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

Isabel Schlangen, Emmanuel Delande, Jeremie Houssineau, Daniel E. Clark

Research output: Contribution to journalArticlepeer-review

40 Citations (Scopus)
69 Downloads (Pure)


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 (SO-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.

Original languageEnglish
JournalIEEE Transactions on Signal Processing
Early online date28 Sept 2017
Publication statusE-pub ahead of print - 28 Sept 2017


  • Bayes methods
  • Computational efficiency
  • Correlation
  • Radio frequency
  • Random variables
  • Reactive power
  • Target tracking

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


Dive into the research topics of 'A second-order PHD filter with mean and variance in target number'. Together they form a unique fingerprint.

Cite this