63. The system of claim 62 , wherein the positional component is given by a second equation x sm ⁡ ( t n , t n - 1 ) = 1 m ⁡ [ x 1 ⁡ ( t n ) + c 1 ⁡ ( t n - 1 ) + x 2 ⁡ ( t n ) + c 2 ⁡ ( t n - 1 ) + … + x m ⁡ ( t n ) + c m ⁡ ( t n - 1 ) ] where t n is a point in time at which the hypotheses x i ε 3 are measured, m is a number of sensors detecting the tag at that instant, and c is a correction factor.
63. The system of claim 62 , wherein the positional component is given by a second equation x sm ⁡ ( t n , t n - 1 ) = 1 m ⁡ [ x 1 ⁡ ( t n ) + c 1 ⁡ ( t n - 1 ) + x 2 ⁡ ( t n ) + c 2 ⁡ ( t n - 1 ) + … + x m ⁡ ( t n ) + c m ⁡ ( t n - 1 ) ] where t n is a point in time at which the hypotheses x i ε 3 are measured, m is a number of sensors detecting the tag at that instant, and c is a correction factor. 71. The system of claim 63 , wherein the rotational component is approximated by applying the second equation to unit direction vectors that form a basis of a rotating coordinate frame within the SOE, and re-normalizing the unit direction vectors.