We investigate the problem of target tracking using a wireless sensor network with asynchronous sensors. To study the impact of sensor clock imperfection on target tracking in practical situations, we build a testbed and collect data from an outdoor experiment. After analyzing the collected data, we find that the TDOA (time-difference-of-arrival) and FDOA (frequency-difference-of-arrival) measurements have notable bias, which is caused by asynchronous sensors or more precisely by the sensor clock drift. Based on the model of clock drift, the measurement bias and the target position are integrated into a state-space model. Both can be estimated in the framework of the extend Kalman filter. In some circumstance, the target trajectory is tracked successfully.
As an emerging wireless service and application, target positioning or tracking using the measurements collected in wireless sensor networks (WSNs) has drawn a lot of attention over the past two decades [
In this paper, we consider the practical case that the involved sensors are not perfectly synchronized. The asynchronism between sensors is caused by the local oscillator drift of sensors. In recent years, the problem of target positioning is investigated jointly with the problem of clock synchronization. In [
Instead of implementing distinct protocols (e.g., two-way message exchange) as the aforementioned work, the work in [
In this paper, we attempt to build an outdoor testbed using radio frequency, which can be used as a platform to test and validate different schemes of joint clock synchronization and localization of the nodes in WSNs. In addition, a simple scheme based on the extended Kalman filter (EKF) is proposed to track the target node’s location and clock parameters, which can deal with the case with nonstationary clock parameters. Recall that most of the existing methods are based on the stationarity assumption on the clock parameters.
The remainder of the paper is organized as follows. The experimental setup is presented in Section
In the outdoor experiment, we use three sensors which are placed at different positions to track the trajectory of a moving target. The target to be tracked is a satellite phone. Someone is sitting in a moving car and making call using the satellite phone. The uplink signal of the phone can be sensed by our sensors, from which we can extract necessary information for tracking purpose, e.g., TDOA and FDOA measurements. The relative positions of sensors and the target trajectory are marked on a Cartesian coordinate plane; see Figure
At the target side, there are mainly three items. First, the involved satellite phone product is Inmarsat IsatPhone pro. Second, an external magnetic mount antenna (i.e., Serial No. AT1595-90) is mounted on the top the car, in order to let the phone calling in the car. Third, a Trimble 5700 GPS Receiver is used to record the instantaneous position of the car, which is considered as ground truth in algorithm implementation.
The sensor is built based on the USRP (Universal Software Radio Peripheral) (https://www.ettus.com) and related peripherals. All the components of the sensor are given in Figure
Sensor components.
Sensor prototype.
We use the GPS-unlocked oscillators (or free-running local clocks) to synchronize the USRP. In this case, the USRPs’ local clocks are initialized roughly through the NTP service before recording the data. The NTP service needs WIFI access which is provided by a mobile phone. The free-running local clocks of the USRPs cause the bias of the TDOA and FDOA measurements, which is analyzed in the next section.
The uplink signal of the Inmarsat IsatPhone Pro is modulated by GMSK with a channel bandwidth of
The amplitude of the uplink signal in the time period 80s-80.1s.
The initial synchronization between sensor clocks via NTP service is not very precise and can lead to the clock difference as large as 1 s. Since we have no prior knowledge of sensor clock parameters, we do manual calibration to achieve the clock difference smaller than 1 ms by inspecting received signal packet pattern. Based on the calibrated signals of three sensors, we use the generalized cross correlation algorithm [
The local oscillator drift or simply the clock drift leads to significant bias when estimating TDOA and FDOA measurements. The biases of estimated TDOA values compared to the true ones are given in Figures
Bias of the estimated TDOA values for Sensor 1 and Sensor 2.
Bias of the estimated TDOA values for Sensor 1 and Sensor 3.
Bias of the estimated TDOA values for Sensor 2 and Sensor 3.
The bias is suspected to be caused by two sources. One is imperfect synchronization between sensors, which can be roughly modeled by line fitting. If there is prior knowledge of the clock drift, e.g., obtained by training data or other sources, the modeling will be more accurate. However, it is not the case in our experiment. The other is propagation error in the channel between the target and sensors, e.g., multipath effect or non-line-of-sight (NLOS) error, which is hard to be modeled. In this paper, we focus on the bias caused by asynchronous clocks. In order to isolate the propagation error and model the synchronization error, only the data, which is suspected to be transmitted via the channel of good quality, is used for line fitting. More precisely, the data between 28 s and 90 s is used for line fitting in Figures
The line fitting of the TDOA bias captures the trend of bias variation with respect to the time. This validates the linear model for TDOA bias caused by the clock drift, which will be presented in the next section. It is worth mentioning that the measurement bias is modeled roughly by the line fitting in this section and will be estimated more accurately in the next section. The result of line fitting is used for the initialization for the estimation procedure.
The estimated FDOA values has relatively small bias and large variance, compared to the TDOA values. The FDOA bias also can be modeled by line fitting. However, the FDOA measurement is not informative as the TDOA measurement in our case. We do not attempt to present the result of the estimated FDOA values here.
To implement tracking algorithm, the measurement bias must be estimated simultaneously with the target position. Therefore, we have to study the mechanism of clock drift producing the measurement bias.
The local time
For a pair of sensors, e.g., Sensor
Since each pair of sensors produces a set of TDOA and FDOA values, we will have
We stack only the Sensor 1 related TDOA and FDOA bias in order into two column vectors:
Now, we can stack the TDOA and FDOA measurements at time step k in order into two column vectors, i.e.,
Let
The target state includes the position and velocity; that is,
If we define
The extended Kalman filter for the state-space model in (
As a summary, the EKF in (
Before implementing the EKF, some initial values should be set appropriately. By inspecting the TDOA and FDOA measurements, we can set
The initial measurement bias
Figures
Estimated trajectory using data from 0 s to 90 s.
Estimated trajectory using data from 40 s to 90 s.
According to the EKF formulation in Section
It can been seen that the estimated trajectory deviates from the true one at the end of target motion (i.e., around 90 s). It is supposed to be caused by model mismatch of the TDOA and FDOA measurement noise. Recall the measurement noise is assumed to be Gaussian distributed with zero mean; see
We build an outdoor testbed in order to jointly track target location and clock parameter. The main challenge of target tracking in our experiment is the nonnegligible measurement bias caused by the sensor clock drift. The collected TDOA and FDOA measurements validates the theoretical state-space model of clock parameters. Following this, the measurement bias can be modeled. The EKF is used to track the measurement bias (or clock parameters) and the target trajectory simultaneously. The tracking result directly depends on the channel quality. When the channel is of good quality, the target trajectory is successfully tracked. The channel effect on the measurements, including multipath and NLOS propagation, is not well studied in this paper. This should be investigated in the future work. Besides, using the developed testbed to validate the existing algorithms is expected to be investigated in the future.
The MATLAB codes used to support the findings of this study are available from the corresponding author upon request. However, the experimental data is not available because of security issues.
The authors declare that they have no conflicts of interest.
The research was supported by the National Natural Science Foundation of China (no. 61601254) and the K. C. Wong Magna Fund in Ningbo University. The experimental data was collected during the first author staying with the Sensor Array Group at Temasek Labs of Nanyang Technological University in Singapore. The authors would like to thank all the group members for their invaluable assistance in preparing the experiment.