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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12 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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40 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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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
29 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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26 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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38 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
77 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
47 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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28 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
88 views

A Fast Power Grid Frequency Estimation Approach Using Frequency-Shift Filtering using numerical example

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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17 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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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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24 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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75 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
34 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
105 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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44 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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51 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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32 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
76 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
109 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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11 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
38 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
51 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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61 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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189 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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70 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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99 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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1answer
117 views

The Wiener Filter for the Time Derivative of the Signal

Assume the observation of the original signal $s(t)$ is $x(t) = s(t) +n(t)$, where the signal and noise are independent. Then we need to design the Wiener filter $g(t)$ to estimate $\frac{d s(t)}{dt}$ ...
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23 views

Dark current rate using Matlab

I have darkcurrentrate (Dark noise) data collected at various ISO speeds such as ISO 55, ISO 99, ISO 198 etc. and the files are in .dng format. Can someone suggest how to calculate the dark current ...
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1answer
149 views

What will be the distribution of a given signal

Suppose I have a signal $$ \mathbf{s} \sim C \mathcal{N}\left(\mathbf{0}, \sigma^{2} \mathbf{I}_{N_{}}\right) $$ The signal going through a channel : $$ {\mathbf{r}}_{}=\mathbf{s}+{\delta \mathbf{n}} ...
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125 views

What is the current “state of the art” in future audio sample prediction, given recent developments in “image inpainting” using deep learning?

In the last few years, there have been many breakthroughs in the image processing world regarding repairing "damaged" images, images with corrupt pixels, or even reversing artefacts from ...
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MAP Estimation Problem for Frequency Band Occupancy Calculation

Consider designing a wireless communication system. Your communication link is not iso- lated in the environment, there are other similar devices trying to communicate in the same general frequency ...
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1answer
67 views

ML estimation - solve for x

I'm trying to solve the following maximum likelihood estimation but for multiplicative noise instead of additive noise: So the goal is to do ML-estimation for a scalar constant $x$, which is ...
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1answer
43 views

Multipath channel estimation in single carrier modulation

I think it’s a basic question, but I couldn’t get it’s clear answer. If we have data symbols $x$ vector of length $N$ x $1$ ; it’s convoluted with a multipath channel $h$ of length $L$ x $1$; the ...
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65 views

Frequency Estimation Using Multiple Signal Classification Algorithm (MUSIC)

I'm working on side research that deals with signals and data in the time domain. currently, I want to use the multiple signal classification algorithm (MUSIC) which is mainly used for frequency ...
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Estimate IR's from single channel speech audio

I have a dataset of single-channel audios containing speech, recorded in a single room. I need to extract the room IR's. The goal is to simulate the room acoustics and adjust new speech audios ...
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Achieve better noise reduction at frequency response function estimation

I have the following problem. I have $M$ synchronized, noisy measurements of a MIMO system (2 inputs, 2 outputs) of all inputs and outputs. The inputs are synchronized (no phase shift, coherent ...
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34 views

How to Use Time Difference of Arrival (TDOA) for a Transmitter Localization

Does anybody know a source that illustrates the algorithm to use TDOA method to locate a transmitter? Would the equations to solve (x, y, z) of the transmitter location linear or non-linear? How about ...
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1answer
96 views

How to calculate time domain SNR using known sequence

I am using the following formula to calculate SNR of a real world complex baseband signal sampled at 1x Nyquist. ...
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2answers
245 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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1answer
39 views

Why SRS signalling is used in 5g?

Since DMRS is also being used as a reference signal in PUCCH and PUSCH channel, so why an extra SRS signalling is required.
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2answers
97 views

Find gaussian in data

I have some time series data (blue line lower plot) with a gaussian added into it (red line upper plot). I would like to estimate where the gaussian is in the data, and the height of the gaussian (...
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37 views

Variance of expectation estimator

Given a set of $N$ iid samples, $x_k$, of random variable $X$ and the expectation estimator, $$E[X] \approx \frac{1}{N} \sum_{k=1}^N x_k,$$ how do I find the variance of this estimator (not the ...
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1answer
47 views

Matlab: xcorr: Having trouble when I try to calculate delay between two sinusoids

I have a problem when I try to use Matlab built-in function for cross-correlation 'xcorr'. Background: I created two sinusoids, one of them delayed in time. I choose center frequencies of these ...
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91 views

How to Improve the Kalman Filter for Tracking the Periodic Motion of a Car?

I have a quite typical Kalman filter to design. I really read a lot of articles about the design of this filter but the performances of my filter are still quite bad. Here is my situation. I have a ...
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Why filtic function does not work for a specific use?

And how can I solve this issue? I designed a filter via bilinear transformation in order to obtein a high-pass filter of Butterworth. When I want to set initial conditions with filtic function, it ...
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1answer
44 views

Justification for Squared $ {L}_{2} $ Data and Smoothness Term as an Error Bound

Often in variational methods (and not only) we have an energy that is of the form: $$E(u) = \frac{1}{2}\|f-u\|^2_2 + \frac{\alpha}{2}\|\psi(u)\|^2_2,$$ where the first term is referred to as the data ...
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81 views

What's the computational complexity of MMSE equalizer in OFDM system

As I know that in case of one tap OFDM equalizer, (ZF equalizer), we should have $N$ division complexity since we divide every subcarriers by its correspondent channel tap in frequency domain. But I ...
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34 views

Estimation of Group Delay from Noisy Frequency Response Measurements

Consider a linear, time-invariant system. Noisy measurements of the magnitude and phase associated with the frequency response of the system are available over some dense generally non-uniform grid ...

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