Time series data appears in a variety of applications such as smart transportation and environmental monitoring. One of the fundamental problems for time series analysis is time series forecasting. Despite the success of recent deep time series forecasting methods, they require sufficient observation of historical values to make accurate forecasting. In other words, the ratio of the output length (or forecasting horizon) to the sum of the input and output lengths should be low enough (e.g., 0.3). As the ratio increases (e.g., to 0.8), the uncertainty for the forecasting accuracy increases significantly. In this paper, we show both theoretically and empirically that the uncertainty could be effectively reduced by retrieving relevant time series as references. In the theoretical analysis, we first quantify the uncertainty and show its connections to the Mean Squared Error (MSE). Then we prove that models with references are easier to learn than models without references since the retrieved references could reduce the uncertainty. To empirically demonstrate the effectiveness of the retrieval based time series forecasting models, we introduce a simple yet effective two-stage method, called ReTime consisting of a relational retrieval and a content synthesis. We also show that ReTime can be easily adapted to the spatial-temporal time series and time series imputation settings. Finally, we evaluate ReTime on real-world datasets to demonstrate its effectiveness.
Long-term scene changes present challenges to localization systems using a pre-built map. This paper presents a LiDAR-based system that can provide robust localization against those challenges. Our method starts with activation of a mapping process temporarily when global matching towards the pre-built map is unreliable. The temporary map will be merged onto the pre-built map for later localization runs once reliable matching is obtained again. We further integrate a LiDAR inertial odometry (LIO) to provide motion-compensated LiDAR scans and a reliable initial pose guess for the global matching module. To generate a smooth real-time trajectory for navigation purposes, we fuse poses from odometry and global matching by solving a pose graph optimization problem. We evaluate our localization system with extensive experiments on the NCLT dataset including a variety of changing indoor and outdoor environments, and the results demonstrate a robust and accurate localization performance for over a year. The implementations are open sourced on GitHub.