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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How do I extract tag values from a stream in Gnu Radio?
I have two MPSK SNR Estimator and MSPK SNR Estimator Probe blocks that insert a tag after a certain number of samples. In my case, tag = "snr" with the value of SNR is inserted every 10000 ...
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Optimum Measurement of Sine Wave Amplitude in Noise
There are many related questions posted about estimating sine wave parameters, and this one is closest: Measuring amplitude of a pure sine wave of known frequency close to the noise floor, but none ...
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Understanding Maximum likelihood detector expression?
Consider the MIMO system which has $N_t$ antennas at transmitter and $N_r$ antennas at receiver and uses Generalized space shift keying (GSSK) modulation. The received signal is given by:
$$Y = H X + ...
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Distribution of Power Spectral Density in white noise
I have a signal $s$, of which the PSD I call as $S$.
So,
$$ S(\omega) = \frac{1}{N} \left|\sum_{n = 0}^{N-1} s(n) \exp(-j\omega n)\right|^2 $$
I have a closed form expectation of the above mentioned $...
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Noise leakage problem with least square estimation in the frequency-distance domain
I have data $d$ recorded from an antenna of sensors. These data are composed of a Gaussian noise $n$ and a signal $s$ which I try to estimate. This signal propagates on the antenna with frequency ...
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Modelling problem
Considering a finite-length impulse response $h[n]$ of length $M $ (which amounts to considering $h[n] = 0,$ for $n \geq M$). The data model, with additive disturbance, is then written as:
$$y[n] = ...
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How to get prior channel knowledge for estimation the channel using MMSE?
I have implemented an OFDM communication system in Matlab. I use the 802.11ac preamble for estimating the channel using the least square estimator. However I would like to implement the MMSE too. I ...
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Generalized distribution of Power Spectral Density at each Frequency Point
I have an expression for the expectation of the power spectral density and I call it $F(\omega, \Theta)$ where $\omega$ is the frequency and $\Theta$ are the parameters. I have some measurements of ...
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How to generate ground truth in constant velocity Kalman simulation?
I'm trying to simulate a particle going from (-3,0) to (3,0) with a constant velocity and some noise (e.g. the particle is a quadcopter trying to fly at constant velocity, but may be pushed by gusts ...
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Variance of Value Expressed as Number of Changing Bits
I consider values physical measurements, expressed as variables of type int16, uint32, float ...
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Clipping detection algorithm for a sinusoidal signal with noise and unknown amplitude in an online fashion
My problem is the following:
I am sampling data from a sine signal
Samples come in a online fashion (more and more data incoming through time).
The device does not have a lot of memory so it is ...
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How to Estimate a Multi Channels and Multi Kernels Convolution Kernel (Deep Learning Style) Given the Input and Output Images
Is it possible that can estimate convolutional kernel that have multi channels and multi filters ?
I saw answer from this to link to estimate kernel for one channel and one filter (Estimating ...
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Estimating the Most Likely Harmonic Signal in a Spectrogram
Experimental data description: below image is from spectrogram of doppler radar return as I walk toward sensor. Bright sinusoid shape modulated with frequency F is from motion of small retroreflector ...
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Noise variance estimation
could anyone recommend some articles how to estimate noise variance for the single carriers system with burst mode transmission (preamble+data TDMA)?
My goal at the beginning is to develop skills how ...
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Mean squared error between white noise and colored noise
While studying the whitening filter, I still can't come up with an intuitive and reasonable explanation of why a whitening filter is needed.
As this question and its answer mentioned, I understand ...
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Estimation of time-varying velocity
Objective:
Estimate the mechanical tension of a cable using the velocity of the waves travelling along it.
Experimental setup:
I have a cable in tension equipped with accelerometers. I measure a ...
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What are the Kalman filter capabilities for the state estimation in presence of the uncertainties in the system input?
I have a question regarding the capabilities of the discrete Kalman filter for estimation of the unmeasurable state variables of a dynamic system.
In the time being I have been using a discrete ...
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Sensor Fusion of Two Same Type of Data
I have an object moving with sinusoidal motion. I estimate the position of the object using lidar and camera separately. Then I want to fuse these two estimation data in the optimal way. For example I ...
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Is there a reconstruction procedure after beamforming for broadband signal?
Consider we have a received data matrix of size $T \times N$ where T is the time samples and N is the number of sensors. As I understand in the frequency domain beamforming we perform Fourier ...
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What's the best way of modeling 3d target motion with only 2d angle observations?
A maneuvering target is flying in 3d cartesian space, but a sensor (passive infrared or mic array, etc.) can only observe it in polar coordinate with 2d orientations
(azimuth, elevation). For ...
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Why does sequential update of Kalman Filter work when you have multiple sensors?
If you are using a kalman filter with multiple sensing sensors there are two ways to fuse them.
One way is doing a single observation step where you include all the sensors in a single vector and a ...
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Why do I need to multiply the frequencies with a number, to get correct "shift" in the bode plot?
Assume that we got a sine wave function
$$u(t) = A\sin(2\pi \omega(t)t)$$
Where the frequency $\omega(t)$ changes over time $t$ and $A$ is the amplitude.
Assume that we apply that $u(t)$ signal onto a ...
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IMU state estimation Covariance updating
EKF filter normally has a predict + update step, I am curious - how do you evolve the covariance of the state without one of the steps?
In essence I want to evolve the state of an object using an IMU ...
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Why MUSIC algorithm fail when the antenna spacing is larger than half wavelength?
I'm studying MUSIC algorithm for far-field DOA estimation. I found that when the antenna spacing $d$ is larger than half wavelength $(\frac{\lambda}{2})$, the algorithm fails and the spatial spectrum ...
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Derivation of the process noise covariance matrix for non linear system in UKF
I have a continuous (in time) non-linear system in the form $\dot{x}=f(x(t)) + Bu(t) + w(t)$ which I would like to track with a UKF. $w(t)$ represent white noise (in particular, the acceleration and ...
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Estimation of the Amplitude of a Sine / Cosine Wave and Its Independence of the SNR / Amplitude of the Wave
Consider a sinusoid in AWGN:
$$Y = A \cos(\omega t+\phi)+n $$
Assume the frequency and phase are known. To estimate $A$ we can use least squares (which in this case is equivalent to the DFT):
$\hat{A} ...
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Bounding Detection and Estimation by SNR in Gaussian Channel
Assume the following problem: A deterministic signal $X$ whose magnitude is known to satisfy $0 \leq \Vert X \Vert_2 < \Delta$ for some known constant $\Delta$ is transmitted through a Gaussian ...
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Estimation of the attenuation of two waves on a linear sensor array
Context and objective
I am trying to estimate the attenuation coefficients ($\alpha_u$ and $\alpha_v$) of two waves ($\overrightarrow{u}$ and $\overrightarrow{v}$). These waves propagate on a linear ...
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Time fusion Kalman filter
Suppose I have a set of estimators, $$\{S^1, S^2, S^3, S^4,\ldots,S^n\}$$ that output at each timestep $t$ a measurement representing an estimate of the true signal $y$, however the output of each ...
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EKF: IMU vs State Transition Model
Suppose you have an object you're interested in estimating the state of, ex position.
Suppose you don't have a state transition model but you do have an IMU.
Can the IMU be used to simulate a state ...
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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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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 $\sigma_i^2$:
$$
x_1[j] = ...
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cramer lower bound, MAE, and MSE
I am quite confused, is there any relation between MSE, CRLB and MAE.
Can we test the efficiency of a Maximum likelihood estimator with the MAE, or must we use CRLB?
Also is it true that CRLB is MSE?
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Difference between Cramer Rao bound and mean absolute error MAE
Difference between Cramer Rao bound and mean absolute error MAE?
I cannot see the difference, or where to use one and not the other. I know that Cramer and MAE are used to measure the quality of an ...
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Localization by Time Difference of Arrival (TDOA) with Chan's Method
In the paper Hyperbolic Position Location Estimation in the Multipath Propagation Environment (Direct PDF link) at page 2, the Chan's method is presented. But, the presentation is made for a 3 base ...
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State estimation in HyperSonic Missiles
I'm curious, what would be the correct approach for state estimation for hypersonic Missiles?
Would it be exclusively GPS and IMU? Historically these are what was used, but I have also seen ground ...
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On-Off keying for wireless communication channel estimation
Let us assume I have $k$ (a fixed number) sensors in a wireless sensor network with unknown channel statistics $\{h_1,h_2 \ldots, h_k\}$.
In my system model, each of these $k$ sensors has an ...
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Kalman Filter State Covariance Matrix for Non Constant Process Noise Matrix in PyKalman
I'm experimenting with the pykalman Python library to learn about Kalman Filters. In the code below, I'm generating a random walk where each step is the last step ...
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Kalman Filter on Sinusoidal Signal
Suppose a system follows this equation:
$$ x(t)=A \cos(\omega t + \phi)+\eta$$
where:
$\omega = 2\pi f $ and $\eta$ is a random error
using Extended Kalman Filter, how does estimated value $\hat{x}$ ...
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Is there a way to measure an image SNR blindly?
Are there known techniques to estimate the SNR of an image in small neighborhoods (say like 11x11) without any knowledge of the clean image, with arbitrary content ? Denoising is not required.
Update:...
user7657
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Multiple frequency estimation - MSE from data
I have a multiple frequency estimation problem at hand according to the signal model
$$
\boldsymbol{x} = \boldsymbol{A}(\boldsymbol{f}) \boldsymbol{s} + \boldsymbol{n}
$$
where $\boldsymbol{x} \in \...
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How to check that the state observer works appropriately?
I have implemented a discrete state observer for a given dynamic system in continuous time domain in following form
$$\bar{\mathbf{x}}(k) = \mathbf{A}_d\cdot\hat{\mathbf{x}}(k-1) + \mathbf{B}_d\cdot \...
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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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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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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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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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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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