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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Search for tracking techniques

I have an image with scatter points. Check the following figures. We can see a line and a sin function in the images, which are corrupted by noises. The tracks of the straight line and the sin ...
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ARIMA in state space and Kalman filter for predicted values [closed]

Given the coefficients of an arima Model arimaM <- arima(y, order = c(1,0,2), transform.pars = FALSE, fixed = c(0.5,2,1.5,NA)) how can I compute the one step ...
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135 views

Univariate Kalman filtering with factor in state-equation

I have a simple Kalman problem: how does one estimate the following local level univariate state-space model, but with some driving factor: ...
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459 views

State space models: Advantage of Stationary State Vector?

Consider a State Space Model, where the observed process is $Y_t$ $$ Y_t = B F_t + \epsilon_t \\ F_t = \Phi F_{t-1} + \nu_t $$ where the error terms are white noise. Later on, I want to compute the ...
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132 views

prior for initial values of Kalman Filter

I'm studying Carter and Kohn's (1994) implementation of the Gibbs sampler for Bayesian analysis of state space models. In their paper, they assume the starting value, call it $\beta_0$, of the state ...
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Kalman filter Welch and Bishop

I am trying to understand Kalman filter from a highly recommended pdf by Welch and Bishop https://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf. I am highly confused with one terminilogy x_k. There ...
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How to use Kalman filter in regression?

I read that Kalman filter can be applied to perform regression with a dynamic beta, calculated on the fly. Can someone please break this down for me, with some simple example of single-variable ...
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253 views

ARIMA and SARIMA state space form

I need to write down a program that place ARIMA(p,d,q) and SARIMA models in state space form, however I cannot figure out the composition of the system matrices. In the book of Koopman (pag. 54) the ...
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163 views

Estimate standard deviation of random-walk using Kalman filter

I'm new to Kalman filters so this might be a stupid question. I created a Kalman filter that takes in time series observations and estimates the mean of that time series. This is simply modeling a ...
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29 views

Number of the samples for an Ensemble Kalman Filter EnKF

Can someone lead me to some references related to how to choose the samples number for the ensemble Kalman filter EnKF.
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The difference between systems with and without direct feedthrough

Generally, in nonlinear state estimation the state space model is defined by the following pair of difference equations in discrete-time: \begin{equation} \begin{aligned} x_k & = f(x_{k-1},u_{k-1}...
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Can Kalman Filtering be done hierarchically - estimated from multiple time series with the same parameters?

I have a large number of of noisy time series recordings (trials), for which I wish to estimate the state transition model underlying them using the Kalman filter. The process generating the time ...
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DLM implementation of the mean reverting model

I am trying to use DLM package in R to estimate a state space repersentation of the term structure model, where observation and state equation are as follows $y(t )= F* x_t +e_t$ $x_t- \mu = G* (x_{...
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estimating weights in lattice recursive least squares (LRLS)

I'm struggling to estimate the weights (W) from the forward and backward prediction coefficients (k) in Lattice recursive least squares (Lattice-RLS). The standard recursive least squares (RLS) ...
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69 views

Have trouble fitting a stationary time series

I've been working on fitting a time series generated from an indicator in stock market, whose frequency is 1 minute and length is 1433. This series is stationary, proved by many stationarity tests. ...
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Combining errors from two groups of measurements

Suppose I have two ways of measuring some quantity, $a$ and $b$, where each method has its own intrinsic error, $\sigma_a$ and $\sigma_b$. I make repeated measurements with each method and produce ...
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ARIMA vs Kalman filter - how are they related

When I started reading about Kalman filter it thought that it is a special case of ARIMA model (namely ARIMA(0,1,1)). But actually it seems that situation is more complicated. First of all, ARIMA can ...
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Cubature Kalman Filter vs. Kalman Filter [closed]

In the context of time series forecasting, does CKF perform better over KF or other Time Series models?
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154 views

Time varying regression in high dimension: cheaper than the Kalman filter

Assume you have a linear regression model $Y=\beta X$ with a high dimensional (say 1 000 000 resulting from dummy coding) vector $X$. You want to use this regression to predict $Y$. But dependence is ...
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82 views

Multi-Target Tracking Filters

I am trying to solve a multi-target tracking problem, which is in some parts different to some filters I have already researched such as the PHD filter. I am asking for advise which filters to start ...
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379 views

Difference between the Kalman filter predictor and the conditional expectation predictor?

We have a model in state space form $$Y_t = G_t X_t + W_t$$ where $$X_t =F_t X_{t-1} + V_t $$ and $W_t,V_t$ are some kind of random noise. I am confused between these two predictions of $X_t$ that ...
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222 views

MLE or joint Kalman filter

I am trying to identify the parameters of a discrete-time nonlinear state space model: \begin{equation} \begin{aligned} x_k & = f(x_{k-1},\theta)+q_{k-1}\\ y_k & = h(x_k,\theta)+r_k \end{...
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Why assume controls are independent of state estimation in Kalman Filter?

Here's the classic graphical model depiction of a Kalman Filter (or any form of Bayes filter for that matter). Why do we assume that the controls are independent of the previous state estimation? For ...
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State Space model identification with Kalman Filter [duplicate]

If I have a standard state-space model where all parameters are unknown (coefficients and covariance matrices for both the state equation and observation equation) and I want to estimate it with the ...
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93 views

Why state vector equation is one time forward in Kalman FIlter? [closed]

After looking various sources (1), I have found following equations for system description in kalman filter: Measurement Equation as: $$ y_t=C_t x_t+r_t \tag{1} $$ and state vector equation as: ...
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interpreting linear minimum mean squared geometrically

LMMSE approach estimates $x$ as $$\hat{x} = \mathbb{E}[xz^H]\mathbb{E}[zz^H]^{-1}z$$ where $z$ is an observation and a function of $x$. However, $\hat{x}$ can be interpreted as a projection of $x$ ...
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269 views

How to interpret the measurement error of Kalman filter

In a Kalman Filter, assume we have the state equation as: $x_t=F_{t}x_{t-1}+e_t$, $e_t \sim N(0,V_t))$ $y_t=H_t x_t+w_t$, $w_t \sim N(0,W_t))$. The measurement equation tells us how the observations ...
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786 views

Trouble training LSTM for sequence to sequence learning of sensor time series

I'm experimenting with using RNNs/LSTMs in place of a Kalman Filter (KF) for sensor fusion. I'm struggling to make much progress, and would appreciate some feedback/advice. I have several multi-...
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Covariance matrix of the measurement in a Kalman filter

I want to fuse the estimation from two vision-based algoritms for a moving robot using Kalman filter. The state of the robot is defined as: $q_{k}=(x,y,\theta)$ where $x$ and $y$ are the coordinates ...
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58 views

How can one fit a kalman filter to an object in 1D without knowledge of the parameters of the model?

How can we use a Kalman filter for tracking an object in 1D for which we we don't know the parameters of the state transition model, and only have estimates? Consider the state transition model for ...
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How is $P(x_k | Z^k ) = P(z_k | x_k) \left[ P(z_k | Z^{k-1}) \right]^{-1} P(x_k |Z^{k-1} )$ an application of Bayes theorem?

We are in the econometric context of a dynamic system given by $$x_{k+1}=\phi_k x_k +w_k$$ $$ z_k = H_k x_k + v_k$$ where $\phi_k \in R$ is the state transition, and $H_k$ is the observation matrix ...
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Dynamics of the Kalman Filter and testing efficacy of the filter [closed]

I have a few questions: What statistical tests should we run to test the performance of the Kalman Filter? Should I expect the difference between the forecast estimates and the observations to ...
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132 views

What information is used to make predictions in the kalman filter, and how do the state predictions differ from the measurement predictions?

In the Kalman Filter, is the one step look-ahead estimate generated before there is an observation, or after? i.e. if we have observations up until time t-1, do we use only this information to ...
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87 views

Zero restrictions in state-space models/ Kalman Filter

I am estimating a state space model using Kalman and the EM algorithm in Matlab, using Kevin Murphy's toolbox (http://www.cs.ubc.ca/~murphyk/Software/Kalman/kalman.html). My question should in ...
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Kalman Filter Vs Recursive Least Squares

Does the Kalman Filter boil down to Recursive (i.e., incremental) Least Squares if the state is constant? I expect it does but I am not sure. Assume that all simplifying assumptions hold (i.e, ...
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Kalman Filter: Adding Noise to Mean-State Vector Correct? [closed]

I am learning about Kalman filters in Udacity's Self-driving Car Nanodegree. In one of the lectures on Unscented Kalman Filters (UKF) the state update equation is confusing me. The Filter in question ...
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Distinguishing between measurement outliers and unmodeled state dynamics in Kalman filter

Consider a linear Kalman filtering scenario with the following state update and measurement equations: $$ \mathbf{x}(k+1) = \mathbf{F}(k) \mathbf{x}(k) + \mathbf{w}(k) \\ \mathbf{z}(k) = \mathbf{H}(k)...
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SMC (Particle Filtering) code [closed]

Does anyone know where I can find particle filtering code for R? In particular I'm looking for code for filtering a forward-rate curve.
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Why is the likelihood in Kalman filter computed using filter results instead of smoother results?

I am using the Kalman filter in a very standard way. The system is represented by the state equation $x_{t+1}=Fx_{t}+v_{t+1}$ and the observation equation $y_{t}=Hx_{t}+Az_{t}+w_{t}$. Textbooks teach ...
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Non-Markov Kalman filtering via an augmented Markov state-space. What are the potential dangers beside increased dimensionality?

I have been experimenting with using an augmented state space in which I store / memorise previous states as new variables at the bottom of the state vector when performing discrete Kalman filtering. ...
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Kalman Smoother with Repeated Measurements

I have a problem that I thought should be easy but is turning out to be quite difficult. Lets say I have 100 measurements of a time-varying processes at time points $t\in {1, \dots, 100}$ which are ...
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2answers
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Simple way to solve Bayesian regression problems?

My question is on Bayesian regression problems, where I want to formulate my problem as: Find the posterior pdf of parameters $\theta$, where model $f_\theta$ relates observations $y_i = f_\theta(\...
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1answer
265 views

Kalman Filter Likelihood

I am trying to implement the exact maximum likelihood estimation of ARMA(p,q) models using the Kalman filter. I wrote the following code in MATLAB and seems right to me, however when i compare the ...
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Kalman filter vs Kalman Smoother for beta calculations

I am trying to calculate the beta of two timeseries by setting up a state-space model, calculating its covariances via the EM algorithm and finally running the kalman filter/smoother. From what I have ...
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How to use a Kalman filter?

I have a trajectory of an object in a 2D space (a surface). The trajectory is given as a sequence of (x,y) coordinates. I know that my measurements are noisy and ...
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199 views

Techniques to estimate constant states with particle filter?

I have an application where some of my states are constant and therefore have no process noise. Over the course of the estimation process, the uncertainty in these states drops several orders of ...
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For regression with time varying parameters, SGD or Kalman filter?

What is the advantage of kalman filters as an online update mechanism instead of the stochastic gradient descent?
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86 views

Calculate projectile trajectory from 3d points

I am trying to calculate the trajectory of a moving object (specifically, a thrown object) through a series of video frames. My tracking algorithm can reliably detect ~90% of the object occurrences ...
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1answer
705 views

multi-factor time-varying CAPM using kalman filter

I am trying to implement a time-varying CAPM model using the kalman filter. I have already found numerous examples in R and python using the DLM and the pykalman packages but the problem is that they ...
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435 views

Efficient forecasting of daily and weekly seasonality in minute data

If I naively apply STL, Holt-Winters or Kalman-Filter approaches to the problem of extracting the seasonality and trend components of a one-minute data stream, I will end up with about 10K cyclic sub-...