This paper develops an estimation algorithm for the time and amplitude of arrival of a known transmitted sequence over a single-path fading channel. The algorithm is optimized to enhance robustness to fast channel fading and low signal-to-noise ratio (SNR) conditions, which are common in wireless location applications. The paper also presents a noise and fading bias correction technique for amplitude of arrival estimation that improves the estimation accuracy significantly. The proposed algorithm is then applied to the case of code-division multiple-access (CDMA) wireless location finding for which the paper gives simulation results that demonstrate significant estimation accuracy improvement over known algorithms.