#  Radar Basics

#### Multilateration Figure 1: The operation of the multilateration
(here the special case of trilateration: three distances to three known points determine a new position) Figure 1: The operation of the multilateration
(here the special case of trilateration: three distances to three known points determine a new position)

#### Multilateration

Multilateration is the process of determining locations of points by measurement of distances from known points. In Air Traffic Management the measurement of distances is performed by various radar methods by devices installed at these known points. In contrast to triangulation, it does not involve the measurement of angles. That's why big directional antennas are not necessary.

##### Functionality
###### Time-synchronous Measurements

The object to be measured is irradiated (primary radar method) or emits a signal on request (secondary radar method). This echo or response signal is received by a fixed receiver using an omni-directional antenna. The runtime is a measure of the distance. Since a direction determination is not yet possible, the object to be measured is located somewhere around the receiver on a circular line with the radius of the measured distance.

The same process using a second receiver gives a second circle around its fixed position. The object to be measured must be located on one of the two intersections of these circles. This result is still ambiguous. The third receiver from a third fixed position gives an unambiguous result because three circles can only have one common point of intersection.

Synchronicity is established by the time of the transmitted interrogation (or the radar pulse). If each receiver transmits the interrogation itself, the ranging is simple like a monostatic radar. It is an equation with only one unknown quantity, that can be easily calculated. If only one central transmitter emits the interrogation, the distance measurement becomes a bit more complicated like with a bistatic radar. There are now two unknown quantities in the calculation: The distance from the transmitter to the object (which is constant for each receiver) and the distance from the object to the respective receiver. Figure 2: Non-synchronous multilateration, also-called hyperbolic navigation Figure 2: Non-synchronous multilateration, also-called hyperbolic navigation

###### Non-synchronous Multilateration

There is also the possibility that the object to be measured regularly transmits a broadcasting message without any interrogation (example given: ADS-B). Here the exact transmission time is unknown. The receivers only recognize the exact arrival time of the transmission signal. It is therefore not possible to measure the runtime between the object and a single receiver, but only the runtime difference in comparison between the leading edge of the signals in two receivers on different sites. (The transit times in the cable connections between the receivers and the server are calibrated and can be deducted.)

Between two receivers, the different runtime differences are represented as a group of hyperbolas. Each hyperbola in this group corresponds to exactly one measured runtime difference. This means that at this given runtime difference, the object to be measured may be somewhere on this hyperbola.

Further pairs of receivers also measure a difference in runtime and also get a dedicated hyperbola from their individual group of hyperbolas. The intersection of all these selected hyperbolas is the position you are looking for.