Energy Expenditure Estimation (EEE) is an important step in tracking personal activity and preventing chronic diseases such as obesity, diabetes and cardiovascular diseases. Accurate and online EEE utilizing small wearable sensors is a difficult task, primarily because most existing schemes work offline or using heuristics. In this work, we focus on accurate EEE for tracking ambulatory activities (walking, standing, climbing upstairs or downstairs) of a common smartphone user. We used existing smartphone sensors (accelerometer and barometer sensor), sampled at low frequency, to accurately detect EEE. Using Artificial Neural Networks, a machine learning technique, we build a generic regression model for EEE that yields upto 89% correlation with actual Energy Expenditure (EE). Using barometer data, in addition to accelerometry is found to significantly improve EEE performance (upto 15%). We compare our results against stateof- the-art Calorimetry Equations (CE) and consumer electronics devices (Fitbit and Nike+ Fuel Band). We were able to demonstrate the superior accuracy achieved by our algorithm. The results were calibrated against COSMED K4b2 calorimeter readings.