The problem considered in this dissertation is that of estimating the state of a system with a linear plant equation but having a measurement function which is a quadratic form in the state. It is first demonstrated by constructive proof that the problem has a solution if the controls have large enough magnitude, and some requirements on the minimum size of the control are discussed.
Three algorithms for estimating the state are obtained, one using the technique of maximum likelihood, the other two utilizing a more general Bayesian approach. In addition, a first-order approximate conditional mean filter is included for comparison.
It is demonstrated by structural comparisons and numerical results that the algorithm for finding an approximate maximum of the posterior density function is the overall best in terms of speed, storage, practicability, and accuracy. It is also shown that good state estimates can be generated for a large class of problems using any of these algorithms if the control largeness conditions are satisfied.
Finally, some extensions are discussed, the main one being the application of the technique of finding an approximate maximum of the posterior density function to systems with more general nonlinear observers.
Level of Degree
Electrical and Computer Engineering
First Committee Member (Chair)
Harold K. Knudsen
Second Committee Member
Third Committee Member
Shipley, James Parish Jr.. "State Estimation in Discrete-Time Linear Systems with Quadratic Form Observers." (1973). https://digitalrepository.unm.edu/ece_etds/471