International Telemetering Conference Proceedings / October 27-30, 1997 / Riviera Hotel and Convention Center, Las Vegas, Nevada / This paper proves theoretically that GDOP decreases as the number of satellites is increased.This paper proposes two recursive algorithms for calculating the GDOP and positioning solution.These algorithms not only can recursively calculate the GDOP and positioning solution, but also is very flexible in obtaining the best four-satellite positioning solution ,the best five-satellite positioning solution and the all visible satellite positioning solution according to given requirements. In the need of the two algorithms,this paper extends the definition of the GDOP to the case in which the number of visible satellites is less than 4.

International Telemetering Conference Proceedings / October 20-23, 2003 / Riviera Hotel and Convention Center, Las Vegas, Nevada / This paper describes key points in the field of Galileo application abroad spacecraft and normal vehicles. On the basis of ephemeris of Galileo constellation, the mathematic model and procession are given in high dynamic signal environment, the digital simulation is also completed, the results are statistics and analyzed and presented. On the topic of navigation satellite constellation orbit and visibility, the paper presents the Galileo frame system, time system, navigation satellite orbit elements, constellation structure, and GDOP calculation. The users include low dynamic as well as high dynamic spacecraft. The analysis for relevant GPS is also showed. About the navigation signal structure, main points are Galileo system working frequency, including E5, E6 and L1 frequency spans, the modulation and navigation data, ets. At the same time, this paper compares Galileo with GPS. On the aspect of signal communication link, Dopplar frequency shift and power level calculation are present as well as compare with GPS system.

In indoor environment, the multi-sensor system can be used as an efficient solution for target location process, in terms of lower estimation cost, due to the factor that sensors have the advantages of low power, simple, cheap, and low operation complexity. However, the location methods and the placements of designed multisensor have great impact on the location performance. Based on the time difference of arrival (TDOA), the present research utilizes linear-correction spherical-interpolation (LCSI) method to estimate the location of its targets. The method is a combination of the linear-correction least-squares method and the spherical-interpolation method. Apart from the usual process of iterative, nonlinear minimization, and consequently, under the influence of noise interference and target-sensor geometry, the spherical-interpolation method will produce better results; therefore, SI method is used in place of the LS part of the LCLS method and named as the LCSI method. The objective is to correct the SI method to generate a better estimate performance. In addition to the performance issues, the limitation of the methods will also be examined. The geometric dilution of precision (GDOP) of the TDOA location method in the 3-D scenario is demonstrated with the effects on location performance of both inside and outside of the multi-sensor formation. Programmed 3-D scenario are used in the simulations, where cases with three different multiple sensor formations and two different target heights are investigated. From the simulation results of various location methods, it can be seen that LCSI has has its advantages over other methods in the wireless TDOA location.

In wireless positioning system, in addition to channel error, the geometric re- lationship between sensor nodes and the target may also affect the positioning accuracy. The effect is called geometric dilution of precision (GDOP). GDOP is determined as ratio factor between location error and measurement error. A higher GDOP value indicates a larger location error in location estimation. Accordingly, the location performance will be poor. The GDOP can therefore be used as an in- dex of the positioning performance. In this thesis, approaches of tracking a moving target with extended Kalman filter (EKF) in a time-difference-of-arrival (TDOA) wireless positioning system are discussed. While the target changes its position with time, the geometric layout between sensor nodes and the target will become differ- ent. To maintain the good layout, the positioning system with mobile sensor nodes is considered. Therefore, the geometric layout can be possibly improved and GDOP effect can be reduced by the mobility of mobile sensor nodes. In order to find the positions that mobile sensor nodes should move to, a time-varying function based on the GDOP distribution is defined for finding the best solutions. Since the simu- lated annealing is capable of escaping local minima and finding the global minimum in an objective function, the simulated annealing algorithm is used in finding the best solutions in the defined function. Thus the best solutions can be determined as the destinations of mobile sensor nodes. When relocating mobile sensor nodes from their current positions to the destinations, they may pass through or stay in high GDOP regions before arriving at the destinations. To avoid the problem, we establish an objective function for path planning of mobile sensor nodes in order to minimize the overall positioning accuracy. Simulation results show that the mobile sensor nodes will accordingly change their positions while the target is moving. All the sensor nodes will maintain a surrounding region to localize the target and the GDOP effect can be effectively reduced.

In indoor environment, the multi-sensor system has been proved to be an efficient solution for target locating process in terms of lower estimation cost. However, the placement of designed multi-sensor has great impact on the location performance in an indoor environment. Based on the time difference of arrival (TDOA), closed-form least-square location methods, including the spherical-interpolation (SI) and the spherical-intersection (SX) methods, are used in the estimation of target locations. The two methods are apart from the usual process of iterative and nonlinear minimization. Consequently, under the influence of noise interference, the performance of the two methods also produce different results. In addition to the above issues, the limitation of these methods will also be examined. The geometric dilution of precision (GDOP) effects of TDOA location on location performance of both inside and outside of the multi-sensor environment in the 2-D scenario have been studied in the past. This thesis aims to further advance the performance of GDOP in 3-D scenarios, analyze the differences, and propose the suitable needs. Programmed 3-D scenario simulations are used in this research, designed according to multiple sensor arrays and the moving latitude of a target. The Setup interprets the degree of multi-sensor separation, and distances from targets to the sensor array. A suitable location algorithm and optimal multi-sensor deployments in an indoor environment were proposed according to the simulation results.

In wireless location system, geometric relationship between the base station (BS) and the mobile station (MS) may affect the accuracy of MS location estimate. The effect is called Geometric Dilution of Precision (GDOP). Given the information of geometric configuration of BS and MS locations, the GDOP value can be calculated accordingly. In fact, the GDOP value is considered as ratio factor between the location error and measurement noise. A higher GDOP value indicates larger location error in the location estimator. Therefore the GDOP can be utilized as an index for observing the location precision of the MS under different geometric layout. The accuracy of location estimation can be improved by changing the BS device element locations. In the thesis, a time different of arrival (TDOA) wireless location system with mobile base station (MBS) is considered. Changing the geometric layout between the BS and the MS by relocating the MBS, the GDOP effect can be reduced and the accuracy of location estimation also can therefore be improved. Since the simulated annealing (SA) is capable of escaping the local minimum and finding the global minimum in an objective function, the SA algorithm is used in finding the best solution in a defined function based on the GDOP distribution. The best solution is then the destination of an MBS in the process of MS location estimation. When relocating an MBS from its initial location to the best location, it is likely that the MBS enters regions with high GDOP effects. To avoid the problem, the steepest descent (SD) algorithm is utilized for path planning. First, we establish the objective function which consists of the GDOP information and the angle of movement. A nearby location that has the minimum value of objective function is selected as the next move. The process continues until the MBS reaches the destination. A variety of cases are investigated by computer simulations. Simulation results show that the proposed approach can effectively find the best locations for MBSs to relocate. Based on the relocation and path planning, the GDOP effects can be reasonably reduced, and therefore the higher location accuracy is achieved.