Indoor WLAN localization via adaptive Lasso Bayesian inference and convex optimization

Figures & data

Table 1. Work notation

Symbol	Meaning
$q_{i,j}^{{(}^{\circ })}(\tau )$	Direction of the orientation
t	Time sample
${\mathrm{\Delta }}_j^{{(}^{\circ })}$	Variance vector
L	Number of aps
N	Number of rps.
${\mathrm{\Delta }}_{i,j}^{{(}^{\circ })}$	Variance for AP i at RP j
${(}^{\circ })$	Orientation
$\alpha ,\beta$	Conjugate exponents
$\gamma$	Absolute Lebsegue integrable
p(x), q(x)	Scalar value
β, α	Conjugate exponents
IPS
ci	Center
Ci’s	Cluster
$\left|C_i\right|$	Cardinality of Ci.
$c_{li}$	Cluster centers
$l_i\in \{1,\dots ..,L\}$	Cluster labels
${\mathrm{\ell }}_1$	Sparse recovery
$\theta =[0,0,1,\dots ..,0{]}^T$	Sparse location vector
$\mathrm{\Psi }$	Fingerprinting database
$\epsilon$	Error vector
y	The RSS measurement
$\epsilon$	Noise measurement
$\begin{array}{rl}& \left(\hat{\theta }\right)=argmin\left[{∥\theta ∥}_1\right]\\ & s\cdot t\cdot y=\mathrm{\Phi }\mathrm{\Psi }\theta ,\end{array}$	Convex optimization
$\epsilon$.	Error measurement
$0\le \alpha \le 1$	Adjustment between Lasso and ridge regression
$\lambda$	Complexity parameter
${\mathrm{\Lambda }}^{-1}$	Diagonal of $\gamma$ and $\gamma =[{\gamma }_1,{\gamma }_2,{\gamma }_3,\dots ,{\gamma }_N{]}^T$
$\gamma$	Hyperparameters
$\mathrm{\Phi }$	AP selection matrix

Figure 1. Signal-to-noise ratio of received strength signal indicator variations over time.

Figure 2. Hölder divergence encompasses the skew Bhattacharyya divergence and the Cauchy-Schwarz divergence.

Figure 3. The layout used in the experimental work in the College of Engineering and Applied.

Figure 4. The comparison results of K-mean Hölder Divergence with K-mean clustering methods with adaptive Lasso and APs randomly selection.

Figure 5. The localization distance error for adaptive Lasso Bayesian inference and CS n with respect to different number of access points, with and without clustering.

Figure 6. The localization distance error of the proposed system under different AP selection schemes.

Figure 7. The localization distance error for WKNN, KDE, CS-based and adaptive Lasso Bayesian inference for various number of access.

Figure 8. The cumulative distribution function (CDF) of localization for the proposed algorithm with some well know localization algorithms.