Resource-Aware Localization in Sensor Networks - Networked Embedded Systems - page 108

P TX

P TX

P TX ,max

P TX ,max

Measuring received signal
strength

Measuring minimal transmission
power P TX by scaling the graph

P RX along the graph

P TX ,2
P TX ,1

P RX ,1
P RX ,2

P RX, min P RX ,min

d d

d 1 d 2 d max d 1 d 2 d max

(a) (b)

FIGURE . Distance estimation between sender and receiver with (a) RSS and (b) MTP.

A new approach to determine a distance was introduced by Blumenthal et al. in [BTB + ] called
minimal transmission power (MTP). his method detects the MTP P TX ,min required at the sender to
transmit a signal to the receiver. P TX ,min canbecalculatedbyrearrangingEquation.using P RX ,min
(Equation .).
In MTP, a sender continuously transmits a signal with an increasing transmission power ( P TX

∶

P TX ,max ). he transmitted signal contains the sender's adjusted transmission
power P TX in terms of a register value R TX , i to setup the transceiver. At a receiver, the signal can be
detected first at P RX ,min depending on the distance d between both nodes. In most cases, the signal
is received more than once with increasing R TX , i .hen,onlythesmallest R TX , i is valid to determine
d by solving Equation ..

P TX ,min < P TX ( R TX )<



P TX ( R TX G TX G RX

P RX ,min L

) λ 

π )

d = ( (.)

In contrast to RSS where received power and distance are related along a graph with a maximum
at P TX ,max (Figure .a), MTP scales and moves the whole graph with its maximum at P TX

( R TX )

(Figure .b).
he distance estimation using MTP is very precise, especially in very short ranges due to preventing
multipath effects. Figure . shows typical results using ESB.

6.3 Positioning Systems and Localization Algorithms

This section gives an overview about both positioning systems and localization algorithms in wireless
sensor networks. he most popular derivatives are described in more detail.

6.3.1 Positioning and Navigation Systems
Existing positioning systems like GPS cannot be integrated on resource limited sensor nodes due
to their high energy, computation, and communication requirements. However, positioning systems
are important for sensor networks where only a limited number of powerful nodes with GPS provide
their position as reference.