Output error method

Abstract

The type of (linear or nonlinear) mathematical model, and the presence of process or measurement noise in data or both mainly drive the choice of the estimation method and the intended use of results. The equation error method has a cost function that is linear in parameters. It is simple and easy to implement. The output error method is more complex and requires the nonlinear optimisation technique (Gauss-Newton method) to estimate model parameters. The iterative nature of the approach makes it a little more computer intensive. The third approach is the filter error method which is the most general approach to parameter estimation problem accounting for both process and measurement noise. Being a combination of the Kalman filter and output error method, it is the most complex of the three techniques with high computational requirements. The output error method is perhaps the most widely used approach for aircraft parameter estimation and is discussed in this chapter, after discussing the concepts of maximum likelihood. The Gaussian least squares differential correction method is also an output error method, but it is not based on the maximum likelihood principle.