# Questions tagged [covariance]

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### In EKF should Kalman Gain converge to a specific value?

I have implemented an EKF using the standard predict and update equations in order to perform state estimation of a vehicle with multiple sensors. The model has process covariance matrix $Q$ and each ...
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### Intuitive understanding of the relationship between the variance of a Wiener process and the variance of white noise

The Wiener process $W(t)$ is said to be the integral of white noise $\xi(t)$ from $0$ to $t$. That is, $$W(t) = \int_{0}^{t} \xi(t')dt'$$ However, the variance of $\xi(t)$ is infinite, but the ...
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### Generalized correlation coefficients

Assume there are given two Gaussian random vectors $\boldsymbol{x}$ and $\boldsymbol{y}$ of equal length $N$ with corresponding means $\boldsymbol{\mu}_x$, $\boldsymbol{\mu}_y$ and covariance matrices ...
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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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### How to determine covariance matrices $\mathbf P$, $\mathbf Q$, and $\mathbf R$ in Extended Kalman Filter

I am implementing an Extended Kalman-Filter and an Unscented Kalman-Filter for state and parameter estimation of a conveyer belt system. The problem is that I don't really know how to determine the ...
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### Ideally Lowpass-filtered White Gaussian Noise: question about a derivation of variance and covariance

Consider white gaussian noise $\omega(t)$ that has passed through and ideal lowpass filter with bandwidth $B$. This filter has the impulse response $$h(t) = 2B\text{sinc}(2Bt)$$ Sampling the filter ...
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### Kalman Filter: Why do we decrease the state uncertainty regardless of the current measurement?

I'm struggling with fully understanding the concept behind a Kalman filter. For the sake of simplicity, let's ingore the input variable $u$ and assume constant process $Q$ and measurement noise $R$. ...
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### Estimating variance in arbitrary, periodic signal

I have a periodic signal $x[m], m \in [0;M-N+1]$ made of modulated templates $s[n],~ n \in [0;N-1],~ N \ll M = NK$ of finite energy and support (i.e. zero outside of its defined interval, which does ...
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### Is there a difference what measurement units use in covariance matrix

The R matrix in the Kalman filter contains measurement noise. Diagonal elements of the matrix is the power of standard deviation. Is there a difference what measurement unit to use for standard error ...
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### Why does it mean that the process/signal is not stationary when its variance varied with time? [closed]

Why does it mean that the process/signal is not stationary when its variance varied with time? that is, $VAR[X(t)]= \alpha \times t$,$t$ is time,and $\alpha$ is a constant,then $X(t)$ is not the WSS ...
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### What Is the Difference Between PCA and Karhunen Loeve (KL) Transform?

I have been reading about Karhunen-Loeve (KL) transform. I see that when it is used to reduce dimension the procedure is identical to PCA, that is, for both methods the covariance matrix of the data ...
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### [Python ]How can I improve my 1D Kalman Filter estimate?

I have written the following code to smooth an (almost) linear function: ...
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### Interpretation of Eigen Values of covariance matrix

I am trying to obtain an intuitive understanding of Eigen Values of covariance matrix and have used a few layman terms because I fully do not understand the concept yet. The following is the code ...
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### Sensor fusion under unknown correlations: can covariance intersection account for delays?

Of late, there has been some interest in cooperative estimation algorithms in robotics, where the information sources are usually sensors such as cameras. When multiple robots observe surrounding ...
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### Estimate standard deviation of random-walk using Kalman filter

I'm new to Kalman filters so this might be a stupid question. I created a Kalman filter that takes in time series observations and estimates the mean of that time series. This is simply modeling a ...
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### 2-D parameter vector: Cramer Rao lower bound

Given a 2-D parameter vector, $\mathbf{X} = [x_1, x_2]$, let the corresponding $2\times2$ Fisher Information Matrix be $\mathbf{F}$. The Cramer-Rao Lower Bound (CRLB) is the inverse of the FIM. I ...
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### Is it possible to estimate variance of noise for a step answer signal?

I know there is not possible to find the true noise of a measured signal. The only way to "find" the noise is to estimate the noise. Noise has the mean 0, but the variance varies. So assume that we ...
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I am programming a Generalised Likelihood Ratio Test (GLRT) detector. When it comes to inverting a covariance matrix $Ri$, I need to do a diagonal loading to fix the problem of sigularity of this ...
### Difference between $\mathbb{E}[\mathbf{x} \mathbf{x}^{\rm{H}}]$ and $\mathbb{E}[(\mathbf{x}-\boldsymbol{\mu}) (\mathbf{x}-\boldsymbol{\mu})^{\rm{H}}]$
Let us have a random vector $\mathbf{x} \sim \mathcal{CN} (\boldsymbol{\mu}, \boldsymbol{\Sigma})$ with $\boldsymbol{\mu} \neq \mathbf{0}$. What can we say about the relationship between the elements ...