7
votes
Estimators for improved spectral subtraction of noise
Maximum likelihood (ML) estimator
Here will be derived a maximum-likelihood estimator of the power of the clean signal, but it doesn't seem to be improving things in terms of root mean square error, ...
- 13.7k
7
votes
Accepted
Estimate and Track the Amplitude, Frequency and Phase of a Sine Signal Using a Kalman Filter
We can build a non linear dynamic model in order to estimate the parameters of a sine signal.
Let's model the signal as $ a \sin \left( \phi \right) $ where $ \phi $ is the instantaneous phase. So the ...
- 20.5k
7
votes
Kalman Filter on Sinusoidal Signal
This isn't quite what you're asking, because it neglects the amplitude, $A$, but it's a relatively straightforward example of application of an extended Kalman filter to the frequency tracking problem....
- 26k
7
votes
Accepted
What sensors can be fused using the Kalman Filter framework
Remark: I will answer this using the Linear framework of the Kalman Filter but the idea is the same.
The Kalman Filter basically propagate and fuses Gaussian Distributions in order to calculate the ...
- 20.5k
5
votes
Estimators for improved spectral subtraction of noise
Update:
I'm sorry to have to say that testing shows the following argument seems to break down under heavy noise. This is not what I expected, so I have definitely learned something new. My prior ...
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5
votes
Why Does the Kalman Filter Remove Only Gaussian Noise?
First of all let us assure that a Kalman filter (estimator) does not only remove Gaussian noise, but can remove (with certain success) any other type of noise as long as it's designed accordingly.
...
- 28.4k
5
votes
Layman Description of the Kalman Filter
Simple Description
Imagine you're in a car that is traveling at 70MPH with cruise control. Because the cruise control isn't perfect, your actual speed might vary slightly. This imperfection is called ...
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4
votes
Accepted
Unscented Kalman Filter Equations for Constant Turn Rate and Velocity Process Model
From a statistical point of view, the noise parameters are zero mean gaussian distribution and that does not mean that at all times the value of noise would be zero. All it says is that if you were to ...
4
votes
What Is the Relationship Between a Kalman Filter and Polynomial Regression?
I suggest this reference regarding the comparison between least-squares and Kalman filters :
Fundamentals of Kalman Filtering: A Practical Approach by P. Zarchan & H. Mussof
Especially Chapter 3 ...
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4
votes
What Is the Relationship Between a Kalman Filter and Polynomial Regression?
A lot has been said already, allow me to add some comments:
Kalman filters are an application of Bayesian probability theory, which means that "a priori information" or "prior uncertainty" can (and ...
4
votes
MMSE Estimation - Fusion of 2 Measurements
*STOP! If you only want a hint and not the complete solution please see Stanley P.'s or Peter K.'s answers. *
Since you do not specify if there is model for the temperature evolving over time $n$, I ...
- 4,144
4
votes
Layman Description of the Kalman Filter
KF is actually a mixture of a deterministic state propagator and a statistical estimator.
Despite it's name including the term filter, Kalman filter is not a simple frequency selective one. It's ...
- 28.4k
4
votes
Accepted
Kalman Filter on Sinusoidal Signal
I'm copying my answer to Estimate and Track the Amplitude, Frequency and Phase of a Sine Signal Using a Kalman Filter which solves a more general problem with example code:
We can build a non linear ...
- 20.5k
4
votes
What sensors can be fused using the Kalman Filter framework
Are there types of measurements that are not compatible for sensor fusion? Can any measurement be fused to better inform the underlying model?
Any sensor that gives you more information about the ...
- 13.3k
3
votes
Accepted
Alternative to Extended Kalman Filter When Prediction Function Is Not Differentiable / Given by a Black Box
I will tell you something, even if it is differntiable, use Unscented Kalman Filter for any non linear case.
This flavor of Kalman Filter, based on the Unscented Transform, is almost always superior ...
- 20.5k
3
votes
Why Does the Kalman Filter Remove Only Gaussian Noise?
Assumption of a Gaussian process allows us to obtain optimality. This uses the facts
A linear( or better affine) map takes a Gaussian random variable and maps to another Gaussian random variable.
A ...
- 522
2
votes
Accepted
Will an Unscented Kalman Filter Be "As Good" as Other Optimization Algorithms for This Problem?
Though this is quite an old question, my two cents might help others in the future.
The UKF is a very nice algorithm, but you need to take care before using it. My concerns are the following:
You want ...
- 146
2
votes
How to Determine Covariance Matrix $Q$ and $R$ in Kalman Filter
R depends on the sensor sensitivity. If this is a real world problem this can be obtained from the manufacturer. If not use the identity matrix multiplied by a scalar that is less than 1.
Q is the ...
- 21
2
votes
MMSE Estimation - Fusion of 2 Measurements
I'm going to assume that we have no information about how $X[n]$ varies with time, so we can just do one-at-time estimation of $X[n]$ using $Y_1[n]$ and $Y_2[n]$.
One way to get an estimate from $Y_1$...
- 26k
2
votes
Kalman Filter - Implementation, Parameters and Tuning
Here is a simple and clean implementation of Kalman Filter that follows notations as in Wikipedia page. https://github.com/zziz/kalman-filter
- 31
2
votes
Accepted
"Bi Directional" Kalman Filter - Kalman Filter for Smoothing
Anuar Y, Welcome to the DSP community.
What you're talking about is called smoothing.
Let me explain, assume we have samples $ {\left\{ x \left[ n \right] \right\}}_{n = 0}^{N - 1} $ and we want to ...
- 20.5k
2
votes
Accepted
Extended Kalman Filter (EKF) for Non Linear (Coordinate Conversion - Polar to Cartesian) Measurements and Linear Predictions
Update
If I understood your model, you have a model of Constant Velocity in 2D (Cartesian Coordinate System).
While your measurement are in Polar Coordinate System.
Pay attention that your measurement ...
- 20.5k
2
votes
Estimators for improved spectral subtraction of noise
An interesting approximative solution of the maximum likelihood (ML) estimation problem is obtained by using the asymptotic formula
$$I_0(x)\approx \frac{e^x}{\sqrt{2\pi x}},\qquad x\gg 1\tag{1}$$
...
- 92.4k
2
votes
Estimators for improved spectral subtraction of noise
Scale-invariant minimum mean square error (MMSE) improper uniform prior estimators of transformed amplitude
This answer presents a family scale-invariant estimators, parameterized by a single ...
- 13.7k
2
votes
Layman Description of the Kalman Filter
See: What is the relationship between a Kalman filter and polynomial regression?
In over-simplified form, eyeball a line though a cloud of data samples, look where that line might point one sample ...
- 35.7k
2
votes
Layman Description of the Kalman Filter
In "traditional" filters the design specifications like gain and bandwidth drive the structure of the filter. This is because with these filters we are interested in transforming a signal ...
- 43
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