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 ...
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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 ...
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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 ...
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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, ...
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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?
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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 ...
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ARIMA vs Kalman filter - how are they related
When I started reading about Kalman filter it thought that it is a special case of ARIMA model (namely ARIMA(0,1,1)). But actually it seems that situation is more complicated. First of all, ARIMA can ...
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RNN vs Kalman filter : learning the underlying dynamics?
Being recently interested in Kalman filters and Recurrent neural networks, it appears to me that the two are closely related, yet I can't find relevant enough litterature :
In a Kalman filter, the ...
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Estimation of ARMA: state space vs. alternatives
I am interested in estimation of ARMA models. I understand that a popular approach is to write the model down in the state space form and then maximize the likelihood of the model using some ...
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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 ...
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State space representation of ARMA(p,q) from Hamilton
I have been reading Hamilton Chapter 13 and he has the following state space representation for an ARMA(p,q). Let $r = \max(p,q+1)$.Then the ARMA (p,q) process is as follows:
$$
\begin{aligned}
y_t -\...
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Can we use bootstrap samples that are smaller than original sample?
I want to use bootstrapping to estimate confidence intervals for estimated parameters from a panel dataset with N=250 firms and T=50 month. The estimation of parameters is computationally expensive (...
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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 ...
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Using Kalman filters to impute Missing Values in Time Series
I am interested in how Kalman Filters can be used to impute missing values in Time Series Data. Is it also applicable if some consecutive time points are missing? I cannot find much on this topic. Any ...
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How to model a biased coin with time varying bias?
Models of biased coins typically have one parameter $\theta = P(\text{Head} | \theta)$.
One way to estimate $\theta$ from a series of draws is to use a beta prior and compute posterior distribution ...
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Kalman filter vs. smoothing splines
Q: For which data is it appropriate to use state-space modeling and Kalman filtering instead of smoothing splines and vice versa? Is there some equivalence relationship between the two?
I'm trying ...
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Why is the likelihood in Kalman filter computed using filter results instead of smoother results?
I am using the Kalman filter in a very standard way. The system is represented by the state equation $x_{t+1}=Fx_{t}+v_{t+1}$ and the observation equation $y_{t}=Hx_{t}+Az_{t}+w_{t}$.
Textbooks teach ...
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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 ...
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How to estimate parameters for a Kalman filter
In a previous question, I inquired about fitting distributions to some non-Gaussian empirical data.
It was suggested to me offline, that I might try the assumption that the data is Gaussian and fit a ...
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Gaussian Process Regression vs Kalman Filter (for time series)?
I'm curious about the similarities and differences between Kalman Filter (KF) and Gaussian Process Regression (GPR). From various sources, I've pieced together that the KF is analogous to a Hidden ...
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How to handle incomplete data in Kalman Filter?
What are some typical approaches to handling incomplete data in the Kalman Filter? I'm talking about the situation where some elements of the observed vector $y_t$ are missing, distinct from the case ...
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Identifiability of a state space model (Dynamic Linear Model)
Take a general linear Gaussian state space model (SSM)(aka Dynamic Linear Model DLM):
\begin{align}
X_{t+1} &= FX_t + V_t \\
Y &= HX_t+W_t \\[10pt]
V_t &\sim N(0,Q) \\
W_t &...
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How does one apply Kalman smoothing with irregular time steps?
I would like to apply Kalman smoothing to a series of data sampled at irregular time points. There is a claim on Stack Exchange that "For irregular spaced time series it's easy to construct a Kalman ...
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Rao-Blackwellization of sequential Monte Carlo filters
In the seminal paper "Rao-Blackwellised Particle Filtering for Dynamic Bayesian Networks" by A. Doucet et. al. a sequential monte carlo filter (particle filter) is proposed, which makes use of a ...
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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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Why is forecasting of ARMA models performed by Kalman filter
What are the advantages of expressing an ARMA model as a state-space-model and do forecasting using a Kalman filter?
This methodology is for example used in the SARIMAX implementation of python-...
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Explaining Kalman filters in state space models
What are the steps involved in the use of Kalman filters in state space models?
I have seen a couple of different formulations, but I'm not sure about the details. For example, Cowpertwait starts ...
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What's the model representation for the first difference of a local level model?
This is my first exercise for space state models and I've a few questions I'd need to resolve before I actually start doing the exercise. Unfortunately, I'm self teaching (I have no professor to ask) ...
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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 ...
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Can anyone point me towards tutorials describing how to use the Kalman filter for forecasting?
I am trying to find any guides on how to use Kalman filters with ARIMA models but the only sources I have found have been highly technical that I can't really understand. Can anyone point me towards ...
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Confusion related to linear dynamic systems
I was reading this book Pattern Recognition and Machine Learning by Bishop. I had a confusion related to a derivation of the linear dynamical system. In LDS we assume the latent variables to be ...
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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 ...
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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 ...
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Why is the Kalman Filter a specific case of a (dynamic) Bayesian network?
Question: How can this be the case? Why are Kalman filters so much more complicated than any other Bayesian network? Are there any Bayesian networks which are intermediate in complexity?
Perhaps one ...
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Introduction to Kalman filters
What are good introductory books on Kalman filters? I like lots of examples and practical techniques, and less theory.
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Kalman filter has a frequentist or bayesian origin?
Following this not-very-formal-discussion here, a question raised in my head: is Kalman filter originally a frequentist or a bayesian tool?
I know that many statistical tools can be interpreted from ...
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Where to start: Unevenly spaced time series, with lots of outliers or randomness
I don't really know what's possible, and would like a pointer in the right direction.
I have measurements of time and position which could be anything from a person walking, a vehicle on a road, or ...
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"Monte Carlo Kalman Filter" vs Unscented Kalman Filter
Recently, I have come across references to the Monte Carlo Kalman Filter (MCKF), which is a variant of the Sigma-Point Kalman Filter (SPKF). The key difference between the MCKF and the remainder of ...
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Unscented Kalman filter-negative covariance matrix
I have recently started working on the unscented Kalman filter. I coded the numerically stable version (i.e., square root Kalman filter) and used MATLAB for implementing. In the final update step, ...
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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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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 ...
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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 ...
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Maximum Likelihood estimation and the Kalman filter
I know the Kalman filter recursions and can derive these but what I don't really get is how to estimate the hyper parameters using maximum likelihood.
I understand that when running the Kalman filter ...
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How can I debug and check the consistency of a Kalman filter?
I understand the basic principles involved in Kalman filtering and I have spent some time implementing several algorithms in MATLAB. The problem I'm facing now is to check if the algorithm and my code ...
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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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Relation between Wiener and Kalman filtering
What is the relationship from an historical point of view between Kalman and Wiener filtering? Can the first be logically seen a consequence of the latter?
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Statistical methods to validate the performance of a linear Kalman filter algorithm [duplicate]
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 ...
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traditional state-space models and LSTMs
I am trying to understand the nature of LSTMs in relation to intuitions from traditional state-space models (e.g., Kalman filtering). The code below aims to simulate a simple univariate linear state-...
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Kalman filter update returns an invalid covariance matrix?
I am trying to work through a simple introduction to the Kalman Filter but I am hitting a brick wall. I want to track the position and velocity of a target but only measure (noisily) the position. My ...
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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 ...
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