On model identification of a class of unbounded systems with application to navigation instrument error modeling

An unbounded system model is proposed to represent the error behavior inherent in many navigation instruments or associated with their environments. The model consists of an unbounded deterministic part with unknown constant parameters plus a stochastic part with unknown probability distributions. A simple robust strategy is given to identify the unknown parameters and the second-order statistics of the stochastic part from data. The strategy is sequential, i.e., the deterministic part is first identified and then the statistics of the stochastic part are identified from appropriate residuals. Convergence properties, including the rate of convergence, of parameter estimates are given in terms of conditions which can be easily verified in practical applications. An example involving the use of experimental data to identify an error model for a shipboard velocity measuring system is presented to illustrate the technique.