Algorithm 2. Improved Viterbi algorithm.
Input:	The proposed HMM tuples $<\mathrm{N}=\left\{n_i|\mathrm{i}=1,2,\dots ,N_N\right\},$ $\mathrm{M}=\left\{m_i|\mathrm{i}=1,2,\dots ,N_M\right\},\mathrm{C},\mathsf{\pi }>$; HAR classification results $\mathrm{H}=\left\{h_i\right|\mathrm{i}=1,2,\dots ,N_H\}$; PDR distance information $\mathrm{D}=\left\{d_i\right|\mathrm{i}=1,2,\dots ,{\mathrm{N}}_{\mathrm{D}}\}$; Initial direction of magnetometer $\mathrm{O}$; Initial pressure of barometer $\mathrm{F}$; ${\mathrm{d}}_{\mathsf{\sigma }}$ is the distance threshold.
Output:	Prediction trajectory.
1:	$O_{start}\leftarrow \mathrm{O}$, $F_{start}\leftarrow \mathrm{F}$/* Determine the initial orientation and floor
2:	for $\mathrm{i}$ from 1 to $N_M$ do
3:	for each path pass through $n_{i-1}$ to $n_i$ do
4:	if ((Distance($\mathrm{d}(n_{i-1}$), $\mathrm{d}(n_i$)) - $d_i$)<$d_{\sigma }$) and ($P\left(n_i\right)$>0) then /* Determine whether the distance between two landmark nodes coincides with the distance information estimated by PDR
5:	$\mathrm{Path}\left({\mathrm{N}}_{\mathrm{s}},\mathrm{P}\left({\mathrm{N}}_{\mathrm{s}}\right)\right)\leftarrow$Obtain the subset data
6:	end if
7:	end for
8:	end for
9:	for ${\mathrm{path}}_{\mathrm{j}}$ in $\mathrm{Path}\left({\mathrm{N}}_{\mathrm{s}},\mathrm{P}\left({\mathrm{N}}_{\mathrm{s}}\right)\right)$ do
10:	$H\left({\mathrm{path}}_{\mathrm{j}}\right)=\left\{h_i\right|\mathrm{i}=1,2,\dots ,N_H\}\leftarrow$Obtain the landmark data set
11:	if $H\left({\mathrm{path}}_{\mathrm{j}}\right)$ match with HAR data $H$ then
12:	$\mathrm{Path}\left(N_f, P\left(N_f\right)\right)\leftarrow$Add this trajectory to the final trajectory data set
13:	end for
14	return Max($\mathrm{Path}(N_f, P\left(N_f\right))$)/* Return the trajectory of the maximum probability