## Question 1## aThe goal of this project is to use least square estimations and appropriate regularization to provide traffic estimates and study spatial traffic patterns in San Francisco. Let represent the average travel time on each link of the network. It is the variable that we try to estimate. For a vehicle, with a path represented by and the travel time , we have where represents some noise in the measurements. ## bThe ordinary least-squares (OLS) problem is a particularly simple optimization problem that involves the minimization of the Euclidean norm of a ‘‘residual error" vector that is affine in the decision variables. Given n measurements of path travel times, we would like to estimate the average travel time on each link of the network using least-square estimation: where , are given. The combination of
if the matrix A is full column rank. |