Using a model of the turtle retina, in this paper we show how the model can be used to discriminate between targets that are moving, with a constant speed, along several different directions. Model of retinal cells are chosen from an earlier work of the authors, described in the PhD thesis of the first author, and a patch has been constructed on the visual streak of the retina. Distributions of intensity sensitive 'A Cells' and direction sensitive 'B cells' are chosen from data already reported in the literature and our model of the retinal patch follows this distribution. The model patch is exposed to point targets moving at constant speed but along several directions that are separated by 2°. The obtained patch response is analyzed by two different methods discussed in this paper. In the first method the patch responses are low pass filtered and projected onto a vector on the principal component space. Detection is performed using maximum likelihood method assuming that the vector is distributed as a Gaussian random process conditioned on the direction of the target. In the second method, the spike rate is computed as an intensity function of a vector Poisson process. The detection algorithm is based on minimizing the distance between the intensity function of an unknown input to the intensity functions of inputs computed for an array of targets. The detection algorithms presented in this paper have been implemented using 'a moving time window of detection' and a window of '20 ms' is presented for the purpose of illustration. Detection results are presented using a root mean square error criterion.