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# 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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### What are disadvantages of state-space models and Kalman Filter for time-series modelling?

Given all good properties of state-space models and KF, I wonder - what are disadvantages of state-space modelling and using Kalman Filter (or EKF, UKF or particle filter) for estimation? Over let's ...
2answers
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### What is the difference between a particle filter (sequential Monte Carlo) and a Kalman filter?

A particle filter and Kalman filter are both recursive Bayesian estimators. I often encounter Kalman filters in my field, but very rarely see the usage of a particle filter. When would one be used ...
2answers
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### What is the difference between Kalman filter and moving average?

I am computing a very simple Kalman filter (random walk + noise model). I find that the output of the filter is very similar to a moving average. Is there an equivalence between the two? If not, ...
2answers
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### Switch from Modelling a Process using a Poisson Distribution to use a Negative Binomial Distribution?

$\newcommand{\P}{\mathbb{P}}$We have a random process that may-or-may-not occur multiple times in a set period of time $T$. We have a data feed from a pre-existing model of this process, that provides ...
4answers
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### R code for time series forecasting using Kalman filter

Does anybody have a good example for Time Series Forecasting/smoothing using Kalman Filter in R?
1answer
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### Difference between Hidden Markov models and Particle Filter (and Kalman Filter)

Here is my old question I would like to ask if someone knows the difference (if there is any difference) between Hidden Markov models (HMM) and Particle Filter (PF), and as a consequence Kalman ...
2answers
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### When will a Kalman filter give better results than a simple moving average?

I recently implemented a Kalman filter on the simple example of measuring a particles position with a random velocity and acceleration. I found that Kalman filter worked well, but I then asked myself ...
1answer
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### LogLikelihood Parameter Estimation for Linear Gaussian Kalman Filter

I have written some code that can do Kalman filtering (using a number of different Kalman-type filters [Information Filter et al.]) for Linear Gaussian State Space Analysis for an n-dimensional state ...
2answers
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### 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 ...
2answers
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2answers
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### Time Varying System Matrices in Kalman Filter

Kalman filter can accommodate time varying system matrices. Equations to run the filter are the same and it preserves its optimality under linear gaussian model. My question is the following: Can ...
1answer
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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 ...
1answer
988 views

### Methods of fitting a dynamic linear model

I'm taking a time series course and am learning about exchangeable time series form of dynamic linear models (DLMs). This is given by: \begin{align*} \mathbf{y}_t' &= \mathbf{F}_t'\boldsymbol{\...
1answer
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### Statistical methods to validate the performance of a linear Kalman filter algorithm

I have a problem with a linear Kalman filter algorithm that gets as input some sensor measurements $z_i$ with known measurement error with standard deviation $\sigma_{i,{measured}}$ (assumed normally ...
4answers
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### Kalman filter equation derivation

I'm studying the Kalman Filter for tracking and smoothing. Even if I have understood the Bayesian filter concept, and I can efficiently use some of Kalman Filter implementation I'm stucked on ...
1answer
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### Why is the Confidence Interval Changing for this Time-Series

I have some R code (which I did not write) and which performs some state space analysis on some time-series. The data itself is shown as dots (scatter plot) and the Kalman filtered and smoothed state ...
1answer
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### Beginner level: Help in learning Kalman Smoother (Part 1) [closed]

Parameter estimation of Linear Dynamical system is a tutorial which explains Kalman Filter, Smoothing, and Expectation Maximization. I have followed the derivation for Kalman Filter. But cannot ...
1answer
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### Tracking and data association with Kalman filters

I am trying to solve tracking problem. At certain points in time I receive object location and I should make decision whether received object location belongs to existing track or not. If not, I ...
1answer
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### Are matrix decomposition based Kalman filter algorithms faster or more robust?

I have been using linear Kalman Filters for several different applications. I wrote the implementation from scratch and it follows Welch & Bishop verbatim in the simplest way. I have also heard ...
1answer
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0answers
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### Possible causes for the state noise variance to become negative in a Kalman Filter?

I am having some trouble debugging an application of a linear discreet Kalman Filter. From time to time, I find that there are diagonal elements of the covariance matrix that become negative. This is ...