The main objective of this master’s thesis is to introduce a mathematical algorithm which is based on Bayes formula of conditional probability. For this purpose, basic definitions and results from theory of probability have been introduced as well as Markov chains. Also, Bayes theorem is explained along with it’s interpretation and application to object tracking problem. Furthermore, recursive Bayesian solution is derived from conditional density function, transition density, prediction density function and maximum likelihood function which are derived from object dynamics equation and sensor measurement equation. From these results a posteriori density function is derived which is used to determine object state. In third chapter optimal Bayes filter is explained which results along with some presumptions is used to derive Kalman filter by using Gaussian product theorem. Algorithm in applications is based on Markov property, prediction and measurements to derive object state at a particular time.