Integrity of Cooperative Perception

Antoine Lima, Véronique Cherfaoui, Philippe Bonnifait

Introduction

Overview of a PhD defended in May 2023

1. T2TF

2. Detectability

3. Trust

1. Track to Track Fusion

Problem

Information loops

Spatio-temporal dependency

\[\neq\]

Traditional Kalman filtering

State of the art

flowchart TD
  A(T2TF) --> B(Explicit Correlation Representation)
  A --> C(Generic Methods)
  C --> D(Probability Hypothesis Density)
  C --> E(Covariance Intersection Filter)

State of the art

flowchart TD
  A(T2TF) --> B(Explicit Correlations)
  A --> C(Generic)
  C --> D(PHD)
  C --> E(CIF)

  style E fill:#517dc9,stroke:#2f5597,stroke-width:2px,color:#f9f9f9,font-weight:bold

CI : Weighted Kalman Update

\[ \small \mathbf{P}^{-1} = \color{green}{w}\mathbf{P}^{-1} + \color{green}{(1-w)}\mathbf{R}^{-1} \]

Consistent but hard to converge

State of the art

flowchart TD
  A(T2TF) --> B(Explicit Correlations)
  A --> C(Generic)
  C --> D(PHD)
  C --> E(CIF)
  E --> F(KF/CIF)
  E --> G(SCIF)

  style E fill:#517dc9,stroke:#2f5597,stroke-width:2px,color:#f9f9f9,font-weight:bold
  style F fill:#C8E6C9,stroke:#2E7D32,stroke-width:2px
  style G fill:#C8E6C9,stroke:#2E7D32,stroke-width:2px

CI : Weighted Kalman Update

\[ \small \mathbf{P}^{-1} = \color{green}{w}\mathbf{P}^{-1} + \color{green}{(1-w)}\mathbf{R}^{-1} \]

Consistent but hard to converge

Split CIF

Promising

Harder tuning

No consistency guarantee

* artist’s rendition

2. Detectability

Concept

Like occupancy grids..

Models:

Absence of objects
Presence of objects

.. with a twist

Models:

Absence of objects
Possibility of seing objects

Example

Usage

Better estimate target existence \(p(\exists)\)..

.. and building trust

3. Trust

Problem

What should we do

Risk missing an object?

Risk stopping on nothing?

Depends on how much we trust the other

Proposal

Joint confirmation & Misbehavior detection

\[ \Omega^\mathcal{T} = \{T, \not{T}\} \]

\(m_j(\{T\})\): \(j\) can be trusted

\(m_j(\{\not{T}\})\): \(j\) cannot be trusted

\(m_j(\{T,\not{T}\})\): \(j\) is undecidable

Estimated over time by accumulating pieces of evidence

Examples

Object Similarity

Size Coherency

Tree Fusion

%%{
  init: {
    'theme': 'neutral',
    'themeVariables': {
      'fontSize': '30px'
    }
  }
}%%
flowchart BT
  obde(Object\n Detectability) --> cohe(Coherency)
  atco(Attribute\n Coherency) --> cohe
  spco(Spatial\n Coherency) --> cohe
  hist(History) --> cons(Consistency)
  obsi(Object\n Similarity) --> conf(Confirmation)
  obdi(Object\n Dissimilarity) --> conf
  ofin(Object - FS\n Incosistencies) --> conf
  fssi(FS\n Similarity) --> conf
  cohe --> obse(Trust)
  cons --> obse
  conf --> obse

  style obde fill:#b8545000,stroke-width:0px,text-align:center
  style atco fill:#b8545000,stroke-width:0px,text-align:center
  style spco fill:#b8545000,stroke-width:0px,text-align:center
  style hist fill:#b8545000,stroke-width:0px,text-align:center
  style obsi fill:#82b36600,stroke-width:0px,text-align:center
  style obdi fill:#b8545000,stroke-width:0px,text-align:center
  style ofin fill:#b8545000,stroke-width:0px,text-align:center
  style fssi fill:#82b36600,stroke-width:0px,text-align:center
  style cohe fill:#b8545000,stroke-width:0px,text-align:center
  style cons fill:#b8545000,stroke-width:0px,text-align:center
  style conf fill:#d79b0000,stroke-width:0px,text-align:center
  style obse fill:#d79b0000,stroke-width:0px,text-align:center