the true noise of a measured signal. The only way to "find" the noise is to estimate the noise. Noise has the mean 0, but the variance varies. So assume that we ...
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2answers
121 views

MMSE - How to minimize a complex error with respect to a set of real parameters

Suppose there's a complex signal $X(k)$ (where $k \in \{0, 1, 2,...,N - 1\}$) corrupted by additive complex noise. Its estimate $\hat{X}(k)$ is a linear combination of a set of real parameters $A_r$ ($...
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4answers
237 views

MMSE Estimation - Fusion of 2 Measurements

Let's say I have 2 measurements of the same phenomenon (for example current temperature) and I want to find the MMSE (minimum mean square error) estimator, i.e to minimize the MSE (mean square error). ...
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1answer
123 views

Period of a quasiperiodic digital signal

I have a signal made of a perturbed square wave, sampled so that there are at least six samples per period, for a total of 15 to 50 periods. The sampling frequency and the signal frequency are ...
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1answer
244 views

Estimate a transfer function from ARX models - Is ARIMAX better?

There is diffrent models which can be used to create a dynamical model by using least squares. Those models are following: ARX ARMAX ARIMAX OE BJ But if my goal with creating a dynamical model is to ...
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0answers
46 views

Parameter estimation of mixture of damped sinusoids

What are the most known methods (algorithms) for the parameter estimation of the superimposed (mixture) of damped (complex) sinusoids? The noiseless signal model (with $P$ sinusoids) is as follows: $...
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1answer
193 views

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

Considering an estimation problem of estimating a scalar deterministic parameter $a$ from the observations $y$ which are corrupted by randomvariable $w$. The observations are $y[n] = a + w[n]$ Least ...
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1answer
631 views

Maximum Likelihood Estimator (MLE), MMSE and LS - Are All of Them Regressor, Estimator and Predictor?

Can all three criteria ML, MMSE, and LS be called regressor, estimator, and predictor ? If not, an intuitive explanation of why they can't be would be good.
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1answer
122 views

Part 1- How to apply Least Squares estimation for sparse coefficient estimation?

The model is expressed as, $$y(n) = \sum_{i=0}^{p-1} r(i) x(n-i) + v(n) \tag{1}$$ where $\mathbf{r} = [r_1,r_2,\ldots,r_p]^T$ is the sparse channel coefficients of length $p$, $\mathbf{x} = [x_1,x_2,....
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1answer
353 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 ...
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2answers
100 views

Help in proper notations and mathematical formulation

For a given series, $S = \{-1,0,-2,1,etc\}$. The number of elements in $S$ is $N = 100$. Each $s_i$ belongs to a alphabet from a finite alphabet set $\mathcal{A} = (a_1=0, a_2=1, a_3=2, a_4=3, a_5=-1,...
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1answer
86 views

Can the Cramér-Rao Lower Bound be constant?

In many text books and research papers, I have seen that for the plot of Cramér-Rao Lower Bound vs Signal to Noise Ratio, the CRLB decreases with increasing SNR. Is it possible that the CRLB remains ...
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1answer
52 views

Spreading sequence and equalization based on a paper

I am having difficulty in understanding how the Authors in this paper, An EM based method for semi blind identification of linear systems driven by Chaotic signals have used the expressions derived ...
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1answer
82 views

Is the calculation of variance correct from an estimator — confusion regarding complex number where I am going wrong?

I have an expression for the varaince of measurement noise obtained from an estimator. The measurement noise is additive white gaussian having values in complex domain. I have squared the term $(.)^2$,...
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1answer
52 views

Notation confusion — What is the correct operator for computation of the log-likelihood expression for complex valued data?

This question is an extension of another question of mine asked earlier here Help in understanding if the maximum likelhood estimation is working properly In that question the inputs were real valued....
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1answer
49 views

Help in understanding if the maximum likelhood estimation is working properly

I am learning estimation theory and need help in understanding for educational purpose how the concept of ML works with the help of a step by step implementation. I am trying to find out the ML ...
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0answers
43 views

Parameter estimation from a measure

I'm doing an exercise where, given a data sample taken from a physical measure, I have to estimate the parameters of the measure where samples $x_i$ are described by the equation: $$ x_i = A \sin(2\pi ...
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1answer
536 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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0answers
155 views

Making Unscented Kalman Filter Robust for Nonlinear Parameter Estimation Problems

So I have built code for an Unscented Kalman filter that can take any specified state and measurement dynamics. I have tested it on various linear problems and it works well, as expected. The main ...
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1answer
196 views

Beginner level : Help in understanding from paper how the log-likelihood term has been obtained

Based on document : Practical Approaches to Principal Component Analysis in the Presence of Missing Values The document explains probabilistic approach to principal component analysis using Maximum A ...
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1answer
197 views

Relationship between information retrieval and source separation in signal processing

In machine learning, for the task of classifying input data (called an example) which are in binary representation, $\mathbf{x}\in \mathbb{R}^D$, $\mathbf{x} \in \{0,1\}^D$ into its multiple class ...
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1answer
77 views

Different results for different orders of estimating AR model using Yule-Walker equations

I'm trying to use MATLAB to estimate the AR parameters to the following filter: $$H(z) = \frac{1}{1-0.5z^{-1}+0.25z^{-2} -0.25z^{-4}}$$ As I can see, the process at the output of this filter depends ...
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1answer
117 views

Estimation of accelerating target using position measurements only

I am currently thinking about approaches to estimating the position and velocity of an accelerating target. At this time, I have tried a few approaches that work alright. I have tried two variations ...
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2answers
95 views

Power estimation

I have data from two channels, $A$ and $B$. The first contains a signal of interest, $s[n]$, plus some additive white Gaussian noise, and the second contains a scaled (real, non-negative) copy of my ...
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2answers
291 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
72 views

Parameter identification for PI controller

I have a PI temperature controller being used in experiments, which I am also trying to simulate. However, using the proportional gain and integral time as used in the experiments gives different ...
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2answers
1k views

Fast pitch recognition

I need to detect pitch (measure signal frequency) while the musicians play music, giving a warning if they are out of tune, but music happens to be a bit too fast for FFT (Fast Fourier Transform). ...
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1answer
209 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,\...