A Second-Order PHD Filter With Mean and Variance in Target Number

Abstract

The Probability Hypothesis Density (PHD) and Cardinalized PHD (CPHD) filters are popular solutions to the multi-target tracking problem due to their low complexity and ability to estimate the number and states of targets in cluttered environments. The PHD filter propagates the first-order moment (i.e. mean) of the number of targets while the CPHD propagates the cardinality distribution in the number of targets, albeit for a greater computational cost. Introducing the Panjer point process, this paper proposes a second-order PHD filter, propagating the second-order moment (i.e. variance) of the number of targets alongside its mean. The resulting algorithm is more versatile in the modelling choices than the PHD filter, and its computational cost is significantly lower compared to the CPHD filter. The paper compares the three filters in statistical simulations which demonstrate that the proposed filter reacts more quickly to changes in the number of targets, i.e., target births and target deaths, than the CPHD filter. In addition, a new statistic for multi-object filters is introduced in order to study the correlation between the estimated number of targets in different regions of the state space, and propose a quantitative analysis of the spooky effect for the three filters.

Vision‐based, terrain‐aided navigation with decentralized fusion and finite set statistics

“…Essentially, a navigator may choose any FISST‐based filter that meets their mapping requirements, since this bookend‐style comparison of “simple” and “complex” filters indicates that vehicle state estimation is relatively unaffected. While the δ ‐GLMB filter produces improved mapping results, it is most likely that the cardinalized PHD filter or the newly developed second‐order PHD filter represent attractive compromises between map estimation and computational cost. Alternatively, an approximation of the δ ‐GLMB filter, known as the labeled multi‐Bernoulli filter may be an attractive option, particularly if the flight processor has parallel computing capabilities …”

“…Their differences lie in the resulting map quality, indicating that a mission can select any of the candidate FISST‐based tools based on the mission's mapping requirements. Previous results in McCabe and DeMars indicate that the cardinalized PHD filter addresses the cardinality estimation issues presented by the PHD filter at a modest increase in computational burden, and the authors note that the recently developed second‐order PHD filter of Schlangen et al may serve as an attractive balance of mapping performance and computational cost.…”

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].…”

Second order multi-object filtering with target interaction using determinantal point processes

“…where (g n ) n≥1 is a sequence of bounded functions converging weakly to the Dirac measure δ x at x ∈ Λ. In the subsequent part of the thesis, we work with the term Dirac delta function δ x (•) which follows the same convention and notation as in [18].…”

“…As such, when the PHD filter propagates a higher mean, it also implies a higher variance. Second-order PHD filters that can propagate separate information on mean and variance parameters have been recently proposed in [18], using e.g. the Panjer cardinality distribution.…”