A reduced-complexity scheme using message passing for location tracking

EURASIP Journal on Advances in Signal Processing

Table 1 The operations carried out for tracking scheme

Operations	$Inputs : N (argument; mean; variance)$	$Output : N (argument; mean; variance)$
oper₁	$N (x; m_{1}, σ_{1}^{2}), N (x; m_{2}, σ_{2}^{2})$	$N (x; \frac{σ_{2}^{2} . m_{1} + σ_{1}^{2} . m_{2}}{σ_{1}^{2} + σ_{2}^{2}}, \frac{σ_{1}^{2} . σ_{2}^{2}}{σ_{1}^{2} + σ_{2}^{2}})$
oper₂	$N (x; m, σ_{1}^{2}), N (y; α x, σ_{2}^{2})$	$N (y; α m, α^{2} σ_{1}^{2} + σ_{2}^{2})$
oper₃	$N (x; m_{1}, σ_{1}^{2}), N (y; m_{2}, σ_{2}^{2}), N (z; α x + β y, σ_{3}^{2})$	$N (z; α m_{1} + β m_{2}, α^{2} σ_{1}^{2} + β^{2} σ_{2}^{2} + σ_{3}^{2})$