Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

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.

0
votes
0answers
10 views

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 ...
0
votes
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: $$\xi_{t+1} = F\xi_t + v_{t+1}$$ $$y_t = H\xi_t + w_{t}$$ ...
0
votes
0answers
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 ...
2
votes
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 ...
0
votes
0answers
22 views

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....
0
votes
0answers
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}...
1
vote
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\...
0
votes
0answers
14 views

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 ...
0
votes
0answers
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 $v_t$...
0
votes
0answers
12 views

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 ...
0
votes
0answers
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 ...
0
votes
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 ...
2
votes
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?
1
vote
0answers
38 views

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 ...
0
votes
0answers
18 views

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 ...
0
votes
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 ...
0
votes
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 $...
0
votes
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 ...
0
votes
0answers
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 ...
1
vote
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 ...
0
votes
0answers
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 ...
2
votes
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 ...
0
votes
0answers
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 <...
0
votes
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 $\bf{y_o}$) ...
0
votes
0answers
38 views

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. ...
0
votes
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 ...
3
votes
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 $X$...
0
votes
0answers
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 ...
2
votes
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 ...
1
vote
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 ...
0
votes
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 ...
1
vote
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 ...
0
votes
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}...
0
votes
0answers
19 views

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 ...
0
votes
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 ...
0
votes
0answers
106 views

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 ...
2
votes
0answers
21 views

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 ...
0
votes
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{...
0
votes
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 ...
1
vote
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 ...
0
votes
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 ...
3
votes
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_{...
2
votes
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 ...
1
vote
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
votes
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
vote
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 ...
0
votes
0answers
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 ...
0
votes
0answers
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 ...
2
votes
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 ...