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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State Space model with autocorrelated errors in state equation [closed]
I'm trying to estimate a state space model with a autocorrelated error component in the state equation. The model that I'm working with has the form:
\begin{equation}
Y_t = \frac{x_t + x_{t-1} + x_{t-...
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State space models and Kalman Filter
I have the following model specification:
$y_t = \mu_t + v_t,$
$\mu_{t+1|t} = \phi \, \mu_{t|t-1} + k\, v_t $
where v_t= y_t - mu_{t|t-1}, v_t|F_{t-1} ~ tv(0, sigma^2).
I was asked to provide the ...
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Representation of Hessian in Augmented State-Space Filtering Problems
Question
Let $z_t := (x_t, x_{t-1}, x_t^2, x_{t-1}x_t,x_{t-1}x_t,x_{t-1}^2)$, and
$R(x_t) := \sum_{(i,j) \in \{\{0,1,2,3,4\} \otimes \{0,1,2,3,4\} : i+j \le 4\}} w_{i,j} x_t^i x_{t-1}^j$,
so $R(\cdot)$...
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Ways to parametrise a positive parameter
I am working with a differentiable state-space model involving a noise variance term $\sigma^2$ which I want to parametrise based on some features, e.g. $\sigma^2 = g(X\beta) > 0$, wherer $\beta$ ...
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Kalman Filter to minimize weighted errors on the states: what's wrong with my derivation
I am thinking about how to implement a "weighted Kalman Filter". Note that the weights here are on the states. Basically the classical KF minimizes $\sum (x_i - \hat{x_i} )^2$ but I want to ...
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Measurement error R in Kalman Filter [duplicate]
I want to calculate the measurement error R for Kalman filter if I have such data:
True value of the golden bar is 18 g. A tool was used to measure the weight of the bar: 17.7, 17.8, 18.1, 17.8.
How ...
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For an ideal Kalman filter, I have that the NEES test passes but NIS test does not?
Sorry if this is more of a debugging question, but I have been stuck on this supposedly simple NIS test for a very long while. If anyone knows any sources which cover the theory or implementation of ...
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What if there is only one measurement equation containing two (or more) state variables while there are two unobservable state variables in a model?
I am learning Kalman Filter and ran into a question about the case in which only one signal is available.
It is commonly assumed that the number of states equals the number of observations (signals) ...
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Bayes rule and terms with expectation
I am reading the following paper in economics;
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On page 495, authors give an expression with Bayes rule. As an example, say that there is a random variable $\beta$ which can be either $\beta_L$ or ...
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kalman filter equations when I have position and velocity but force is unknown
I have a car for which I measure position and velocity using GPS receiver, but I do not know forces, which change the car velocity. I wonder how to build equations for Kalman filter. For measurements ...
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Covariance inversion for Gaussian process
Background
Let $x=f(u_x)\in\mathbb{R}$ and let $y=[f(u_y^1)\cdots f(u_y^{N})]\in\mathbb{R}^N$ for some function $f:u \in \mathbb{R}\mapsto \mathbb{R}$.
Given $y$, $u_x$, $u_{y}^1,\dots, u_{y}^{N}$, I ...
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How to Interpret and Address Non-Gaussian Measurement Post-Fit Residuals of a Kalman Filter?
I'm using a Kalman filter, optimized via hyperparameter search for both the feature matrix (about 300 variables post my most recent hyperparameter grid search), a ridge regression-based observation ...
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Best way to approach sensor fusion
I'm fusing acceleration data from an accelerometer and the derived acceleration from a distance sensor to learn about sensor fusion. The derived acceleration (2nd derivative) from the distance sensor ...
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Computing the Kalman filter measurement covariance matrix directly from measurement data?
I'm looking into methods for estimating the parameters of a Kalman Filter, in particular the covariance matrices. I have seen it suggested a couple times (for example here) that the measurement ...
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Looking for books and/or other resources for Multivariate Statistics for Optimal Estimation
I was trying to familiarize myself with state estimation theory by going through Optimal State Estimation and I realized I don't have the required background in Multiple Random Variables and ...
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