Questions tagged [estimators]

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How do you "split apart" the output of a linear estimator?

Let's say I have a true signal $x$ which is corrupted by noise $n$ such that: $y = x + n$ I am attempting to use a Weiner filter to estimate the true signal $x$. This estimator is of the form: $\hat{x}...
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Why using a secondary observation increases the estimation variance?

The output of a 2-input 2-output communication channel is given by: $x^{(i)}(t) = \sum_{j=1}^{2}\sum_n {a^{(j)}_n}h_{ij}(t-nT-\tau^{(j)})$, where $x^{(i)}(t)$ is the i-th output, $\{a^{(j)}_n\}$ are ...
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How sensitive is parameter estimation to uncertainty in time?

Suppose I have the following deterministic system that is a function of time: $y = k*t + b$ Now let's say I have the ability to measure this system but there is a zero-mean noise component in the ...
Izzo's user avatar
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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 ...
Land's user avatar
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Help in understanding from book expression of variance of an estimator : PRBS vs real valued input

The question is based on Book : Fundamentals of Statistical Signal Processing by Steven Kay, Chapter 4 : Eq(4.21). The expression for the variance of the estimated coefficients when the input is PRN ...
Ria George's user avatar
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2 answers
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Bias of random variable

I have a really simple question of definition. Consider that I have an estimator $\widehat{a}$ and a variable $a$. I know that we define the bias of $\widehat{a}$ by $B(\widehat{a})=\mathbb{E}(\...
StarBucK's user avatar
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Need help in understanding minimum variance estimator and CRLB concept using an example

I am reading the book, Fundamentals of Statistical Signal processing, Estimation Theory Volume 1 by Steven M. Kay. In Chapter 2, there is a Fig 2.5 which illustrates which estimator to select based ...
SKM's user avatar
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Why Would Pre Filtering Measurement Data Affect the Least Squares Estimate?

In estimating parameters in a discrete time model I've often seen the use of filters applied to the input data, before its applied to least squares processing. I've been told that the filters are ...
docscience's user avatar
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Estimate High Frequency

I'm smoothing a signal with an little algorithme and I can control the amount of smoothing dynamically. Now it could be interesting to drive that amount with a measure depending of the frequency ...
snoob dogg's user avatar
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Phase Estimation in speech enhancement

I am reading a recent paper titled "Phase Estimation of Speech Enhancement - unimportant, important, or impossible?" by Grekmann et al. published in the 2012 the IEEE convention. The paper proposes an ...
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Conceptual question on entropy and its relation to information

Learning Informative Statistics: A Nonparametric Approach paper presents an approach to parameter estimation by entropy minimization. There are other related works "Minimum-entropy estimation in semi-...
Ria George's user avatar
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minimizing the mean squared error?

I'm reading this book "Applied Optimal Estimation" by A. Gelb. In the example 1.0-1, there are two measurements $z_{1}$ and $z_{2}$ with some noise for measuring $x$ as following $$ z_{1} = x + v_{1} ...
CroCo's user avatar
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2 answers
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Minimum Mean Square Estimator - Equivalent Expressions to Minimize

Given $ M \in \mathbb{R}^{N \times N} $ which is a Positive Definite Matrix. Let $ \hat{x} $ the MMSE of $ x $ given $ z $, namely $ \hat{x} = \mathbb{E} \left[ x \mid z \right] $. Prove the ...
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How to detect specific behavior in time series?

I was not quite sure what the right SE for this was, so I posted this also here on SciComp. Please tell me which one to remove :) Problem statement I have a few hundred unrelated time series, say $...
Rody Oldenhuis's user avatar
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1 answer
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Estimation of the amplitude of a frequency component in a signal

I'm working on a device that produces a signal with sampling rate of 100 kHz. Every 40 ms, I receive 16000 points, from which I have to extract a frequency close to 3.55 kHz. I have developed a method ...
The Quantum Physicist's user avatar
6 votes
1 answer
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Noisy Frequency Estimation using Hilbert Transform

I'm looking for a way to estimate instantenous frequency with low time-variation. The following MATLAB function (save as test_fest.m) does this using the Hilbert ...
Nordlöw's user avatar
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7 votes
2 answers
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Probability distribution of windowed cross-correlation

This question is in the context of time-delay estimation. Say I have a stationary Gaussian stochastic process $g$, and I know its autocorrelation function $R_g(\tau)$. To do time-delay estimation, I'm ...
Matt's user avatar
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2 votes
1 answer
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Finding the friction coefficient by using experimental data

I have the differential system equation with some unknown parameters (friction coefficients) Also I have experimental data. What I want is to determine the friction coefficients which best fit the ...
maximus's user avatar
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10 votes
2 answers
4k views

Estimate Taylor series coefficients from samples of a function

Say I have measurements of a function $y = y(x)$, sampled at $x_i$ with some noise, that could be approximated by a Taylor series expansion. Is there an accepted way of estimating the coefficients for ...
Matt's user avatar
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23 votes
2 answers
1k views

How should I pre-process a real valued signal in order to use Kay's estimator?

I have 100,000 samples of a signal $x[n]$ that was sampled at 20kHz. The data is vibration data from a rotating machine, and contains a significant spectral component related to the speed of the ...
Peter K.'s user avatar
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