The kalman-filter tag has no wiki summary.
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Time Series Forecasting using Particle Filter
I have searched high and low for a practical example of using a Particle Filter to assist with short term price forecasting using the local trend of a time series.
Could someone please share how a ...
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11 views
Parameter MLE for dlmModReg: why not include both V and W?
I'm fitting a univariate regression model using the dlm R package, and was able to get sensible results (compared to least squares, PCA) only after I dropped the process noise covariance term $W$ from ...
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30 views
Maximum likelihood parameter estimates for Kalman filter with time-varying state transition
I'm currently studying Kalman filter, and the model I'm trying to fit is a uni-variate regression:
$Y_t = \beta_t \mathbf{X_t} + v_t$
$\beta_t = \beta_t-1 + w_t$
where $v$ and $w$ are both ...
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0answers
36 views
Kalman- Bucy filter: prior mean change
I have a question on Kalman-Bucy filter:
the prior distribution is $g \sim N(0,σ_g^2 )$, signal is $ds=(μ+g_t )dt+σdZ_t$, posterior distribution becomes $g_t \sim N((\hat{g_t},\hatσ_t^2)$. ...
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Time variation in coefficients
Given $x_t, y_t$ ($t=1,\ldots,240$), I want to estimate $y_t = \alpha_t + \beta_t x_t$ and test $H_0: \alpha_1=\ldots=\alpha_T=0$. It is crucial to allow for time variation in the regression ...
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32 views
State space representation using KFAS package
I am using KFAS package for R.
You can run
install.packages("KFAS")
library(KFAS)
?regSSM
...
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0answers
23 views
Looking for special case for EKF and PEM parameter identification
In system identification is very much of methods. I was discusing extended kalman filter (EKF) used for parameter identification and prediction error method (PEM). For ARMAX model this two methods ...
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39 views
Formulas for fitting the parameters of a linear dynamical system
Using the expectation-maximization algorithm one can fit all the parameters of a linear dynamical system. I know the theory behind it, and I know how to derive the updated parameters from the Kalman ...
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2answers
181 views
Implementing Kalman filter in R
I am attempting to implement a Kalman filter in R. Working from "Time Series Analysis" by Hamilton the state space equations are defined as:
State: $z(t) = F_z(t-1) + v(t)$
Observation: $y(t) = ...
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0answers
43 views
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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57 views
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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0answers
79 views
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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1answer
100 views
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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1answer
87 views
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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1answer
153 views
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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129 views
Unscented Kalman Filter-Negative Covariance Matirx
I have recently started working on the Unscented Kalman Filter. I coded the numerically stable version (i.e Square root Kalman filter) and use matlab for implementing.
In the final update step , ...
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19 views
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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1answer
83 views
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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1answer
125 views
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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1answer
216 views
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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66 views
Filtering error covariance of kalman filter
Hi the P matrix of kalman filter is defined as the conditional variance :
Vt(x_t-xhat_t)
where x_t is the latent state variable at time t.
xhat_t is the filtered value of the latent state variable ...
2
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1answer
116 views
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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1answer
228 views
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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1answer
108 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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107 views
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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1answer
106 views
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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1answer
387 views
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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2answers
167 views
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. ...
3
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1answer
120 views
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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0answers
87 views
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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3answers
323 views
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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1answer
349 views
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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2answers
143 views
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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1answer
165 views
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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1answer
124 views
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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5answers
736 views
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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1answer
305 views
Estimating State Space Model in R with MARSS package and shared parameters between Q and R
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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2answers
323 views
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.
...
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266 views
optim() is very slow to converge for my Kalman Filter
I am using kalman filter to estimate my state variables for a time series data.
...
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0answers
131 views
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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1answer
195 views
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 ...
1
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1answer
295 views
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 ...
0
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1answer
101 views
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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1answer
164 views
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 ...
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1answer
1k views
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, ...
3
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1answer
289 views
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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1answer
593 views
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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2answers
166 views
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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2answers
392 views
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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110 views
How to derive $P$ in continuous Kalman filter?
I want to derive the equation
$\dot P = K'P+PK'^T + Cov(Kv-Gw)$
from the system
$\dot x=Fx+Gw \ \ \ \ \ \ w \sim N(0,Q)$
$z=Hx+v \ \ \ \ \ \ v \sim N(0,R)$
given
$\dot {\hat ...
