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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A Machine Learning Based Algorithm as an Alternative to the Matched Filter

Consider we have to detect a known signal added with Gaussian noise. In this scenario, the matched filter is known to be an optimal filter for SNR. The question: is there any machine learning ...
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Maximum possible CFO that can be estimated

I was trying to model the CFO (Carrier Frequency Offset) estimation in MATLAB. The Frame I was working on is of the following structure, yellow being the information data. How CFO was introduced? ...
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Convolution between a vector and another symmetric vector

Let's have the vector $y = h * x$ where $*$ is the convolution operation, $h$ is the channel with length $N$ and $x$ is a symmetry vector which means $x = [x_M, x_{M-1}, ....,x_0, 0 , x_0, x_1, .... ...
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9 votes
2 answers
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What sensors can be fused using the Kalman Filter framework

I was recently introduced to the concept of Kalman filtering in the context of projectile tracking. A classmate recommended this to me, and what intrigued me most was its ability to fuse different ...
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Optimal weighting in case of unknown noise variances

Let's consider $n$ multiple measurements $x_i[j]$ of the same desired signal $s[j]$ but with different uncorrelated zero-mean additive noise $n_i[j]$ with different variances $\sigma_i^2$: $$ x_1[j] = ...
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2 votes
1 answer
66 views

cramer lower bound, MAE, and MSE

I am quite confused, is there any relation between MSE, CRLB and MAE. Can we test the efficiency of a Maximum likelihood estimator with the MAE, or must we use CRLB? Also is it true that CRLB is MSE?
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Difference between Cramer Rao bound and mean absolute error MAE

Difference between Cramer Rao bound and mean absolute error MAE? I cannot see the difference, or where to use one and not the other. I know that Cramer and MAE are used to measure the quality of an ...
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1 vote
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Localization by Time Difference of Arrival (TDOA) with Chan's Method

In the paper Hyperbolic Position Location Estimation in the Multipath Propagation Environment (Direct PDF link) at page 2, the Chan's method is presented. But, the presentation is made for a 3 base ...
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3 votes
0 answers
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State estimation in HyperSonic Missiles

I'm curious, what would be the correct approach for state estimation for hypersonic Missiles? Would it be exclusively GPS and IMU? Historically these are what was used, but I have also seen ground ...
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1 vote
1 answer
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On-Off keying for wireless communication channel estimation

Let us assume I have $k$ (a fixed number) sensors in a wireless sensor network with unknown channel statistics $\{h_1,h_2 \ldots, h_k\}$. In my system model, each of these $k$ sensors has an ...
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7 votes
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Kalman Filter State Covariance Matrix for Non Constant Process Noise Matrix in PyKalman

I'm experimenting with the pykalman Python library to learn about Kalman Filters. In the code below, I'm generating a random walk where each step is the last step ...
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How to choose appropriate discretization method for the state estimator?

Let's say I have following open loop state estimator of a dynamic system in the continuous time domain $$ \begin{bmatrix} \frac{\mathrm{d}\hat{\psi}_{r_\alpha}}{\mathrm{d}t} \\ \frac{\mathrm{d}\hat{\...
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10 votes
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Kalman Filter on Sinusoidal Signal

Suppose a system follows this equation: $$ x(t)=A \cos(\omega t + \phi)+\eta$$ where: $\omega = 2\pi f $ and $\eta$ is a random error using Extended Kalman Filter, how does estimated value $\hat{x}$ ...
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0 votes
2 answers
71 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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2 votes
1 answer
113 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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1 answer
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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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4 votes
1 answer
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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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4 votes
1 answer
81 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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1 vote
1 answer
62 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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0 votes
2 answers
52 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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0 answers
37 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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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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2 votes
2 answers
55 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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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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6 votes
1 answer
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Estimate the Image Using Multi Realizations of Its Convolution with a Known Filters Using Wiener Filter

Suppose we have a corrupted image $Y = H*X + \epsilon$ formed by taking an image $X$, convolving it with a point-spread function $H$, and adding gaussian noise $\epsilon$. Then we know that the Wiener ...
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9 votes
5 answers
1k 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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0 votes
3 answers
119 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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8 votes
1 answer
394 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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0 answers
21 views

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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0 votes
1 answer
100 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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3 answers
77 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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1 vote
0 answers
68 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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0 votes
1 answer
80 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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1 vote
0 answers
203 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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1 vote
1 answer
56 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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8 votes
4 answers
452 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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0 votes
1 answer
33 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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0 votes
1 answer
56 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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5 votes
2 answers
114 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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2 votes
1 answer
84 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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1 vote
1 answer
178 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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1 vote
0 answers
45 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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1 vote
2 answers
142 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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0 votes
0 answers
28 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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11 votes
2 answers
141 views

Does the Wiener Filter Achieve the Cramer Rao Lower Bound (CRLB)?

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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0 votes
1 answer
66 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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0 votes
0 answers
80 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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  • 113
1 vote
1 answer
47 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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6 votes
1 answer
287 views

LMS Convergence and the Step Size ($ \mu $) Parameter

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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0 votes
0 answers
142 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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