# Tag Info

### 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, ...
• 13.5k
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 ...
• 19.3k

### 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....
• 25.2k
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 ...
• 19.3k

### 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. ...
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### 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 ...
• 7,520
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 ...

### 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 ...
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### 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 ...

### 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 ...
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 ...
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### 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 ...
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### 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
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 ...
• 19.3k

### 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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• 19.3k

### 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 $Y_1$...
• 25.2k

### 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
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 ...
• 19.3k
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 ...
• 19.3k

### 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 $$I_0(x)\approx \frac{e^x}{\sqrt{2\pi x}},\qquad x\gg 1\tag{1}$$ ...
• 88.8k