Optimal Inputs for Nonlinear Process Parameter Estimation

The sensitivity of observed data to an unknown parameter is enhanced by utilizing optimal inputs. The derivation is given for the optimal input of an nth-order nonlinear differential equation. To obtain the optimal input, the solution of 4n two-point boundary value equations is required. Numerical resutis are given for a second order linear example. The optimal return is compared with the return obtained for a step input. The existence of a critical time length is demonstrated.     

A Comparison of Numerical Methods for Solving Optimal Control Problems

Linear systems with quadratic performance criteria typically lead to two-point boundary value problems. The numerical solution of such problems is often difficult because of roundoff and truncation errors. In this paper numerical methods for digital computer solutions are considered for a system described by a given second-order linear differential equation and the results are compared. The results show that where accurate analytic solutions cannot be obtained, the invariant imbedding technique yields more accurate results, for a given integration grid interval, than the other methods considered.     

Automatic Solution of Nthorder Optimal Control Problems

An automatic method for obtaining the numerical solution of a certain class of nth-order nonlinear optimal control problems is described. The derivatives required for the solution of the two-point boundary value problem are computed automatically. The user of the program need only input the Hamiltonian function by calling the appropriate Fortran subroutines. This paper extends the methods described by the authors in previous papers in that it increases the order of the system that can be handled by the program from second order to the general nth order.     

Linear Regression Filtering and Prediction for Tracking Maneuvering Aircraft Targets

A Cartesian coordinate linear regression filter is utilized for tracking maneuvering aircraft targets. Measurements of target position are made in a line-of-sight coordinate frame, but filtering is performed in Cartesian coordinates. Numerical results are given for optimizing the truncation time constant such that a good balance is obtained between the dynamic errors and the standard deviations. Lower bounds on the dynamic errors are established for the Cartesian coordinate linear regression filter and compared with a line-of-sight coordinate Kalman filter.     

Passive Position Location Estimation Using the Extended Kalman Filter

Several papers have been published recently using the method ofleast squares for passive position location estimation. While the Kalman filter is mentioned as an alternative approach in most ofthese papers, none of the papers actually compare the performanceof the Kalman filter with the method of least squares. In this paper,the performances of the extended Kalman filter and the iteratedextended Kalman filter are compared with the method of leastsquares. Monte Carlo results are given showing how the a prioricovariance matrix influences the accuracy of the extended Kalmanfilter.