The design of an energy-efficient tracking framework is a well-investigated issue and a prominent sensor network application. The current research state shows a clear scope for developing algorithms that can work, accompanying both energy efficiency and accuracy. The prediction-based algorithms can save network energy by carefully selecting suitable nodes for continuous target tracking. However, the conventional prediction algorithms are confined to fixed motion models and generally fail in accelerated target movements. The neural networks can learn any non-linearity between input and output as they are model-free estimators. To design a lightweight neural network-based prediction algorithm for resource-constrained tiny sensor nodes is a challenging task. This research aims to develop a simpler, energy-efficient, and accurate network-based tracking scheme for linear and non-linear target movements. The proposed technique uses an autoregressive model to learn the temporal correlation between successive samples of a target trajectory. The simulation results are compared with the traditional Kalman filter (KF), Interacting Multiple models (IMM), Current Statistical model (CSM), Long Short Term Memory (LSTM), Decision Tree (DT), and Random Forest (RF) based tracking approach. It shows that the proposed algorithm can save up to 70% of network energy with improved prediction accuracy.