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Questions tagged [covariance]

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What Does Make an Error Surface Convex? Is It Determined by the Covarinace Matrix or the Hessian?

I am currently learning about least-squares (and other) estimations for regression, and from what I am also reading in some adaptive algorithm literatures, often times the phrase "... and since the ...
8k views

Covariance vs Autocorrelation

I'm trying to figure out if there is a direct relationship between these concepts. Strictly from the definitions, they appear to be different concepts in general. The more I think about it, however, ...
2k views

Question on covariance matrix of 2 spatial signals

Every time I think I have understood the covariance matrix, someone else comes up wih a different formulation. I am currently reading this paper: J. Benesty, "Adaptive eigenvalue decomposition ...
2k views

Cross-correlation or cross-covariance of non-zero mean signals

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 (...
146 views

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 ...
2k views

Is there a way to reduce the covariance matrix of several source signals to the dominant source signal?

The problem I have can be seen in the context of DoA estimation or blind source signal separation and similar fields, where several source signals are observed by several antennas (or by an antenna ...
3k views

Why does diagonal loading of a covariance matrix make an adaptive beamformer more robust in the case of a perturbed array?

It has been shown that 'diagonal loading' a covariance matrix derived for an adaptive beamformer can improve robustness of the beamformer when the antenna array is perturbed, albeit at the expense of ...
200 views

Help in understanding from book expression of variance of an estimator : PRBS vs real valued input

The question is based on Book : Fundamentals of Statistical Signal Processing by Steven Kay, Chapter 4 : Eq(4.21). The expression for the variance of the estimated coefficients when the input is PRN ...
383 views

How to Extract Nonorthogonal PCA Principal Components

My problem is essentially a 'blind source separation' problem. I have 3 non-orthogonal sources (or basis functions) and $N$ random linear combinations (mixes) of said sources. My problem is to obtain ...
2k views

Variance of a filtered signal

I'm using a very simple 1st order Butterworth Filter shown in Matlab code: order = 1; cutOff = 0.1; [b, a] = butter(order, (2*cutOff)/SampleRate, 'high'); So ...
199 views

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Testing for changes in auto-covariance

I am working with uniformly-spaced time series data where I am interested in knowing whether there are changes in temporal auto-covariance. The mean can be assumed constant. Visually, there are no ...
369 views

Determining the covariance of point clouds in real-time

So basically I have a set of multidimensional data that I need to determine the covariance of between dimensions in real-time. Each point that comes in is a vector. I have gotten the mean and variance ...