# Tagged Questions

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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### Maximum likelihood estimation using kalman filter for an economical two factor model, whats the measurement noise?

I'm trying to implement a Kalman Filter for the parameter estimation of a linear gaussian two factor model in Matlab. (Schwartz Smith model for commodity prices) In other words: I try to compute the ...
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### How to initiate value for dlmModPoly?

I'm trying to build a model to predict a product's sale price. I'm researching the dlm package. Looks like I should use dlmModPoly, dlmMLE, dlmFilter, dlmSmooth, and finally dlmForecast. I'm looking ...
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### Logistic regression state-space representation

Consider this univariate time series Logit model: $\text{Pr}(X_{t}=1)=\frac{e^{\beta_{1}+\beta_{2}x_{t}+\epsilon_{t}}}{1+e^{\beta_{1}+\beta_{2}x_{t}+\epsilon_{t}}}$, then ...
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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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### Multivariate exponential smoothing and Kalman filter equivalence

Suppose the time-series $X$ is hidden state Gaussian random walk and we observe $Y = X + e$, where $e$ is gaussian white noise independent of $X$. The Kalman estimator of $X$ in this case has a ...
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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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### State Space formulation of Hodrick-Prescott ﬁlter

I would like to apply the Kalman filter in order to get a causal Hodrick-Prescott ﬁlter. The Hodrick-Prescott ﬁlter models a time series $(y_t)_{t=0}^T$ as $$y_t = \tau_t + c_t$$ where $\tau_t$ is ...
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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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### How it temporal correlation modelled in linear dynamic systems

This might be a vague question but I want to know how is temporal correlation modelled in linear dynamic system?
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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 ...
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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. ...
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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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### 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. Many thanks. I have measurements of time and position which could be anything from a person walking, a vehicle on ...
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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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### 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 ...
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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 ...
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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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### 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. ...
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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: ...
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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 ...
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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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### Relative predictive power of predictors used in time series models like kalman filter

How would we measure the predictive power of predictors in time series models. For e.g. in linear regression we have the magnitude and direction of the regression co-efficients and their p-values. Is ...
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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.