Robust Linear Rules for Nonlinear Systems

Abstract

In [Hager, 1988] we proposed a framework for describing sensor data fusion problems in terms of data representations, sensors, and sensing tasks. One approach to solving such problems is to use linear updating rules to update representation parameters based on sensor observations. This approach is particularly attractive when fast updates for dynamic systems are required. The disadvantage of this approach has traditionally been the amount of heuristic “tuning” required to ensure the method has accurate, stable behavior. In this article we refine the results found in [Hager & Mintz, 1989b] to study the behavior of linear rules for nonlinear systems. The resulting solutions have an interesting nature, and suggest an interesting relationship between the complexity of computing a rule, and the efficiency with which the rule makes use of information. We point out analogous results for other methods we have studied, and discuss their implications for sensor data fusion.