Accelerated ageing of cross-linked polyethylene (XLPE) insulated aerial bundled cables (ABC) installed at coastal regions for electric power distribution is a topic of major concern. Sudden failures caused by rapid insulation deterioration initiate unexpected power shutdowns. Accurate prognosis of incipient failures in cables will enable maintenance agencies to plan repair or replacement activities well on time thus improving the reliability and availability of the transmission grid. In this research work, historical non-destructive evaluation (NDE) data was generated using infrared thermography of ABCs to ascertain cable degradation parameter. Historical NDE data embodies the progressive degradation experienced by the ABCs installed at harsh marine environment. The degradation growth in cable insulation, when subjected to rough environmental conditions, is non-linear coupled with non-Gaussian / multimodal noise distributions. Therefore, a renowned nonlinear Bayesian estimator namely Particle Filter (PF) is applied on the historical database to determine degradation growth evolution over time. The proposed framework is further complimented with f-step prediction scheme in future time to quantify the prediction accuracy of cable degradation growth in future where measurement data is not available. The so predicted results are then compared to the actual degradation in future. The prediction accuracy demonstrates the efficacy of proposed technique for prognosis of ABCs installed at different locations. Accurate state prediction in different life phases of ABCs further displays robustness of proposed technique in estimating actual degradation growth during the different life stages.