One-step solution for the multistep out-of-sequence-measurement problem in tracking

Abstract

In multisensor target tracking systems measurements from the same target can arrive out of sequence. Such "out-of-sequence" measurement (OOSM) arrivals can occur even in the absence of scan/frame communication time delays. The resulting problem-how to update the current state estimate with an "older" measurement-is a nonstandard estimation problem. It was solved first (suboptimally, then optimally) for the case where the OOSM lies between the two last measurements, i.e, its lag is less than a sampling interval-the 1-step-lag case. The real world has, however, OOSMs with arbitrary lag. Subsequently, the suboptimal algorithm was extended to the case of an arbitrary (multistep) lag, but the resulting algorithm required a significant amount of storage. The present work shows how the 1-step-lag algorithms can be generalized to handle an arbitrary (multistep) lag while preserving their main feature of solving the update problem without iterating. This leads only to a very small (a few percent) degradation of MSE performance. The incorporation of an OOSM into the data association process is also discussed. A realistic example with two GMTI radars is presented. The consistency of the proposed algorithm is also evaluated and it is found that its calculated covariances are reliable.

Rao–Blackwellized Particle Filters With Out-of-Sequence Measurement Processing

“…See [16] for an overview of initial work spanning to the late 1990's. Two suboptimal algorithms are given in [17], [18]. An algorithm that is optimal in the mean-square sense is found in [19].…”

Analysis of Kalman filter based approaches for fusing Out-of-Sequence measurements corrupted by systematic errors

“…The delayed information is incorporated by computing the update of the state at time t k with the residual of the OOSM and the retrodicted state to the time κ as well as the covariance matrices between the states at t k and t κ . In [14,15] BarShalom et al extend the presented one-lag algorithm to deal with multi-lag OOSMs by virtually compressing the information of the updates between t κ and t k into one update. This approach is further extended to a multi-model approach in [16].…”

“…For sake of discussion we will only consider the OOSM processing algorithm Al1 of [15] referred to as ADVA as it is best suited for the presented exemplary scenario.…”

Multirate Signal Processing

“…The initial work on this topic focused on tracking systems with linear state and measurement models (see [2] and references therein). In order to address nonlinear models, researchers began to explore methods for efficiently processing OOSMs within particle filters.…”