An Introduction to Optimal Estimation
Linear algebra; Nonlinear and linear dynamic systems; Elementary concepts of probability theory; Random dynamic systems; Linear estimation theory; Discrete dynamic system estimation; Continuous dynamic system estimation.
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Nonlinear and Linear Dynamic Systems
Elementary Concepts of Probability Theory
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algebra assume assumption average calculate coefficient components computation constant continuous random correlation covariance matrix defined density function derived diagonal elements diagonal matrix differential equation discrete distribution dot product dynamic system equations of motion error matrix estimation problem estimation theory event Example expected value given identity matrix initial conditions input integral interval inverse Kalman form last equation latter equation linear system matrix form matrix multiplication mean square error measurement process nonlinear Note observation obtain optimal estimate optimum filter polynomial priori estimate probability function procedure quadratic form random process random variable reader real number sample space satisfy second moment matrix sinh solution solve square matrix step process Suppose symmetric theorem transition matrix transpose true variance verify voltage weighted least square zero