Clock model and synchronization

TDOA-based localisation presents stringent requirements on the time synchroniza- tion accuracy between multiple sensors that are used to receive signal and calcu-

Distance (m) Distance (m) (a) Noiseless −4 −2 0 2 4 6 8 −10 −5 0 5 10 15 20 25 30 35 S1 _S2 S3 S4 Target Distance(m) Distance(m) (b) Noisy measurements −4 −2 0 2 4 6 8 −10 −5 0 5 10 15 20 25 30 35 S1 _S2 S3 S4 Target

Figure 3.19: Hyperbolas of 3 independent TDOAs from four sensors in noiseless and noisy case

late TDOA measurements. Small time synchronization error can cause large dis- tance error as the propagation speed of the electromagnetic signal is very high (≈ 3∗108m/s). Assume the clock model of the local oscillators of ith SDR to be

Ci(t) =αi∗t+βi (3.10)

where αi and βi denote clock skew and clock offset. For an ideal clock, we assume

α0 = 1 and β0 = 0, however, in practice, there are some clock skew and clock

offset between the local clocks of different SDR units. Figure 3.20 shows an intuitive expression of how local clocks perform differently as a function of time. Here we assume the clock skew is constant. With different intrinsical time offsets and clock skews, the time stamps on the received samples will not be accurate such that time synchronization error is produced; therefore, accurate time synchronization solutions are required to correct the difference of the clock skews and clock offsets of different SDRs.

In general, time synchronization is mainly achieved through distributed methods using mutual communications between sensors or centralized methods using the ref- erence broadcasting signal. Distributed methods usually require mutual communica- tions between different sensors; however, in this source localisation implementation, different SDRs are far from each other (several kilometers), so the mutual commu- nication between them is not available. Even if the communication between SDRs is possible, the SDRs which can actively send signals that carry time synchronization information must be developed, which will make the system more complex and con- sume more energy than current receiver-only-based implementation. Therefore, the centralized synchronization methods are chosen. Three methods are evaluated for the time synchronization of multiple SDRs, including NTP (Network Time Protocol), MIMO (Multi-input Multi-output) cable and the GPSDO.

NTP NTP can be used to synchronize PCs running a Linux operating system to the time on a common network server. Using NTP, the hosts to which the USRP units are

0 t Loc al clock 𝛼3< 𝛼1< 𝛼0< 𝛼4< 𝛼2 𝛽1< 𝛽3< 𝛽0< 𝛽4< 𝛽2

Figure 3.20: Different local clock running on different SDRs

attached can be connected to the Internet and all of them can be calibrated against public time servers. The process for using NTP involves installing NTP server in Ubuntu, configuring NTP server by running commend editing /etc/ntp.conf and then running ntpdate plus server name to synchronize the PC to the public server. In order to obtain a highly accurate result, it is recommended to use local country (national) servers, e.g. server 0.au.pool.ntp.org and listen to multiple servers.

Another method to use NTP was also attempted. Rather than calibrating time against a public server, a different approach is to set up a local area network consist- ing of multiple SDRs, where one SDR acts as the NTP server and others are clients. The same method as described above can then be used to synchronize the SDRs. The accuracy of this approach is similar to the previous one.

However, there are some limitations to the NTP-based synchronization method. Firstly, the time resolution of the NTP is 0.1 ms, which is not accurate enough for the TDOA-based localisation. This time resolution corresponds to 30 kilometers in distance. It means that, to use this synchronization method, the minimum distance (baseline) between two SDRs needs to be 30km, which is too far for experiments. Another major drawback of this method is that the NTP synchronizes the time of the host PCs, not the time reference of the USRP N210s directly. This introduces a second synchronization problem to be solved between the SDR and its host PC, which is not straight forward to tackle.

MIMO The MIMO expansion cable has a length of 0.5m and is used to link a pair of USRP N210 devices together. This method relies on physical connection to synchro- nize a pair of USRPs. The MIMO cable allows two connected USRPs to communicate clock and time reference information. To use it, one USRP must be configured as

the master and the other as the slave. The USRP reads the status of "mimo locked" sensor either "locked" or "unlocked" to indicate whether the two devices are synchro- nized through the MIMO cable. With correct setting, two devices are synchronized immediately after they are powered on. The synchronization accuracy is high as time deviation between the USRPs is 0. However, it can only be used to synchronize a pair of closely placed SDRs at a time, which is not suitable for multi-SDR-based applications.

GPSDO To achieve high-accuracy synchronization among multiple spatially dis- tributed SDRs in a large area, GPSDOs can be used. By installing one GPSDO unit on the motherboard of each USRP, the time and frequency reference of SDRs can be provided by GPSDOs. As opposed to physical cable connection, time synchroniza- tion using GPSDOs only requires the SDRs have access to the GPS satellites. Without working with the GPSDO, the local oscillator of the USRP is TCXO (Temperature Compensate crystal Oscillator) which gives 2.5 ppm (parts per million) frequency reference. Different USRPs begin to count individually after each power cycle such that they do not have an agreed time to support synchronized operation. After the GPSDO is used, the local oscillator of the USRP is disciplined by the GPS signal to achieve higher frequency accuracy. The frequency output of GPSDO is 10 MHz and the frequency reference accuracy is enhanced to 0.01 ppm, which is equivalent to +/- 0.1Hz frequency error. GPSDOs not only offer more accurate frequency output, but also provide an agreed time reference which is synchronized to the global GPS time among different USRPs. With this agreed time reference, synchronization based applications can be implemented using multiple SDRs. The 1 PPS time references of GPSDOs is synchronized to Coordinated Universal Time (UTC) and the achieved 1PPS accuracy is +/-50 nanoseconds.

To use the GPSDO to synchronize the SDRs, an appropriate external GPS antenna is required with a good view to the sky. SMA male straight black GPS antennas are used to compile with the connector of GPSDOs. It takes a few minutes for the GPSDO to lock on to the GPS signal. By checking the status of "gps locked" sensor on the USRP motherboard, the GPS receiver will declare "locked" or "unlocked". Once the GPSDO is locked to the GPS signal, the time of different USRPs is synchronized to the UTC time. By default, if a GPSDO is detected at startup, the USRP will be configured to use it as a frequency and time reference. The time output of GPSDO includes integer second and fractional second, e.g. "1333767848.21354165s".