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• A Kalman filter can be used to predict the state of a system where there is a lot of input noise.
• The Kalman Filter estimates the true state of an object given noisy input (input with some inaccuracy).
• In the case of this simulation, the Kalman Filter estimates the true position of your cursor when there is random input noise.
• We used the Kalman Filter on an Aldebaran NAO humanoid robot as part of a class project.
• After reading the first part, you will be able to understand the concept of the Kalman Filter and develop the "Kalman Filter intuition".
• After reading the second part, you will be able to understand the math behind the Kalman Filter.
• Kalman filters are ideal for systems which are continuously changing.
• The math for implementing the Kalman filter appears pretty scary and opaque in most places you find on Google.
• That’s a bad state of affairs, because the Kalman filter is actually super simple and easy to understand if you look at it in the right way.
• The Kalman filter assumes that both variables (postion and velocity, in our case) are random and Gaussian distributed.
• This document gives a brief introduction to the derivation of a Kalman filter when the input is a scalar quantity.
• Kalman filter was proposed in the early 1960s and has been extensively used for the state estimation of dynamic systems.
• I would like to first explain the idea of ​​the Kalman filter (according to Rudolf Emil Kalman ) with only one dimension .
• The Picture Illustrates the Kalman Filter ‘s Predition step in various time-stages.
• This part of the Kalman filter now dares to predict the state of the system in the future.
• The Kalman filter has made a prediction statement about the expected system state in the future or in the upcoming time-step.
• P_{k\mid k-1}} The Kalman filter keeps track of the estimated state of the system and the variance or uncertainty of the estimate.
• The Kalman filter also works for modeling the central nervous system's control of movement.
• In the prediction step, the Kalman filter produces estimates of the current state variables, along with their uncertainties.
• Optimality of the Kalman filter assumes that the errors are Gaussian.
• Both dynamic meteorological and static socioeconomic factors were selected as the vector containing controls in the Kalman filter.
• The HFMD incidence was the explained variable in GWR model, as well as the measurement Y in the Kalman filter.
• Moreover, the state vector X in the Kalman filter contains the HFMD incidence and the socioeconomic factors.
• The Bayesian probabilistic approach is proposed to estimate the process noise and measurement noise parameters for a Kalman filter.
• Before we can run the Kalman filter we must initialize the state vector.

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