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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2answers
62 views

Is there a way to measure an image SNR blindly?

Are there known techniques to estimate the SNR of an image in small neighborhoods (say like 11x11) without any knowledge of the clean image, with arbitrary content ? Denoising is not required. Update:...
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1answer
97 views

Multiple frequency estimation - MSE from data

I have a multiple frequency estimation problem at hand according to the signal model $$ \boldsymbol{x} = \boldsymbol{A}(\boldsymbol{f}) \boldsymbol{s} + \boldsymbol{n} $$ where $\boldsymbol{x} \in \...
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35 views

How to check that the state observer works appropriately?

I have implemented a discrete state observer for a given dynamic system in continuous time domain in following form $$\bar{\mathbf{x}}(k) = \mathbf{A}_d\cdot\hat{\mathbf{x}}(k-1) + \mathbf{B}_d\cdot \...
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1answer
71 views

How to linearize this state space model and write it in discrete form?

This might not be trivial nor short so in advance thank you all who read this in attempt to help. I'm building a Kalman filter in matlab and I'm fairly certain the software itself is working correctly ...
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1answer
74 views

Kay Statistical Signal Processing Estimation Theory Example 7.14

Example 7.14 from Kay Estimation Theory A common WSS random process has the ACF $$r_{xx}[k]= \begin{cases} 1+b[1]^{2}+b[2]^{2} & \text{k = 0}\\ b[1] +b[1]b[2] & \text{k=1}\\ ...
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1answer
41 views

Noise model as Sinc function

In "Fundamentals of signal processing: estimation theory", example 3.13 Kay has used a model of band-limited Gaussian noise with a uniform PSD and a sinc autocorrelation function. I expected ...
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2answers
32 views

Real time estimation of room impulse response using the sine sweep method

I am working on real time Room Impulse Response estimation using sine sweep. $x(n)$ is my sine sweep signal. $f(n)$ is its amplitude modulated inverse. $beep$ consists of 3 sine sweeps with a delay ...
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0answers
30 views

Radar beamforming receiver combining vector estimation

I don't have much experience with radar signals. I know in the cellular system, the channel directional vector can be estimated using pilot symbols based on MMSE, EW-MMSE, and LS. Then, we can use the ...
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38 views

Estimating Correlation Matrices

I am trying to obtain the correlation matrices of two random signals. Both of them, $ X $ and $ Y $, are white Gaussian Noise, with unitary variance. However, they are correlated, with correlation ...
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2answers
53 views

Methods for time series estimation in time domain

I am trying to estimate the clean form of a time series, $u(t)$ that is corrupted by additive White Gaussian noise $w(t)$ at a particular SNR. The received signal is: $$y(t) = u(t) + w(t)$$ My first ...
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52 views

Frequency offset estimation accuracy

To improve frequency offset estimation, we could: Use the second order interpolation / equation in the frequency domain based on the coarse estimation fc, e.g. BPSK frequency offset estimation; Zero ...
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1answer
54 views

Estimate the Image Using Multi Many Realizations of Its Convolution with a Known Filters Using Wiener Filter

Suppose we have a corrupted image $Y = H*X + \epsilon$ that is formed by taking an image $X$, convolving it with a point-spread function $H$, and adding gaussian noise $\epsilon$. Then we know that ...
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790 views

Simple and Effective Method to Estimate the Frequency of a Single Sine Signal in White Noise

Given a sinusoidal signal, how can we efficiently determine its frequency?
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107 views

Why, for a musical instrument, the first harmonic has more power than the fundamental and last longer?

In analyzing the audio recording of a string instrument, I am struggling with pitch estimation. I am using the pYIN algorithm and every pitch estimation I'm obtaining is off by one octave. I assume ...
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1answer
187 views

Estimate and Track the Amplitude, Frequency and Phase of a Sine Signal Using a Kalman Filter

There is sinusoidally controlled signal, which other than being noisy, can change values for amplitude, frequency, phase and offset. At every new sample a new sine is fitted for the last N samples. ...
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Podcasts or video channels on applied signal processing

There is already a good list of text media on signal and image processing here. I'm curious if anyone is making audio or video media about new techniques or interesting applications across ...
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1answer
53 views

Phase offset analysis in real trsnsmitted signal

Assume we are transmitting a real signal $x(t)$ through a channel $h$ in passband as : $y(t) = x(t)cos(2πf_c t + ∅) * h(t)$ = $Re(x(t)e^{j2πf_c t})*h(t)$ where $f_c$ is the carrier frequency and $t$...
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3answers
72 views

Noise variance estimation under known channel

I have $N$ observations $\{y_i\}_{i=1..N}$ $$y_i = h_i x_i + w_i$$ where $\{x_i\}_i$ are the realizations of uniform distributed QPSK symbol $x$, i.e. $x_i \in \{\pm\frac{1}{\sqrt{2}} \pm j\frac{1}{\...
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54 views

Mixing Kalman filter and least-squares

I'm not sure it is the right department. I try my chance I am wondering if there is a way to make a hybrid formulation of a least-square problem and a Kalman filter. Let me explain what I mean: The (...
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1answer
44 views

I want to perform aec on a wav file and calculate erle

I am trying to evaluate the performance of an AEC by comparing the i/p and output wav file. I want to calculate echo return loss enhancement to predict how much(db) echo has been attenuated but i am ...
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14 views

Cramer-Rao Lower Bound with different constants

Suppose we have two observarions such as; $x[0] = A + w[0]$ $x[1] = B + w[1]$ where $w[0]$ and $w[1]$ are WGN with variances $\sigma_0^2$ and $\sigma_1^2$, relatively. We are given two estimators; $\...
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101 views

Accelerometer Bias estimation with kalman filter

I have to estimate biases of a 3-axes accelerometer by modyfying an existent kalman filter mounted on a drone. The biases are assumed constant. The filter has 9 states: position (xyz), velocity (xyz) ...
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32 views

Bispectrum estimation methods

I am trying to understand whether to use the indirect method(with Parzen as our window) or the direct method to better estimate the bispectrum of X(k). I get the following plot for the indirect ...
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1answer
48 views

Channel estimation using bit reversed order of FFT matrix

Is it possible to use the bit-reverse order of FFT instead of FFT to estimate the channel? Based on my reading, I found that bit reversed order of FFT matrix can diagonalize the channel, but ...
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4answers
279 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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1answer
32 views

How do you "split apart" the output of a linear estimator?

Let's say I have a true signal $x$ which is corrupted by noise $n$ such that: $y = x + n$ I am attempting to use a Weiner filter to estimate the true signal $x$. This estimator is of the form: $\hat{x}...
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1answer
32 views

correlation matrix for complex white noise does not equal to identity matrix?

I generate 8 time series of gaussian white noise and want to compute the correlation matrix at a frequency bin between them. The following is the matlab code I use ...
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2answers
68 views

How Are Unmeasured Properties (Velocity and Covariance of Velocity) Handled with a Kalman Filter?

I'm trying to understand how I can update a Kalman filter with a state variable for position and velocity when I only measure position. I have a covariance matrix of the position measurements. But ...
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1answer
82 views

How to handle a logarithmic term in Kalman filter?

I am trying to implement a Kalman filter for an echo pulse detection application as similar to this paper. (an open source version is here (pg 16)) The measurement variable is $h(x,t)=A_0 (\dfrac{t-\...
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1answer
104 views

Estimating the SNR of 2-FSK

I have some iq data recordings of a 2-FSK waveform that I've created periodograms from. How do you estimate the SNR of this waveform in the frequency domain? I've heard two opinions: One: Integrate ...
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32 views

estimating peak frequency close to bin zero

Given a half complex spectrum (positive frequency bins from DC to Nyquist) as the result of a real FFT, to estimate the true (non integer) peak frequency I usually rely on Eric Jacobsen's estimator: $$...
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2answers
138 views

A Fast Power Grid Frequency Estimation Approach Using Frequency Shift Filtering

I have read the paper A Fast Power Grid Frequency Estimation Approach Using Frequency Shift Filtering. I want to prove it using a numerical example, I have problem how to calculate the ...
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21 views

Forming the estimation manifold for a 2-D beamformer

Given an array of L sensors in a uniform planar array, with known positions in space, I would like to estimate both the angles of arrival and delays from a point source under multipath conditions ...
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84 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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1answer
51 views

Offline State Estimation

Imagine I have a nonlinear system: $$ \frac{\text{d} x}{\text{d} t} = f(x,t)\\ y = g(x). $$ I can design a nonlinear observer to estimate the state $x$ based on the measurements $y$. However, this ...
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76 views

Estimating a Filter's Envelope

Are there any established techniques for estimating the envelope of a swept filter? I tried a first order piece-wise polynomial approximation using the SHGO global minimizer algorithm (Python code ...
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1answer
40 views

where we use estimation and detection in communication system?

I read from the book that we use estimation when we are dealing with analog signal or continuous random variable and the term detection when the transmitted signal is a discrete value even if a ...
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1answer
188 views

LMS convergence and step size $\mu$

I am running the LMS algorithm based on Haykin's Adaptive filter theory. I aim to plot the cost function $\mathbf{J}$ and calculate $\mathbf{J}_{\tt min}$ and the simulation excess mean square error $\...
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93 views

Can the numerical variance be lower than Cramer-Rao Lower Bound?

For a sample mean unbiased estimator, which achieves the CRLB, I plotted the variance and compared it to the theoretical CRLB. The plot below shows what I got. I have small number of samples to ...
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1answer
58 views

time-domain channel estimation based on two vectors optimization

Let's the input data vector $X = [X_1, X_2, X_3, X_4, X_5,X_6,X_7,X_8];$ where $[X_7,X_8]$ are well known, and the vector $y = h*X$ where $*$ is the convolution operation and $h = [h_1,h_2]$ is the ...
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36 views

Transceiver for TDoA measurements

Could someone advise me on some module for making the TDoA position system for my research work? I need to have measurements with an accuracy of a few meters. It equals a bandwidth of about 20 MHz. I ...
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2answers
81 views

MSE of an estimator

In the book Fundamentals of Statistical Processing, Volume I: Estimation Theory by Steven M. Kay on page 19, it say that the mean square error of an estimator, $\hat{\theta}$, given the true value, $\...
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1answer
114 views

Signal Estimation after detection Part 2

I have a binary information source signal $s(t)$ that is corrupted by additive White Gaussian noise $w(t)$ at a particular SNR. The received signal is: $$x(t) = s(t) + w(t)$$ Then I have created a ...
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12 views

Uplink Pilot Design in TDD based OFDM system

In a paper “Design of Orthogonal Uplink Pilot Sequences for TDD Massive MIMO under Pilot Contamination”,it was mentioned that, In the uplink channel estimation, if each user occupy all available ...
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1answer
43 views

Estimating a phase for a frequency band

I'm looking for a way (preferably already implemented in eg. python) of estimating a phase for a specified freq band. When I'm performing FFT on the signal, I can determine components frequencies as ...
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1answer
59 views

What Are Intuitive Explanations for Shrinkage in the Context of Image Denoising?

I have occasionally come upon the term "shrinkage", mostly in the context of denoising methods. My rough understanding is that it refers to the part where the real distribution might not be ...
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62 views

Optimal sampling rate for the HMM forward-algorithm

I have a system with a binary-state. The system state is estimated by an HMM forward-algorithm. Also, the system allows a varying sampling rate. Considering that the system state transition takes a ...
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2answers
818 views

Understanding the H1 and H2 estimators

So the $H_1$ and $H_2$ frequency response estimators for SISO systems are defined according to: \begin{align} H_1 &= \frac{P_{yx}}{P_{xx}}\\ H_2 &= \frac{P_{yy}}{P_{xy}} \end{align} Where $\...
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2answers
77 views

Speed from Depth/Pressure sensors

I have a pressure based Depth sensor. For reference, MS5837-02BA. All depth measurements I've been able to read are very accurate (±1cm) I tried experimenting to find out the speed of the body by ...
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0answers
155 views

Find the Autocorrelation and Cross Correlation of The Wiener Filter

I am dealing with a problem with Wiener filter. Assume the original function is $s(t)$ with observation $x(t) = s(t) + n(t)$. And $s(t)$ and $n(t)$ are WSS (wide sense stationary) and they are ...

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