Patent ID: 11867512
Assignee: GEOTAB INC.
Field: Control (Instruments)
Classification: CPC G | IPC G

Claim 11:
12. The asset tracking device of claim 11, wherein the distances are minimum distances and wherein the controller is configured to determine each minimum distance for a sample point in the target set of data to the reference line by determining a reference point on the reference line that is minimally distant from that sample point by evaluating tmin in the following equation:, t
   min
  
  =
  
   
    
     t
     p
    
    +
    
     
      ∑
      
       n
       =
       1
      
      N
     
     
      
       (
       
        
         y
         
          p
          n
         
        
        -
        
         y
         
          0
          n
         
        
       
       )
      
      *
      
       a
       n
      
     
    
   
   
    1
    +
    
     
      ∑
      
       n
       =
       1
      
      N
     
     
      a
      n
      2
     
    
   
  
 

wherein,
tp represents the time value (t) at the sample point (p),
N represents the total number of non-time dimensions in the target set of data,
n represents the nth dimension in the target set of data,
ypn represents the value (y) of the sample point (p) in the nth dimension (n),
y0n represents the value (y) of the first point (0) in the nth dimension (n), the first point (0) being first with respect to time,
an represents the slope (a) of the reference line in the nth dimension (n) with respect to time, and
tmin represents the time (t) at the reference point, the point at which the reference line is minimally distant (min) from the sample point; and

determining the distance from that sample point to the reference point by the following equation:, ❘
    "\[LeftBracketingBar]"
   
   
    R
    ⁡
    (
    
     L
     ,
     p
    
    )
   
   
    ❘
    "\[RightBracketingBar]"
   
  
  =
  
   
    
     
      (
      
       
        t
        min
       
       -
       
        t
        p
       
      
      )
     
     2
    
    +
    
     
      ∑
      
       n
       =
       1
      
      N
     
     
      
       (
       
        
         y
         
          0
          n
         
        
        +
        
         
          a
          n
         
         *
         
          t
          min
         
        
        -
        
         y
         
          p
          n
         
        
       
       )
      
      2
     
    
   
  
 

wherein,
tmin, tp, N, n, y0n, an, and ypn are defined as in the previous equation, and
|R(L, p)| represents the distance (R) from the sample point (p) to the reference point on the reference line (L).