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A new globally convergent nonlinear observer called the modified gain extended Kalman observer (MGEKO) is developed for a special class of systems. The stochastic stability of this observer used as a filter (now called the MGEKF), is analyzed in the probabilistic Hilbert space L2. Sufficient conditions for the MGEKF to be asymptotically stable are established. Finally, the MGEKO and the MGEKF are applied to the three-dimensional bearing only measurement problem (BOMP) where the EKF often shows erratic behaviors.