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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Books on systematic risk(beta)
I am looking for some reference material on beta (systematic risk in market model regression). I want to calculate time varying beta for stocks using kalman filter. First I would like to go through ...
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3answers
51 views
Kalman filter parameter estimation
From what I've known about Kalman filter, it requires all the parameters of the underlying state space model. Say the state space model is:
$$\xi_{t+1} = F\xi_t + v_{t+1}$$
$$y_t = H\xi_t + w_{t}$$
...
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14 views
How do I tell if the sensors that feed a Kalman filter has diverged?
I have a time varying variable $x$ that I want to estimate. I have two sensors A and B that measure $x$. I feed their measurements to a Kalman filter.
Sometimes, one of the sensors degrades for a ...
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0answers
15 views
State space estimation with state dependent state variance
I am estimating a state space of the following form
$$Y_t= A X_t + \epsilon_t$$
$$X_{t+1} = B X_{t} + \sigma \sqrt{( a-X_t)(X_t-b)} \eta_t$$
Considering the variance of the state error is state ...
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Kalman filter on stock sentiment time series
I was wondering if & how I can use a Kalman filter on my dataset which contains closing prices of stocks + sentiment scores of tweets about that stock for each day in a timeframe of 1 month.
e.g....
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60 views
DLM regression with parameter restriction
Good afternoon,
I am attempting to fit a state space regression model of the form:
$Y_{t} = \beta_{1}Y_{t-1} + (1-\beta_{1})[i^* + \beta_{2}X_{t}] + \epsilon_{1,t}$
$i^* = i^*_{t-1} + \epsilon_{2,t}...
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1answer
35 views
Parameter estimation in Dynamic Linear Models
I am currently developing a DLM of the following form
$$\underset{k \times 1} {y_t} = \underset{k \times n}A \underset{n \times 1}{\theta_t} + \epsilon_t$$
$$\theta_t = \mu + \underset{n \times n}B\...
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Smoothing detected vehicle positions from camera given my own vehicle's location, velocity and acceleration
I have a dashcam which detects the position and estimated depth of other vehicles on the road relative to my own. Given my own vehicle's global co-ordinates, I can convert the detected vehicle's ...
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76 views
Kalman Filter with MLE giving bad estimates
I am trying to learn and implement the Kalman filter. Yesterday I successfully implemented a non linear kalman filter of the form:
$$
x_t = a(x_{t-1}) + u_t \\
y_t = Gy_{t-1} + v_t
$$
$u_t$ and $v_t$...
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Kalman/HMM for (short) multivariate time series from a sample with missing values
The problem in short:
I want to estimate (?) a lag-1 Markovian hidden process for offline multi-variate discrete-time time series with continuous distributions via smoothing, with no dimensionality ...
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17 views
Calculating travel distance from GPS updates
I am learning about Kalman filters but struggle to apply them for the following problem: tracking the distance traveled from GPS data. The GPS provides position updates every second and an estimate of ...
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0answers
57 views
Statsmodels Kalman Filter: simple equivalent to pykalman set up (partly answered)
Following some examples on Chad Fulton's blog and in statsmodels' tests,
I have tried to come up with an equivalent of a pykalman implementation.
The original question was deemed unclear and was ...
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0answers
48 views
What is the difference between using a Kalman filter and just recursively applying the Bayes rule as new data comes in?
I'm having a hard time wrapping my head around the Kalman filter: Is it just Bayes rule applied over and over with each new measurement? Or is there more to it?
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Multilevel dynamic linear models in R
I am interested in fitting a multilevel bayesian structural time series with a hierarchical structure of the dynamic regression coefficients. The reason I want to do this is is that I have a number of ...
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Covariance matrix for a 2D state vector
I'm performing Optimal Interpolation (which in fact is a simplified Kalman filter with constant $\mathbf{K}$). My state variable is a 2D concentration field with a size of 370 x 400 on which I try to ...
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1answer
27 views
Custom Space State model using DLM in R
DLM package in R can model linear space state models of the form:
I have a different category of equation which is also a linear polynomial equation of order 1 with constant coefficients. I would ...
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0answers
30 views
Parameters estimation using Kalman filter
I have a model like this:
$$P_t=\alpha_t+gP_{t-1}+u_t$$
$$\alpha_t=\alpha_{t-1}+d+n_t$$
Where {$u_t$} and {$n_t$} are normal, iid with 0 mean but unknown variance.
I want to estimate the parameters $...
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0answers
23 views
Updating the kalman filter and RTS with multiple measurements at each time step
I am currently working with kalman filter in area of target tracking. The sensor we are using gets me multiple measurements at each time step. Number of measurements is not fixed, meaning that in one ...
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32 views
Noise reduction with known noise distribution
I have a time signal with a known noise distribution parameters (gaussian, sd is known). I would like to estimate the true value statistically and in the best case obtain a confidence interval.
As I ...
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1answer
30 views
Kalman filter-ish model, is this identifiable?
Time series of observations $y_t$. The proposed model is that there's unobservable scalar series $x_t$:
$$x_t=\phi x_{t-1}+B_tu_t+w_t$$
where $u_t$ - vector predictirs and $w_t$ - noise.
Then there's ...
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12 views
In a LGSSM how do we know that the prediction distribution is Gaussian?
I am trying to follow lecture notes regarding the Kalman Filter from a course taught at Stanford. The lecture notes can be found here.
The linear Gaussian state space model (LGSSM) is introduced as
...
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0answers
38 views
Time varying representation of Okun's law
I've estimated a dynamic linear model to capture time varying parameters in an Okun's law type of model:
I set the starting values for the state vector all equal to zero and estimate the system ...
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22 views
Auto.arima differencing order test for the model with external regressors
Suppose that we have a regression model with ARIMA errors. We need to determine the appropriate level of differencing, so that the errors from the regression are actually stationary. In Hyndman's <...
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1answer
37 views
Observation Operator - Data Assimilation
In data assimilation, one assumes the existence of a observation operator $\mathcal{H}$ that maps the model-state vector $\bf{x_b}$ to $
\bf{y_b}$ (the model-equivalent of the observations $\bf{y_o}$) ...
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Fixed-Delay Kalman smoother with/without augmented measurements
There are several algorithms regarding fixed-lag Kalman smoothing.
In most cases, an augmented state vector is defined in which the elements are the current and delays of the original state vector.
...
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1answer
47 views
Is a Kalman filter ever the optimal way to estimate a dynamic value given a full history of measurements?
I'm trying to get some intuition for Kalman filtering, and I conceived this toy example:
Say that I have a sensor that tracks a moving 1-dimensional target. Say that the measurements from the sensor ...
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0answers
144 views
ARMA process forecasts and maximum likelihood parameters
I have some trouble understanding the forecasting/inference process of ARMA models.
From Hamilton (which I am reading now), we can obtain forecasts at $Y$ from any linear process with r.v. values $X$...
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19 views
Trouble replicating the experiments in “On-line Novelty Detection Using the Kalman Filter and Extreme Value Theory”
I'm trying to replicate the online novelty detection algorithm from "On-line Novelty Detection Using the Kalman Filter and Extreme Value Theory" by Hyoung-joo Lee and Stephen J. Roberts. In the first ...
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1answer
80 views
Math questions in Kalman filter equation derivation
I am interested in data analysis. While my working data (actually it's shopping mall's daily sale) is accumlating, I wish to find some statistical laws underlying business phenomena. I left school for ...
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1answer
231 views
Kalman Filter vs. Regression
I'm an economics undergraduate with a fundamental understanding of regression and some experience with machine learning models (e.g. regression trees, boosting). To my knowledge, Kalman Filter is ...
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1answer
58 views
(Online) intuitive explanation of state space models
I have a similar question to the one in the link below:
Intuitive explanation of state space models
In the link they recommend the book by Commandeur and Koopman. I have this book already.
I was ...
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0answers
27 views
How to create the initial ensemble samples for EnKF
As we know, for the ensemble Kalman filter (EnKF), we need to create a set of samples in the beginning and then to run the predict and analysis step.
But for now I have a question of how to create the ...
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1answer
258 views
Examples of state space models where the filtering problem can be solved analytically
Background
A discrete-time, Markovian state space model takes the form
\begin{align}
\mathbf{y}_t&\sim p(\mathbf{y}_t\,|\,\mathbf{s}_t,\,\boldsymbol{\theta})\\
\mathbf{s}_t&\sim p(\mathbf{s}...
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How can I not show the initialization of the estimation in the Extended Kalman Filter?
I'm making estimates through the Extended Kalman Filter and I have a problem related to the vertical axis of my figure, it's too big, so I can not see population dynamics. However, I wish it did not ...
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1answer
53 views
Tracking Moving Objects with Kalman Filters— Over-fitting over time?
I've been learning about Kalman Filters, and the classic example given is tracking an object via radar/gps. My issue here is that each time you get a new data point, you update the error in the ...
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How can one use Kalman filtering to estimate stochastic volatility models?
Assume that we have returns modelled by a stochastic volatility model with parameters that are unknown. Say we want to estimate the parameters with Quasi-Maximum Likelihood estimation and the ...
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0answers
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Are there any R code examples for estimating the state space vector in this case?
I couldn't make sure Whether the model I'm using is a local level model with multiplicative components (state vector $\times$ regressor vector) or a linear gaussian state-space model. And couldn't ...
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1answer
84 views
How to sample an unobserved Markov process using the forward-backward algorithm?
The setup
Let $X = (x_1, \ldots, x_T)$ denote a state variable that follows a Markov process, where $x_t \in S$. The transition distribution is denoted by
\begin{equation}
p(x_{t}|x_{t-1}) .
\end{...
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0answers
40 views
How to interpret log-likelihood score as compared to mse
Say one has a linear dynamic system as follows:
$x_k = Fx_{k-1} + v_k$
$y_k = Hx_{k-1} + w_k$
with $v \sim (0, Q)$ and $w \sim (0, R)$.
I am estimating $(x)_k$ using a normal Kalman Filter and ...
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1answer
73 views
State-space model with contemporaneous effects
I have the following system of equations:
$$
\begin{align}
y_t^{(1)}&=y_t^{(2)}-x_t+\epsilon_t\\
y_t^{(2)}&=x_t+\nu_t\\
x_t&=\alpha x_{t-1}+u_t
\end{align}
$$
where $y_t^{(1)}, y_t^{(2)}$ ...
1
vote
2answers
53 views
Probability of a measurement with uncertainty covariance being generated by a normal distribution
I have the following situation:
A set of Kalman filters with the same model, each with its own
current estimated state and state covariance.
A measurement with a covariance matrix expressing its ...
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1answer
49 views
Proper Imputation and bias-correction on degrading signal with Kalman Filtering?
A signal degrades in its quality. Some signals are far more robust to degradation while others are not. We will simulate degradation by randomly removing values from a function and then applying ...
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1answer
96 views
State Space Model Form for Equations
I have a set of equations which I have to write in state space model form but unfortunately I'm having a bit of difficulty doing so. They are given as:
$y_{t} = x_{t} + z_{t}$
$x_{t} = x_{t-1} + w_{...
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1answer
125 views
Deriving a filter like a Kalman filter from a non-Gaussian state space model
Assume we specify a state space model as
$$Y_t = a X_t + W_t$$
and
$$X_{t+1} = b X_t + V_t$$
where $b,a \in R$, $E[W_t] = E[V_t] = 0 \quad \forall{t }$ and $W_t $ and $V_t$ are indipendent for ...
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1answer
32 views
Student doubts about maximmization
I am an economics student and I am having doubts about optimization.
For example, at some point in my course I will estimate a state space model via kalman filter and I will need to find parameters ...
2
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0answers
58 views
Using Kalman Filters with different dimensionality in an Interacting Multiple Model Algorithm
I am currently reading a lot about Kalman Filtering and am especially interested in the IMM - Interactive Multiple Model Algorithm.
In the literature (e.g. here), IMM is used for Kalman Filters with ...
1
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1answer
38 views
Why is Qk not included in the cost function that is optimised by the Kalman filter?
Assume the following linear discrete system:
$x_k = Fx_{k-1} + w_{k-1}$ where $w_{k} \sim N(0, Q)$
$y_k = Hx_k + v_{k}$ where $v_{k} \sim N(0, R)$
One way to prove that the Kalman filter is optimal ...
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59 views
Chi^2 Test: Alpha and it's Relation to Sigma
I'm using an Extended Kalman Filter and the $Chi^2$ test to test a part of it's residual during the update. Here I want to determine if the residual lays within 3 Sigma and reject outliers that are ...
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82 views
How to approach SSM models for time series forecasting in general?
I have worked on SSM model using KFAS package (https://cran.r-project.org/web/packages/KFAS/KFAS.pdf) in R. Package suggests me to use one of the Box_Jenkins method to implement SSM. So we convert ...
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0answers
69 views
What is the difference between Noise, error and residuals?
I was reading about Kalman filter. http://web.mit.edu/kirtley/kirtley/binlustuff/literature/control/Kalman%20filter.pdf
They talk about additive noise and error. I need to understand difference ...
