Sequential Likelihood Ratio Test based on the Distributed Kalman Filter for Multi Sensor Track Extraction

In the research literature there are numerous publi- cations on Track-to-Track fusion and Track-to-Track association. All these algorithms assume that the problem of target existence is solved on a per sensor basis. In this paper the distributed computation of the track existence by means of the likelihood ratio score is presented. The approach is based on the Distributed Kalman Filter where a single target likelihood function is used which allows to model uniformly distributed clutter with a fixed clutter rate. Numerical examples show that the fused track existence score is close to equivalent to a centralized approach. I. INTRODUCTION For challenging surveillance tasks, algorithms which en- hance the situational awareness by fusing sensor informa- tion are inevitable. Nowadays it has become very popular to improve the performance of systems by linking multiple sensors. This implies some challenges to the sensor data fusion methodologies such as sensor registration, communi- cation delays, and correlations of estimation errors (1), (2). In particular, if the communication links have limited bandwidth, data reduction techniques have to be applied at the sensor sites, that is local tracks have to be computed. Once recieved at a fusion center (FC), the tracks then are fused to reconstruct a global estimate. It is a well known problem that the estimation errors of tracks which refer to the same object are mutually correlated whenever process noise is present (3). To cope with these correlations, algorithms have been developed and recent publications show that this is still an active topic in the research community. Among the most popular methodologies are tracklet fusion (5), the Bar-Shalom-Campo formula (6), the Federated Kalman Filter (7), nafusion and the least squares estimate. However, all these approaches have assume that the problem of target existence is solved on a per sensor basis or generally not addressed at all. In this paper, a closed form solution for a distributed computation of the target existence decision based on a sequential likelihood ratio (LR) test in a two sensor study is presented. The approach generalizes the derivations in (8) to an arbitrary number of sensors. Also, a single target likelihood function is used which simplifies the closed form computation. Also in this paper a numerical example is provided. Structure: This paper is organized as follows. In the next Section, the problem of distributed track extraction is presented. In Section III a summary of the Distributed Kalman filter is provided to conclude its assumptions and possible approximations. The Distributed Kalman filter is then used in Section IV to compute the required parameters of a local sensor which are fused by the FC to obtain a global likelihood ratio score. A numerical example is provided in Section V and the result of the distributed algorithm is compared against a centralized approach. This paper is concluded in Section VI.