# 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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### 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 $p(y) \approx N(m_y, S_y)$ ...
1 vote
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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} \...
1 vote
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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 ...
1 vote
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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 ...
1 vote
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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 ...
1 vote
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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 ...
1 vote
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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 ...
1 vote
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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 ...