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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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Stochastic process inference from partial observations

Consider a set $U$. My signal is a piece-wise constant "function" $Sig: t \mapsto s$, i.e. the signal at time $t$ equals to some subset $s \subset U$. One can see $Sig(t)$ as a stochastic process. ...
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Finding the parameters and endpoints of a sinusoid

Suppose I have some signal $$ s(t) = n(t) + \left\{\begin{aligned} &0 &&: t < t_0\\ &A e^{i (2 \pi f t + \theta_0)} &&: t_0 \le t \le t_1\\ &0 &&: t > t_1 \...
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121 views

Unbiased estimation of square in presence of Gaussian noise

I have a single scalar observation, $y$, of a scalar parameter $x$ in presence of additive Gaussian noise. That is $y = x + n$ where $n$ is the Gaussian noise. The variance $n$ is known to be $\sigma^...
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110 views

Problem using MMSE estimation of channel frequency response

I need to model the minimum mean square error (MMSE) performance in estimating channel frequency response. I have channel's power delay profile (PDP) as a table with tap delays and powers. The ...
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74 views

When Does $ {L}_{1} $ Regularization 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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1k views

4th order cumulant of signal

I'm trying to implement some code for watermarking on audio based on a scientific paper. I'm stuck in the part of the pseudo code where they calculate the fourth order cumulant of the approximation ...
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717 views

What is the proper way to select the time-bandwidth product when doing multi-taper spectral estimation?

Frequently programs for calculating the spectrum of a signal using the multi-taper method require the user to specify the time-bandwidth product. What considerations must be made when selecting the ...
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25 views

how to robustly estimate low and up envelope of signal with trend, few level constant steps and noise

I am looking for robust estimation method of low and up envelope of the signal consisting from smooth trend component, constant steps between few fixed levels and additive noise (+ outliers of course)....
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148 views

Deterministic method to compute “Process noise covariance matrix, Q” for a Kalman filter when parameter variations of the model is known apriori

I am implementing a Kalman filter (for a linear ODE system for now). My model represents a physical device that has 6 "parameters", i.e. those values of the device do not evolve over time (within a ...
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129 views

Optimal method to calculate Fractional Fourier for Chirp signals

There are several method exist in the literature to calculate fractional Fourier transform. My interest is in chirp signals and want to find time delay estimation using fractional Fourier transform (...
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4k views

Digital low pass filter vs Kalman filter

I have experience with the design of FIR, IIR digital filters. I also know about the Kalman filter, but I am not skilled at using them. Consider the case of a low frequency signal from discrete ...
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178 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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114 views

Iterative Auto and Cross Correleation Estimates

I'm looking for literature or other information that covers iteratively estimating the auto- and cross-correlation vectors and the auto-correlation matrix. Initially, I can assume the signal is wide-...
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382 views

How to model/estimate channel in discrete time with different sampling time?

I want to estimate a channel based on LTE 3GPP EVA with given power delay profile (set of average power and delay of channel taps). ...
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112 views

Voice sample prediction scheme

I have some telephone voice audio with occasional "blips" in the audio. The blips appear to come from an IP link buried in the PSTN (this is a conceptual explanation, so don't worry about things like ...
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1k views

Equivalent number of looks (ENL) calculation

As stated in gagnon1997speckle in paragraph 2.2, under the unit-mean noise assumption one can say that: \begin{equation} ENL = \left(\frac{\bar{y}}{\sigma_{y}} \right)^2 = \frac{1}{\sigma_{n}^2} \end{...
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110 views

How to estimate an auto-regressive model?

Given a periodic impulse train and it's impulse response, how is an auto-regressive model of this system computed or estimated?
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29 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 ...
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47 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 ...
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39 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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26 views

Estimating a discrete summer with constrained input bandwidth

I have a discrete-time system which can be described as: $$ Y_m = \sum_{r=-N_g}^{R-1+N_g} c_r x[R(m-1) + r] $$ The unknowns are $c_k$ but I know that they have the following approximate behavior: $$...
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35 views

EKF smoothing for prediction at t=0 when no there is no measurement

I have a simple first-order reaction batch system for which I have some discrete measurements ($0<t_{k}\le t_{endbatchsample}$). I have an initial guess for $x_0$ and $P_0$ and from here I ...
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112 views

Parseval's Theorm and Effective Bandwidth

This question says that RMS bandwidth (effective bandwidth) is defined based on the carrier frequency of a signal. This makes intuitive sense to me that the carrier frequency shouldn't determine the ...
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81 views

Sensor fusion under unknown correlations: can covariance intersection account for delays?

Of late, there has been some interest in cooperative estimation algorithms in robotics, where the information sources are usually sensors such as cameras. When multiple robots observe surrounding ...
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125 views

Why does noise prevent a (kalman) filter from diverging?

I'm using a filter (not exactly kalman) of the following form to estimate angles by fusing gyroscope with accelerometer and gyro with magnetometer: $(1)\quad \hat{\theta}_k = \hat{\theta}^-_{g,k} + \...
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46 views

Get slopes of integer shift of an image in radians

I tried to reproduce the result from this paper, However I'm stuck at the Section III of the paper which involve integer shift. Two images which their phase correlation $\theta(k_1,k_2)$ was ...
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197 views

Kalman filer for estimating velocity

The goal is to use a Kalman filter to estimate velocity from noisy position measurements. I am attempting to implement a version of the filter used in the example on the Wiki page Kalman Example for ...
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1k views

1/f noise parameter characterization

I would like to characterize 1/f noise in some time series data. I would like to estimate the 1/f noise corner, and the standard deviation of the 1/f noise component and white noise component. The ...
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149 views

RLS Algorithm Convergence

I am looking for some help to understand the concept how RLS converges? If possible to present it graphically that would be best. It is very easy to understand the understanding of convergence in case ...
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0answers
248 views

Optimality of Kalman Filter for Process Noise dependent on magnitude of state

Consider I have a dynamical system $\dot{x} = Ax + w(t)$, $x \in \mathbb{R^2}$ where $w(t)$ is a Gaussian random variable with mean $E(w(t)) = C\|x\|^2$ where $C \in R^2$ is a constant and covariance ...
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13 views

Temporal window $\{v(t)\}$ of Welch estimator

The Welch estimate [1] of PSD (power spectral density) is determined as: $$\hat{\phi}_W(\omega)=\frac{1}{S}\sum_{j=1}^S \hat{\phi}_j(\omega)$$ where $$\hat{\phi}_j(\omega)=\frac{1}{MP}\left|\sum_{t=1}^...
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57 views

Solving an array signal processing estimation problem based on the Rayleigh quotient

The Rayleigh quotient for a covariance matrix $\mathbf{C}$ and a non-zero steering vector $\mathbf{a}$ is given by $$ R(\mathbf{C},\mathbf{a}) := \frac{\mathbf{a}^H\mathbf{C}\mathbf{a}}{\mathbf{a}^H\...
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100 views

Spectral estimation from noisy time-series data

This is the first time I'm posting a question on here so I hope I'm doing it right. I've tried searching on here for an answer but haven't found anything particularly relevant. I have some data ...
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648 views

What are variance and bias in spectral estimation (specifically periodogram spectral estimation)?

So far, I have read that all the non-parametric estimation techniques decrease the frequency resolution in order to decrease the variance in the spectral estimate What is the general "overview" ...
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152 views

Incorporating delayed data in Kalman filter

my guide has told me to get familiarized with state estimates and kalman filter ....the problem is that: 1) I am totally new to this topic and finding it really difficult to understand due to lack of ...
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242 views

Symbol timing recovery algorithms

I am trying to implement the symbol timing recovery loop and for that I have chosen two algorithm to compare my results one is feedforward and Gardner TED. One thing that is confusing me is smoothing ...
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2k views

Prony method for frequency estimation in matlab

i am interested if where can i find matlab code for Prony method for frequency estimation.there is pdf article about prony https://www.google.ge/#site=&source=hp&q=prony+method+for+...
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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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24 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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41 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 ...
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77 views

Estimation of the frequency response data using Matlab command invfreqz?

I would like to determine frequency response and then impulse response of the displacement equation (eq. 1 please see screen shot of the task below). In this example we study a response of the finite ...
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85 views

Estimating frequency when there's little isolation between signal and noise frequencies

Say I have a signal which is guaranteed to have a frequency between 110-120 Hz but is corrupted by interference signals that're very close to this frequency range. For example, let the interference ...
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80 views

What is the difference between Statistical Signal Processing and Estimation and Detection?

Looking at the syllabus of Statistical Signal Processing in different university I see a lot of correlation with that of Estimation and Detection? In some universities, these are seen the same. For ...
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52 views

Best equalizer for a perfect CSI

Assuming a MIMO system and a perfect CSI (the channel matrix is known), what can be the best equalizer? ZF or others?
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70 views

2-D parameter vector: Cramer Rao lower bound

Given a 2-D parameter vector, $\mathbf{X} = [x_1, x_2]$, let the corresponding $2\times2$ Fisher Information Matrix be $\mathbf{F}$. The Cramer-Rao Lower Bound (CRLB) is the inverse of the FIM. I ...
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46 views

Parameter estimation of mixture of damped sinusoids

What are the most known methods (algorithms) for the parameter estimation of the superimposed (mixture) of damped (complex) sinusoids? The noiseless signal model (with $P$ sinusoids) is as follows: $...
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25 views

Methods of combing two parameter estimates

If you have two different methods of calculating a continuous parameter (eg. heart rate), each with their own uncertainty, what would be some common methods of combining these parameters to create a ...
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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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34 views

Is TOA is different for extended target?

The time of arrival (TOA) or time difference of arrival (TDOA) beteen two signals are seen extensively in literature. Are these algorithm applicable for point target as well as extended target? For ...
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39 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 ...