Limited Memory Prediction for Linear Systems with Different types of Observation

Abstract — This paper is concerned with distributed limited memory prediction for continuous-time linear stochastic systems with multiple sensors. A distributed fusion with the weighted sum structure is applied to the optimal local limited memory predictors. The distributed prediction algorithm represents the optimal linear fusion by weighting matrices under the minimum mean square criterion. The algorithm has the parallel structure and allows parallel processing of observations making it reliable since the rest faultless sensors can continue to the fusion estimation if some sensors occur faulty. The derivation of equations for error cross-covariances between the local predictors is the key of this paper. Example demonstrates effectiveness of the distributed limited memory predictor. Index Terms — limited memory, multisensory, Kalman filter, prediction —————————— —————————— 1 I NTRODUCTION N many applications, multiple sensors observe a com-mon origin, for example, system state [1, 2]. If there are no constraints on communication channels and proces-sor bandwidths, complete measurements can be brought to a central processor for data processing. In this case, sensors act as simple data collectors and do not perform any data processing. One of the advantages of this centra-lized processing is that it involves minimal information loss. However, it can result in severe computational over-head. Also, there needs to be a somewhat ideal assump-tion on the environment mentioned above. In practice, especially when sensors are dispersed over a wide geographic area, there are limitations on the amount of communications allowed among sensors. Also, sensors are provided with processing capabilities. In this case, a certain amount of computation can be performed at the individual sensors and a compressed version of sensor data can be transmitted to a fusion center where the re-ceived information is appropriately combined to yield the global inference. The advantage of the distribution of fil-ters is that the parallel structures would lead to increase the input data rates and make easy fault detection and isolation. However, the accuracy of the distributed filter or predictor is generally lower than of the centralized fil-ter. Various distributed and parallel versions of the stan-dard Kalman filter have been reported for linear dynamic systems [2-8]. To get a more accurate estimate of a state of system under potential uncertainty, various kinds of techniques have been introduced and discussed. Among them, a limited memory technique called receding horizon, which is ro-bust against temporal uncertainty, has been rigorously investigated [9-12]. In this paper, we study the distributed receding horizon fusion prediction for the continuous-time linear systems with multiple sensors. The local re-ceding horizon predictors (LRHPs), which we fuse, utilize finite measurements over the most recent time interval [9-12]. It has been a general rule that the LRHPs are often robust against dynamic model uncertainties and numeri-cal errors than the standard filters, which utilize all mea-surements. Based on the LRHPs [10, 12] and the optimal fusion formula with matrix weights [8, 13], we propose a distributed receding horizon predictor which has a better accuracy than every LRHP, and it has the reduced com-putational burden as compared to the centralized reced-ing horizon predictor (CRHP). This paper is organized as follows. The problem is set up in Section II. The CRHP is described in Section III. In Section IV, we present the main result regarding the dis-tributed receding horizon predictor (DRHP) for multisen-sor environment. Here the key equations for cross-covariances between LRHPs are derived. In Section V, example illustrates performance of the CRHP and DRHP. In Section VI, concluding remarks are given