# Moon Sensor Station to Improve the Performance of Lunar Satellite Navigation Systems
## 5 Independent Source of Localization
Concerning the dimensions of each field, they were chosen similar to the dimensions of analogous fields used in other long-time tested protocols such as the ADS-B protocol [47; 48]. The preamble is used to synchronize the reception and to perform the measurements; its dimension will be discussed later. The \"type\" field is 8 bits long and is used to specify what type of message is being sent and/or different submessage types. A parity check field that keeps the checksum value of the entire message is 16 bits long. The data field will be different for different types of messages: UI and LER messages contain the user and the local sensor IDs, which are assumed to be 16 bits long. The LER message also contains the measured angle information: 16 bits for the elevation and 16 bits for the azimuth, as well as 16 bits for the ID station. The LEI message comprises the ID of the local sensor and its position information, i.e., latitude, longitude, and altitude. The latitude and longitude are 32 bits and the altitude is 24 bits. Note that this is only a possible implementation, subject to improvement and changes, but, for the scope of the paper, it is enough to have a first assessment of channel occupancy, AOA, and range measurement accuracy. Under these conditions, the maximum number of data bits in each message, without considering the preamble, is 128 bits, and the length of the preamble can be chosen as long as possible to increase the accuracy of the angle and range measurement. In fact, the preamble bits will be used to make \(N\) different measurements on the same messages, obtaining \(N\) as the integration factor. To set a value for the preamble size in terms of number of bits, which corresponds to the integration factor \(N\), the message time duration must be selected: the message should be as long as possible to improve the AOA measurement performance, but it also has a constraint due to the channel occupancy. A derivation to set a value of the message's time length (in terms of number of users and probability of successful localization) follows. Assuming we have \(N_{user}\) users transmitting interrogations, each with a rate \(r\), that the message is \(t_{int}\) seconds long, and that to assure the service it is enough to take at least one measurement over \(M\) (e.g., at least one measurement over 5 s with an interrogation rate of 1-second means one measurement over 5, \(M=5\)), the following formula gives the successful transmission probability:  
\[P_{succ}=1-(1-Pr(0))^{M};\;Pr(0)=e^{(-2\lambda t_{int})} \tag{31}\]  
where \(\lambda=N_{user}\cdot r\), and the expected probability of no collision, \(Pr(0)\), is approximated by the Poisson distribution [49]. Note that \((1-Pr(0))\) is the probability that a collision occurs for one message, \((1-Pr(0))^{M}\) is the probability that collisions occur for \(M\) messages, and \(P_{succ}=1-(1-Pr(0))^{M}\) is the probability of having at least a message without collision on \(M\) received messages. Figure 3: ISL working principle and data communication chart. Fixing the number of simultaneous users \(N_{user}\) to 10, the signal time duration of 1 ms, the packet transmission rate, \(r\), to 2 packets per second, and requiring at least one measurement every one second, the probability of successful transmission for the user is 0.9985. Recalling that a 2 MHz bandwidth BPSK modulation was proposed, a bit-rate of 1 Mbit/s is obtained, i.e., the total number of bits for a single message can be slightly higher than 1000 (accepting \(P_{succ}\) on the order of 0.99). Summing up, a message with a time-size in the order of one millisecond allows high performance in terms of probability of correct transmission and allows a preamble bit-size in the order of one thousand (i.e., \(N=1000\)). In Table 1, a summary of the assumptions is reported: with a preamble of ca.