Finding the Truth From Uncertain Time Series by Differencing

Time series data is ubiquitous and of great importance in real applications. But due to poor qualities and bad working conditions of sensors, time series reported by them contain more or less noises. To reduce noise, multiple sensors are usually deployed to measure an identical time series and from these observations the truth can be estimated, which derives the problem of truth discovery for uncertain time series data. Several algorithms have been proposed, but they mainly focus on minimizing the error between the estimated truth and the observations. In our study, we aim at minimizing the noise in the estimated truth. To solve this optimization problem, we first find out the level of noise produced by each sensor based on differenced time series, which can help estimating the truth wisely. Then, we propose a quadratic optimization model to minimize the noise of the estimated truth. Further, a post process is introduced to refine the result by iteration. Experimental results on both real world and synthetic data sets verify the effectiveness and efficiency of our proposed methods, respectively.