In this section, we analyze the performance of our proposed IBST system through extensive simulations and validate the proposed scheme by comparing it with the following two previous methods: (1) RSSI localization system, which estimates the object’s position based on the trilateration of RSSI values only [
20]; and (2) INS system, which the results from the inertial and magnetic sensors are used to determine tag location [
19]. As will be shown, our proposed system gives precise and stable localization results, even in sparse and random reader deployment scenarios.
5.1. Simulation Environment and Parameter Setting
In our numerical evaluation, we consider N mobile readers in an area of 100m by 100m. The tagged object moves in two different paths within this track area. Readers are assumed to have a maximum detection range of 20m. The simulation is executed under sparse and dense deployments of random readers, with 5 and 20 readers, respectively. In addition, two paths are tested as tracks for the tag a rectangular back-and-forth track and a circular track.
The rectangular back-and-forth track starts at the point (10,20) meters and the circle track starts at (50,20) with respect to a relative Cartesian origin at the bottom left corner of the track area as in
Figure 10a,b and
Figure 11a,b. The starting point is assumed to be stored in the tag memory; hence, it will be known to the readers once the tag is detected. The values of
and
in the covariance matrix
of the inertial sensors readings process noise are set to 0.1 m/s2 and 0.1 m/s [
19]. The log-normal shadowing path loss model is used as the signal propagation model and the value of the noise variance in RSSI (
) is set to two meters with path loss exponent of 3. The selection of the above values is based on the typical settings of low cost IMUs under indoor/outdoor walking speed conditions [
19]. As the main focus of this paper is to provide an estimation of the absolute tag location based on inertial sensors readings and overlapped and non-overlapped readers, providing more accurate RSSI measurements or precise inertial sensors readings is beyond the scope of this work.
5.2. Simulation Results
The first scenario is the circular track of the tag with 500 steps to return to the starting x-y coordinate of (50,20). We consider a dense reader deployment of 20 readers in the track area. The readers are deployed randomly, and the tag advertises itself continuously to surrounding readers; if the tag is detected by three or more readers, RSSI location can be estimated; otherwise, RSSI trilateration outage is considered (i.e., location cannot be estimated). The tag in IBST will also advertise itself continuously to the readers, however, as in Algorithm II, the detection by one or more readers will be enough to provide a location estimation.
Figure 10a shows a scenario of dense and random deployment of 20 readers within a 100 m
2 localization area. The actual circular track (in purple) and the tracks based on IMU, RSSI, and IBST after 500 steps. Note that the drifting in the IMU readings is significant after two turns, and with no referencing mechanism, the drift from the actual location will continue to accumulate. RSSI is following the actual track whenever the track passes through three readers simultaneously. If an RSSI localization outage occurs, once the tag passes by three or more readers again, the line connecting between the current estimated location and the one before the outage is considered the track during the outage. IBST track, on the other hand, is continuously referenced to the estimated intersection points due to the dense coverage of the readers.
In
Figure 10c, the mean error between the actual track and the track by RSSI, IMU, and IBST is plotted. IMU error is accumulating due to the drift in inertial sensor readings, which causes an incremental, yet cyclic, error as the number of steps increases. RSSI track error is non-cumulative; however, the actual track is not always passing by points where at least three readers’ ranges exist. Note that when RSSI trilateration is not available, a straight line is used to connect the last available and next available locations, causing a deviation from the actual track, which in turn is represented in periodic error areas. IBST error is none-cumulative and not constrained by three readers simultaneous detection; hence, it is the lowest with continuous update to the displacement vector to follow the actual track. The average mean errors for IMU, RSSI, and IBST from the simulation scenario in
Figure 10c are 11.47 m, 3.66 m, and 1.43 m, respectively.
Similarly,
Figure 10b shows a sparse and random deployment of 5 readers, the tracks from inertial sensors only, an actual track, and IBST. In this deployment scenario, the drifting in the IMU readings is comparable to the one in
Figure 10a as IMU readings are not influenced by the number of readers. RSSI, on the other hand, had no estimated locations as the actual track does not pass by three or more readers simultaneously. As a result, no track can be estimated based on RSSI trilateration. Conversely, more deviation is observed in the IBST track from the actual track. This is due to the lower availability of readers, which results in longer inertial sensors readings before finding an intersection point to represent the estimated actual tag location. The effect of lack of any point within the test area that is covered by three readers or more on the performance of IBST is less severe than the RSSI-based track. In fact, the performance of IBST is significantly superior as shown in
Figure 10d, with much lower error than both RSSI and IMU. The average mean errors for IMU, RSSI, and IBST from the simulation scenario in
Figure 10d are 10.91 m, 32.84 m, and 2.34 m, respectively.
Another example of a localization scenario is depicted in
Figure 11a was a dense and random deployment of 20 readers within 100 m
2 localization area. The track starts at the point (10,20) and is rectangular with sharp turns to emphasis the effectiveness of IBST over IMU. Note that the drifting in the IMU readings is significant after two turns. Between steps 240 and 290, outage in RSSI localization occurs, causing an increased localization error as shown in
Figure 11c. The average mean errors for IMU, RSSI, and IBST from the simulation scenario in
Figure 11c are 10.25 m, 5.77 m, and 2.40 m, respectively.
In
Figure 11b, a scenario of sparse and random deployment of 20 readers within the localization area. In this scenario, no points on the actual track are covered by three or more readers; hence, RSSI is in an outage for all steps in the track as the estimated location is the start point (10,20). This is reflected in high localization error as shown in
Figure 11d. The error of IBST track is higher than the one in
Figure 11c as this scenario suffers from the lack of more than three readers to enhance the location estimation. Nevertheless, the mean error is significantly lower than IMU and RSSI. The average mean errors for IMU, RSSI, and IBST from the simulation scenario in
Figure 11d are 10.47 m, 51.69 m, and 1.69 m, respectively.
The above circular and rectangular tracks were executed 1000 times each for:
- (a)
5, 10, 20 readers
- (b)
5, 20 m reader ranges
The mean error in meters (for 1000 runs) in addition to standard deviation of such mean are provided in
Table 3 and
Table 4, for circular and rectangular tracks, respectively. The superiority of the IBST technique is evident. The number and range of readers affect the accuracy of both RSSI and IBST. However, RSSI is more prone to localization errors in small and large numbers of readers with high variance around the mean error. This is because of the dependency on passing through an area covered by three or more readers. IBST, on the other hand, is less dependent on the number and range of readers. The reason behind this stability of IBST mean error is that passing by a single reader will provide a location that is near the actual track. IMU is independent of the number or range of readers. However, the drifting in IMU readings without referencing causes a consistent high error in both track scenarios.
We would like to stress here that IBST is a location estimation algorithm that combines asynchronous inertial and range readings to estimate the location; IBST is not an optimization algorithm of ranging nor inertial sensor readings. Therefore, any improvement in ranging methods can replace RSSI in this work (e.g., AoA, TDoA, hybrid RSSI-TDoA, etc.). Similarly, any enhancement in inertial sensors accuracy or drift-reduction algorithms can replace the “IMU” results. Note that any reduction in inertial sensor or ranging errors will improve the accuracy of IBST, as well.