# Questions tagged [covariance]

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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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### Kullback-Leibler Distance of Spectral Data

I am currently reading through Music Structure and Analysis from Acoustic Signals and am having some difficulty in understanding how the modified Kullback-Leibler distance is calculated. (I am just ...
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### Covariance matrix $P$ and $Q$ for complex valued data

The equations for the Kalman filtering are IM = H*X; IS = (R + H*P*H'); K = P*H'/IS; X = X + K * (y-IM); P = P - K*IS*K'; The covariance matrix in my ...
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### Problem with Covariance matrix using diagonal loading involved in calculation of eigenvalues

I have the following problem : I'm calculating the sample covariance matrix in the frequency domain ( $y_{k}$ is the FFT of a time domain $k_{th}$ symbol vector signal , basically a simulated ...
Cross-correlation for uniformly sampled signals is defined as  $$(f \star g)[n]\ \stackrel{\mathrm{def}}{=} \sum_{m=-\infty}^{\infty} f^*[m]\ g[m+n].$$ Cross-covariance for wide-sense stationary (...