## 1 Introduction  
Noise pollution continues to be a major health problem in the modern world, leading to various negative effects on human beings, such as cardiovascular effects, rising blood pressure, annoyance, sleep disorders, and learning impairment [1; 2; 3; 4; 5; 6]. Noise is a major issue that should be considered during the design and construction of new transportation systems, as well as in the improvement of existing systems [7; 8; 9; 10]. Road traffic noise is caused by the combination of rolling noise, consisting of friction noise between the road surface and the car tyres, and the propulsion noise caused by the exhaust systems or engines. The emission of traffic noise is influenced by many factors such as type of engines, exhaust systems and tyres interacting with the road, weather, and road conditions. For instance, [PERSON] et al. [11] revealed the influence of tyres on the use of the Close Proximity Method (CPX) for evaluating the effectiveness of a noise mitigation action based on low-noise road surfaces. Further, some studies have been proposed to address the effects for pavement age, pavement texture, and other pavement characteristics on traffic noise emission [12; 13; 14; 15; 16]. Traffic noise prediction models are required as aids in the design of highways and other roads, and sometimes in the assessment of existing or envisaged changes in traffic noise conditions [17; 18]. However, due to the complexities of urban traffic systems, extensive uncertainties exist in the traffic noise prediction model.  
Previously, a number of uncertainty analysis methods have been applied to traffic noise prediction models. For example, [PERSON] and [PERSON] [19] assessed the impact of traffic noise based on probabilistic and fuzzy approaches under uncertainty, in which the input (i.e., traffic flow, speed, and component) of the traffic noise prediction model was represented by probability distributions. [PERSON] and [PERSON] [20] introduced a stochastic model to describe and predict the noise levels, in which a Gaussian Ornstein-Uhlenbeck model is used to represent the dynamics of the noise levels, and the mean-reversion properties and seasonal volatility for each day of the week are studied separately. [PERSON] and [PERSON] [21] presented the development and evaluation of a stochastic dynamic traffic noise prediction model based on noise curves for vehicle classes and their speed. [PERSON] et al. [22] evaluated the influence of speed distribution in road traffic noise prediction. [PERSON] et al., [23] used the entropy-copula method for modelling the dependence between traffic volume and traffic noise on the highway. However, previous studies of the uncertainty assessment in traffic noise predictions were mainly focused on inputs, such as the probabilistic characteristics of the road traffic flows [24]. Few studies have been conducted on the parameter estimation and uncertainty quantification of the traffic noise prediction models.  
Therefore, in this study, a nested ensemble filtering (NEF) approach, as an extension of previous ensemble Kalman filter (EnKF) and particle filter methods, will be proposed for parameter estimation and the uncertainty quantification of traffic noise models. The proposed NEF method will improve upon the ensemble Kalman filter (EnKF) method by incorporating the sample importance resampling (SIR) procedures into the EnKF update process. Compared with the EnKF method, the proposed NEF approach can avoid the overshooting problem (abnormal value (e.g., outside the predefined ranges, complex values) in parameter or state samples) existing in the EnKF update process. The proposed NEF method will be applied to traffic noise prediction on the Trans-Canada Highway in the City of Regina to demonstrate its applicability.