>> doit


Starting...


Solve the system using multivariate Newtons method...
U[0] = x
U[1] = y
U[2] = z
U[3] = d

ans =

         -19.0538453256602
          11.3182159043034
          6370.25197283455
     -0.000425998681307362



Test the conditioning of the GPS problem...
R[] = satelite ranges
T[] = travel times

phi =

          0.69915584090742         0.731982200210962          1.32924149477362          0.31831772503192


theta =

          5.85476366840607          2.63045218448402          3.29963044881334          4.22316426632253


R =

          21376.3140754387          15430.6026955574          10702.0691403308          30882.6203802394


T =

        0.0714037086324523        0.0515709502650577        0.0357982600954252         0.103113333244826



Find the condition number...

condition_number =

          4.19374052244009



Find the condition number (tightly grouped satelites)...

phi =

          1.31651337490734          1.34498832481472          1.36863177147797          1.34941706433005


theta =

         0.123398704955571         0.104467627536503         0.123840551740472         0.112229143822628


R =

          6395.53657268653          6215.51527676166          5609.36662111004          6045.36249017118


T =

        0.0214332137017487         0.020832727294833        0.0188108330160529         0.020265158691788


condition_number =

          2735.58348495999



Add more satelites...

phi =

  Columns 1 through 4 

         0.478491840956378         0.303840949969001         0.475581208624155         0.236990716748664

  Columns 5 through 8 

         0.594346919363667          1.34091834359469         0.779982764054642          1.29061206767065


theta =

  Columns 1 through 4 

          1.19162964003996          4.28653493468607          3.40343720009581          4.38502548712483

  Columns 5 through 8 

           5.4036122798288          3.72946577095605          5.65341646127879           4.0520914504143


R =

  Columns 1 through 4 

          21798.5246312091          31382.5271965149           21378.479770392          32181.6411911449

  Columns 5 through 8 

          27589.2853704439          18165.5561655263          23235.9882519246          23012.4090037047


T =

  Columns 1 through 4 

        0.0728120514526388         0.104780842893369        0.0714109326132282         0.107446400259158

  Columns 5 through 8 

        0.0921279501175573        0.0606937730612498        0.0776069139728812        0.0768611338765058


condition_number =

          4.30562912650122

>>