In signal processing, estimation is a technique for approximating an unobserved signal from an observed signal containing noise.

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Beginner Level : How to perform channel estimation using Least Square estimates and CRLB for channel estimation

Paper : Cramer-Rao bounds for semi-blind, blind and training sequence based channel estimation by E De Carvalho http://www.eurecom.fr/en/publication/1782/download/cm-decael-970416.pdf also mentions ...
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Beginner level : Model representation and Is this estimator valid for Blind identification?

This is in continuation to a Question asked : http://stats.stackexchange.com/questions/154674/help-in-crlb-for-linear-model In the Answer, the estimator and the CRLB when a linear FIR model is ...
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10 views

Difficulty in understanding how to derive the CRLB and maximization

An univariate autoregressive process AR(p) process is expressed as $$y(n) = \sum_{j=1}^p a_jy(n-j) + u(n) $$ is excited by Gaussian sequence, $u$. Is there a resource / reference for a lucid ...
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12 views

MLE of minimum code distance in Bit error rate formula

In paper Performance analysis of communication system based on chaotic symbolic dynamics, Eq(12) contains an expression for the Bit error rate and the MLE of the parameter $w_{min}$ is presented in ...
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1answer
47 views

What is the estimator used in this paper for system identification?

Paper : System Identification using Symbolic Chaotic Sequence download link proposes EM-UKS estimator for system identification of a linear FIR channel when excited by non-linear input. In Fig 3 of ...
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121 views

Expectation maximization of moving average with binary source input

I am trying to do blind system identification of a univariate linear FIR model: \begin{align} z(n) &= h_1 u(n-1) + h_2 u(n-2) + u(n) \tag{1} \\ y(n) &= \mathbf{h^Tz(n)} + w(n) \tag{2} ...
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23 views

Parameter estimation from unknown noise pdf

I have a noisy time series assumed to be the output of a linear process. My problem is that I do not know the pdf so that I can estimate the parameters of the process model. I apply density ...
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43 views

Trying to understand particle filters

I have gone through some of the posts on particle filters as well as papers and lecture videos. I believe I have a good hold of systems theory etc, and a very basic understanding of probability ...
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13 views

Carrier frequency estimation - dependency on symbols rate

I am working on the problem of estimating the carrier frequency of some PSK modulation around a carrier. The PSK symbols are unknown (Non-data-aided) and I do not wish to estimate them (considered ...
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18 views

How to estimate minimum of a random variable

Let $X_i, i =1,\ldots,N$ be vectors of random varaibles. Each of them has $m$ components representing the dimension, $X_{ij}, j=1,2,\ldots,m$. Specific values $x_{ij}$ are observations or data. From, ...
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50 views

how to extract meaning from signal (distance estimation)?

I have 3 times series representing detected rssi signal power from 3 emitting devices. The devices are at 1 meter distance from the receptor, plotting the 3 time-series gives the following results : ...
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28 views

Discrete sinusoidal to state space

I'm looking to apply an optimal LQR filter to a discrete signal of the form $x[n]=A\sin[\omega_0n + \phi]+ v[n]$ The amplitude $A$ and the phase $\phi$ are unknown variables I want to estimate using ...
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1answer
43 views

I'm looking for the concept about estimated standard deviation

I am looking for the concept about estimate standard deviation. Actually I'm not sure how can I get a concept the estimate standard deviation ? If you know the concept, then would you let me know ...
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1answer
35 views

What does it mean when one model fit the data better than does a comptitor model?

I'm trying to review MLE (maximum likelihood estimation). What does it mean when one model fit the data better than does a comptitor model?
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1answer
145 views

What do we espect Likelihood function used for?

In my understanding, I let make a example. For example, you can see in the following picture. Consequently, We want to find ^sigma. and We have already known the observation data(which is random ...
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22 views

Sparse Channel Estimation in OFDM System

Compressive sensing methods are used in channel estimation when the channel is thread as sparse where there are zero points in the signal representation. I am in the beginning of the sparse signal ...
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2answers
103 views

How do can we cancel out noises while listening voice on headphones?

It's a common problem that while talking with the another person on Smart phones with the help of regular headphones,we get very annoying sounds at background . The opposite person's voice gets mixed ...
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1answer
59 views

How to estimate the noise of an image?

I want to know how to estimate the noise of an image? Also is this represent the camera's noise? Does anyone know how to estimate the noise of an image or camera? Update: Especially, I want to ...
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1answer
16 views

Frequency and amplitude estimation with missing samples

My input signal is given by $$ x[n] = A\sin(2\pi f n/F_s + \varphi)$$ The signal is uniformly sampled at a sampling rate of $F_s $[Hz]. However some of the samples are missing. Assume that there are ...
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2answers
151 views

Signal decompositon

I am not a good in writing algorithm but please follow below steps 1.There are 4 1D sinusoidal periodic signals.3 of them are given by \begin{cases} x(t)=4\sin(10\pi t) \\ y(t)=8\cos(20\pi t) \\ ...
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1answer
29 views

How does the OFDM system receiver decide the OFDM symbol length? [duplicate]

I am trying to understand how the receiver decides the length of OFDM symbol in time domain before it goes into DFT process at the receiver. The complete OFDM symbol (with Cyclic Prefix added) is ...
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34 views

Is there a principled way to distinguish between these signals?

Consider these two signals: They both describe a biological process going on in the same subject. The blue one is obtained at rest and the red one after the subject is perturbed. Is there a ...
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28 views

Estimation of Hit Time Using Kalman

I have the following model for Kalman Filter. The Dynamic Equation: $$ \begin{bmatrix} {r}_{k} \\ {v}_{k} \end{bmatrix} = \begin{bmatrix} 1 & -T \\ 0 & 1 \end{bmatrix} \begin{bmatrix} ...
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3answers
155 views

How to estimate the period of a pulse train?

I am trying to find the period of a pulse train like signal. I have reviewed the following questions but I did not find a clear-cut answer to the problem, 12892, 16502, 6260. I do not know the ...
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160 views

How to estimate for an exponential in WGN

Question: Formulating a Maximum likelihood estimator: So, the likelihood will be $p(y;\mathbf{h}) = \frac{1}{{(2 \pi \sigma_\eta^2)}^{T/2}} \exp{(-(y - y_0(t))^2)/ 2\sigma_\eta^2}$. Then, I ...
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1answer
55 views

What is an AMDF?

The wikipedia page for Average Magnitude Difference Function/Formula (AMDF) appears to be empty. What is an AMDF? What are AMDF's properties? What are AMDF's strengths and weaknesses, as compared ...
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28 views

can measurements go out of the uncertainty bounds?

In the below picture, the measurements are inside the $\pm 3 \sigma$ bounds. In my experiment, the measurements sometimes go out of the uncertainty bounds. This is a snapshot of my plot where the ...
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3answers
156 views

FFT bin interpolation for low frequency with DC offset

I have a noisy signal in I/Q format with a peak frequency that constantly changes between 0.5Hz and 4Hz. The sample rate is 64Hz. I want an output showing the current peak frequency with a maximum lag ...
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1answer
43 views

Does the OFDM MMSE Channel Estimator Require Prior Channel Knowledge?

The OFDM MMSE channel estimator seems to require a-priori knowledge of the channel to calculate the MMSE estimate. See equation 8 here: http://cache.freescale.com/files/dsp/doc/app_note/AN3059.pdf. ...
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1answer
170 views

Duration of unknown rectangular pulse with additive white Gaussian noise

Problem. There is a discrete signal $f[i]$ (example below). It is known, that $f[i]$ have a form of rectangular pulse with additive white Gaussian noise. $f[i] = s[i] + n[i]$, $s[i] = ...
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51 views

Distribution of a signal covariance matrix

A common estimation problem in signal processing assumes the following signal model \begin{equation} \mathbf{r} = \sum_{i=1}^{Q}\alpha_i\mathbf{s}\left(w_i\right)+\mathbf{n} \end{equation} where ...
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50 views

Estimate Image power spectrum of the noise

I want to implement Wiener filter. I have original image and image blured with linear motion. The one thing I am lack of(to implement it) is Noise power spectrum. I know that it is hard task. I've ...
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53 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
126 views

What is the Intuitive description of circular symmetric complex zero mean white Gaussian noise?

Suppose we have an added discrete noise signal defined as: $$y[n]=x[n]+w[n], $$ where $w$ is zero mean white Gaussian noise. Question: When we say white noise, is it sufficient to say that it is ...
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1answer
117 views

dominant eigenvectors of an unknown matrix

Do you have any idea about how we can find the principle eigenvectors of an unknown matrix ${H}$? The elements of $H$ are unknown in general. If you are familiar with channel estimation procedure in ...
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9 views

GAPES- like estimation methods

I'm searching for a-parametric methods for gap estimation. These methods don't have to relay on spectral analisis. I need these algorithms for comparison between GAPES with other algorithms. thanks.
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29 views

Conceptual queston on Z transforms and time series model (Part2)

I am learning the fundamentals of signal processing and time series models and I am having a hard time to follow due to lack of basics related to $z$ transforms and autoregressive model. I am facing ...
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Coefficient Estimation

In the classic paper "Channel Estimation in Narrowband Wireless Communications Systems" by Arslan and Bottomley, section 3.1 talks about estimating the channel coefficients. The text reads "One of the ...
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17 views

Estimating plant parameters from noisy frequecy response data

I have to estimate the parameters of a 1st order transfer function, namely, the coefficients, through experiment. I ran a few experiments and I have a bunch of input-output data vectors. The ...
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1answer
66 views

Effect of Sampling frequency on RMS estimation

I have a simple, but interesting question for you. I have to compute the RMS (root mean square or standard deviation) value of a time signal which represents in my case a velocity mesasurement over ...
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1answer
129 views

Discrete algorithm for low pass filter

I am working on a position controller for a marine vessel. I have an measurement signal containing the y-position of the vessel that consists of both low frequency (<.1 rad/s) and high frequency ...
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1answer
64 views

How to periodically estimate states of a LTI if the output is measured irregularly?

How can I periodically estimate the states of a discrete linear time-invariant system in the form $$\dot{\vec{x}}=\textbf{A}\vec{x}+\textbf{B}\vec{u}$$ $$\vec{y}=\textbf{C}\vec{x}+\textbf{D}\vec{u} ...
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100 views

How to learn MUSIC algorithm?

I was actually preparing for my semester project and decided to take up Frequecncy estimation.I ll directly come to the point that I want to know how should I learn MUSIC algorithm. How do I start it? ...
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88 views

why adding noise enhances the accuracy sometimes?

I am applying simple FFT to estimate the frequencies of the oscillations. The real values of frequencies are known to me as I made a synthesis signal for simulation.Thus, I can calculate the error ...
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29 views

Prediction error in least squares with a linear model

In the classical linear model with $$Y=X\beta +\epsilon,$$ where $Y \in \mathbb{R}^n$ is the observation, $X\in \mathbb{R}^{n\times p}$ is the known covariates, $\beta \in \mathbb{R}^p$ is the ...
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Estimate the Discrete Fourier Series of a Signal with Missing Samples

Assuming we have a discrete signal $ { \left\{ x \left[ n \right] \right\}}_{n = 1}^{N} $. Which has a Discrete Fourier Series. Now, assume I'd like to estimate its Discrete Fourier Series ...
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62 views

Hardware Transfer Function Estimation

Suppose you have the ability to inject any arbitrary waveform into a piece of analog rf hardware and collect and digitize the output for analysis. If you wanted to characterize/estimate the transfer ...
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When does l1 regularisation give a sparse solution?

I was maximising a likelihood function, which is convex. I know that the system has a K-sparse solution. I wanted to know the conditions (or some sufficient conditions) on the likelihood function ...
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The Standard Deviation of The Derivative of a Signal

Given a signal with zero mean and a standard deviation of 0.1 sampled at 5000 Hz. What would be the Standard Deviation of its 1st, 2nd and 'n' derivative? For instance, let's say we measure the ...
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1answer
138 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 ...