# 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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### Using Bayesian statistics in time series forecasting

I would like to forecast demand count time series of taxi fleets at different locations on the map at different points in time. I.e. multivariate demand Time series forecasting. Given hierarchinal ...
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### How can mahalanobis and chi2-test be used to determine of an observation is acceptable?

Assume that you have a model $$\dot x = Ax + Bu$$ $$y = Cx$$ And this model is SISO. Single input and single output. You got the mission to determine of an observation is acceptable for the kalman ...
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### Assessing probability that one set of measurements extends the other with Kalman smoother

I have two sets of N-dimensional measurements following each other with a certain time gap in between. Let's name those sets $A$ and $B$, respectively. All observations have constant Gaussian white ...
1 vote
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### Exact diffuse initialization of the Kalman Filter: what does the design matrix look like?

I am using Python (statsmodels) to create a dynamic factor model on which I apply the Kalman filter. Thanks to earlier questions on this forum, I landed upon using exact diffuse initialization. My ...
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### Kalman Filter Terminology: Prediction vs Estimation

The linear dynamical system model underlying the Kalman filter technique involves a random process $(x_{0}, v_{1}, w_{1}, x_{1}, z_{1}, v_{2}, w_{2}, x_{2}, z_{2}, \ldots)$ where $x_{k}$ represents ...
1 vote
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### Why do popular ML and statistical packages simply ignore classical estimation and detection algorithms for statistical signal processing? [closed]

For those who had a hard time to study and understand classical estimation and detection algorithms, and unfortunately realized that these algorithms are simply ignored by many packages that have the ...
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### Derivation of posterior distribution of Kalman filter

I am following this article on Understanding the Kalman filter by Meinhold, and I can understand all the derivation up until equation (4.4). However, I cannot understand how they arrive at the ...
1 vote
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### Proving consistent/inconsistency of a fusion of KF estimates

I have a distributed fusion scenario with a single target where two sensor nodes $i,j$ estimate the true state $\mathbf{x}$ using a local Kalman filter. The (linear, Gaussian) measurement errors of ...
1 vote
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### Smoothing of GPS tracks - remove noise and stop-go clusters

I know there are several posts about this, but I could not find exactly what I need. I have GPS track data (from an underwater vehicle) for short intervals of 1 second (time-stamps on data). The data ...
1 vote
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### Instantaneous propagation of process covariance matrix modification's effect on state

I am trying to build a zero-delay kalman filter which udates its process noise covariance matrix $Q_k$ depending on the value of the residues $z_k - H\cdot x_k$. My problem is, I have adopted a 1D ...
1 vote
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### Inferring a random walk from noisy "images"

I'm interested in the following inference / filtering problem in a hidden Markov model setting. Suppose we have a simple random walk $x_t\in\mathbb{Z}$ and observations are "images" ...
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### What is the null hypothesis and p value in the lagged autocorrelation of innovations in Kaman filter

I am using statsmodels.tsa.stattools.acf to calculate the lagged autocorrelation of innovations in Kalman filter with alpha=0.05....
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### Negative value of likelihood function in Kalman filter

I use kalman filter algorithm, where I minimize the value of likelihood function. But after some iteration I got negative value of likelihood function. Is that a problem?
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### Extended Kalman Filter for estimating angle using tan measurement function and two measurements

I'm attempting to implement an extended Kalman filter (EKF) to estimate an angle $\alpha$ given measurements of two scalars $x$ and $y$ where the measurement function is $\alpha=atan(\frac{y}{x})$. ...
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### How do I calculate the standard error of Kalman Filter parameter estimates?

I am trying to implement the Schwartz-Smith (2000) commodity pricing model from the paper Short-term variations and long-term dynamics in commodity prices The model is estimated using the Kalman ...
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### Parameter estimation of state-space models with hidden variables

I have a time-series analysis problem, that I am having trouble finding a suitable regression technique for. I have a coupled linear three dimensional system \begin{align*} X_{t} & =\left(1+J\...
1 vote
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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 ...
1 vote
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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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### 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 ...
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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### 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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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 ...