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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Estimating spectrum with regularly missing samples from data
Suppose:
$$
s(t) = \sin(2\pi{f_0}t)
$$
Suppose I'm sampling the signal with a sample frequency $f_s >2f_0$ .
However, every $M$ samples there is a dead-time of $L$ samples.
Traditionally, the (...
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Calculation of the LMMSE Channel Estimator
Consider a MIMO system equipped with $N_t$ transmit antennas and $N_r$ receive antennas.
The received signal over $L$ snapshots are given by
$$Y = H X + Z,$$
where $X$ is the $N_t \times L$ transmited ...
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How to implement maximum likelihood (ML) detector in MATLAB?
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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How can I estimate the 2 parameters of this signal?
I have a digital signal of fixed length (e.g. 100 samples). Somewhere within this signal is a contiguous region characterized by "low variance". The remainder of the signal is characterized ...
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Proof that the estimation error in the LMS filter is uncorrelated
I need to demonstrate that the estimation error in the LMS adaptive filter is white.
The LMS equations are the following:
$y(n)={\mathbf{\hat{w}}}(n)^H\mathbf{u}(n)$
$e(n)=d(n)-y(n)$
${\mathbf{\hat{w}}...
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What is the adjoint of a linear operator and why is it useful?
The concept of linear operators and their adjoints arises frequently in some corners of signal processing, but is not particularly well documented, at least from a signal processing perspective (you ...
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Smallest Eigenvalue in the Derivation of the MUSIC Algorithm
I am seeking clarification on a particular step in the derivation of the MUSIC algorithm as presented in a specific paper. Here, there is an intermediate step I cannot follow and I would appreciate ...
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Variance of phase estimation using FFT as a function of SNR, frequency and signal length
I have looked at previous questions on this topic but I am still unsatisfied. I want to predict how accurately I can estimate the phase of a tone as a function of signal SNR, tone frequency, and the ...
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Implementation of biased estimators
In Fundamentals Of Statistical Signal Processing: Estimation Theory page 19, Kay mentions a biased mean square error estimator for $\mu$ where the samples $x\sim\text{N}(\mu, \sigma^2)$.
The suggested ...
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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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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 $$
Assume the frequency and phase are known. To estimate $A$ we can use least squares (which in this case is equivalent to the DFT):
$\hat{A} ...
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Unscented Kalman Filter for Parameter Estimation (Tracking) of Amplitude Frequency and Phase of a Multi Component Harmonic Signal
I'm trying to implement an Unscented Kalman Filter that tracks the amplitude, frequency, and phase of a multi-component oscillatory signal. Below is an attempt using the ...
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Bounding Detection and Estimation by SNR in Gaussian Channel
Assume the following problem: A deterministic signal $X$ whose magnitude is known to satisfy $0 \leq \Vert X \Vert_2 < \Delta$ for some known constant $\Delta$ is transmitted through a Gaussian ...
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Estimation of the attenuation of two waves on a linear sensor array
Context and objective
I am trying to estimate the attenuation coefficients ($\alpha_u$ and $\alpha_v$) of two waves ($\overrightarrow{u}$ and $\overrightarrow{v}$). These waves propagate on a linear ...
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Time fusion Kalman filter
Suppose I have a set of estimators, $$\{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] = ...
3
votes
1
answer
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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 ...
- 818
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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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