  The localization problem in a wireless sensor network is to determine the
coordination of sensor nodes using the known positions of some nodes (called
anchors) and corresponding noisy distance measurements. There is a variety of
different approaches to solve this problem such as semi-definite programming
(SDP) based, sum of squares and second order cone programming, and between
them, SDP-based approaches have shown good performance. In recent years, the
primary SDP approach has been investigated and a variety of approaches are
proposed in order to enhance its performance. In SDP approaches, errors in
approximating the given distances are minimized as an objective function. It is
desirable that the distribution of error in these problems would be a delta
distribution, which is practically impossible. Therefore, we may approximate
delta distribution by Gaussian distribution with very small variance. In this
paper, we define a new objective function which makes the error distribution as
similar as possible to a Gaussian distribution with a very small variance.
Simulation results show that our proposed method has higher accuracy compared
to the traditional SDP approach and other prevalent objective functions which
are used such as least squares. Our method is also faster than other popular
approaches which try to improve the accuracy of the primary SDP approach.
