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A Kalman Filter/Smoother is fully specified by its initial conditions ().
These parameters define a probabilistic model from which the unobserved states and observed measurements are assumed to be sampled from.
The difference is that while the Kalman Filter restricts dynamics to affine functions, the Unscented Kalman Filter is designed to operate under arbitrary dynamics.
The advantages of the Unscented Kalman Filter implemented here are: .
Given a sequence of noisy measurements, the Kalman Filter is able to recover the “true state” of the underling object being tracked.
Common uses for the Kalman Filter include radar and sonar tracking and state estimation in robotics.
The Kalman Filter, Kalman Smoother, and EM algorithm are all equipped to handle this scenario.
To make use of it, one only need apply a Num Py mask to the measurement at the missing time step: In order to understand when the algorithms in this module will be effective, it is important to understand what assumptions are being made.
The Kalman Filter is a unsupervised algorithm for tracking a single object in a continuous state space.
To make notation concise, we refer to the hidden states as , the measurements as , and the parameters of the These assumptions imply that that is always a Gaussian distribution, even when is observed.
If this is the case, the distribution of and are completely specified by the parameters of the Gaussian distribution, namely its The Gaussian distribution is characterized by its single mode and exponentially decreasing tails, meaning that the Kalman Filter and Kalman Smoother work best if one is able to guess fairly well the vicinity of the next state given the present, but cannot say Like the Kalman Filter, the Unscented Kalman Filter is an unsupervised algorithm for tracking a single target in a continuous state space.
class comes equipped with two algorithms for prediction: the Kalman Filter and the Kalman Smoother.
While the former can be updated recursively (making it ideal for online state estimation), the latter can only be done in batch. Functionally, Kalman Smoother should always be preferred.
Unlike the Kalman Filter, the Smoother is able to incorporate “future” measurements as well as past ones at the same computational cost of where is the number of time steps and class implements the Expectation-Maximization algorithm.