Questions tagged [estimation]

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

69 questions with no upvoted or accepted answers
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164 views

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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0answers
88 views

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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1answer
144 views

How to prevent Octave Jumping in ACF of Speech Signal?

I'm working with speech signals and my aim is to estimate the fundamental frequency $\ F_0$ of this signal often called as "pitch". The main idea is taking small blocks of the speech signal such ...
3
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126 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^...
3
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0answers
116 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 ...
3
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0answers
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 ...
3
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0answers
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 ...
3
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0answers
743 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 ...
3
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2answers
619 views

DOA estimation 2 sources time delay estimation uniform array

I am new to signal processing, so sorry if the question is superbanal. I have been spending more days than I would admit on this and can't find the error. I have two triangle waves that are emitted ...
2
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0answers
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)....
2
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0answers
161 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 ...
2
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0answers
135 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 (...
2
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0answers
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 ...
2
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0answers
183 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 $\...
2
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0answers
123 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-...
2
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0answers
385 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). ...
2
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0answers
113 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 ...
2
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0answers
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{...
2
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0answers
112 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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0answers
32 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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0answers
60 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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0answers
40 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 ...
1
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1answer
76 views

Symbol Timing recovery for modulation producing ISI

I am interested in understanding why the common timing recovery algorithms function for modulation schemes which produce ISI. For example, suppose you are receiving at the output of a matched filter ...
1
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0answers
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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0answers
40 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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2answers
240 views

Harmonics to Noise Ratio Estimation

I'm willing to estimate the Harmonics to Noise Ratio (HNR) of a speech signal x[k] and using autocorrelation method. Theoretically, HNR is given as, $\ HNR = \frac{R_{xx}[T_0] }{R_{xx}[0]-R_{xx}[...
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0answers
120 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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0answers
90 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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0answers
139 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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1answer
370 views

Cramer Rao Lower Bound for Cross Correlation (Time Shift Estimation)

UPDATE 2 Okay, I think I understand now why the defined CRLB is not applying to my use case. In my use case, we have very high SNR, and the the first signal $x_1$ is always the same. So the classical ...
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0answers
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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0answers
215 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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0answers
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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0answers
152 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
262 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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0answers
14 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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2answers
589 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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0answers
61 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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0answers
105 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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0answers
669 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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0answers
153 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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0answers
249 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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0answers
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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0answers
38 views

Method for determining the X mid-point of a rectangular function in the presence of noise

Let's say I have a rectangular function that has been polluted with noise. The objective is to determine the X (independent) variable that corresponds to the middle of the rectangle. One method for ...
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0answers
23 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 ...
0
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0answers
18 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 \...
0
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0answers
50 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 ...
0
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0answers
29 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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0answers
43 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 ...