This article proposes two algorithms for the localization or motion analysis of a moving target, by using a number of stationed sensors observing the frequency of the emitted target signal. This is a challenging problem due to the complicated non-linear relation between the target location parameters and the observations. The first algorithm is closed-form through algebraic evaluation that is computationally efficient. The second is derived from semidefinite programming by relaxationthat is robust against noise. The situations of having target frequency known but erroneous and completely unknown are investigated, as well as the presence of sensor position errors. Sequential algorithms for motion analysis are proposed in addition to the two for reducing latency and complexity. The algorithms are analyzed and their performance is able to achieve the CRLB accuracy under Gaussian noise.