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
41 views

Find gaussian in data

I have some time series data (blue line lower plot) with a gaussian added into it (red line upper plot). I would like to estimate where the gaussian is in the data, and the height of the gaussian (...
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1answer
20 views

Variance of expectation estimator

Given a set of $N$ iid samples, $x_k$, of random variable $X$ and the expectation estimator, $$E[X] \approx \frac{1}{N} \sum_{k=1}^N x_k,$$ how do I find the variance of this estimator (not the ...
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1answer
21 views

Matlab: xcorr: Having trouble when I try to calculate delay between two sinusoids

I have a problem when I try to use Matlab built-in function for cross-correlation 'xcorr'. Background: I created two sinusoids, one of them delayed in time. I choose center frequencies of these ...
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3answers
59 views

How to improve the Kalman filter for tracking the periodic motion of a car?

I have a quite typical Kalman filter to design. I really read a lot of articles about the design of this filter but the performances of my filter are still quite bad. Here is my situation. I have a ...
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0answers
20 views

Why filtic function does not work for a specific use?

And how can I solve this issue? I designed a filter via bilinear transformation in order to obtein a high-pass filter of Butterworth. When I want to set initial conditions with filtic function, it ...
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1answer
33 views

Justification for Squared $ {L}_{2} $ Data and Smoothness Term as an Error Bound

Often in variational methods (and not only) we have an energy that is of the form: $$E(u) = \frac{1}{2}\|f-u\|^2_2 + \frac{\alpha}{2}\|\psi(u)\|^2_2,$$ where the first term is referred to as the data ...
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1answer
38 views

What's the computational complexity of MMSE equalizer in OFDM system

As I know that in case of one tap OFDM equalizer, (ZF equalizer), we should have $N$ division complexity since we divide every subcarriers by its correspondent channel tap in frequency domain. But I ...
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29 views

Estimation of Group Delay from Noisy Frequency Response Measurements

Consider a linear, time-invariant system. Noisy measurements of the magnitude and phase associated with the frequency response of the system are available over some dense generally non-uniform grid ...
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38 views

On the channel estimation based on vector

I have a matrix $X$ of size .i.e $(8,8)$ with $M$ columns and $N$ rows. Suppose I took it's $iFFT$ column wise resulting matrix $x$ of size $(8,8)$ too, $x = F^HX_{(:,m)}, $ ...... (1), where ...
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1answer
30 views

How to calculate pitch fundamental frequency f( 0) ) in time domain?

I am new in DSP, trying to calculate fundamental frequency ( f(0) ) for each segmented frame of the audio file. The methods of F0 estimation can be divided into ...
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1answer
72 views

Source Localization with the BLUE Estimator

I'm trying to implement BLUE estimator in MATLAB for source localization and after my research I've come up with a theoretical example in Steven Kay's "Fundamentals of Statistical Signal Processing: ...
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1answer
69 views

KLT vs DCT basis restriction error

I want to implement 8x8 DCT and 8x8 KLT matrices to the 8-length vectors of 256x256 Lena image (e.g. each row of image there is 32 vectors 256/8 = 32 and for all rows 256x32 = 8192). I do the eigen ...
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2answers
115 views

Estimating Convolution Input Under the Assumption of Sparsity and Constant Non Zero Values Using Compressive Sensing Approach

I was wondering about if there is compressive sensing algorithm to estimate the sparse vector where the number of non-zeros values and amplitude of every non-zeros value are known. For example, assume ...
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0answers
9 views

Whats the Correct Approach to Estimate the PSF of a Moving Detector

In lab, I did a bunch of scans using a radiation source and a detector. My source emits a gaussian beam (whose dimensions I know), and my detector is a uniform 7mmx7mm square. These are stationary and ...
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1answer
85 views

The use of LS estimation with Vector OFDM

I work in Vector OFDM, but I had an issue in channel estimation in that scheme. For example, I try to use LS channel estimation but I can't get the performance back. However, in conventional OFDM, I ...
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1answer
54 views

Kalman Filter | Difference Between Minimizing the Mean Square Error (MMSE) & Maximizing Likelihood Value in Bayesian Estimation

I am going through data assimilation slides on Multi Sensor Data Fusion by Hugh Durrant Whyte and it mentions: The Kalman Filter, and indeed any mean-squared-error estimator, computes an estimate ...
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1answer
95 views

Zero forcing vs matched filtering vs LMMSE

In what scenarios would you choose each of Zero forcing, LMMSE and matched filtering receivers: Possible points to consider are: Receiver SINR, High Interference levels, Low interference levels, ...
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1answer
74 views

Channel estimation and interpolation by vector in OFDM

I have V-OFDM system (Vector OFDM) where every symbol is organized as in below figure: The black cirles are pilots and white circles are data. First, iFFT operation it taken per column, and then ...
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1answer
49 views

OFDM pilot allocation block type and comb type

As known, the pilot insertion in OFDM can be either bock type or comb type, I think comb type is appropriate for double-selective channel while block type is for frequency selective channel: In the ...
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2answers
43 views

OFDM time vs. frequency domain channel estimation/equalization

In OFDM, the majority of Equalizers are used in frequency domain. I mean the signal is transmitted in time domain (after performing iFFT), then to estimate the channel we should perform FFt to use ...
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3answers
137 views

Understanding the Difference Between MAP Estimation and ML Estimation

There are a number of possible criteria to use in making decisions. Can someone elaborate on the difference between ML and MAP for a sequence of BPSK symbols impaired by Gaussian noise ?
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156 views

Residual error when setting measurement matrix in compresssive sensing

I have an issue when implementing compressive sensing to recover sparse vector. Assume I have sparse vector $x$ of length, for example, $(256,1)$. $x = [x_1,x_2,.....x_{256}]$. This vector is ...
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1answer
101 views

On the Measurement Matrix Used for Compressing Sensing

Assume we have a matrix $x$ of size $(8,8)$ where each column is considered to be sparse with degree of sparsity equals to $4$. it means that every column can have $4$ zeros and $4$ non-zeros values ...
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1answer
40 views

On the Use of OMP Algorithm to Estimate Sparse Vector

As known, Orthogonal Matching Pursuit (OMP) Algorithm is to recover the sparse channel after convolution with another vector. But when I implement that in MATLAB, I don't get the sparse vector ...
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47 views

How to simulate (in matlab or c) power spectrum of random brownian noise signal?

I have a semi random noise signal, it does have some periodicity however. I can estimate the power spectrum (of the blue signal, I thought that it would be more clear, because white noise is flat, ...
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1answer
29 views

Variance of circular vector correlation

Say I have two zero-mean vectors, with a size of N and the translation between them is k. Say the image signal std is $\sigma_s$ and the noise std is given by $\sigma_n$. What is the variance of the ...
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35 views

Weiner filter vs Analytical Linear optimal estimator

I've been learning recently about estimation of stochastic processes in general, and linear estimation in particular. On one hand I've seen the following estimation of $X[n]$ from $Y[n]$ - $X_{opt} ...
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1answer
82 views

Estimate Instantaneous Frequency Using LMS Algorithm

I hope someone can help me with the following problem: I want to estimate the frequency of a sound file that is composed of a sinusoidal with varying frequency and additive white noise: $$ x \...
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0answers
17 views

How to estimate the channel in DS CDMA system

I am working with DS-CDMA system based on multi-path Rayleigh channel,My question, how can I estimate the channel from the received signal to cancel the effect of channel? for example in OFDM system ...
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1answer
37 views

Detection of “constant” signal

I have the positions of a computer mouse, sampled at a high frequency, with a good amount of noise. When the user stops moving the mouse, instead of going to zero the velocity reported by the mouse is ...
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1answer
61 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
72 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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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) ...
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1answer
94 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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29 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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58 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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63 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
41 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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6 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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21 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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26 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
92 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 ...
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1answer
74 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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1answer
58 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
93 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 ...
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1answer
199 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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37 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
88 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
27 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
285 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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