page_title: Multilateration
section_title: TOT algorithm principle
hierarchical_section_title: Multilateration / Principle / TOT algorithm principle
caption_attribution_description: English: Illustration of multilateration surveillance system time-of-transmission (TOT) algorithm concept
context_page_description: Multilateration is a navigation and surveillance technique based on measurement of the times of arrival of energy waves having a known propagation speed. Prior to computing a solution, the time of transmission of the waves is unknown to the receiver.
  A navigation system provides position information to an entity on the subject 'vehicle'; a surveillance system provides 'vehicle' position information to an entity not on the 'vehicle'. By the reciprocity principle, any method that can be used for navigation can also be used for surveillance, and vice versa. For surveillance, a subject of interest transmits to multiple receiving stations having synchronized 'clocks'. For navigation, multiple synchronized stations transmit to a user receiver which can determine the time of transmission. To find the user's coordinates in dimensions, at least TOAs must be measured. Almost always, or.
  One can view a multilateration system as measuring at least TOAs using a clock with an unknown offset from actual time.
context_section_description: The TOT concept is illustrated in Figure 2 for the surveillance function and a planar scenario (). Aircraft A, at coordinates , broadcasts a pulse sequence at time . The broadcast is received at stations ,  and  at times ,  and , respectively. Based on the three measured TOAs, the processing algorithm computes an estimate of the TOT , from which the range between the aircraft and the stations can be calculated. The aircraft coordinates  are then found. 
  When the algorithm computes the correct TOT, the three computed ranges have a common point of intersection which is the aircraft location (the solid-line circles in Figure 2). If the algorithm's computed TOT is after the actual TOT, the computed ranges do not have a common point of intersection (dashed-line circles in Figure 2). Similarly, if the algorithm's computed TOT is after the actual TOT, the three computed ranges do not have a common point of intersection. It is clear that an iterative TOT algorithm can be found. In fact, GPS was developed using iterative TOT algorithms. Closed-form TOT algorithms were developed later. 
  TOT algorithms became important with the development of GPS. GLONASS and Galileo employ similar concepts. The primary complicating factor for all GNSSs is that the stations (transmitters on satellites) move continuously relative to the earth. Thus, in order to compute its own position, a user’s navigation receiver must know the satellites’ locations at the time the information is broadcast in the receiver’s time scale (which is used to measure the TOAs). To accomplish this: (1) satellite trajectories and TOTs in the satellites’ time scales are included in broadcast messages; and (2) user receivers find the difference between their TOT and the satellite broadcast TOT (termed the clock bias or offset). GPS satellite clocks are synchronized to UTC (to within a published offset of a few seconds) as well as with each other. This enables GPS receivers to provide UTC time in addition to their position.
caption: Fig. 2. Multilateration surveillance system TOT algorithm concept
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