Optimality analysis of one-step OOSM filtering algorithms in target tracking

Abstract

In centralized multisensor tracking systems, there are out-of-sequence measurements (OOSMs) frequently arising due to different time delays in communication links and varying pre-processing times at the sensor. Such OOSM arrival can induce the "negative-time measurement update" problem, which is quite common in real multisensor tracking systems. The A1 optimal update algorithm with OOSM is presented by Bar-Shalom for one-step case. However, this paper proves that the optimality of A1 algorithm is lost in direct discrete-time model (DDM) of the process noise, it holds true only in discretized continuous-time model (DCM). One better OOSM filtering algorithm for DDM case is presented. Also, another new optimal OOSM filtering algorithm, which is independent of the discrete time model of the process noise, is presented here. The performance of the two new algorithms is compared with that of A1 algorithm by Monte Carlo simulations. The effectiveness and correctness of the two proposed algorithms are validated by analysis and simulation results.out-of-sequence measurement (OOSM), OOSM filtering, target tracking, data fusion In a centralized multisensor tracking system, the processing of the measurements from all the sensors is done at the central fusion node. Due to different time delays in communication links and varying pre-processing times at the sensor platforms, the central fusion node receives the measurements from the same target which will arrive out of sequence. In the standard filtering algorithm (e.g. Kalman filtering), it is supposed to process in-sequence measurements. For such out-of-sequence measurement (OOSM) case [1][2][3] , however, one faces the problem of updating the current state with the delayed measurements. Assume the delayed measurement with time stamp τ , and after the state of the target has been already updated to time , the OOSM can occur when t 0 t τ − < . This is also known as the "negative-time measurement update" problem (called so when t τ − is negative) [4][5][6] , which is quite common in real multisensor tracking systems [7] .

Distributed Kalman filtering: a bibliographic review

“…A globally optimal state trajectory update algorithm for a sequence with arbitrary delayed OOSMs including the case of interlaced OOSMs with less storage is given in [110]. Other publications classified with distributed OOSM are [105, 111–144]. Remark 7 An exhaustive review of OOSM, a subdivision of DKF, have been contained in Table 6.…”

Distributed Kalman Filtering

“…A globally optimal state trajectory update algorithm for a sequence with arbitrary delayed OOSMs including the case of interlaced OOSMs with less storages is given in [279]. Other publications classified with distributed OOSM are [61], [62], [63], [64], [81], [82], [83], [84], [85], [86], [87], [88], [89], [90], [141], [163], [165], [166], [167], [168], [188], [195], [207], [208], [224], [225], [225]- [229], [230], [231], [280], [301] and [302]. …”

The Nonsequential Fusion Method for Localization from Unscented Kalman Filter by Multistation Array Buoys

“…In order to solve the problem of OOSM, Bar-Shalom et al [7,8] put forward a series of suboptimal algorithms; the purpose is to use the out-of-sequence measurements for the current moment to update the target state, in order to obtain more accurate state estimation and its error covariance matrix. Zhou et al [9] analyzed theoretically the optimality algorithm which is put forward by Bar-Shalom, point out that its optimality is associated with the discretization of process noise model, and propose an improved algorithm based on discrete time model, improving the accuracy of the filter. Bar-Shalom et al [10] used the method of equivalent observation data in the original literature which extended one-step-lag OOSM to the multistep lag OOSM.…”