Multisensor CPHD filter

Abstract

The single sensor probability hypothesis density (PHD) and cardinalized probability hypothesis density (CPHD) filters have been developed in the literature using the random finite set framework. The existing multisensor extensions of these filters have limitations such as sensor order dependence, numerical instability or high computational requirements. In this paper we derive update equations for the multisensor CPHD filter. The multisensor PHD filter is derived as a special case. Exact implementation of the multisensor CPHD involves sums over all partitions of the measurements from different sensors and is thus intractable. We propose a computationally tractable approximation which combines a greedy measurement partitioning algorithm with the Gaussian mixture representation of the PHD. Our greedy approximation method allows the user to control the tradeoff between computational overhead and approximation accuracy.Index Terms-Random finite sets, multisensor CPHD filter, multisensor PHD filter, multisensor multitarget tracking.

A Multisensor Multi-Bernoulli Filter

“…The result of the differentiation in (15) requires the partitioning of the measurements Z 1:s,k+1 . Therefore, we introduce notation similar to [14]. Let W i ⊂ Z i,k+1 be a measurement subset that contains at most one measurement from sensor i, i.e., |W i | ≤ 1.…”

“…i (·) denoting the n-th derivative of the clutter probability generating function C i (·). Then the differentiation of the functional (14) with respect to all the sensors evaluated at (0, . .…”

“…Other filters, such as [12] and [13], rely on the δ-Generalized Labeled multi-Bernoulli RFS in order to achieve approximate multi-sensor multi-target tracking. A generalized multi-sensor CPHD (MS-CPHD) filter was proposed in [14] along with computationallytractable implementations. In a different setting, in [15], [16] distributed multi-target filtering is achieved using an unlabeled version of the Generalized Labeled multi-Bernoulli RFS and the Generalized Covariance Intersection method [17], [18] for the fusion of posterior densities.…”

“…Hence, a greedy partitioning mechanism is employed which associates likely measurement subsets with individual target densities from the predicted PHD function. The MS-PHD and MS-CPHD filter implementations of [14] constrain the PHD function to be a Gaussian mixture and assume that each Gaussian component represents a potential target.…”

Measurement-Driven Multi-Target Multi-Bernoulli Filter

“…On the basis of the PHD filter, the Cardinalized PHD (CPHD) filter propagates the first-order moment as well as the cardinality distribution without making the Poisson assumption [3]; thus the cardinality estimation of the CPHD filter is more accurate and stable than the PHD filter. Recently, further researches have been made to reduce the computational cost and improve the robustness of the PHD and CPHD filters [4][5][6], and the multi-sensor extensions have also been developed [7].…”