A fixed-lag smoothing solution to out-of-sequence information fusion problems

Abstract

Abstract. Multi-sensor tracking using delayed, out-of-sequence Information (OOSI) is a problem of growing importance due to an increased reliance on networked sensors interconnected via complex communication network architectures. In such systems, it is often the case that information (in the form of raw or processed measurements) is received out-of-time-order at the fusion center. Owing to compatibility with legacy sensors and limited communication bandwidth most practical fusion systems send track information rather than raw measurements to the fusion node. This paper presents a unified Bayesian approach to handling this out-of-sequence information problem and provides implementable sub-optimal algorithms for both cluttered and non-cluttered scenarios involving single and multiple time-delayed measurements/tracks. Such an approach leads to a solution involving the joint probability density of current and past target states. A fixed-lag smoothing framework, developed by John Moore and his students almost 30 years ago, forms the basis of our algorithm. Under linear Gaussian assumptions, the Bayesian solution reduces to an Augmented State Kalman Filter (AS-KF). Computationally efficient versions of the AS-KF are considered in this paper. Simulations are presented to evaluate the performance of these solutions.

Multisensor Out of Sequence Data Fusion for Estimating the State of Discrete Control Systems

“…This section compares IFAsyn with other OOS algorithms for solving (1) whose optimality holds when the delays are bigger than one time lag (f t , a > t + 1) [5]- [11]. We skip [12], optimal for any delay too, because it restarts the fusion process from the time stamp of the incoming £ s t We also consider [13]-A1, although its degree of suboptimality is a few percent of MSE and is less general because (Fk,i, Qk,i, k < I) has to be available for arbitrary k and I.…”

“…This lets the fusion center obtain the same estimates as if it had received the data without delays, increasing its memory and computational needs. To reduce these needs, several OOS estimators have been recently developed, such as [1] and [5]- [13] for the KF, and [14]- [16] for Particle Filters (PF).…”

“…The first, designed for linear systems and originally proposed in [17], [18], finds the same solutions as the KF or Information Filter (IF) when the measurements are not delayed. It is computationally more efficient, simple to implement and general in scope than [5]- [12]. The second, for nonlinear systems, is a novel approach inside the EKF and Extended IF (EIF), significantly different to the OOS PF [14]- [16] or the use of linear OOS algorithms for linearized systems [19].…”

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

“…This enables the information fusion to incorporate measurements corresponding to past states in an optimal, elegant way but is computationally enormous expensive [27] (optimal multilag filtering algorithm for linear systems). To overcome the computationally expensive augmented state algorithm, Challa and Wang introduce the iterated augmented state algorithm [28]. In [29], they additionally describe the use of these algorithms in scenarios with clutter.…”

A Finite Memory Structure Smoother with Recursive Form Using Forgetting Factor

“…Recently, to overcome the resulting problems of existing fixed-lag Kalman smoother with the infinite memory structure (IMS) in [1][2][3][4][5], the fixed-lag smoother with the finite memory structure (FMS) has been developed for state estimation in discrete time-invariant systems [6][7][8][9] and discrete time-varying systems [10]. This FMS smoother has been known to have some good properties such as unbiasedness and deadbeat, which cannot be obtained by the IMS smoother.…”