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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Is there some standard way to diagnose a structural time series model (also called simple unobserved components model)?

I am dealing with a structural time series model (also called a simple unobserved components model), and I wonder if there is some standard way to diagnose this sort of models. In most reference books ...
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Mutlisensory data fusion for infering the state (on/off) of a system

I have a machine that could take 2 states---on or off. My goal is to sense the state of the machine by fusing observations from multiple sensors that observe the state of the system. The sensors (say ...
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Is there a probabilistic or bayesian interpretation of the kalman filter gain?

The Kalman filter makes sense to me as the repeated application of Bayes' theorem - if you correctly propagate the gaussian prior at each step and then update on new observation, you get a gaussian ...
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How to apply Kalman filter to improve my model?

I'm trying to build a model that predicts humidity W This is the data I'm working with : ...
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State-Space model with time-varying error in R

I am trying to estimate the following local level model in R: $y_t = \theta_t + v_t$ $\theta_t = \theta_{t-1} + w_t$ where $y$ is the observable variable and $\theta$ is the latent variable. This ...
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Kalman forecast of AR(1)

I'm trying to work out the details of the proof of the following statement: Suppose $\xi_t = \rho \xi_{t-1} + \epsilon_t$ is an AR(1) process. Using Kalman filter, one can prove that $\mathbb{E}_t\{\...
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Using ML in the prediction step of a kalman filter

I am trying to design a kalman filter to model an athlete's "skill". Each time they compete, we have a new data point - call it their "score". I am taking each score they receive ...
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What is the scope of application of Kalman filter?

Recently I learned some basics about Kalman Filter 1D As I know, Kalman Filter is useful in Telecommunication and GPS positioning. My estimation goal is to measure the reliability of the Circuit using ...
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DLM package in R: No convergence

I am trying to decompose an observable time series $y$ into a permanent component $\bar{y}$ and a transitory component $\tilde{y}$. In my model, the transitory component follows a stationary $AR(1)$ ...
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Approximating a 1-d Kalman Filter with non-Gaussian Observation Noise

I'm looking for a Bayesian filter where observations are generated according to $s_t = \gamma s_{t-1} + w_p$ and $w_p \sim Normal(0, \sigma_p^2)$. Both $\gamma$ and the variance of the process noise $\...
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Fixed-leg Kalman filter smoother (Rauch–Tung–Striebel) error bounds

Although very intuitive and with plenty of results that talk about the asymptotic convergence of the estimate I wasn't able to track down any paper stating explicitly convergence bounds based on the ...
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Kalman Filter with External Control Input in R

I am facing a problem with Kalman filtering. I am not possible to find some package in RStudio with state equation containing Control Input (x_k=Fx_{k-1}+Gu_{k-1}+q_{k-1}). Does anybody know some ...
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On the noiseless Kalman filter

Introduction I've implemented a simple Kalman filter and I'm facing some difficulties into filtering out the noise of the measurements. If I set a small initial state covariance and a null process ...
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Is the state covariance matrix (or estimate uncertainty) in a Kalman filter in 1D equal to the variance of the current normal distribution?

I'm trying to use a Kalman-filter for some kind of anomaly detection. But I think that maybe I have misunderstood something fundamental about the filter. I'm following this "guide". I'm ...
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(Co)variance interpretation in Kalman filter

Let's say I have a device which uses Kalman filter to fuse sensor data and produce an optimal estimate of the system parameters. As it should, it also estimates parameter covariance matrices at each ...
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Unscented Transform - Combination of multiple Sets of Sigma Points?

Given an initial state distribution $x \sim N(m_x, S_x) \in R^{n_x}$ and transition function $y = f(x)$ one can use the unscented transform to approximate the distribution $p(y) \approx N(m_y, S_y)$ ...
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Kalman filter: updating the state-transition model

I am currently reading lots of material on the Kalman filter (in order to do some experiments), and there is something that I don't get, and I can't get a clear understanding. I'll stick to the ...
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Prove that innovation (residual) of Kalman filter is orthogonal to all future state prediction

The question is to prove that $$v(k) \perp \hat{x}(j|k-1) \space \forall j>k-1$$ where v(k) is innovation (residual) at time k and $\hat{x}(j|k-1)$ is the estimate state at time j given ...
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Gaussian Process Regression vs Kalman Filter (for time series)?

I'm curious about the similarities and differences between Kalman Filter (KF) and Gaussian Process Regression (GPR). From various sources, I've pieced together that the KF is analogous to a Hidden ...
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Is the mode probability of IMM filter in a multi-sensor problem formulated by pseudo measurement or just a probability product?

I would like to use IMM filter to solve a multi-sensor problem, but it seems that there are two ways of calculating mode probability $\mu_k$. The first way can be written as follows, \begin{aligned} \...
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Where is a good place to start with (hidden) state-space models?

I'm interested in (hidden) state-space models. My language here might be poorly articulated as I'm quite new to this area of math. The topic of Kalman filters has come "across my desk" a ...
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Why are there two forms of cubature kalman filters?

When I read cubature Kalman filter (CKF) related papers, I have seen two forms of corvariance $P_{xz}$. I don’t know what is the difference, or are they equivalent? The first form is form the orignal ...
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Unknown parameter - augmenting state equation (Kalman filter)

First, we have a state space model with mean reversion and $\mu$ is unknown $y(t )= F* x_t +e_t$ $x_t- \mu = G* (x_{t-1}-\mu) +n_t$ There is a option to add unknown parameters to the state vector and ...
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Is this the right way to set up a kalman filter in dlm based on random walk?

I have just started learning the filter for forecasting (please be gentle...), as well as the dlm package and its applications. I have the following code stolen from link but instead of ARMA I used a ...
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In-sample forecast accuracy of Beta (Kalman filter)

One can calculate time-varying betas (known from the CAPM) using the Kalman filter. For example, one can calculate the in-sample forecast accuracy using the MAE. $MAE = \frac{1}{T}\sum_{t=1}^T|\hat{R}...
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Understanding questions regarding the Kalman filter

I have a few questions about the Kalman filter in R (dlm package): Given the function dlmFilter, there is the output time ...
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Sigma-point Kalman filter (CDKF)

I am completely stuck on the below series of questions. Specifically 3/4/5. I know what some of the correct answers are but I do not understand the steps to get there (especially the input matrix X). ...
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Choice of covariance matrices in Kalman filtering?

I am attempting to learn about Kalman filtering. I understand the state vector, call it $\mathbb{x}$, comes with a covariance matrix call it $P$. I can initially choose my $\mathbb{x}$ by my pre-...
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Moving mean reverting model - Beta off the charts? (Kalman Filter)

I have implemented the moving mean reverting model with the FKF package, but unfortunately the beta as well as beta mean is way off as you can see in the chart. Is there anything I have not considered?...
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Understanding "Kalman Filter" intuitively

What is the cleanest, easiest way to explain to someone the concept of "Kalman Filter"? What does it intuitively mean? It's a concept that I have difficulty articulating - especially when ...
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EM Algorithm for Kalman Filters

Say I have the following dynamical system with unknown covariances for $w,v$. $$ z_n = Az_{n-1}+w\\ x_n = Bz_n +v $$ where $w \sim \mathcal{N}(0,Q)$ and $v \sim \mathcal{N}(0,R)$. I want to apply the ...
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What is the cost function that needs to be minimized in a Kalman Filter?

I keep finding different cost functions (in discrete and continuous forms) on the internet and it has me confused. Given a simple problem where the error of the state must go to zero, what is the cost ...
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Prediction Interval for the Kalman Filter

I am considering using the Kalman filter for an online regression for the state space system \begin{align} \beta_t &= \beta_{t-1} + \eta_t \\ Y_t &= X_t \beta_t + \varepsilon_t \end{align} ...
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Maximum likelihood parameter estimation for state space model (Kalman Filter)

it´s about a state space model that I want to run using the Kalman filter. However, certain parameters are unknown and must be estimated by the maximum likelihood method. The state space model is as ...
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Does Normalized Estimation Error Squared (NEES) and Normalized Innovation Error Squared (NIS) Only Apply to Kalman Filtering?

Regarding the NEES and NIS metrics, do they only apply to Kalman Filtering? Or can I use them for any estimator that outputs a prediction and has a covariance matrix? I have never seen NEES applied to ...
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In stochastic filtering, can observations depend on lagged observation values?

Say I have a latent state like $$ dX_t = dW_t $$ and observations like $$ dY_t = f(X_t - Y_t)dt + dZ_t $$ Can I get filtering estimates of $X_t$ using a standard Kalman filter framework despite the ...
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Kalman filter for stock price return

I am trying to use the Kalman filter to predict daily stock returns, where I have access to about 2000 trading days of daily price data, denoted $y_t$ as well as simulations of the same dimension ...
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Extended Kalman Filter Non-Linear Regression Implementation R, Correct?

I am working on the Kalman Filter and its applications. I tried to implement a model for a nonlinear regression problem of the form: $$ y = \exp(-(X\beta)) + q,\quad q \sim \mathcal{N}(0, I) $$ using ...
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Getting started with Bayesian Dynamic Networks?

Dagum developed DBNs to unify and extend traditional linear state-space models such as Kalman filters, linear and normal forecasting models such as ARMA and simple dependency models such as hidden ...
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State space representation of VECM-GARCH

Can someone help me write a state-space representation for the VECM-GARCH model to estimate the time-varying parameters using Kalman Filtering in Matlab? I am struggling with specifying the GARCH ...
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How to design a filter to remove the influence of factors on the values of a measurement

Is anybody aware of methods that are appropriate to modify the values of a time series to account for factors that are known to artificially inflate or deflate the measurement. An example of the ...
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Learning resources for Bayesian Dynamic Networks?

Increasingly, I've stumbled on the term Bayesian Dynamic Network(s). The field seems to be at the intersection of probabilistic graphical models, time series, Kalman filters, etc. Because there's so ...
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On the predictive distribution of a Bayesian structural time-series model

I am trying to understand the structure and, in particular, normality properties of the predictive distribution of a Bayesian structural time-series model. My reasoning is as follows. The posterior ...
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how to make Kalman filter results equivalent to linear regression? [duplicate]

Statistics gurus, Kalman filter appears to be a powerful estimator for linear problems. I understand one can tune the performance by adjusting parameters like process noise and measurement noise. Is ...
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How to make Kalman filter results equivalent to linear regression?

Kalman filter appears to be a powerful estimator for linear problems. I understand one can tune the performance by adjusting parameters like process noise and measurement noise. Is it possible to ...
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How to treat data for Bayesian VARs

I am working on a project where I need to implement a time varying structural VAR. From my understanding this uses the Kalman filter and is basically a Bayesian tool. From frequentist time series ...
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Stabilize pose estimation keypoints

I'm currently facing a problem of stabilizing the generated key points from the HRNet as in this repository. I created my personalized dataset where the key points mark the extreme locations of an ...
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How to verify Kalman filter performance without true data

I am implementing a Kalman filter for GPS/INS data, but I do not have data that can be considered "true" (i.e. a deterministic state). The only data I have for the problem is the collection ...
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Can anyone point me towards tutorials describing how to use the Kalman filter for forecasting?

I am trying to find any guides on how to use Kalman filters with ARIMA models but the only sources I have found have been highly technical that I can't really understand. Can anyone point me towards ...
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Why are covariance matrices projected by both right and left multiply?

I've been doing a lot of Kalman filtering work recently. I've derived all the equations starting from a basic linear inverse problem, so strictly speaking I know where everything comes from. I also ...
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