Questions tagged [estimation]
In signal processing, estimation is a technique for approximating an unobserved signal from an observed signal containing noise.
428
questions
0
votes
1
answer
29
views
Looking for an online course
I work for a company with expertise in electromagnetics physics, specifically dealing with time domain-based simulation software. We routinely need to transform our results into frequency domain, ...
- 11
0
votes
0
answers
11
views
Advantages of Euler vs Quaternion vs Axis-Angle Paramertization
I have spent a bit of time studying attitude estimation and I noticed that uncertainty of orientation can basically be represented in three forms.
Euler angles, Axis Angle and Quaternions. Quaternions ...
- 834
0
votes
0
answers
19
views
Fusing multiple IMUs in EKF framework
What is the approach to fuse multiple IMUs in EKF framework?
Normally you take the IMU as the motion model and the sense step to consist of other sensors but when have multiple IMUs operating, what is ...
- 834
0
votes
1
answer
49
views
How to estimate temperature based on resistance thermal dependency?
My question is tightly related to my different question. Let's say I have an inverter fed three phase induction motor drive where in the braking phase (when the motor operates in a generator mode) the ...
- 395
1
vote
0
answers
30
views
Temperature estimation via Kalman filter
Based on the recommendation I would like to ask you for your opinion regarding my question I have asked on different forum.
- 395
0
votes
0
answers
32
views
Does it make sense to have diverging Kalman gain and covariance when system accuracy worsens over time?
I've developed an UKF for a system, whose dynamics change slowly over time. The state & measurement equations are quadratic and linear equations fitted to experimental data in the following form:
$...
0
votes
1
answer
26
views
IMU gravity tracking
I'm interested in tracking the gravity vector for a UAV supposing we don't have external input or GPS.
I think a solution to the problem is as a follows:
We have a past gravity direction vector which ...
- 834
0
votes
0
answers
19
views
MatLab - System Identification Toolbox vs Code - discrepancies and small fit percentages
I need help understanding what in what is wrong with what I am doing, or why is this happening.
So basically I have two tables and one variable:
...
- 11
2
votes
0
answers
82
views
What happens when Kalman filter is applied on a memoryless system?
I'm trying to set up a Kalman filter for my system
$$ x_{k+1} = f(u_k) $$
$$ z_{k+1} = g(x_{k+1}) $$
and found that while the filter "works" (able to reduce rmse from 1.5% in the open loop ...
1
vote
0
answers
24
views
How to tune the coefficients of Polynomial Models in MatLab System Identification toolbox
I have such setting:
Where $Y_M(S)$ is the transfer function of the model I am trying to approximate with $Y_U(S)$, what I have is the data of the signal corrupted with noise.
I am trying to create a ...
- 11
4
votes
1
answer
205
views
FFT-based phase estimation better than CRLB in MATLAB simulation
I am trying to understand the concept of CRLB for a simple sinusoid in AWGN with a simulation in MATLAB.
According to Kay (p. 57) the CRLB for phase estimation is:
$var\{\phi\}=\frac{2(2N-1)}{SNR\cdot ...
- 43
0
votes
0
answers
15
views
Finding oscillation frequency in a harmonic polluted signal [duplicate]
I would like to find periodicity and the oscillation frequency in a signal. I used this simple MATLAB code which works find for some signals, but for a harmonic polluted signal like the one given ...
0
votes
0
answers
31
views
Value of EKF when fusing two estimates of the same state
I'm looking at fusing the output of two SLAM packages.
In the examples code given an EKF is referenced for this fusion but I can't find the implementation.
I don't understand the value of the EKF ...
- 834
4
votes
2
answers
135
views
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 (...
- 113
1
vote
1
answer
122
views
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 ...
- 11
1
vote
0
answers
138
views
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 + ...
- 73
1
vote
3
answers
229
views
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 ...
- 183
1
vote
0
answers
38
views
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}}...
- 31
8
votes
1
answer
627
views
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 ...
- 1,767
4
votes
2
answers
296
views
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 ...
- 145
0
votes
0
answers
83
views
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 ...
- 195
1
vote
2
answers
133
views
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 ...
- 1,156
0
votes
0
answers
96
views
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 ...
- 1
2
votes
0
answers
70
views
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 ...
- 51.1k
4
votes
1
answer
129
views
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 + ...
- 73
7
votes
1
answer
206
views
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 ...
- 85
0
votes
0
answers
46
views
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] = ...
- 1
1
vote
2
answers
115
views
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 ...
- 11
1
vote
0
answers
45
views
Variance of Value Expressed as Number of Changing Bits
I consider values physical measurements, expressed as variables of type int16, uint32, float ...
- 305
2
votes
2
answers
146
views
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 ...
- 21
4
votes
1
answer
72
views
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 ...
- 43
3
votes
1
answer
176
views
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 ...
- 31
0
votes
0
answers
83
views
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 ...
- 45
1
vote
0
answers
116
views
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 ...
- 155
2
votes
0
answers
65
views
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 ...
- 85
1
vote
1
answer
70
views
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 ...
- 395
1
vote
0
answers
171
views
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 ...
- 51
1
vote
1
answer
76
views
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 ...
- 11
2
votes
1
answer
1k
views
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 ...
- 834
0
votes
2
answers
204
views
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)$$
Where the frequency $\omega(t)$ changes over time $t$ and $A$ is the amplitude.
Assume that we apply that $u(t)$ signal onto a ...
- 405
1
vote
1
answer
145
views
IMU state estimation Covariance updating
EKF filter normally has a predict + update step, I am curious - how do you evolve the covariance of the state without one of the steps?
In essence I want to evolve the state of an object using an IMU ...
- 834
0
votes
0
answers
155
views
Why MUSIC algorithm fail when the antenna spacing is larger than half wavelength?
I'm studying MUSIC algorithm for far-field DOA estimation. I found that when the antenna spacing $d$ is larger than half wavelength $(\frac{\lambda}{2})$, the algorithm fails and the spatial spectrum ...
- 73
1
vote
0
answers
190
views
Derivation of the process noise covariance matrix for non linear system in UKF
I have a continuous (in time) non-linear system in the form $\dot{x}=f(x(t)) + Bu(t) + w(t)$ which I would like to track with a UKF. $w(t)$ represent white noise (in particular, the acceleration and ...
- 53
7
votes
2
answers
646
views
Estimation of the Amplitude of a Sine / Cosine Wave and Its Independence of the SNR / Amplitude of the Wave
Consider a sinusoid in AWGN:
$$Y = A \cos(\omega t+\phi)+n $$
Assume the frequency and phase are known. To estimate $A$ we can use least squares (which in this case is equivalent to the DFT):
$\hat{A} ...
- 384
3
votes
0
answers
575
views
Unscented Kalman Filter for Parameter Estimation (Tracking) of Amplitude Frequency and Phase of a Multi Component Harmonic Signal
I'm trying to implement an Unscented Kalman Filter that tracks the amplitude, frequency, and phase of a multi-component oscillatory signal. Below is an attempt using the ...
- 243
0
votes
1
answer
62
views
Bounding Detection and Estimation by SNR in Gaussian Channel
Assume the following problem: A deterministic signal $X$ whose magnitude is known to satisfy $0 \leq \Vert X \Vert_2 < \Delta$ for some known constant $\Delta$ is transmitted through a Gaussian ...
- 65
4
votes
1
answer
174
views
Estimation of the attenuation of two waves on a linear sensor array
Context and objective
I am trying to estimate the attenuation coefficients ($\alpha_u$ and $\alpha_v$) of two waves ($\overrightarrow{u}$ and $\overrightarrow{v}$). These waves propagate on a linear ...
- 85
1
vote
1
answer
105
views
Time fusion Kalman filter
Suppose I have a set of estimators, $$\{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 ...
1
vote
1
answer
236
views
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 ...
- 834
7
votes
2
answers
1k
views
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 ...
- 188