Networked Data Fusion with the Asynchronous Observations at Multiple Rates

Most of the earlier works are based on the measurements observed by sensors with synchronous samples at the same sampling rate [10, 20, 23, 28, 39]. Only a few pieces of work deal with asynchronous multirate multisensor data fusion. Based on continuous time systems, Alouani with his group [4] and Bar-Shalom et al. [10, 8] present some effective algorithms for asynchronous multisensor systems. As far as the discrete time systems are concerned, the related researches include the approaches based on multiscale system theory [72, 11, 12, 195, 211, 226], the batch process methods [104], and the algorithms based on the designing of multirate filter banks [42], etc. In the literature listed above, the missing of observations is rarely concerned, which is inclined to encounter in many application fields including communication, navigation, etc. For filtering of incomplete measurements, there are some interesting results. Among these, the algorithms presented by the team of Wang are promising that it has proper computation complexity and can generate nearly optimal state estimate [194]. Based on a discrete-time linear dynamic system, Kalman filtering with intermittent observations is studied in [169], where the arrival of the observations is modeled as a random process, and the statistical convergence property of Kalman filter is given. The modified Riccati equation is studied by Boers and his group [15]. Some useful results are presented as far as a single sensor observing a single target which is described by a linear state space model is concerned. Kalman filtering with faded measurements is studied in [173]. By use of peak covariance as an estimate of filtering deterioration caused by packet losses, the stability of Kalman filtering with Markovian packet losses is studied in [81] based on a linear time-invariant system. Bar-Shalom studies the state estimation with out of sequence measurements based on a time-invariant dynamic system [8]. Xia, Shang, Chen and Liu study the networked data fusion with packet losses and variable delays, and an optimal state estimate is generated [206]. However, in all these interesting papers, multirate systems are not concerned. The multi-rate linear minimum mean squared error state estimation problem is solved by use of the lifting technique [99]. While, asynchronous sampling and data losses are not concerned in this reference. To sum up, there are few results on the fusion of multirate sensors that sample asynchronously with measurements randomly missing. This motivates us for the present study.