An Alternative Algorithm for Discrete-Time Filtering
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The discrete-time Kalman filter is a conditional mean estimator of the states of a linear stochastic process, conditioned on the previous state and current measurements. It assumes that the states and noise inputs can be represented as jointly Gaussian random variables. The influence diagram is a decision analysis tool. Under certain conditions, it can represent continuous, jointly Gaussian random variables. The conditioning order of the random variables may be changed using Bayes rule so that any random variable can be conditioned on any other subset of random variables in the diagram. Under these conditions, an influence diagram can represent the states, measurements, and initial conditions of a linear stochastic process. It too can be a conditional mean estimator of the states of a linear stochastic process, and is an alternative algorithm for the Kalman filter. The influence diagram algorithm for the Kalman filter uses a factored covariance matrix. It is similar to other factored forms of the Kalman filter such as the U-D filter. It can be faster than other factored forms of the Kalman filter, but retain their improved numerical properties.
- Numerical Mathematics
- Statistics and Probability