Complex nonlinear parameter estimation (CNPE) and obstacle shape reconstruction

The complex nonlinear parameter estimation (CNPE) formula and a robust algorithm are introduced. The formula is simple. However, it is exact, explicit, and systematic. The algorithm is flexible, accurate, fast, and robust. It can be applied to many different complex nonlinear parameter estimation problems as well as complex nonlinear least squares (CNLS) problems. The algorithm is applied to an obstacle shape reconstruction problem to show the power of the formula and the algorithm. The problem is known to be highly nonlinear and severely ill-posed.