WSN Localization Using RSS in Three-Dimensional Space—A Geometric Method With Closed-Form Solution
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Proposed in this paper is a wireless sensor network source localization algorithm in the three-dimensional space. By using the measurements of the received signal strength (RSS), two closed-form none-ambiguous estimators are proposed to geometrically locate the source position under the shadowing noise in the wireless channel. The dynamic adjustment scheme has been applied in the localization algorithm to combat the measurements error in the ranging. With multiple measurements of the RSS, a lower bound of the source localization error is also derived. The numerical simulations show that the proposed estimators outperform the conventional least squares estimator, especially under the adverse scenario when the reference sensor nodes are close to be coplanar. Comparing with the maximum likelihood estimator that approaches the localization lower bound, the proposed estimators result in significantly lower computational burden, but without showing much degradation of localization accuracy.Keywords:
RSS
Cramér–Rao bound
Ranging
Shadow mapping
Position (finance)
This paper analyzed the resolution of ultra wideband(UWB) ranging/imaging system based on the parameter estimation theory.The structure and features of DS-UWB were presented,which was advised to be applied for ranging/imaging. The evaluation algorithms of Cramer-Rao inequality and Fisher information in parameter estimation were introduced.The Cramer-Rao lower bound formula of UWB ranging/imaging system resolution was developed.The simulation results show that the decrease of the impulse duration time and the increase of the SNR help improve the resolution,which gives a theoretical explanation why the impulse has high resolution.
Ranging
Cramér–Rao bound
Impulse Radio
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The Cramer-Rao lower bound (CRLB) provides a useful tool for evaluating the performance of parameter estimation techniques. Several techniques for the computation of the CRLB for ARMA and AR-plus-noise models are presented. It is shown that the CRLB can be expressed as an explicit function of the model parameters.
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Performance of received signal strength (RSS) based localization techniques are directly related to the employed RSS model. Hence, localization performance can be enhanced by improving the accuracy of the RSS model. Lognormal mixture shadowing model for wireless channels, generated by taking distinct scattering clusters into account, characterizes RSS variable more accurately than classical lognormal shadowing model. In this paper, lognormal mixture is applied to localization techniques by means of the derived maximum likelihood estimator. Through simulations performed making use of an exemplary microcellular network structure, it is demonstrated that the mixture model significantly increases the performance of RSS based localization systems compared to the classical model.
RSS
Log-normal distribution
Shadow mapping
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Localization based on received signal strength (RSS) has drawn great interest in the wireless sensor network (WSN). In this paper, we investigate the RSS-based multi-sources localization problem with unknown transmitted power under shadow fading. The log-normal shadowing effect is approximated through Fenton-Wilkinson (F-W) method and maximum likelihood estimation is adopted to optimize the RSS-based multiple sources localization problem. Moreover, we exploit a sparse recovery and weighted average of candidates (SR-WAC) based method to set up an initiation, which can efficiently approach a superior local optimal solution. It is shown from the simulation results that the proposed method has a much higher localization accuracy and outperforms the other
RSS
Shadow mapping
Signal strength
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The Cramer-Rao lower bound (CRLB) provides a useful tool for evaluating the performance of parameter estimation techniques. Several techniques for the computation of the asymptotic form of the CRLB for ARMA models are presented. It is shown that the asymptotic CRLB can be expressed as an explicit function of the model parameters.
Cramér–Rao bound
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The estimation accuracy of conventional parameter estimation methods, including the maximum likelihood (ML) estimator and subspace-based estimation methods, diverges from the Cramer-Rao lower bound (CRLB) under low signal-to-noise (SNR) ratio conditions. Conventional stochastic resonance (SR) technique has shown appealing weak signal improvement advantages under low SNR, but it still needs a priori information such as the probability density functions (pdfs) of weak signal and channel noise. In this study, to address the channel parameter estimation for weak signal conditions, a novel channel parameter estimation algorithm based on dynamic stochastic resonance networks (SRN) is introduced. Since the signal statistical properties are altered by the SRN processing, the CRLB of the wireless channel parameter estimation employing the SRN-enhanced signal is derived, and then the corresponding ML estimator is presented. Theoretical analyses show that the CRLB is lower than those from the original signal and stochastic-resonance-enhanced signal. Computer simulations are performed to verify the effectiveness of the theoretical CRLB expressions. Both simulation and real experimental results indicate that the proposed SRN processing approach outperforms the conventional SR processing through achieving the CRLB improvement, the ML estimation performance enhancement under low SNR conditions, and the hardware complexity reduction.
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The term "ranging" is often used to indicate the operations that make it possible to estimate the distance between two nodes by processing some signals generated and/or received by the nodes. In wireless systems, a very popular ranging method makes use of the radio signal strength (RSS), which is a measure of the received radio signal power. However, RSS-based ranging is considered very inaccurate, particularly in indoor environments, mainly because of the randomness of the received signal power. In this tutorial paper, we provide an in-depth analysis of the main factors that affect the variability of the received signal power and the accuracy of the RSS measurements. Starting from a survey of the most common and widely accepted models for the radio signal propagation and the RSS-based ranging, we then focus our attention on some technological and procedural pitfalls that are often overlooked, but may significantly affect the accuracy of the RSS-based ranging, and we suggest possible techniques to alleviate such problems. The theoretical argumentation is backed up by a set of empirical results in different scenarios. We conclude this paper by providing some best-practice recommendations for proper RSS-based ranging estimation in wireless networks and discussing new approaches and open research challenges.
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RSS
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The problem of Cramer-Rao bound for parameter estimation in norrowband bistatic Multiple-Input Multiple-Output (MIMO) radar system is considered. In this paper, we propose a new narrowband signal model to accurately estimate parameter from a moving target. The Cramer-Rao bound for target parameter estimation is derived and computed in closed form which shows that the optimal performance is achieved. Target location and parameter estimation performances are evaluated and studied theoretically and via simulations.
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Narrowband
SIGNAL (programming language)
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Abstract. The received signal strength (RSS) fingerprint based localization is a widely used technique for location estimation in the indoor environment with the fifth generation (5G) wireless communication. However, the RSS feature is easily affected by the noise and other variations of the propagation channel, thus limiting the localization accuracy. In this paper, we propose a multiple RSS fingerprint based localization scheme in the reconfigurable intelligent surface (RIS) assisted system, where the RSS values under different RIS configurations are leveraged as the fingerprints. However, it is challenging to set the favorable RIS configurations. To tackle this challenge, we design an optimization method based on Cramér-Rao Lower Bound (CRLB) to derive the optimal RIS configurations to achieve a robust and accurate location estimation, where the CRLB is minimized, and projected gradient descent (PGD) method is applied to solve this optimization problem. After the fingerprints are collected, deep neural network (DNN) is employed for location estimation. Simulation results reveal that the proposed scheme performs well in terms of localization accuracy and stability.
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Cramér–Rao bound
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Due to robustness against multi-path effect, channel state information (CSI) of Orthogonal Frequency Division Multiplexing (OFDM) systems is supposed to provide accurate distance measurement for indoor localization. However, we find that the original CSI ranging model is biased, so the model cannot be used to directly derive Cramer-Rao lower bound (CRLB) of positioning error for CSI-ranging based localization scheme. In this paper we first analyze the estimation bias of the original CSI ranging model according to indoor wireless channel model. Then we propose a negative power summation ranging model which can be used as an unbiased ranging model for both Line-Of-Sight (LOS) and Non-LOS scenarios. Subsequently, based on the proposed model, we derive both the CRLB of ranging error and the CRLB of positioning error for CSI-ranging localization scheme. Through simulation we validate the bias of the original ranging model and the approximately zero bias of our proposed ranging model. Through comprehensive experiments in different indoor scenarios, localization errors by different ranging models are compared to the CRLB, meanwhile our proposed ranging model is demonstrated to have better ranging and localization accuracy than the original ranging model.
Ranging
Cramér–Rao bound
Robustness
Channel state information
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