Fusion of multi-resolution data for estimating speed-density relationships

Estimating traffic flow models, such as speed-density relationships, using data from multiple sources with different temporal resolutions is a prevalent challenge encountered in real-world scenarios. The resolution incompatibility is often intuitively addressed by averaging the high-resolution (HR) data to synchronize with the low-resolution (LR) data. This paper shows that ignoring the variability of HR data within the LR interval during the averaging process could lead to systematic data point distortions, resulting in biased model estimations. The average absolute biases of models estimated from the average data increase with the lost variability of HR data within the LR intervals. Subsequently, it proves that for any given complete average data dataset, there must exist an optimal dataset that minimizes the average absolute bias in model estimations introduced by the averaging process. A novel procedure for determining the practical optimal dataset is proposed. To test the proposed method, real-world HR data from four sites in Hong Kong and Nanjing, China were collected to mimic situations with multi-resolution data. Results demonstrated that the proposed method can significantly reduce the average absolute biases of models estimated from the determined practical optimal dataset, as compared to models estimated from the complete average dataset.