A train positioning method based on received signal strength for urban rail transit

Figures & data

Table 1. Comparison of train positioning methods.

Train positioning methods	Advantages	Disadvantages
Speed measuring based	Simple principle	Large accumulated error
Balise based	High positioning accuracy	Cannot be positioned continuously
Track circuit based	Simple to implement, low cost	Low positioning accuracy
Inductive loop based	Non-contact, continuous positioning	Susceptible to electromagnetic interference
Satellite based	Less equipment for easy maintenance	Not suitable for Non-Line of Sight (NLOS) environment

Figure 1. Structure of DNN.

Figure 2. Schematic of DA.

Table 2. Illustration of parameters in DNN.

Variable name	Explanation	Type	Dimensions
$I_i$	the ith neuron of the input layer	symbol	–
$h_j^{\left[i\right]}$	the jth neuron of the ith hidden layer	symbol	–
$O_i$	the ith neuron of the output layer	symbol	–
l	number of DNN layers, excluding the input layer	integer	–
$n^{\left[i\right]}$	number of neurons in the ith layer	integer	–
N	number of input layer neurons, equal to $n^{\left[0\right]}$	integer	–
K	number of output layer neurons, equal to $n^{\left[l\right]}$	integer	–
M	number of samples	integer	–
X	the input sample set	matrix	$N\times M$
$W^{\left[i\right]}$	the weight of the ith layer	matrix	$n^{\left[i\right]}\times n^{[i-1]}$
$b^{\left[i\right]}$	the bias of the ith layer	matrix	$n^{\left[i\right]}\times 1$
$Z^{\left[i\right]}$	the linear output of the ith layer	matrix	$n^{\left[i\right]}\times M$
$a^{\left[i\right]}$	the output of the ith layer	matrix	$n^{\left[i\right]}\times M$
$\hat{y}$	the output of the output layer, equal to $a^{\left[l\right]}$	matrix	$K\times M$
y	the label set corresponding to sample set	matrix	$K\times M$
$g^{\left[i\right]}\left(x\right)$	the activation function of the ith layer	function	–

Figure 3. Schematic diagram of offline training and online positioning.

Figure 4. DNN training process.

Figure 5. Schematic of simulation environment.

Figure 6. Model accuracy with different section lengths.

Table 3. Model accuracy with different section lengths and velocity.

$L\left(m\right)$
$v\left(km/h\right)$	20	30	40	50
40	79.38%	85.4%	88.5%	92.7%
50	82.8%	83.7%	89.4%	91.4%
60	79.7%	84.4%	89.4%	93.3%
70	76.4%	84.5%	90.3%	92.3%