Recursive algorithm of the passive location in sensor networks based on measurement of the received signal strength

Abstract

Introduction. Broad application for monitoring and control of surrounding space is found by sensor networks. For the passive location of radio sources (RS) in the sensor networks uses the method of RSS (received signal strength). It brings together a group of procedures, the hallmark of which is the application to determine the location of RS of the measured strength values of a received signal. In the known RSS algorithms received on the basis of the least squares method, the error of measurement of the ranges, calculated on the measured values of power isn't considered. At the same time definitions of location of RS is performed after receipt of the measurements from all sensors.

Statement of the problem. It is believed that during the propagation of the signal from RS to sensor network, its coordinates don’t change. It is required to synthesize an algorithm which after formation of entry conditions on the basis of measurements of power of signals from three sensors, allowed to specify recurrently location of RS in process of receipt of measurements from other sensors in which the error of measurement of power is considered.

The main part. The vector of the estimated parameters includes coordinates of position of a RS on the plane. The recurrent algorithm of estimation is received on the basis of the extended Kalman filter and belongs to the class of quasi-optimal algorithms with Gaussian approximation of a posteriori density of probability. The initial vector of an assessment of coordinates of RS and correlation matrix of an error of assessment are defined on the basis of the method of least squares in the presence of three measurements of the signal power.

Analysis of the effectiveness of the algorithm. The analysis of efficiency of recurrent algorithm and its comparison with the known algorithms are carried out by means of statistical modeling. Sensor network includes eight sensors. The RS settles down on a circle with a radius of 600 m. Comparison of precision characteristics of the considered algorithms with the lower bound of Rao-Cramer is carried out.

Conclusions. The algorithm is developed belongs to the class of RSS algorithms, which after formation of initial conditions on the basis of measurements of power of signals from three sensors, allows recurrently clarify the location of RS in process of receipt of measurements from other sensors. For the considered example, the values of the circular MSD of an error of assessment of location of RS the developed algorithm is close to potentially achievable values of circular MSD of lower limit of the Cramer-Rao, and less than those of known algorithms on 36-44.4 %. The received algorithm can be also easily extended to a case of a trajectory filtration of a RS at which parameters of his movement are estimated.