ABSTRACT The thesis aims to study the GPS navigation system,set—membership estimation theory and application of embedded issues of state bounding estimation and its application in GPS filtering are discussed in details based on the framework of unknown but bounded noise addition,the design of GPS mobile tracking terminal is includes the following research works. GPS has e all important tool both in navigation and in precise point ,GPS navigation system prehensive described,and the structure and development of GPS system are we investigate the GPS measurement princiFIle and the analysis of error the other hand the mathematical model of GPS positioning is discussed. In linear system state bounding estimation with ellipsoidal set description of uncertainty,a recursive state bounding estimation algorithm using ellipsoidal sets to describe the state uncertainties and to bound the process and observation noises is algorithm optimizes stage of time updating according to the minimum—volume and minimum-trace bounding ellipsoid and measurement updating according to minimum—radius bounding results and performance comparisons with traditional set—membership algorithm and Kalman filter show its ,We extend the algorithm to GPS filtering problem and the estimation result is satisfaction. In nonlinear system state bounding estimation,an extended optimal bounding ellipsoid(EOBE)state estimation algorithm is in the EKF,the EOBE linearizes the state equations about the current state the EKF,the EOBE does not neglect the linearization ,the linearization errors are considered as part of bounded analysis shows that the state estimation error is bounded and non—divergent in the case of sufficiently small initial estimation error and noise algorithm not only reduces putation,bu