## 3 The Conventional and Proposed UWB Localization Approaches
### UIWB Model  
The model presented in Reference [26] is used for the UWB simulation. Figure 2 shows the flow chart of the UWB localization system. The UWB localization system consists of UWB signal generation, transmission of UWB signals through indoor channel, cross relation of received UWB signals with reference signal, TOA estimation of UWB signals, distance estimation from TOA and finally estimate the current user position using the trilateration approach. To generate the UWB pulses as input signal for UWB simulation, we use the Gaussian pulse and is defined as  
\[y\left(t\right)=\frac{A}{\sqrt{2\pi\sigma^{2}}}e^{-\left(\frac{t^{2}}{2\sigma^ {2}}\right)}, \tag{1}\]  
where \(A\) is the amplitude of the signal and \(\sigma\) is the standard deviation related to the pulse shape factor. The simulation uses the pulse width of 0.5 \(ns\) and Figure 3 shows the generated UWB pulse for transmission. The UWB transmitted signal is expressed as [26]  
\[s(t)=\sum_{i=0}^{N-1}p\left(t-i\times T_{\text{int}}\right), \tag{2}\]  
where \(p(t)\) is the UWB pulse, \(T_{\text{int}}\) is the sum of guard time and pulse width, \(N\) is the number of pulses. Then the received signal is expressed as  
\[r(t)=h(t)\times s(t)+n(t), \tag{3}\]  
Figure 2: UWB based localization algorithm. where \(h(t)\) is the channel impulse response and \(n(t)\) is the AWGN noise. When we consider the average time of received signal, the noise term is eliminated and is expressed as  
\[r_{\text{avr}}(t)=\sum_{i=0}^{N-1}\,\{p(t)\times h_{i}\,(t+i\times T_{\text{int}} )\}. \tag{4}\]  
After the average operation of received signal, we perform a correlation between the averaged signal and the template signal and is expressed as  
\[S_{\text{Crr}}(t)=\int_{0}^{T_{\text{int}}}r_{\text{avr}}\,(\tau)\times p\,(t- \tau)\,d\tau. \tag{5}\]  
The correlated output signal from one anchor node to UWB tag is shown in Figure 4.  
The correlated output signal is used in the peak detector for estimating the TOA of signal. In the simulation process, we considered IEEE 802.15 4a UWB channel model [27], which characterizes  
Figure 4: Correlated output signal. Figure 3: UWB pulse. industrial LOS environment. The UWB pulses propagate through a large number of paths and the channel impulse response is expressed as  
\[h(t)=\sum_{l=0}^{L}\sum_{k=0}^{k}\alpha_{k,l}\exp\left(j\phi_{k,l}\right)\delta \left(t-T_{l}-\tau_{k,l}\right), \tag{6}\]  
where \(\alpha_{k,l}\) is the multipath gain coefficient, \(T_{l}\) is the delay of the \(l^{th}\) cluster and \(\tau_{k,l}\) is the delay of the \(k^{th}\) multipath component relative to the \(l^{th}\) cluster arrival time \((T_{l})\). The phases \(\phi_{k,l}\) are uniformly distributed in the range \([0,2\pi]\) and the number of clusters \(L\) are assumed to be the Poisson distribution. Table 1 shows the parameter settings for the UWB simulation. The overall UWB simulation stages are summarized in \[s(t)=\sum_{i=0}^{N-1}p\left(t-i\times T_{\text{int}}\right), \tag{2}\]0 To generate the UWB simulation data, our simulation ran on MATLAB and defined an indoor experiment area in the MATLAB simulation environment. The anchors positions are defined and the UWB tag moved in the predefined trajectories. In the UWB transmitter, we generated Gaussian pulses for transmission and these signals are transmitted through the indoor UWB channel. On the receiver side, the UWB receiver receives the UWB signal with Gaussian noise through the UWB channel. To remove the Gaussian noise, the receiver took the average of the signal and passed the signal onto the correlation block. In the correlation block, correlation between the received signals and reference signal is performed and the correlation output is used in the peak detector block. The peak detector block estimates the TOA of the UWB signal based on the threshold setting and the overall UWB transmission-reception is illustrated in Figure 5 as a block diagram.