# Geolocation and Tracking by TDOA Measurements Based on Space-Air-Ground Integrated Network
## 1 Introduction  
Passive source localization has been an important study aspect in the area of electronic reconnaissance. The localization method can be classified as single station [1; 2; 3] or multi-station [4; 5] by the number of observers. Localization approaches can also be divided by the type of observers: ground-based [6], air-based [7] and space-based localization [8]. Commonly used signal measurements include time of arrival (TOA) [9], time difference of arrival [10; 11], frequency difference of arrival (FDOA) [12] and angle of arrival (AOA) [13; 14]. The attitude of observer should be measured accurately for the localization approach with AOA. Clock synchronization between observer stations should be precise to ensure position accuracy when using TDOA or FDOA. In practice, clock synchronization is commonly precise to the level of a nanosecond. Hence, many popular passive localization approaches utilize TDOA measurements. Over the years, many approaches have been proposed, such as the iterative Taylor-series method [15], two-step least squares [10], Hough transform [16], particle swarm optimization [17], semi-definite relaxation [18] and so on. However, most current research focuses on the single-station type. Localization accuracy and detection range could not accommodate usability requirements while using aircraft or ground stations only. There are few studies on source localization using different observation platforms. Due to the development of manufacturing and launch technology for satellites, there are now more and more satellite networks. Hence, cooperative reconnaissance is possible to implement among satellite networks, aerial vehicles and ground stations. Therefore, it is highly expected to enhance passive localization performance by using SAGI networks. With the development of communication technology, SAGI communication is envisioned to achieve significant performance gain in coverage, reliability and flexibility, which has attracted great interests over the past few years [19]. Many companies have also made extensive efforts in the area of SAGI communication [20; 21], such as SpaceXand Google. Therefore, it is viable to realize source localization based on SAGI networks. [PERSON] et al. [22] developed an active cooperative localization method for SAGI networks based on TOA measurements. The authors also analyzed the effects of clock offset among ground agents. However, there is no literature about the problem of passive localization based on SAGI networks. In this paper, we study the method of geolocation and tracking by TDOA measurements based on SAGI networks. The conference article [23] presented some preliminary work about performance analysis of geolocation based on SAGI networks. The contributions of this paper mainly include the following. 1. We derive the CRLB of the source localization in different coordinate systems. Most research about the CRLB of geolocation is derived in the standard Earth-centered Earth-fixed (ECEF) coordinate system [24; 25]. Under the constraint conditions of source position and velocity on the Earth, the Fisher information matrix (FIM) of the source location in the ECEF coordinate system may be occasionally nonreversible. For the purpose of more accurate estimation, we also derive the CRLB for the target modeled in the geodetic coordinate system. 2. Our second contribution is to analyze the effects of different system errors, such as clock synchronization error, position bias of the observers, elevation bias of the target and non-horizontal velocity of the target. Meanwhile, most existing research focuses on the effect of random errors [26; 27; 28]. However, it should be remarked that system biases are common in the scenario of passive geolocation based on SAGI networks, where accurate synchronization among observers is an impractical assumption. 3. Note that most previous research concentrates on estimation of source position and TDOA measurements.