# Questions tagged [covariance]

The tag has no usage guidance.

68 questions
Filter by
Sorted by
Tagged with
17 views

### Finding the error in the total integrated intensity of a fitted 2D Gaussian

I have been trying to fit signals to a 2D Gaussian function, and while I have bene able to use sciKit-image's curve_fit function to find the covariance matrix for ...
19 views

### How would I modify a squared-exponential covariance kernel to be periodic?

I want to create a Gaussian process that resembles one generated by an exponential kernel (smooth and with a lot of variance) with a single caveat: I need the final value to be the same as the initial ...
20 views

122 views

### 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 ...
83 views

### 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 ...
91 views

### 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 ...
910 views

### What Is the Difference Between PCA and Karhunen Loeve (KL Transform)?

I have been reading about Karhunen-Loeve or also known as KL transform and I see that when it is used to reduce dimension the procedure is identical to PCA, that is, for both methods the covariance ...
1k views

### [Python ]How can I improve my 1D Kalman Filter estimate?

I have written the following code to smooth an (almost) linear function: ...
69 views

### 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 ...
107 views

### 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 ...
273 views

### 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 ...
95 views

### 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 ...
294 views

### 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 ...
328 views

### How to calculate the Diagonal loading factor evaluate calculate the inversion of a covariance matrix

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 ...
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 ...
314 views

### How to estimate covariance matrix using Fourier representation?

So, I have multidimensional time-series $X \in R^{(d \times T)}$, and I want to determine the covariance matrix of that signal in a specific frequency band. I might filter the signal to that specific ...
1k views

217 views

37 views

### 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 ...
404 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 ...
1k views

### Calculating covariance matrix for MVDR beamforming

I am trying to calculate the covariance matrix that is required for the calculation of an MVDR beamformer. I am getting confused as to how to calculate it. I have an array of 3 microphones each with a ...
423 views

### Relation between Covariance matrix & Energy of a random signal

Let's say I have the below random signal: $Y[n] = [y(n), y(n-1), y(n-2), \ldots, y(1)]$ I have two random variables now: The first one $X_1$ which express the maximum eigenvalue of the covariance ...
105 views

### Best way to find an object in a picture

I'm trying to find an object in a picture, my solution is to take the picture and a photo of the object and find the maximum of the mutual covariance, this is my ...
125 views

### Can I model process noise as a known “error” in my dynamics while designing a Kalman Filter?

Consider I am modelling the dynamics of a robot and using a Kalman filter to obtain estimates of some state. I have certain terms in my equation which correspond to data not accessible to this robot ( ...
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 ...