# A second-order PHD filter with mean and variance in target number

## TL;DR

This paper introduces a second-order PHD filter that propagates both mean and variance of target number, offering a computationally efficient alternative to the CPHD filter with improved responsiveness to target number changes.

## Contribution

It proposes a novel second-order PHD filter using Panjer point process, which models mean and variance of target count with lower computational cost than CPHD.

## Key findings

- The second-order PHD filter reacts faster to target number changes.
- It has lower computational cost than the CPHD filter.
- The filter provides better modeling versatility.

## 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.

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Source: https://tomesphere.com/paper/1704.02084