Patent Document ID: 20120059621
Application ID: 13147959
Patent Flag: 0

Claim One:
1. A method for localizing an object moving in an unknown environment, comprising: providing k position marks at undetermined positions p 1 , p 2. .. , p k that are spaced apart from one another, where {p 1 ,. .. , p k }ε , where k is a natural number greater than or equal to 3; repeatedly measuring distances between the object and each of the position marks independently of one another at uncontrolled instants, such that the distance values {r 1 ,. .. , r n }ε are present at the instants {t 1 ,. .. , t n }ε ; and determining a motion curve x(t)ε according to x ( t ) = ∑ i = 1 n α i k ( t , t i ) , where n number of distance measurements used and each function k(t, t i ) is a positively defined kernel function, and where {α 1 ,. .. , α n }ε are coefficient vectors that are estimated using smoothness conditions by based on a regularization term formed with the kernel functions.