Optimal Solution to Matrix Riccati Equation – For Kalman Filter Implementation
Kinjal Bhar, Adam S. Charles, Lanre M.A., Aliyu M. Aliyu · InTech eBooks · 2012
Matrix Riccati Equations arise frequently in applied mathematics, science, and engineering problems. These nonlinear matrix equations are particularly significant in optimal control, filtering, and estimation problems. Essentially, solving a Riccati equation is a central issue in optimal control theory. The needs for such equations are common in the analysis and synthesis of Linear Quadratic Gaussian (LQC) control problems. In one form or the other, Riccati Equations play significant roles in optimal control of multivariable and large-scale systems, scattering theory, estimation, and detection processes. In addition, closed forms solution of Riccti Equations are intractable for two reasons namely; one, they are nonlinear and two, are in matrix forms. In the past, a number of unconventional numerical methods were employed for the solutions of time-invariant Riccati Differential Equations (RDEs). Despite their peculiar structure, no unconventional methods suitable for time-varying RDEs have been constructed, except for carefully re-designed conventional linear multistep and Runge-Kutta(RK) methods.