The Error Propagation Analysis of the Received Signal Strength-Based Simultaneous Localization and Tracking in Wireless Sensor Networks

The Error Propagation Analysis of the ReceivedSignal Strength-Based Simultaneous Localizationand Tracking in Wireless Sensor Networks



Simultaneous localization and tracking (SLAT) inwireless sensor networks (WSNs) involves tracking the mobiletarget while calibrating the nearby sensor node locations. In practice,localization error propagation (EP) phenomenon will arise,due to the existence of the latest tracking error, target mobility,measurement error, and reference node location errors. In thiscase, the SLAT performance limits are crucial for the SLATalgorithm design and WSN deployment, and the study of localizationEP principle is desirable. In this paper, we focus on theEP issues for the received signal strength-based SLAT scheme,where the measurement accuracy is assumed to be spatialtemporal-domain doubly random due to the target mobility,environment dynamics, and different surroundings at differentreference nodes. First, the Cramer–Rao lower bound (CRLB)is derived to unveil both the target tracking EP and the nodelocation calibration EP. In both cases, the EP principles turn outto be in a consistent form of the Ohm’s Law in circuit theory.Second, the asymptotic CRLB analysis is then presented to revealthat both EP principles scale with the inverse of sensor nodedensity. Meanwhile, it is shown that, the tracking and calibrationaccuracy only depends on the expectation of the measurementprecision. Third, the convergence conditions, the convergenceproperties, and the balance state of the target tracking EPand the location calibration EP are examined to shed light onthe EP characteristics of the SLAT scheme Finally, numericalsimulations are presented to corroborate the EP analysis.


  • The EP principles of mobile target tracking and sensor location calibration in the SLAT issue are revealed, which turn out to resemble the Ohm’s Law in circuit theory. The obtained EP principles can be readily extended to linear Gaussian and nonlinear non-Gaussian filtering problems.
  • The convergence conditions and the properties of tracking and calibration EP behaviors are studied to shed lights on the localization information exchange for the mobile target prediction, tracking and the reference node location calibration.
  • The asymptotic performance limits are derived to reveal the impact of those dependent factors like reference node density, reference node location errors, target transition model and measurement accuracy on the SLAT performance, which is important for practical algorithm development and network design.


 SIMULTANEOUS localization and tracking (SLAT) of amobile target has attracted tremendous interests with therapid advances in wireless sensor networks (WSNs) ,e.g., the location-based services , warehousing management, location-aware security , location-based network routing , and shopping mall navigation.

The SLAT problem is to track the mobile target location(referred to as “tracking” hereafter) while calibrating thelocations of network nodes around (referred to as “calibration”hereafter). In principle, the mobile target tracking can beconsidered as the localization cooperation in the temporaldomain, while the sensor node location (and the cooperative network localization as well) can be regarded asthe localization cooperation in the spatial-domain . It ishighly desirable to study the performance limits of the SLATscheme and its error propagation (EP) behaviours for bothalgorithm design and wireless sensor network deployment.The EP phenomenon arises from the uncertainties (e.g., theprevious mobile tracking error, target mobility, measurementerror and reference node location errors) propagating withinthe target tracking and the sensor node location calibration inthe SLAT process.


  1. Haeberlen, E. Flannery, A. M. Ladd, A. Rudys, D. S. Wallach andL. E. Kavraki, “Practical Robust Localization over Large-Sclae 802.11Wireless Networks,” Proc. ACM MobiCom, 2004.
  • The EP issue is studied for the SLAT scheme in wireless sensor networks based on the received signal strength (RSS) measurements, due to its compatibility to the communication infrastructure
  1. Wymeersch, J. Lien, and M. Z. Win, “Cooperative localization inwireless networks.” Proceedings of the IEEE 97.2 (2009): 427-450.
  • The RSS measurement is a promising choice in closed indoor environments (g., shopping mall or underground parking) where the global positioning system (GPS) signal is unavailable.


  • Highly desirable to study the performance limits of the SLAT.
  • EP phenomenon arises from the uncertainties (g., the previous mobile tracking error, target mobility, measurement error and reference node location errors).


In this paper, the error propagation is investigated for bothmobile target tracking and sensor node location calibration ofthe SLAT scheme in WSNs.The spatial-temporal-domain random measurements owingto different levels of shadow fading, device orientation, strengths of thermal noises, surrounding backgrounds, targetmobility and dynamic environments (such as the shoppingmall crowded with moving people) have been taken intoconsideration in the EP analysis to reveal their impact on theSLAT performance.


The Error Propagation Analysis of the ReceivedSignal


Network Model

The WSN under study is depicted in Fig. 1, where all sensornodes are assumed to be randomly and uniformly distributedinside a deployment area. Due to the inevitable errors in theinitial location acquisitions of sensor nodes, we assume that

all sensor node locations are inaccurate. Let si denote the true(but unknown) location of the ith sensor node, i = 1 : M,where M denotes the total number of sensor nodes inside thetracking area. A mobile target moves inside this area, whoselocation at time instant t is denoted by a D-dimensional vectorxt, which is unknown and to be tracked.

Once completing the target tracking, the SLAT scheme startsto calibrate those reference senor nodes with the assistance ofthe localized target and other sensor nodes nearby.3 For thelocation calibration of the objective node sit, we assume that,there are Nt 0 nearby sensor nodes available as referencenodes in addition to the mobile target. Let the index set ofreference cluster formed by these sensor nodes be denoted as

Let’s define a vector associated with reference sensor nodesof the objective node siIn addition, when Nt = 0, the SLAT problem under studyis simplified to the traditional case where only the localizedtarget helps calibrate the objective node.


  • Temporal-spatial-domain localization cooperation in the SLAT scheme for WSNS.
  • The presented EP analysis framework can also provide an intuitive way to capture all dominate factors for both linear Gaussian filtering and nonlinear non-Gaussian filtering problem.
  • The asymptotic performance limits over dependent factors, such as shadow fading, target mobility, reference sensor node density and sensor node location errors are also revealed.



  • System : Pentium Dual Core.
  • Hard Disk : 120 GB.
  • Monitor : 15’’ LED
  • Input Devices : Keyboard, Mouse
  • Ram : 1GB


  • Operating system : Windows 7.
  • Coding Language : MATLAB
  • Tool : MATLAB R2013A


Bingpeng Zhou, Member, IEEE, Qingchun Chen, Senior Member, IEEE, and Pei Xiao, Senior Member, IEEE, “The Error Propagation Analysis of the ReceivedSignal Strength-Based Simultaneous Localizationand Tracking in Wireless Sensor Networks”, IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 63, NO. 6, JUNE 2017.


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