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Questions tagged [estimators]

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Comparison Between Mahoney Filter and Kalman Filter in Euler Angles (Yaw, Pitch, Roll) Estimation

What are the advantages of Mahoney Filter over Kalman Filter for Euler Angle (Yaw, Pitch, Roll) estimation? Could anyone compare them for Angular State Estimation? Resources Mahoney Filter ...
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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
198 views

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 ...
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2answers
326 views

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}(\...
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2answers
152 views

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 ...
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0answers
17 views

Why would prefiltering 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 ...
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1answer
37 views

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 ...
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1answer
129 views

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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1answer
110 views

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-...
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1answer
584 views

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} ...
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2answers
133 views

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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1answer
261 views

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 $...
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1answer
336 views

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 ...
6
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1answer
1k views

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 ...
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2answers
701 views

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 ...
2
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1answer
221 views

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 ...
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2answers
2k 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 ...
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3answers
856 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 ...