A Simple Iterative Solution for Mixed Additive and Multiplicative Random Error Model with Inequality Constraints

Objectives With the development of modern observation techniques, the processing methods which only consider additive errors cannot meet the requirements. Most of the existing methods for dealing with inequality constraints are based on additive error models, including Gaussian-Markov model and errors-in-variables model, while the processing methods for mixed additive and multiplicative (MAM) random error models are rare.

Methods Based on the least squares principle and the ideas of zero and infinite weights, we construct a penalty function with the given inequality constraints, and derive the simple iterative method (SIM) for the estimation of MAM parameters under the inequality constraints. Then, we add a penalty factor increasing with the number of iterations before the penalty term to address the defects of the original SIM.

Results Two sets of cases show that the improved SIM can effectively solve the problem that the original method does not converge when used to deal with MAM error models with inequality constraints. The structure of improved SIM is simple and easy to implement. And it can obtain better parameter estimation compared with other schemes.

Conclusions The feasibility and effectiveness of the improved SIM for parameter estimation of MAM error models with inequality constraints are verified, and it can be applied to the processing of large batches of data.