# 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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### Kalman Filter vs. Regression

I'm an economics undergraduate with a fundamental understanding of regression and some experience with machine learning models (e.g. regression trees, boosting). To my knowledge, Kalman Filter is ...
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### (Online) intuitive explanation of state space models

I have a similar question to the one in the link below: Intuitive explanation of state space models In the link they recommend the book by Commandeur and Koopman. I have this book already. I was ...
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### How to create the initial ensemble samples for EnKF

As we know, for the ensemble Kalman filter (EnKF), we need to create a set of samples in the beginning and then to run the predict and analysis step. But for now I have a question of how to create the ...
664 views

### Examples of state space models where the filtering problem can be solved analytically

Background A discrete-time, Markovian state space model takes the form \begin{align} \mathbf{y}_t&\sim p(\mathbf{y}_t\,|\,\mathbf{s}_t,\,\boldsymbol{\theta})\\ \mathbf{s}_t&\sim p(\mathbf{s}...
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### How can I not show the initialization of the estimation in the Extended Kalman Filter?

I'm making estimates through the Extended Kalman Filter and I have a problem related to the vertical axis of my figure, it's too big, so I can not see population dynamics. However, I wish it did not ...
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### Tracking Moving Objects with Kalman Filters— Over-fitting over time?

I've been learning about Kalman Filters, and the classic example given is tracking an object via radar/gps. My issue here is that each time you get a new data point, you update the error in the ...
152 views

### How can one use Kalman filtering to estimate stochastic volatility models?

Assume that we have returns modelled by a stochastic volatility model with parameters that are unknown. Say we want to estimate the parameters with Quasi-Maximum Likelihood estimation and the ...
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### Are there any R code examples for estimating the state space vector in this case?

I couldn't make sure Whether the model I'm using is a local level model with multiplicative components (state vector $\times$ regressor vector) or a linear gaussian state-space model. And couldn't ...
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### How to sample an unobserved Markov process using the forward-backward algorithm?

The setup Let $X = (x_1, \ldots, x_T)$ denote a state variable that follows a Markov process, where $x_t \in S$. The transition distribution is denoted by \begin{equation} p(x_{t}|x_{t-1}) . \end{...
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### How to interpret log-likelihood score as compared to mse

Say one has a linear dynamic system as follows: $x_k = Fx_{k-1} + v_k$ $y_k = Hx_{k-1} + w_k$ with $v \sim (0, Q)$ and $w \sim (0, R)$. I am estimating $(x)_k$ using a normal Kalman Filter and ...
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### State-space model with contemporaneous effects

I have the following system of equations: \begin{align} y_t^{(1)}&=y_t^{(2)}-x_t+\epsilon_t\\ y_t^{(2)}&=x_t+\nu_t\\ x_t&=\alpha x_{t-1}+u_t \end{align} where $y_t^{(1)}, y_t^{(2)}$ ...
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### Probability of a measurement with uncertainty covariance being generated by a normal distribution

I have the following situation: A set of Kalman filters with the same model, each with its own current estimated state and state covariance. A measurement with a covariance matrix expressing its ...
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### Proper Imputation and bias-correction on degrading signal with Kalman Filtering?

A signal degrades in its quality. Some signals are far more robust to degradation while others are not. We will simulate degradation by randomly removing values from a function and then applying ...
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### kalman filter in R when restoring missing values

I did not know, where it would be more correct to ask my question, on CrossValidate or on stakoverflow, but decided here. If I'm wrong, just let me know, I'll delete the post and create it on a ...
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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 ...
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### 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: ...
410 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 ...
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### 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 ...
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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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### 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}...
I am trying to use DLM package in R to estimate a state space repersentation of the term structure model, where observation and state equation are as follows $y(t )= F* x_t +e_t$ \$x_t- \mu = G* (x_{...