Definitions of estimates •ML Maximum Likelihood •MAP Maximum A Posteriori •LS Least Squares •MMSE Minimum Mean square Error Measures of quality of estimates •Unbiased, variance, consistency,the Cramer-Rao lower bound, Fisher information, Efficiency
Linear Estimation in Static Systems
•Minimum Mean Square Error (MMSE) •MMSE estimation of Gaussian random vectors •Linear MMSE estimator for arbitrarily distributed random vectors •LS estimation of unknown constant vectors from linear observations, batch form, recursive form. •Apply the LS technique
• Gaussian pdf, mean and covariance • Stochasticsequences, Markov property • Discrete-time linear stochastic dynamic systems Prediction, propagation of the mean and covariance • Continuous-time linear stochastic dynamic systems, Propagation of mean and covariance
State Estimation in Discrete Time Linear Dynamic Systems (= Kalman Filter)
•The estimation of the state vector of a stochastic linear dynamic system is considered. •The state estimator for discrete-time linear dynamic systems driven by white noise —the (discrete-time) Kalman filter —is introduced. •Estimation of Gaussian random vectors.
The multiple model (MM) algorithms; Hybrid systems —the system behaves according to one of a finite number of models, it is in one of several modes (operating regimes), both discrete (structure/parameters) and continuous uncertainties.
The static MM algorithm —for fixed (nonswitching
The optimal dynamic MM algorithm —for switching models —Markov chain, two suboptimal approaches: Generalized pseudo-Bayesian (GPB) ; Interacting multiple model (IMM)
Adaptive estimation algorithms —in many practical situations the “parameters of the problem” are partially unknown and possibly time-varying. The state estimation techniques that can “adapt” themselves to certain types of uncertainties