# 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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### 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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### Confusion related to Kalman filters density view

I was reading this book related to Kalman filters and I didn't understand a couple of things. I have also attached the screenshot of the pages from the book where I had confusion. The book is Shumway,...
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### Pointers for understanding the derivation of inference in linear dynamic systems

I am trying to learn about the inference and maximization basically EM of the linear dynamic systems(Kalman filters for example) from Bishop's book of Pattern Recognition and Machine Learning. However,...
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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 ...
1answer
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### Role of kalman filter prior, the 'right' prior?

We can solve the Riccati equation and get the steady state priors for a Kalman filter. So why are people still allowed to have any prior they want? They can solve Riccati equation ex-ante and use ...
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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 ...
2answers
938 views

### 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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### Kalman filter consistency checks and debugging

I understand the basic principles involved in Kalman filtering and I have spend some time implementing several algorithms in Matlab. The problem I'm facing now is to check if the algorithm and my code ...
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 ...
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 ...
2answers
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### Combining a linear Kalman Filter with additional linear constraints?

This question contains a relatively long prelude, since I want to explain as clearly as possible the motivation for the question. It may well be the case that I am asking the wrong question (i.e. ...
2answers
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### Minimal state vector for a Kalman filter

I'm trying to work my way through a text on robotics and specifically trying to make sense of Kalman filters. I've used them before but I'd like to be able to understand and make my own for new ...
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### Filter out information in Kalman Filter

I have a disagreement with friend over if an observable that depend on lagged observable, should be called a state variable. I have the following system: ...
3answers
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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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### 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 ...
2answers
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### Learning a mapping from one time series to another with a Kalman Filter

I am interested in finding the relation between two (possibly multi dimensional) time series $x_{1:T}$ and $y_{1:T}$. I wonder how I can do that with a linear dynamical system/Kalman filter. My ...
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### Assumption of Gaussian distribution of acceleration

I have a data set consisting of noisy position values of a trajectory of a human hand. I want to estimate a generative model of these trajectories, and the obvious choice is a Kalman Filter/linear ...
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### Introductory book for multivariate statistics

I am looking for an introductory book that helps building some skills in working with multivariate distributions. For example, I want to be able to work with multivariate normal easily, something ...
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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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### Estimating State Space Model in R with MARSS package and shared parameters between Q and R [closed]

I am trying to estimate the following unobserved components model using the MARSS package $y_t = \mu_t + \varepsilon_t$ $\mu_t = \mu_{t-1} + \beta_{t-1}$ $\beta_t = \beta_{t-1} + \zeta_{t}$ with ...
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### Which R package can estimate parameters in my Kalman Filter

I am using Kalman Filter to estimate my state variables for a time series data. But all my parameters in KF are unknown. ...
0answers
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### Predicting outlier series in Kalman filter

I have built a Kalman Filter model for flu forecasting as shown below. Y - Target Variable X1 - Predictor1 X2 - Predictor2 While forecasting into the future, I will NOT have data for all three ...
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### What's the difference between dlmSmooth and dlmFilter in R's dlm package?

Could someone please explain what the difference is between the two, and perhaps avoid the worst statistical jargon? I am currently using the dlm package to model ...
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### Kalman smoothing of returns vs. prices with dlmSmooth in R's dlm package?

So I am using the R code behind Fig. 3.14 in Dynamic Linear Models With R (p. 124-5) to make a dynamic version of a simple pair trading model: $$Y = \alpha + \beta X.$$ If I use log returns (<...
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### Problem with zero epsilon value for Kalman filter

I am coding a Kalman filter in R and I am trying to estimate the parameters dV and dW using the methods as provided in Vignette section2. However I get Epsilon=0 (which is dV for Kalman filter) for my ...
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### Error while using dlmModReg

I have started coding a Kalman filter in R. I am using dlmModreg to build an object of class dlm, which I am planning to use as my input to dlmFilter. But, I am stuck in the dlmModreg step itself. I ...
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, ...
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### Maximum likelihood estimation procedures for state-space linear models

State-space models are represented by a state equation and an observation equation (or system of equations to be more precise). These equations are parametarized by components including a transition ...
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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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### Density of multivariate normal given linear condition

Given a variable $X \sim N(\mu, \Sigma)$ What is the density of $X$ given $HX = d$, $H$ and $d$ both constant I.e. we observe $X$ with rank-deficient linear operator $H$ and obtain some value $d$. ...
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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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### Likelihood function of DSGE model using Kalman filter

In Frank Schorfheide's class notes on likelihood functions of DSGE models, he expresses the value of the likelihood function for a given vector of parameters $\theta$, and time series $Y^T$ as: p(Y^...
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### What is the Unscented Kalman Filter?

What is the Unscented Kalman Filter and when is it used in preference to other types of filters? edit: I find the Wikipedia explanation a bit too technical to be readily understood.
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### Rewriting AR model in State-Space form

How can I rewrite an AR(p) model in state-space form? Max(p)=5 and I want to use Kalman Predictor.
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?
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 ...