Multilateration

Multilateration is a navigation and surveillance technique based on the measurement of the times of arrival (TOAs) of energy waves (radio, acoustic, seismic, etc.) having a known propagation speed. The time origin for the TOAs is arbitrary. (By the reciprocity principle, any conceptual method that can be used for navigation can also be used for surveillance, and vice versa.) For surveillance, a subject of interest – in cooperative surveillance, often a vehicle – transmits to multiple receiving stations having synchronized 'clocks'. For navigation, multiple synchronized stations transmit to a user receiver. To find the coordinates of a user in n dimensions (typically, n = 2 or n = 3), at least n + 1 TOAs must be measured. Multilateration systems are also called hyperbolic systems, for reasons discussed below.    (1)    (2)    (3)    (4)    (5)    (6)    (7) Multilateration is a navigation and surveillance technique based on the measurement of the times of arrival (TOAs) of energy waves (radio, acoustic, seismic, etc.) having a known propagation speed. The time origin for the TOAs is arbitrary. (By the reciprocity principle, any conceptual method that can be used for navigation can also be used for surveillance, and vice versa.) For surveillance, a subject of interest – in cooperative surveillance, often a vehicle – transmits to multiple receiving stations having synchronized 'clocks'. For navigation, multiple synchronized stations transmit to a user receiver. To find the coordinates of a user in n dimensions (typically, n = 2 or n = 3), at least n + 1 TOAs must be measured. Multilateration systems are also called hyperbolic systems, for reasons discussed below. One can view a multilateration system as measuring n + 1 TOAs, and then either: (a) determining the time of transmission (TOT) and n user coordinates; or (b) ignoring the TOT and forming n time difference of arrivals (TDOAs), which are used to find n user coordinates. Systems and algorithms have been developed for both concepts. The latter (b) is addressed first, as it was the first implemented (roughly, pre-1975); in practice, those systems largely determine a user/vehicle location in two dimensions. A TDOA, when multiplied by the propagation speed, is the difference in the true ranges between the user and the two stations involved (i.e., the unknown TOT cancels). The former (a) is addressed second (it was implemented, roughly, post-1975). In practice, TOT/non-TDOA systems largely determine a user/vehicle location in three dimensions. A TOA, when multiplied by the propagation speed, is termed a pseudo range. However, there is no conceptual reason that TDOA or TOT algorithms should be linked to a number of dimensions. For surveillance, a TDOA system determines the difference in the subject of interest's distance to pairs of stations at known fixed locations. For one station pair, the distance difference results in an infinite number of possible subject locations that satisfy the TDOA. When these possible locations are plotted, they form a hyperbolic curve. To locate the exact subject's position along that curve, multilateration relies on multiple TDOAs. For two dimensions, a second TDOA, involving a different pair of stations (typically one station is one of the first two, and one station is new), will produce a second curve, which intersects with the first. When the two curves are compared, a small number of possible user locations (typically, one or two) are revealed. Multilateration surveillance can be performed without the cooperation or even knowledge of the subject being surveilled. TDOA multilateration was a common technique in earth-fixed radio navigation systems, where it was known as hyperbolic navigation. These systems are relatively undemanding of the user receiver, as its 'clock' can have low-performance/cost and is usually unsynchronized with station time. The difference in received signal timing can even be measured visibly using an oscilloscope. This formed the basis of a number of widely used navigation systems starting in World War II with the British Gee system and several similar systems deployed over the next few decades. The introduction of the microprocessor greatly simplified operation, increasing popularity during the 1980s. The most popular TDOA hyperbolic navigation system was Loran-C, which was used around the world until the system was shut down in 2010. The widespread use of satellite navigation systems like the Global Positioning System (GPS) have made TDOA systems largely redundant, and most have been decommissioned. GPS is also a hyperbolic navigation system, but also determines the TOT in order to provide accurate time.