# Questions tagged [kalman-filter]

The Kalman filter is an algorithm for estimating the mean vector and variance-covariance matrix of the unknown state in a state space model.

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### Search for tracking techniques

I have an image with scatter points. Check the following figures. We can see a line and a sin function in the images, which are corrupted by noises. The tracks of the straight line and the sin ...
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### ARIMA in state space and Kalman filter for predicted values [closed]

Given the coefficients of an arima Model arimaM <- arima(y, order = c(1,0,2), transform.pars = FALSE, fixed = c(0.5,2,1.5,NA)) how can I compute the one step ...
135 views

### Univariate Kalman filtering with factor in state-equation

I have a simple Kalman problem: how does one estimate the following local level univariate state-space model, but with some driving factor: ...
459 views

### State space models: Advantage of Stationary State Vector?

Consider a State Space Model, where the observed process is $Y_t$ $$Y_t = B F_t + \epsilon_t \\ F_t = \Phi F_{t-1} + \nu_t$$ where the error terms are white noise. Later on, I want to compute the ...
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### prior for initial values of Kalman Filter

I'm studying Carter and Kohn's (1994) implementation of the Gibbs sampler for Bayesian analysis of state space models. In their paper, they assume the starting value, call it $\beta_0$, of the state ...
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### Kalman filter Welch and Bishop

I am trying to understand Kalman filter from a highly recommended pdf by Welch and Bishop https://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf. I am highly confused with one terminilogy x_k. There ...
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### How to use Kalman filter in regression?

I read that Kalman filter can be applied to perform regression with a dynamic beta, calculated on the fly. Can someone please break this down for me, with some simple example of single-variable ...
253 views

### ARIMA and SARIMA state space form

I need to write down a program that place ARIMA(p,d,q) and SARIMA models in state space form, however I cannot figure out the composition of the system matrices. In the book of Koopman (pag. 54) the ...
163 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 ...
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### Number of the samples for an Ensemble Kalman Filter EnKF

Can someone lead me to some references related to how to choose the samples number for the ensemble Kalman filter EnKF.
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### The difference between systems with and without direct feedthrough

Generally, in nonlinear state estimation the state space model is defined by the following pair of difference equations in discrete-time: \begin{equation} \begin{aligned} x_k & = f(x_{k-1},u_{k-1}...
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### Can Kalman Filtering be done hierarchically - estimated from multiple time series with the same parameters?

I have a large number of of noisy time series recordings (trials), for which I wish to estimate the state transition model underlying them using the Kalman filter. The process generating the time ...
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### Kalman Filter Likelihood

I am trying to implement the exact maximum likelihood estimation of ARMA(p,q) models using the Kalman filter. I wrote the following code in MATLAB and seems right to me, however when i compare the ...
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### Kalman filter vs Kalman Smoother for beta calculations

I am trying to calculate the beta of two timeseries by setting up a state-space model, calculating its covariances via the EM algorithm and finally running the kalman filter/smoother. From what I have ...
17k views

### How to use a Kalman filter?

I have a trajectory of an object in a 2D space (a surface). The trajectory is given as a sequence of (x,y) coordinates. I know that my measurements are noisy and ...
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### Techniques to estimate constant states with particle filter?

I have an application where some of my states are constant and therefore have no process noise. Over the course of the estimation process, the uncertainty in these states drops several orders of ...
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### For regression with time varying parameters, SGD or Kalman filter?

What is the advantage of kalman filters as an online update mechanism instead of the stochastic gradient descent?
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### Calculate projectile trajectory from 3d points

I am trying to calculate the trajectory of a moving object (specifically, a thrown object) through a series of video frames. My tracking algorithm can reliably detect ~90% of the object occurrences ...