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This paper presents an adaptive scheme to estimate the time-derivative of a signal without any knowledge of its dynamics. The adaptive estimator is formulated as an adaptive observer with the σ-modification update law. The algorithm is applied to an adaptive differential filter for the detection of moving objects within a scene acquired by a stationary camera. We adopt four nonlinear intensity functions to reduce the influence of measurement noises. The MATLAB simulations are performed to demonstrate its performance.

Time-Derivative Filter for Detection of Moving Objects by Adaptive Identification Method