Yoo, Kyunghwan

Real-time Angle Average

N = count

V = value

A = average

Average

A_1 = V_1/1

A_2 = (A_1 + V_2)/2

A_3 = (2 A_2 + V_3)/3

…

A_n = ((N - 1) A_ (n - 1) + V_n)/N

Angle Average

A_1 = ArcTan[Cos[V_1/1], Sin[V_1/1]]

A_2 = ArcTan[(Cos[A_1] + Cos[V_2])/2, (Sin[A_1] + Sin[V_2])/2]

A_3 = ArcTan[(2 Cos[A_2] + Cos[V_3])/3, (2 Sin[A_2] + Sin[V_3])/3]

…

A_n = ArcTan[((N - 1) Cos[A_ (n - 1)] + Cos[V_n])/N, ((N - 1) Sin[A_ (n - 1)] + Sin[V_n])/N]

Example

ArcTan[Cos[θ], Sin[θ]]

n = 10 ; A_ (n - 1) = -150 ; V_n = 150 ;

N[ArcTan[((n - 1) Cos[A_ (n - 1) * π/180] + Cos[V_n * π/180])/n, ((n - 1) Sin[A_ (n - 1) * π/180] + Sin[V_n * π/180])/n] * 180/π]

-155.209

N[((n - 1) A_ (n - 1) + V_n)/n]

-120.