AIT Chapter 5 Sensor Networks

1. Node local with L_i(t) = theta_i*H_i(t) + Phi_i

2. With drift rate theta_i and phase shift Phi_i // Modified by algorithm

1. Compare node time to external real time

2. Accurate if |L_i(t)-t| < delta for all nodes

3. One node needs access to external time scale

1. Compare local times of nodes

2. Nodes agree on time if |L_i(t)-L_j(t)| < delta for all i,j

1. Random switch on of nodes → random phase Phi_i

2. Oscillators have random deviations due to drift and skew

1. Deviations are specified in pulses per million (ppm)

2. Cheaper oscillators have larger average deviation

3. Values from 1ppm (1s/11d) to 100ppm (1s/2.8h) assumed

4. Factors are time, temperature, pressure, supply voltage

1. Physical VS logical time

2. External VS internal synchronization

3. Global (all) VS local (few) algorithms

4. Absolute VS relative time

5. HW VS SW based mechanisms

6. A-priori VS a-posteriori // Before and after event

1. GPS

2. Galileo

3. GLONASS receiver

4. German BC: time signal from DCF77 Mainflingen

5. Loran-C

1. Heavyweight

2. Costly

3. Energy-consuming

4. Line-of-sight to at min 4 satellites required

1. Save local timestamp of event

2. Synchronizes

3. Convert timestamp accordingly

1. Pair-wise and 2. network-wide step

1. Lightweight time synchronization (LTS)

2. Hierarchy referencing time synchronization (HRTS)

1. One reference clock with e.g. GPS access

2. Consider only phase shifts and no drift rate

1. Compute Delta = L_i(t₁) – L_j(t₁)

2. Assumptions L_i(t₂) – L_i(t₁) = L_j(t₂) – L_j(t₁) and L_i(t₃) – L_i(t₂) = L_j(t₃) – L_j(t₂)

3. Solution Delta = (L_i(t₃)–L_j(t₂))/2 – (L_j(t₃)–L_i(t₂))/2

1. MAC delay

2. Interrupt latencies upon receiving packets

3. Delay of packet interrupts to timestamps

4. Delay of OS and protocol stack

1. Node i timestamps after MAC delay before sending first bit // No uncertainty due to OS, protocol stack and MAC delay

2. Node j timestamps directly // No uncertainty due to packet interrupts and leaves only interrupt latencies

3. Difficult for standard HW

4. Easy if full source code of MAC and HW

Timestamp happens in interrupt routine

1. Normal random variable rv

2. Mean = 0

3. Stddev sigma = 11.1 mye s

1. Total uncertainty is zero-mean normal rv with variance 4*sigam²

2. For normal rv 99% of all outcomes have a max distance of 2.3*sigma to mea

3. Max synchronization error is with 99% smaller than 2.3*2*sigma

1. 1hop neighbors synchronizes with R (lev1)

2. 2hop neighbors synchronizes with 1hop (lev2)

3. Spanning tree created

4. Minimal depth minimizes errors

1. All nodes synchronize with reference node R

2. R computes offset to perform synchronization

3. Only three packets necessary

1. Estimating O_R,i

2. Setting t₂=t₂’

1. Timestaps outgoing packets as late as pos

2. Timestaps incoming packets as early as pos

3. Use extra channel for synchronization

Relevant e.g. monitoring or geographic routing

1. Physical as absolute coordinates

2. Logical as relative coordinates or symbolic reference

1. Accuracy // Distance of estimated to real position

2. Precision // Accuracy for repeated localizations

3. Costs

4. Energy consumption

1. Scene analysis

2. Proximity

3. Overlapping connectivity

4. Approximate point in triangle

5. Trilateration

6. Triangulation

1. Use radio environment

2. Which access points or base stations can be received

3. What is the signal strength?

4. Measure beforehand

5. Compare with current situation // Wireless fingerprints

Node’s position is adapted from closest base station

Compare overlapping signals and determine center

1. Determine triangles of anchor nodes

2. Check if node is inside given triangle

Use distance for position estimates

1. Received signal strength indicator (RSSI)

2. Time of arrival (ToA)

3. Time difference of arrival (TDoA)

1. Send signal with P_tx

2. Receive signal with P_recv with loss coefficient c

3. Estimate distance d P_recv = c* P_tx/d^a ↔ d = sqrt^a(cP_tx/P_recv)

Highly error-prone process