Estimation of Physical Layer Performance in WSNs Exploiting the Method of Indirect Observations
Abstract
:1. Introduction
- we designed a new process for the monitoring of the physical layer in WSNs making use of a completely passive methodology. From data sniffed by external nodes, we first estimate the position of the nodes in the WSN by applying the Weighted Least Squares (WLS) to the method of indirect observations. The resulting information on the nodes position is then used to estimate the status of the communication links among the network nodes;
- we performed a significant number of measurements on the field to evaluate the accuracy of the proposed approach in both indoor and outdoor environments. In the experiments, the proposed method achieved an accurate estimation of the channel links status so that we could acquire the status of the channel links with an average error lower than 1 dB, which is around 5 dB lower than the error introduced without the application of the proposed method.
2. State of the Art
3. Estimation of Node Position Using Indirect Observations
3.1. Multilateration Problem
3.2. WLS Applied to the Method of Indirect Observations
4. Proposed Method for Physical Layer Performance Estimation
4.1. Reference Scenario
4.2. Proposed Power Estimation Algorithm
- Step 1: each anchor i measures and stores the received signal for the packets transmitted during a timeframe T and related to Sik packets per blind node k. From these measures the anchors compute the received signal power TAik.
- Step 2: on the basis of information about the ambient environment, each anchor makes use of a channel model for each of the blind nodes k, namely FAik, to estimate the distances DAik.
- Step 3: for any k, we set a vector r = DAik, for k= 1, ...,NB. We then write the system Equation (3) and apply the OLS method described in Section 3.1 to obtain the estimation of the position of each blind node. These estimations are then referred to as
.
- Step 4: for any k, we also compute the estimated residual by applying Equation (5). From this step on, we enter an interactive WLS algorithm applied to the indirect observations described in Section 3.2.
- Step 5: we compute the coefficients of matrix A∂, which represents the partial derivates of Ap in dx and dy. This is performed by a linearization of each function in the system Ap by a Taylor expansion around the point estimate in Step 3. The general equation for the linearization of a multivariable function f(X) at a point Q is: f(X) ≈ f(Q) + ▽ f|Q(X− Q)
- Step 6: we then apply Equation (14) to obtain the estimation of the correction to be applied to the initial position of each blind node k at each iteration s: δPkB,s. We compute again the new estimated position:
.
- Step 7: for any blind node k we go back for another iteration if δPkB,s< ε, where ε is a threshold set as the stop criterion. Otherwise we go ahead with the next step.
- Step 8: from the estimated position of the blinds nodes and making use of the most appropriate channel model FBjk (this is selected again on the basis of the ambient environment), the transmission power of node k seen by the blind node j is computed.
5. Experiments
5.1. Setup
- Development kit case provided by Telit Wireless Solutions. This kit is made of five ZigBee radio boards that are based on the Texas Instruments CC2530 System on Chip with the Embedded Telit Z-One ZigBee-PRO Stack. The antennas are external dipoles characterized by an omnidirectional pattern. Four modules are used to create the network under analysis whereas the fifth works as the sniffer, for which a specific firmware has been developed to correctly capture all the packets on air.
- The software used to inspect the packet content is Wireshark. To analyze the performance of the network from the Wireshark output and to conduct network discovery and commissioning, a specific tool has been developed by Telit Wireless Solution in collaboration with our lab and named SRManager Tool. In this experiment, this tool has been used to collect the RSSI values observed from the different nodes in the network.
Scenario | Size | Description | Link type |
---|---|---|---|
Conference room | 6.3 m × 5.4 m | The room includes 12 desks with around 40 chairs. The room was empty when making the measurements. | LOS |
Office room | 4.5 m × 9.5 m | The room includes 5 desks, 5 personal computers, and 4 people were working when making the measurements. | LOS |
Small flat | around 85 m2 | The flat has 5 rooms (kitchen, living room, corridor and 2 bedrooms) with typical furniture | LOS/NLOS |
ANCHOR | 00-00 | 28-1F | 95-4C | 1E-57 |
---|---|---|---|---|
Conference room | ||||
A1 | 30.03 | 26.92 | 28.00 | 36.00 |
A2 | 23.99 | 10.13 | 22.00 | 40.00 |
A3 | 27.03 | 28.00 | 8.95 | 33.99 |
A4 | 27.92 | 21.95 | 22.88 | 30.00 |
A5 | 31.97 | 7.52 | 26.75 | 24.02 |
A6 | 24.95 | 34.00 | 30.00 | 11.90 |
A7 | 20.97 | 31.01 | 24.00 | 28.84 |
A8 | 25.68 | 30.15 | 36.00 | 13.65 |
A9 | 35.00 | 20.28 | 16.77 | 24.00 |
A10 | 28.00 | 20.96 | 36.83 | 17.97 |
Office room | ||||
A1 | 24.10 | 7.63 | 34.00 | 24.35 |
A2 | 25.62 | 42.00 | 12.50 | 33.36 |
A3 | 29.21 | 6.20 | 39.98 | 20.31 |
A4 | 29.27 | 14.54 | 38.00 | 25.21 |
A5 | 23.01 | 30.00 | 20.55 | 36.45 |
A6 | 13.60 | 30.00 | 10.85 | 43.07 |
A7 | 27.09 | 23.03 | 21.96 | 29.59 |
A8 | 41.96 | 15.30 | 19.63 | 21.87 |
A9 | 33.81 | 26.26 | 21.44 | 21.96 |
A10 | 9.60 | 34.49 | 23.53 | 28.02 |
Flat | ||||
A1 | 13.17 | 5.01 | 23.00 | 20.28 |
A2 | 21.98 | -0.54 | 18.00 | 25.00 |
A3 | 16.00 | 16.92 | 36.00 | 16.00 |
A4 | 28.10 | 12.00 | 4.73 | 9.29 |
A5 | -8.48 | 29.08 | 22.51 | 9.97 |
A6 | 4.91 | 6.86 | 22.00 | 35.02 |
A7 | 7.57 | 18.98 | -0.90 | 27.50 |
A8 | 10.15 | 5.96 | 7.33 | 32.00 |
A9 | -1.17 | 36.00 | 13.17 | 15.00 |
A10 | 39.74 | -5.29 | 13.90 | 16.33 |
5.2. Propagation Models
5.3. Analysis of Results
Node tx | Node rx | Conference room | Office | Flat |
---|---|---|---|---|
00-00 | 28-1F | 3.52 m | 3.14 m | 7.11 m |
-00 | 95-4C | 2.20 m | 2.08 m | 5.36 m |
-00 | 1E-57 | 3.21 m | 2.85 m | 3.87 m |
-4C | 28-1F | 2.52 m | 1.78 m | 3.38 m |
-1F | 1E-57 | 3.59 m | 1.11 m | 3.36 m |
-4C | 1E-57 | 4.46 m | 2.31 m | 3.78 m |
Node | Multilateration—Error | Proposed method-Error | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
TX | RX | RSSI | distance | RSSI | distance | RSSI | ||||
[dB] | a.v.[m] | [%] | a.v.[dB] | [%] | a.v.[m] | [%] | a.v.[dB] | [%] | ||
Conference room | ||||||||||
00-00 | 28-1F | 10 ÷ 18 | 0.25 | 7.6% | 0 | 0% | 0.33 | 10.3% | 0 | 0% |
00-00 | 95-4C | 18 ÷ 26 | 0.96 | 77.4% | 2 | 7.7% | 0.73 | 49.6% | 0 | 0% |
00-00 | 1E-57 | 12 ÷ 20 | 0.98 | 43.9% | 0 | 0% | 0.96 | 42.7% | 0 | 0% |
95-4C | 28-1F | 16 ÷ 24 | 0.06 | 0.7% | 0 | 0% | 0.62 | 19.7% | 0 | 0% |
28-1F | 1E-57 | 9 ÷ 17 | 0.04 | 1.1% | 0 | 0% | 0.33 | 10.1% | 0 | 0% |
95-4C | 1E-57 | 6 ÷ 14 | 1.33 | 42.5% | 0 | 0% | 0.89 | 24.9% | 0 | 0% |
mean | 0.60 | 28.9% | 0.33 | 1.3% | 0.64 | 26.2% | 0 | 0% | ||
variance | 0.55 | 30.9% | 0.56 | 0.1% | 0.27 | 16.6% | 0 | 0% | ||
Office | ||||||||||
00-00 | 28-1F | 12 ÷ 20 | 2.52 | 44.5% | 7 | 35 % | 0.01 | 0.3% | 0 | 0% |
00-00 | 95-4C | 19 ÷ 27 | 2.32 | 52.7% | 10 | 37 % | 0.25 | 13.7% | 0 | 0% |
00-00 | 1E-57 | 14 ÷ 22 | 0.98 | 25.6% | 1 | 4.5 % | 0.57 | 25% | 0 | 0% |
95-4C | 28-1F | 22 ÷ 30 | 2.51 | 58.5% | 12 | 40 % | 1.3 | 42.2% | 6 | 20% |
28-1F | 1E-57 | 31 ÷ 39 | 1.10 | 49.8% | 9 | 23 % | 0.02 | 1.8% | 0 | 0% |
95-4C | 1E-57 | 18 ÷ 26 | 0.10 | 4.1% | 0 | 0 % | 0.02 | 0.9% | 0 | 0% |
mean | 1.58 | 39.2% | 6.5 | 68.2% | 0.36 | 14.0% | 1 | 3.3% | ||
variance | 1.01 | 20.5% | 24.3 | 59.7% | 0.51 | 16.9% | 6 | 0.5% | ||
Flat | ||||||||||
00-00 | 28-1F** | –18 ÷ –10 | 0.63 | 8.1% | 2 | 20% | 0.7 | 8.9% | 0 | 0% |
00-00 | 95-4C** | –12 ÷ –4 | 0.51 | 8.7% | 1 | 25% | 1.31 | 19.7% | 0 | 0% |
00-00 | 1E-57** | –6 ÷ 2 | 1.76 | 31.3% | 8 | 400% | 0.7 | 15.3% | 0 | 0% |
95-4C | 28-1F* | 2 ÷ 10 | 1.68 | 33.2% | 7 | 70% | 0.23 | 6.4% | 0 | 0% |
28-1F | 1E-57* | 1 ÷ 9 | 1.39 | 27.7% | 9 | 100% | 0.41 | 10.2% | 0 | 0% |
95-4C | 1E-57** | -6 ÷2 | 1.56 | 29.2% | 10 | 50% | 1.39 | 26.9% | 2 | 100% |
mean | 1.25 | 23.0% | 6.17 | 170.5% | 0.79 | 14.6% | 0.33 | 16.7% | ||
variance | 0.55 | 11.5% | 14.16 | 418% | 0.47 | 7.7% | 0.67 | 13.2% |
6. Conclusions
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Colistra, G.; Atzori, L. Estimation of Physical Layer Performance in WSNs Exploiting the Method of Indirect Observations. J. Sens. Actuator Netw. 2012, 1, 272-298. https://doi.org/10.3390/jsan1030272
Colistra G, Atzori L. Estimation of Physical Layer Performance in WSNs Exploiting the Method of Indirect Observations. Journal of Sensor and Actuator Networks. 2012; 1(3):272-298. https://doi.org/10.3390/jsan1030272
Chicago/Turabian StyleColistra, Giuseppe, and Luigi Atzori. 2012. "Estimation of Physical Layer Performance in WSNs Exploiting the Method of Indirect Observations" Journal of Sensor and Actuator Networks 1, no. 3: 272-298. https://doi.org/10.3390/jsan1030272