Sensor fusion plays an important role in many applications. The abundance of sensory data from different sources does not guarantee better quality information. It is reasonable to assume that not all sensors have the same levels of accuracy and precision. This needs to be taken into consideration when sensor fusion or integration is performed. In many applications it is difficult to measure the sensors' accuracy and precision, which could be dynamic variables. This paper explores different approaches to address the problems related to competitive sensor fusion. The paper focuses on optimal weight assignment and nonlinear weight functions using artificial neural networks as well as simultaneous fusion and calibration of multi-sensor systems. Optimal weight assignment is formulated as a constrained optimization problem and solved using the Karush-Kuhn-Tucker conditions to minimize the variance. Single and multi-layer artificial neural networks are used to determine linear and nonlinear weight functions for sensor fusion. Although they require training data, neural networks are particularly effective when little statistical information about the sensors is available. Several examples are presented to demonstrate the proposed methods.