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Questions tagged [estimation]

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

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1answer
26 views

Estimation of transfer function with noisy output signal

I have a question regarding the estimation of the transfer function of my system. The system is a lowpass-filter of second order (a damped spring mass system). White noise is added to the output of ...
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1answer
45 views

Amplitude estimation of sinusoid in known spiky spectral noise

What is the "best" way to estimate amplitude of a known-frequency sinusoid in the presence of known spiky spectral noise (i.e. noise comprising a few spectral peaks at known frequencies)? By "best", ...
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2answers
56 views

Idea for Noise Level Estimation / Automatic Thresholding in the Presence of Peaks

I have the fft of some signal, and want a rough estimate of the noise level in order to choose an appropriate threshold for our peak detection algorithm. In general, the fft contains mostly noise with ...
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0answers
8 views

Estimate the environment shape by traveled distance and angle

Consider a robot that randomly moves in a closed environment. Every time it encounters an obstacle, it performs a rotation and proceeds in the new direction. It can measure the angle (with a compass) ...
3
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1answer
70 views

How to Linearly Combine Two Unbiased Estimators of One Parameter without Knowledge of Their CoVariance?

I have two unbiased estimators of one parameter, $\tau$. The first estimator, $r_1$, is the better estimator with lower variance than the second estimator, $r_2$. I also have: $ \mathbb{E} \left[ {r}...
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0answers
28 views

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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0answers
56 views

Problem with 1st order PLL update equation

The output of a communication channel is given by: $x(t) = \sum_n{a_n}h(t-nT)$, where $\{a_n\}$ are BPSK symbols, $h(t)$ is the channel response, and $T$ is the symbol period. If there is an ...
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0answers
47 views

Pulse shape estimation

Given a captured noisy BPSK signal, how do I formulate the maximum-likelihood problem so as to estimate the matched filter? The model of interest would be baseband BPSK with AWGN: $$c(t) = \sum_{\ell=...
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1answer
30 views

Why is the concept of a “state covariance matrix” necessary in estimation?

I'm currently taking a course in optimal estimation (and it's still very early in the course). Much of our work is based around the idea of a measurement model $y=Hx + v$ This model assumes our ...
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0answers
5 views

Clutter Model in MOT: joint distribution of a random matrix and its column size variable

Suppose $C_k$ is a random matrix contains columns of measurement vectors that are random variables: $$C_k=[c_k^1,...,c_k^{m_k^c}]$$ $m^c_k$ is the number of columns as well as a random variable. All ...
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0answers
19 views

How to form the data matrix for channel estimation?

I want to estimate a channel (its length is $L_c$) with a preamble (its length is $L$) and a least square estimator. Let $p_r$ the preamble received. I have a problem to build the data matrix $X$ for ...
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0answers
23 views

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 ...
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1answer
77 views

On the signal recovery in OFDM after estimation

Given a modulated signal X which is transmitted based on OFDM with N = 256 sub-carriers through channel ...
2
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1answer
65 views

Frequency estimation of circularly shifted single tone signal

I have a discrete signal $y[n] = <e^{j ~ 2 \pi f ~ n}>_J + ~w[n]$ with $n \in [0, N[$ and $w[n]$ AWGN, $<x[n]>_K$ denotes the signal $x[n]$ circularly shifted by $K$ samples. Let's define $...
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0answers
20 views

On the use of OMP for sparse channel estimation based on pilots

Given an OFDM frame whose length is 256 sub-carriers, the length of guard interval CP is 64, and the transmitted known pilots 'in red' are 64 too as below: where the received signal is suppose to ...
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1answer
49 views

Estimation / Reconstruction of an Image from Its Missing Data 2D DFT

Given the 2D DFT of an image i.e. a NxM matrix of complex numbers, with some missing lines (or even partial lines), considering we have zeros in the missing positions. Any suggestions for an ...
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2answers
55 views

Correlation between a signal segment and its stretched replica

In my application the measurements are affected by temperature and the signal is stretched over time, though preserving relatively similar structure. I want to find incremental stretching between ...
3
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1answer
104 views

Which Noise Reduction Algorithms Are Used in Commercial RAW Image Processors?

I'm trying to guess what noise reduction algorithms are used in commercial processors for raw images from digital cameras. I find this fairly easy to do for the sharpening algorithms (most use unsharp ...
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0answers
35 views

Time length difference estimation between a waveform and its stretched and a bit distorted copy

I'm trying to solve the following problem and will appreciate your help. In the example I have two signals. The 1st is the original signal and the 2nd is a some slightly stretched version of it. The ...
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1answer
70 views

Correlation between frequency and initial phase estimates using FFT

Why is there a high negative correlation between frequency estimation errors and initial phase estimation errors when measured using FFT? I have a simple code showing this negative correlation. is ...
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0answers
26 views

Extracting 'structure' post permutation

I have particle activity as shown in the left pane of animation below. The activity is clustered and it moves slowly. Sometimes these clusters merges together. On the right side of it, its shuffled ...
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2answers
111 views

Frequency response of a microphone using a sine sweep

I want to determine the frequency response (magnitude, phase) of a microphone. I have another "good" reference microphone whose frequency response I know. I understand that I can use a good speaker ...
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1answer
130 views

Generate signals with a particular variance and SNR

Consider a system model of the form: $y_n = ax_n + v_n$ where $x_n$ is the input that is corrupted by $v_n$ which is an Additive White Gaussian Noise of zero-mean and variance 1 for $n = 1,2,...,N$ ...
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0answers
29 views

Spread Spectrum (CDMA) signal phase noise measurement

A CDMA signal is considered for this application. I would like to have an information on the generated signal oscillator's quality using a phase noise measure. If the signal was a pure carrier, it ...
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0answers
14 views

Tracking a signal

I have two signals representing steering wheel angles, one representing the driver’s inputs (red), while the other one represents the system’s reference signal (blue). I want to estimate in real time ...
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0answers
20 views

DOA estimation of moving, radiating source in the near-field with nonuniform Doppler shifting

I am trying to estimate the DOA of a radiating source using two passive sensors. In the case of a stationary source, I find the lag $k$ of the maximum in the sample cross-covariance sequence $E \...
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1answer
48 views

Does there exist a simple regression method to fit a single sinusoid period to a data set?

I'm currently working on a project where I want to fit a single sinusoid period to a data set. Essentially I have very good control/knowledge of the signal's dominant frequency, so I'm only sampling ...
3
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1answer
113 views

SRF-PLL discretization problem

So I've been working on how to digitally implement a static reference frame PLL (SRF-PLL), which is a quite popular PLL used for extracting three-phase grid angle. This PLL works by using the DQ0 ...
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0answers
25 views

How to get PSD from frequency domain representation of time-series data [duplicate]

Let's say we have a realization (time-series data) of a random process. I take fft() of that to get its frequency domain representation. Then how can I estimate the PSD of this random process by ...
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1answer
72 views

Is it possible to do better than Cramér Rao lower bound for different estimation methods

I’m new to learning about the Cramér Rao lower bound. Does the calculation of the CRLB imply that only particular estimation algorithms can be used (e.g. estimating delay and Doppler from a complex ...
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0answers
72 views

Finding time-varying coefficients for a VAR model by using the Kalman Filter

I'm posting this again, since after my last post i've been able to advance the code quite alot. I'm still trying to write some code in R to reproduce the model i found in this article. The idea is to ...
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1answer
113 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
53 views

Amplitude Estimating Using a Windowed DFT

Let's say we want to estimate the amplitude A of a mono-frequent signal using a windowed DFT. The frequency of the signal is unknown, and the frequency resolution of the DFT is limited, thus it cannot ...
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1answer
36 views

Is match filter a solution of some differential equation?

Matched filter is very common and termed as optimal filter for detection purpose. The question is : can we formulate a differential equation and show that the solution is matched filter.
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0answers
31 views

Training Fractionally Spaced Channel Estimator and Equalizer

If you are attempting least squares channel estimation with a fractionally spaced channel estimator, do you want the training sequence to also be fractionally spaced or symbol spaced? It looks like ...
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1answer
47 views

Channel estimation

In single-carrier systems, at the receiver, when we need to do channel estimation and equalization? Do we need to do before timing synchronization and CFO correction or before it? And, please let me ...
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0answers
41 views

Recovering signal statistics from non-uniform sampled signal

I'm interested in estimating the mean and standard deviation of a signal that was sampled non-uniformly. Assuming I have an estimate of the signal bandwidth, what algorithms would provide estimates of ...
1
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1answer
102 views

Equivalence of Maximum Likelihood (ML) and Discrete Fourier Transfrom (DFT) Peak Finding for Single Tone Estimation

My understanding is Maximum Likelihood and DFT Peak Finding for a single tone produce the same results assuming the ML is restricted to the same frequencies as the DFT. I was wondering if there was ...
1
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2answers
113 views

Solving a Linear Mean Square Estimation the Easy Way

I have an exercise which is quite trivial. However I got stuck and I'm not sure if this the end-result. I assume there has to be a way to get this result much quicker. Given are two randomly ...
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0answers
60 views

Transfer function estimation of a noisy system

Overall description I am trying to estimate a filtering system’s transfer function, given its input and output. This system takes $x$ as input . This signal is low pass filtered and added to a WGN by ...
3
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1answer
111 views

Ratio of expected values of squares of errors in power quantities, in dB

An amplitude quantity $a$ is estimated by two estimators $\hat a_1$ and $\hat a_2.$ The error of estimator $\hat a_2$ is compared to that of $\hat a_1$. One possible comparison is the ratio of ...
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5answers
528 views

Estimators for improved spectral subtraction of noise

Real zero-mean Gaussian white noise, independent of a clean signal $x$ and of known variance is added to $x$ producing a noisy signal $y.$ Discrete Fourier transform (DFT) $Y$ of the noisy signal is ...
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1answer
79 views

number of samples and Amplitude accuracy,what's the solution to this problem

I'm colleceting data samples from a device (temporal signal) in order to analyze it with FFT function in MATLAB R2015b,first i get N=4063 data points with (delta_t=0.000015s) so my frequency ...
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1answer
263 views

Periodogram and Welch periodogram comparison

I'm trying to compute the PSD using the periodogram method. I have a signal that is periodical at 5kHz. The frequency resolution sought for is 1.221Hz. It's a PRBS signal that has its energy drop to ...
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4answers
81 views

Spectrum estimation

When calculating the spectrum estimation of a signal $x(t)$ with random noise, why do we use ($E$ for expectation) $$E[|X(\omega)|^2]$$ but not $$E[|X(\omega)|] $$ If it is because the random ...
2
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4answers
378 views

Sequential Form of the Least Squares Estimator 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 ...
1
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0answers
82 views

Resolution of MUSIC algorithm

MUSIC algorithm has been known to provide super-resolution imaging capabilities, and it is implemented in target recognition radar system, however, I couldn't find a definite expression for its ...
1
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1answer
82 views

Sparsity Representation of a Signal Using the DCT Matrix

I have a signal $\mathbf x$, and I need to know how to obtain the matrix which is the corresponding sparsity basis $\mathbf\Psi$ such that $\mathbf x = \mathbf{\Psi\theta}$, where $\mathbf\theta$ is ...
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0answers
46 views

Advances in Blind SNR estimation beyond $M_2M_4$

In Pauluzzi and Beaulieu, various SNR estimation methods are compared. Among the blind methods considered, the $M_2M_4$ estimator seemed to be unambiguously the best. However, it has been shown that ...
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2answers
40 views

Summing over constants [closed]

I'm following some notes and I came across an example which said that for this x_n with a proposed estimator of the mean, that it is an unbiased estimator for the DC level. I'm trying to do it out ...