Faster Complex Lyapunov Equation Solution Selection

Complex Kalman filters are used to process complex signals that are ubiquitous in many fields of science and engineering. The augmented complex Riccati equation appears for time-invariant augmented or widely linear models. The augmented complex Lyapunov equation is derived in the infinite measurement noise case. Iterative per step and doubling algorithms for the solution of the complex Lyapunov equation are derived. The computational requirements of the per step and doubling algorithms are derived, leading to the ability to select the faster algorithm.