( 1 ) Initialize belief 𝑏 ( 0 ) ( 𝐱 ( 0 ) 𝑖 ) = 𝑝 ( 𝐱 ( 0 ) 𝑖 ) , 𝑖
( 1 ) for 𝑡 = 1 to 𝑇 do { time index}
( 2 ) for all 𝑖 do { mobility update}
( 5 )   Mobility update:
    ̃ 𝑏 ( 𝑡 ) 𝑖 ( 𝐱 ( 𝑡 ) 𝑖 )
     𝑝 ( 𝐱 ( 𝑡 ) 𝑖 | 𝐱 ( 𝑡 1 ) 𝑖 ) 𝑝 ( 𝑧 ( 𝑡 ) 𝑖 , s e l f | 𝐱 ( 𝑡 1 ) 𝑖 , 𝐱 ( 𝑡 ) 𝑖 )
     × 𝑏 ( 𝑡 1 ) 𝑖 ( 𝐱 ( 𝑡 1 ) 𝑖 ) 𝑑 𝐱 ( 𝑡 1 ) 𝑖       (A-1)
( 6 ) end for
( 7 )  Initialize 𝑏 ( 𝑡 ) 𝑖 ( 𝐱 ( 𝑡 ) 𝑖 ) = ̃ 𝑏 ( 𝑡 ) 𝑖 ( 𝐱 ( 𝑡 ) 𝑖 ) , 𝑖
( 8 ) for 𝑙 = 1 to 𝑁 i t do { iteration index; begin cooperative
  update}
( 9 )   for all 𝑖 do
( 1 0 )    for all 𝑗 𝑆 ( 𝑡 ) 𝑖 do
( 1 1 )   Receive and convert 𝑏 ( 𝑡 ) 𝑗 ( 𝐱 ( 𝑡 ) 𝑗 ) to a distribution
   𝑐 ( 𝑙 ) 𝑗 𝑖 ( 𝐱 ( 𝑡 ) 𝑖 ) :
      𝑐 ( 𝑙 ) 𝑗 𝑖 ( 𝐱 ( 𝑡 ) 𝑖 )
       𝑝 ( 𝑧 ( 𝑡 ) 𝑗 𝑖 | 𝐱 ( 𝑡 ) 𝑖 , 𝐱 ( 𝑡 ) 𝑗 ) 𝑏 ( 𝑡 ) 𝑗 ( 𝐱 ( 𝑡 ) 𝑗 ) 𝑑 𝐱 ( 𝑡 ) 𝑗     (A-2)
( 1 2 )   Update and broadcast 𝑏 ( 𝑡 ) 𝑖 ( 𝐱 ( 𝑡 ) 𝑖 ) :
    𝑏 ( 𝑡 ) 𝑖 ( 𝐱 ( 𝑡 ) 𝑖 ) ̃ 𝑏 ( 𝑡 ) 𝑖 ( 𝐱 ( 𝑡 ) 𝑖 ) 𝑘 𝑆 ( 𝑡 ) 𝑖 𝑐 ( 𝑙 ) 𝑘 𝑖 ( 𝐱 ( 𝑡 ) 𝑖 )   (A-3)
( 1 3 )    end for
( 1 4 )   end for
( 1 5 ) end for  {end cooperative update}
( 1 6 ) end for  {end current time step}
Algorithm 1: SPAWN.