# Enhancing Positioning Accuracy through Direct Position Estimators Based on Hybrid RSS Data Fusion

TL;DR: It is suggested that typical median estimator must be replaced by maximum likelihood estimator (mode) to enhance the positioning accuracy in future hybrid localization systems.

Abstract: In this paper, localization based on Received Signal Strength (RSS) is investigated assuming a path loss log normal shadowing model. On the one hand, indirect RSS-based estimation schemes are investigated; these schemes are based on two steps of estimation: estimation of ranges from RSS and then estimation of position using weighted least square approximation. We show that the performances of this type of schemes depend on the used estimator in the first step. We suggest that typical median estimator must be replaced by maximum likelihood estimator (mode) to enhance the positioning accuracy. On the other hand, a new direct RSS-based estimation scheme of position is proposed; Monte Carlo simulations show that the new estimator performs better than indirect estimators and can be reliable in future hybrid localization systems.

## Summary (2 min read)

### Introduction

- Nowadays, Location Based Services (LBSs) are more and more required by people and industries.
- This is the scope of the FP7 WHERE project [2].
- The proposed direct approach consists in the estimation of position directly from RSS measurements without going through ranges.
- These different estimators are evaluated by Monte Carlo simulations and show that mode estimator is the best indirect estimator and that the new direct estimator performs better than all direct schemes.

### II. LOG NORMAL SHADOWING PATH LOSS MODEL

- The simple analysis often used in coexistence studies limits the propagation characteristics to the large scale of the signal at given distances .
- In mathematical terms, the mean received power (around which there will still be shadowing and multipath) will vary with distance with an exponential law.
- The measured loss varies about this mean according to a zero-mean Gaussian random variable, Xσsh , with standard deviation σsh.
- For each environment or/and radio link, a characteristic value of each parameter, np and σsh, is used.
- Taking this into account, a constant level of noise can result in ever increasing error when RSS is used to estimate distance; if RSS noise is sufficient that the authors cannot tell the difference between 1 and 1.5m, they also cannot tell the difference between 10m and 15m.

### A. Estimation of range from RSS

- Thus, this estimator may be practical when no information about shadowing is available.
- Once the MS get this knowledge, the best estimator will be the mode which is the ML estimator.
- To better evaluate the performances of these different estimators, the authors derived for each estimator its variance.

### IV. PROPOSED RSS-BASED DIRECT ESTIMATOR

- The mathematical formulation of the proposed direct estimation scheme is described.
- The authors notice that it has an additional trivial solution at origin which hopefully can be easily eliminated if it comes out from the optimization algorithm.

### V. SIMULATIONS RESULTS AND DISCUSSIONS

- The authors evaluate the performances of the set of studied estimators described in section III and IV through Monte Carlo simulations.
- The different steps of the simulation are the following: The Fig. 2 and Fig. 3 are obtained respectively for indoor and outdoor scenarios with the parameters described in Table III.
- Moreover, these figures suggest that the new proposed direct estimator performs better than direct schemes in the two different cases (indoor and outdoor).
- Thus, the authors believe that the direct RSS-based estimation scheme of MS’s position may enhances the positioning accuracy.

### VI. CONCLUSION

- The authors studied hybrid RSS-based localization estimators assuming a path loss log normal shadowing model.
- The authors distinguished direct from indirect schemes.
- Indirect estimation schemes consist in two steps: estimation of ranges from RSS using mean, median or mode estimators; and estimation of location using weighted least square approximation on previously estimated ranges.
- Furthermore, a new direct scheme for location estimation from RSS is proposed and analyzed.
- Next step will be to evaluate performance in more realistic scenarios and especially by using more realistic path loss model with adequate parameters.

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##### Citations

50 citations

### Cites background or methods from "Enhancing Positioning Accuracy thro..."

...By deriving these likelihood functions, we obtain easily the different ML estimators for respectively RSSI, TOA, and TDOA [5], [6]....

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...This paper considered non-hybrid and hybrid localization techniques using RSSI, TOA, and TDOA....

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...Assuming Gaussian models independence between considered LDP measurements, the likelihood functions are given receptively for RSSI, TOA, and TDOA by [5], [6]: ⎧⎪⎪⎪⎪⎪⎨ ⎪⎪⎪⎪⎪⎩ fRSSI(X) = p∏ k=1 1√ 2πdkSk e − (ln dk−Mk) 2 2S2 k fTOA(X) = q∏ k=p+1 1√ 2πσk e − (cτk−dk) 2 2σ2 k fTDOA(X) = K∏ k=q+2 1√ 2πσk(q+1) e − (cτk(q+1)−dk(q+1))2 2σ2 k(q+1) (10) where Sk and Mk are defined for each k respectively by [5]: Sk = −σsh k ln 10 10np (11) Mk = (P0 − Pk) ln 10 10np + ln d0 (12) By deriving these likelihood functions, we obtain easily the different ML estimators for respectively RSSI, TOA, and TDOA [5], [6]....

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...The use of WLS technique is quite different for RSSI, TOA, and TDOA....

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...CDFs of positioning error using WLS and ML estimators applied on the fusion of RSSI, TOA, and TDOA. fusion of LDPs on positioning accuracy....

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44 citations

### Cites background from "Enhancing Positioning Accuracy thro..."

...GSM, GPS, and Bluetooth [91], [103]–[105] because most wireless receivers can provide RSS measurements....

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31 citations

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##### References

3,865 citations

### "Enhancing Positioning Accuracy thro..." refers methods in this paper

...Fingerprinting with RSS refers to the type of algorithms that first collect RSS fingerprints of a scene and then estimate the location of the MS by matching on-line measurements with the closest location fingerprints [5]....

[...]

542 citations

### "Enhancing Positioning Accuracy thro..." refers background in this paper

...The total pathloss at a distance, d, will then be L, often modelled as [10]:...

[...]

352 citations

### "Enhancing Positioning Accuracy thro..." refers background in this paper

...1, changes in RSS due to distance become small relative to noise, even if the level of noise remains the same over distance [11]....

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