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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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874 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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2answers
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have position, want to calculate 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: ...
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3answers
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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 ...
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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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1answer
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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 ...
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3answers
1k views

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
270 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 ...
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2answers
4k views

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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5answers
459 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 ...
6
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1answer
526 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(\...
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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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1answer
185 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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1answer
261 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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1answer
727 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 ...
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0answers
163 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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4answers
237 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). ...
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2answers
315 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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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 ...
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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 ...
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2answers
298 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 ...
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3answers
2k views

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 ...
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1answer
2k views

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
44 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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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 ...
4
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2answers
408 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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1answer
245 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
131 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
217 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 ...
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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
2k views

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 ...
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1answer
3k views

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 ...
3
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3answers
558 views

How to estimate the mean of a clipped signal?

An accelerometer is used on a high vibration environment (a bicycle) to measure gravity. The signal clips, so data higher than a clipping value is clamped to that value. So, simply filtering the ...
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2answers
6k views

Hermitian symmetry in OFDM systems

I am trying to understand the usage of Hermitian symmetry in OFDM systems and have a couple of questions regarding this. What is the reason of using the Hermitian symmetry in OFDM? How can we arrange ...
3
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3answers
249 views

How to determine, calculate and plot a probability distribution for a given set of numbers?

A device is rotating with a particular wind speed and producing such pulse frequencies in a minute: ...
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2answers
254 views

How do you combine 2 least squares estimates?

Say you want to compute the least squares estimate of $w$ from a data-set: $$ \begin{bmatrix}d_1 \\d_2 \\\vdots\\d_N \end{bmatrix} =\begin{bmatrix} x_1 \\x_2 \\ \vdots \\x_N\end{bmatrix}w + \begin{...
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1answer
202 views

Fitting fixed number of complex exponentials to complex signal

I have a complex data series, and I would like to fit a fixed number (in this case, two) of complex exponentials of the form $Ae^{jBn}$, where A, B are complex. Not interested in the phase (i.e. arg ...
3
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1answer
197 views

What is meant by optimal estimator and how to determine optimality?

Considering an estimation problem of estimating a scalar deterministic parameter $a$ from the observations $y$ which are corrupted by randomvariable $w$. The observations are $y[n] = a + w[n]$ Least ...
3
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1answer
336 views

Estimation of the amplitude of a frequency component in a signal

I'm working on a device that produces a signal with sampling rate of 100 kHz. Every 40 ms, I receive 16000 points, from which I have to extract a frequency close to 3.55 kHz. I have developed a method ...
3
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1answer
198 views

Help in understanding from book expression of variance of an estimator : PRBS vs real valued input

The question is based on Book : Fundamentals of Statistical Signal Processing by Steven Kay, Chapter 4 : Eq(4.21). The expression for the variance of the estimated coefficients when the input is PRN ...
3
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1answer
117 views

How does this FLL work?

I'm trying to get my head around how band-edge frequency locked loops work. In particular, a diagram from this paper: Specifically, what does the Tanh() function and the conjugate product of the two ...
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2answers
2k views

An explanation of parts of the MUSIC Algorithm for someone without a background in signal processing?

I've been looking at every tutorial and paper I can find, but I keep losing the intuition behind what's going on when they get into the matrix operations. There is a step in which the signal vector ...
3
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2answers
311 views

How to understand the type of noise

Suppose that I am receiving RF signals contaminated with noise through antenna. This signal is digitally sampled. How can I understand the type of noise(Gaussian,Uniform etc). Any algorithm is there ...
3
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1answer
109 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 ...
3
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1answer
701 views

How to distinguish signal and noise eigenvalues of autocorrelation matrix for MUSIC algorithm?

MUSIC (multiple signal classification) algorithm is introduced in Schmidt, Ralph. "Multiple emitter location and signal parameter estimation." IEEE transactions on antennas and propagation 34.3 (1986):...
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1answer
117 views

Estimation of accelerating target using position measurements only

I am currently thinking about approaches to estimating the position and velocity of an accelerating target. At this time, I have tried a few approaches that work alright. I have tried two variations ...
3
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2answers
705 views

How do can we cancel out noises while listening voice on headphones?

It's a common problem that while talking with the another person on Smart phones with the help of regular headphones,we get very annoying sounds at background . The opposite person's voice gets mixed ...
3
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1answer
159 views

How to periodically estimate states of a LTI if the output is measured irregularly?

How can I periodically estimate the states of a discrete linear time-invariant system in the form $$\dot{\vec{x}}=\textbf{A}\vec{x}+\textbf{B}\vec{u}$$ $$\vec{y}=\textbf{C}\vec{x}+\textbf{D}\vec{u} $$...