Predicting the Remaining Useful Lifetime (RUL) of a system has become one of the primary goals of engineering and reliability researchers. RUL prediction is based on the measurement data collected from sensors (e.g. vibration data, temperature data). The collected data is may be inaccurate owing to sensor problems. These problems are often ignored or modeled by a Gaussian noise in most previous work. However, due to various operation circumstances and the aging impact, the sensor itself will ultimately deteriorate and its performance will deteriorate. The Gaussian noise with a constant mean is then not appropriate to fully capture the sensor degradation. In this context, this study focuses on predicting the RUL considering the sensor degradation. For this purpose, a joint model of sensor degradation and system degradation is firstly developed. In this model, the sensor degradation is modeled by Wiener and Gamma processes instead of Gaussian noise. Then, different estimation methods based on the particle filter, a popular model-based technique, were proposed to predict the RUL based on the joint degradation model. To study the performances of our methods, numerical analyzes were carried out. The obtained results confirm the performance and advantages of the proposed methods.