Real Time RSSI Error Reduction in Distance Estimation Using RLS Algorithm Rajesh Mehra
Abhishek Singh
Dept. of Electronics & Communication Engineering NITTTR Chandigarh, India
[email protected]
Dept. of Electronics & Communication Engineering RGGI Meerut, India
[email protected]
Abstract—Recently received signal strength (RSS)-based distance estimation technique has been proposed as a low complexity, low-cost solution for mobile communication node with minimum RSSI error. After investigating the existing algorithm of location technique, it is observed that the distribution of RSSI-value at each sample point is fluctuant even in the same position due to shadow fading effect. Therefore, here present a novel method for RSSI error reduction in distance estimation using recursive least square (RLS)-algorithm to the existing deterministic algorithms. The proposed method collects RSSI-values from the mobile communication node to build the probability model. Once the probability models are estimated for different standard deviation related to path loss exponent using adaptive filtering in real time, it is possible to accurately determine the distance between the mobile communication node and fixed communication node. From simulation results it is shown, that the accuracy of RSSI-value for mobile communication node in real time distance estimation is improved in changing environments. Keywords— Adaptive Filters; Received Signal Strength (RSS); Distance Estimation
I.
INTRODUCTION
Due to the lack of precision of conventional location systems such as Global Positioning System (GPS) in indoor and urban environments, the research on location methods based on other types of wireless networks is attracting more and more attention in recent years [1]. Different location systems are based on the estimation of a mobile communication node position by using the values of certain measurements taken from radio-frequency signals that travel between the mobile communication node and the fixed node. These measurements can be time-of-arrival (TOA), time-difference-of-arrival (TDOA), received-signal-strength (RSS), and angle-of-arrival (AOA) [2]. The TOA technique needs strict time synchronization of the whole wireless network and in realistic application; it is very difficult to implement the time synchronization between beacon nodes and unknown nodes. This approach is therefore costly and difficult to deploy in real systems. Although the TDOA uses the difference of time arriving at wireless nodes to calculate the distance, it reduces the tight of time synchronization, but it also uses the time method that requires the synchronization. In AOA method, sensor nodes have to be equipped with an array
c 978-1-4673-4529-3/12/$31.00 2012 IEEE
to define the angle that the signal arrives from other wireless nodes. Thus, it is prominent in cost, size, and power consumption [3]. By received signal strength indication (RSSI) method, flexible positioning is possible without additional hardware installation and modification from communication resources such as Wi-Fi. According to IEEE802.11TGn Channel Model, the wireless signal strength follows the Log-distance path loss model and log-normal shadow fading. So the effects of shadow fading in indoor RSSI range and convergence with pedestrian dead reckoning by using Extended Kalman Filter are presented [4]. An optimization algorithm to automatically calibrate the propagation channel model by using a Least Mean Squares technique: RSS samples gathered in a number of reference points (with known positions) are used by a LMS algorithm to calculate those values for the channel model's constants that minimize the error computed by a hyperbolic triangulation positioning algorithm. Preliminary results on simulated and real data show that the localization error in distance is effectively reduced after a number of training samples [5]. In this paper, proposed method shows the RSSI error reduction using RLS algorithm for solving problems on to estimate the distance of mobile communication node from fixed communication node. Simulation results prove that its performance is usually much better than using conventional methods designed to filter RSS value. II.
EMPIRICAL MODEL OF PATH-LOSS
A. Log-normal shadowing model The empirical model used to define path-loss is the lognormal shadowing model, as in
Pd dBm
P0 100 lo log10
d d0
X .
(1)
where d is the distance between the transmitter and receiver; d0 is the reference distance; Ʉ is the path-loss exponent which defines the rate at which the power falls; generally takes the values of 2-4; Xσ is the Gaussian random noise variables with zero mean and mean variance of σ; P0 is the signal strength at d0 of the distance transmitter; Pd is the signal strength at d of the distance transmitter; P0 can be obtained through the
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experience, or it can be received from the defines of hardware specification. In this way, the distance d can be obtained through the signal strength Pd [6]. In free-space the value of η is equal to 2, and in practice can vary depending on the surrounding environment. The variance of the shadowing is also dependent on the surrounding environment and can increase significantly in complex environments. Table I show the value of path loss exponent η depends on the surroundings and building type and can be calculated via the pre-measurements [7]. Equation (2) is used to calculate the path loss exponent. RSSI ddBm A 10l 10log((d )
(2)
where A is obtained in a no-obstacle one-meter distance signal strength measurements from the reference node [8]. Table II show the relationship between the path loss exponent η and standard deviation responsible for the variance of the shadowing for different types of environment. B. RSSI dependend on distance The fixed node will measure the RSS-value received from mobile communication node and determines the distance between the fixed node and the mobile node according to their RSS-values, as in
d 10 III.
RSSI dBm A dB 0 10
.
(3)
RLS-RSS ESTIMATION ALGORITHM
A. Adaptive Filtering Algorithm Adaptive filters are dynamic filters, which iteratively alter their characteristics in order to achieve an optimal desired output. An adaptive filter algorithmically alters its parameters in order to minimize a function of the difference between the desired output and d(n) its actual output y(n). This function is known as the cost function of the adaptive algorithm. TABLE I.
VALUES OF PATH LOSS FOR DIFFERENT TYPES OF ENVIRONMENT
Environment
Path Loss Exponent (η)
Free space Urban area cellular radio In-building LOS
2.0 2.7~3.5 1.6~1.8
Obstructed in-building
4~6
Shadowed urban area cellular radio
3~5
Metalworking factory, LOS Metalworking factory, obstructed LOS
Free space Retail store Grocery store Office, hard partitions Office, soft partitions
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Path Loss Exponent (η) 2.0 2.2 1.8 3.0 2.6
5~8 6.8
The Recursive Least Square (RLS) algorithms are known for their excellent performance when working in time varying environments. The adaptive filter algorithm updates the filter tap weight vector in adaptive noise cancellation to achieve an estimated output [9? B. Proposed RLS-RSS Estimation algorithm The proposed Recursive Least Square – Received Signal Strength algorithm (RLS-RSS algorithm) has two phases. The first phase starts with the mobile node broadcasting a signal, then the fixed or reference node receives and measures the strength of the signal. In the second phase, all the measured RSS-values will be sent to the RLS-Received Signal Strength adaptive estimator to be further processed. In this current variables are updated within the iteration they are to be used, using values from the previous iteration and proceed the iteration of RLS algorithm finite times for same measured RSS-values and updated filter tap weight vector and inverse matrix. Fig. 1 shows the adaptive RLS-RSS estimation system. To implement the RLS-RSS algorithm, the following steps are executed in the following order. Step1. In the first step, based on the RSS-value measurement system, path loss log-normal shadowing model with the gaussian random noise variables is built, which has non-linear function between the distance values and the RSSI values, as in 4 cd 0 d 0 log g10 10 log10 (4) 4 RSSI dBm 20 X . (4) f d0 where c is the speed of light; f is the frequency of the transmitting signal for the wireless device. In the RSS measurement system that includes one fixed communication node, denote the received shadow faded RSSI vector of the mobile communication node, as in
RSSI dBm
RSSI1, R RSSI 2 ,
, RSSI N .
(5)
where RSSIN stands for the Nth signal strength of mobile node. The received signal strength is measured by dBm. Similarly Equation (6) is defined the RSSI vector for the ith mobile node.
RSSIi dBm
RSSIi1i1, RSSIi 2 ,
TABLE II. RELATIONSHIP BETWEEN PATH LOSS AND STANDARD DEVIATION FOR DIFFERENT TYPES OF WIRELESS ENVIRONMEN Environment
1.6 3.3
Standard Deviation 8.7 5.7 7.0 14.1
2013 3rd IEEE International Advance Computing Conference (IACC)
, RSSIiN .
(6)
Step8. The inverse matrix is calculated, as in
p n
p n 1
T k n Noisemavg n p (n 1)
.
(13)
Step9. Go to Step4 and iterate N total number of iterations. Step10. The median value of the estimated RSSI data for ith mobile nodes is calculated, as in
ERSSI i
median( median( ERSSI i1 , ERSSI i 2 ,...., ERSSI iN ).
(14)
Step11. The distance between fixed node and the mobile node is estimated by solving the non-linear equation, as in ERSSIi dBm dB
di
Figure 1. Adaptive RLS-RSS Estimation System.
Here all RSSI data of fixed communication node will form the M X N fixed communication node matrix, where M is the number of mobile nodes and N is the total RSSI samples of each mobile communication node. Step2. Equation (7) is used to generate the Gaussian random noise vector M X N (NoiseGaussian ) for each mobile node and passes from low pass FIR filter and moving average filter, as in (8).
NoiseGaussian Noisemavg
normrnd d 0, SD, M , N ffilter l
mavg
7
,1, 1 NoiseGaussian
8
where ωmavg the coefficients of moving average filter; SD is the standard deviation for environment. Step3. Initialize filter tap weights; w (0) = 0 and inverse matrix; P (0) = δ-1I, where δ is small positive constant; I is identity matrix. Step4. The filter output is calculated using the filter tap weights from the previous iteration and the current input vector, as in
y n
wT n 1 Noisemavg n . ma
(9)
Step5. Equation (10) is used to calculate the intermediate gain vector.
p n 1 Noisemmavg n
k n
T N i mavg Noise n p n 1 Noisemavg n m
(10)
where λ is a forgetting factor lying in the range 0< λ
