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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14
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1answer
1k views

Kalman Filter - Optimal Way to Handle “Derived” Measurements?

Ie, if you have as state variables position (p) and velocity (v), and I make low-frequency measurements of p, this also indirectly gives me information about v (since it's the derivative of p). What ...
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7answers
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Obtain a signal's peak value if it's frequency lies between two bin centers

Please suppose the following: The frequency of a signal's fundamental has been estimated using FFT and some frequency estimation methods and is lying between two bin centers The sampling frequency is ...
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Given Position Measurements, How to Estimate Velocity and Acceleration

This is simple i thought, but my naive approach led to a very noisy result. I have this sample times and positions in a file named t_angle.txt: ...
11
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2answers
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How to do prediction using frequency domain data?

Both linear regression and Kalman filtering can be used to estimate and then predict from a time domain sequence of data (given some assumptions about the model behind the data). What methods, if ...
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3answers
4k views

Filtering RANSAC Estimated Homographies

I am using RANSAC algorithm for homography estimation between pairs of images taken with cameras which do not have any translation between them (pure rotation and change of scale/zoom). It works well ...
9
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1answer
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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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818 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] = \alpha(\...
9
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1answer
6k views

Measuring time delay of audio signals

Before anyone yells at me I fully realize that this question has been asked numerous times. I assure you that I've read through the existing questions and answers but I am still confused about part of ...
9
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1answer
313 views

Filter order estimation

Assume some unknown but small and finite number of poles and zeros in the complex Z plane, all with complex conjugates, producing some response. Strictly from the absolute value of a set of equally ...
8
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5answers
709 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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3answers
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Determining optimal binary decision rule threshold from observations with unknown priors?

Given only observations of a binary signal perturbed by Gaussian noise with unknown prior information, how can I estimate the optimal decision threshold? ( No, this is not a homework question) ...
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2answers
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How to define SNR for multiple signals in noise?

I have to estimate the number of signals present in a measurement contaminated by additive noise given $n$-dimensional snapshot vectors $\bf x$, modeled as $ \bf x = \bf A \bf s + \bf z $ where $\bf s$...
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1answer
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Maximum Likelihood Estimation in Presence of Colored Noise

I am trying to test system identification in presence of measurement noise (1) A white Gaussian noise (2) Colored noise - pink, violet. When we are estimating parameters we do so in presence of iid, ...
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4answers
388 views

MMSE Estimation - Fusion of 2 Measurements

Let's say I have 2 measurements of the same phenomenon (for example current temperature) and I want to find the MMSE (minimum mean square error) estimator, i.e to minimize the MSE (mean square error). ...
5
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1answer
305 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 ...
5
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1answer
116 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 ...
5
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2answers
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Extended Kalman Filter (EKF) for Non Linear (Coordinate Conversion - Polar to Cartesian) Measurements and Linear Predictions

I'm new to Kalman filtering and state estimation and I'd like some guidance on EKFs. Currently, I'm trying to use a linear prediction model coupled with nonlinear measurements to estimate the state ...
5
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3answers
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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 ...
5
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1answer
530 views

Estimate the Discrete Fourier Transform / 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 Transform / Series. Now, assume I'd like to estimate its Discrete Fourier ...
5
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1answer
188 views

Expectation maximization of moving average with binary source input

I am trying to do blind system identification of a univariate linear FIR model: I am unsure if the approach is correct or not and any help to further proceed with the maximization will be great. ...
5
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2answers
2k views

Is there a way to reduce the covariance matrix of several source signals to the dominant source signal?

The problem I have can be seen in the context of DoA estimation or blind source signal separation and similar fields, where several source signals are observed by several antennas (or by an antenna ...
5
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1answer
298 views

How to detect specific behavior in time series?

I was not quite sure what the right SE for this was, so I posted this also here on SciComp. Please tell me which one to remove :) Problem statement I have a few hundred unrelated time series, say $...
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2answers
974 views

Estimating Plane Pose Without Knowledge of Intrinsic Camera Parameters

Assume a camera has no skew, and has square pixels, that is, its camera-calibration matrix, $K$, looks like: $$ K = \left[\begin{matrix} \alpha&0&u_x\\0&\alpha&u_y\\0&0&1 \end{...
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1answer
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Pose from Homography matrix - Zhang method

This post also contributes to the post at Step by Step Camera Pose Estimation for Visual Tracking and Planar Markers by Jav_Rock (since I cannot add any comment there and I don't know why) It can be ...
5
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0answers
72 views

Is the Wiener filter operating at the Cramér–Rao bound?

I have been told (Wikipedia agrees) that the Wiener filter is optimal when signal and (additive) noise are WSS. Optimal in the sense that it minimizes the mean-square error. The Cramér–Rao bound is ...
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164 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 ...
5
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0answers
172 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. ...
4
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1answer
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What would be the variance for complex number?

When $x$ is a zero mean random variable then $$\sum_{n=1}^N x_n x_n^T = N \sigma^2_x\,\text,$$ where the variance is $\sigma^2_x$. I'm considering Complex Normal Distributions where the real and ...
4
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4answers
994 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 ...
4
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2answers
386 views

Why is PSD estimated, and not simply computed?

I apologize if this comes as a basic question, but I am struggling to understand why the PSD can only be estimated and not directly computed. For example, this thread discusses several such PSD ...
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4answers
167 views

Estimation of Amplitude, Frequency and Phase of Linear Combination of Harmonic Signal Beyond the Leakage Resolution of DFT

How can I find a rough ( as accurate as possible) Amplitude of each frequency when there is spectral leakage. Currently, I am dealing with a system that contains special leakage which seems ...
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2answers
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Kalman Filter for estimating position with nonconstant velocity & acceleration

I am trying to estimate the position & head direction of a rodent going through a 2D environment (a circular surface of 1m radius). Above his head is an overhead camera which records 4 LEDs ...
4
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1answer
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Tracking a Sine Wave with Kalman Filter - How to Account for Offset (DC Signal)?

I am attempting to create a Kalman filter to track a sine wave (I am using a linear Kalman filter example assuming I already know the frequency of the sine wave) - the example I am using is derived on ...
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2answers
3k views

Estimate the Transfer Function of an Unknown System

Suppose you have a system, H, that you want to estimate its transfer function. You have a finite number of complex input samples, x, and noisy complex (magnitude and phase) output samples, y: In ...
4
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2answers
332 views

Minimum SNR Requirements for Maximum Likelihood Frequency Estimation

In certain applications, you have enough SNR available to, for example, perform an FFT and identify peak location and hence the signal frequency. If my understanding is correct, parameter estimation ...
4
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2answers
104 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 ...
4
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1answer
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What Is Uncorrelated Noise

In many applications such as estimation theory, when we need to estimate a parameter then we usually consider in presence of white gaussian noise of zero mean and some standard deviation. During ...
4
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1answer
82 views

Concept About Estimated Standard Deviation

I am looking for the concept about how to 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 ...
4
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1answer
88 views

Variance of an Implicit Function of Kalman State Vector

Given a state vector given by $ x = {[r, v, a]}^{T} $ (Range, Velocity, Acceleration) the Time to Hit is the the time which holds the following: $$ r + v {T}_{tth} + \frac{a {T}_{tth}^{2}}{2} = 0 $$ ...
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2answers
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How Is the Formula for the Wiener Deconvolution Derived?

Wikipedia - Wiener Deconvolution shows this formula: $$ \ G(f) = \frac{H^*(f)S(f)}{ |H(f)|^2 S(f) + N(f) } $$ Could someone explain the derivation? Specifically, where does the squaring ($|H(f)|^2$) ...
4
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1answer
107 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 ...
4
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2answers
156 views

Minimum Mean Square Estimator - Equivalent Expressions to Minimize

Given $ M \in \mathbb{R}^{N \times N} $ which is a Positive Definite Matrix. Let $ \hat{x} $ the MMSE of $ x $ given $ z $, namely $ \hat{x} = \mathbb{E} \left[ x \mid z \right] $. Prove the ...
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2answers
452 views

Peak location estimation for a triangle wave in AGWN?

Is there a more optimal peak location estimator specifically for triangle waves in AGWN, compared with peak estimation for generic waveforms? For a "smooth" waveform in noise, a common peak locator ...
4
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2answers
226 views

Derivation of the LMMSE (Linear Minimum Mean Squared Error) Estimate and the MMSE Under Gaussian Prior

I am learning estimation theory through Steven M. Kay - Fundamentals of Statistical Signal Processing, Volume 1: Estimation Theory. In the ...
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3answers
438 views

Question on Wiener Filtering

I have read that a Wiener filter is a filter used to produce an estimate of a desired or target random process by linear time-invariant (LTI) filtering of an observed noisy process. Now, my doubt ...
4
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2answers
402 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}[...
4
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1answer
351 views

Direct Correlation (DC) Time Delay Estimation: Variance Keeps Decreasing for Increasing SNR?

I'm trying to reproduce the results from this paper "Discrete time techniques for Time Delay Estimation" doi:10.1109/78.193195, for both the correlation and Least Squares. I've generated a random (...
4
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1answer
159 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 ...
4
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2answers
236 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 ...
4
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1answer
136 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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