With the development of deep learning technology, it has been widely used in indoor fingerprint-based localization. Existing indoor fingerprint localization methods based on deep learning carefully design the network structure of the model by manual means, and are used for location estimation in diferent environments. However, the spatial structure of diferent environments makes the signal propagation characteristics, location information and signal intensity distribution diferent, resulting in the universality of these methods when applied to diferent positioning scenarios. In this paper, a fingerprint localization system based on automatic design neural network structure is proposed, and the optimal network structure is carried out based on the two-layer optimization of micro-network architecture search algorithm. It can better extract the high-dimensional position information of the signal for location estimation of diferent spatial structure scenes. The model defines the unit module and simplifies the search of the whole network structure to the optimal unit structure. We conducted experiments in laboratory and library scenarios, which validated NAS-FL's superior performance in positioning accuracy and stability. The results show that this method can efectively improve the positioning accuracy and enhance the universality of the model in diferent positioning scenarios.
The complex building structure of indoor environment makes the signal face the problems of multipath
propagation, non-line-of-sight transmission, signal attenuation and so on. The movement of people and
ever-changing signal interference makes dynamic high-precision indoor positioning challenging[
Indoor positioning systems need to adapt to changes such as personnel movement, equipment
switching, and building structure changes to maintain accuracy, and it has become a growing trend
to design adaptive network models for diferent indoor environments. Neural architecture search
(NAS)[
Inspired by the Neural Architecture Search (NAS) framework, this paper proposes an automatic design of neural network architecture for fingerprint localization: NAS-FL, which designs SOTA models for diferent indoor environments through search algorithms, and the automatically designed models can extract high-dimensional spatial location information in the environment, so that the localisation system has good generalisation ability under diferent spatial structures, and realises high accuracy and high robustness under the complex and variable indoor environment to achieve highly accurate and robust indoor positioning in complex and variable indoor environments. The system is shown in Fig. 1. The methodology and contributions of this work can be summarised as follows: • First, define a rich search space, which simplifies the search of the entire network structure to the search of the optimal unit structure. • Secondly, design a microizable network architecture search algorithm based on two-layer optimization. The algorithm adjusts the network architecture by gradient information, and can find a better network structure in less iterative steps. • Finally, experiments on two indoor fingerprint data sets with diferent spatial structures show that the proposed method achieves excellent localization performance in diferent environments.
Fingerprint localization:Deep learning is an efective technique for feature extraction and
fingerprint matching. The fingerprint location algorithm based on deep learning can extract higher-order
features from the original data and find the function between the data and the location, reducing the
need for traditional feature engineering. In 2017, Chen[
Neural Network Framework Search : Neural network Architecture Search (NAS) is a method of
automatically learning and designing network structures to find an eficient neural network architecture
for a specific task and data set. There are three main approaches to NAS[
In this paper, a WiFi based automatic design neural network framework for fingerprint localization (NAS-FL) is proposed, aiming at high robustness and high accuracy localisation in diferent dynamic indoor environments. The system framework diagram is shown in Fig.1. Based on the WiFi signals collected under diferent environmental spatial structures, the search strategy selects an architecture A from the predefined search space , passes the architecture to the performance estimation strategy, and the performance estimation strategy returns the estimated performance of A to the search strategy. The search strategy fully exploits the spatial location information contained in the WiFi signals under diferent spatial structures, and trains the search strategy through the above feedback mechanism to obtain the optimal network framework for the scenario. The training is carried out under this network framework to finally complete the location estimation in this scenario.
Our proposed NAS-FL adopts the Cell-Based Network Architecture search method, which is divided into two kinds of structures, Normal Cell and Reduction Cell, and will constitute a complete network by splicing after the search is completed respectively. The core method is shown in Fig. 2.
A cell is a directed acyclic graph consisting of an ordered sequence of N nodes. Each node () is a latent representation (e.g.a feature mapping in a convolutional network), and each directed edge (, ) is associated with some operation (,) that transforms (). We assume that the cell has two input nodes and one output node. For normal cells, the input node is defined as the cell output of the first two layers. For reduction cells, the input is defined as the input of the current step and the state carried from the previous step. The output of the cell is obtained by applying an approximation operation to all intermediate nodes. Each intermediate node is calculated on the basis of all its predecessors: () = ∑︁ (,) ︁(
())︁ <
The task of learning a cell is reduced to learning the operations on its edges, and the possible operations between two nodes are selected in the search space. A well-designed search space is important for NAS methods. On the one hand, a good search space should be large enough and expressive enough to simulate various existing CNN models, thus ensuring that the performance of the models it searches is competitive. On the other hand, the search space should be small and compact enough to save computational resources. The expressiveness of a neural network model depends on the properties of diferent aggregation functions, so we design an expressive and simplified search space: • Node Aggregators: We chose six node aggregators with good results according to the popular
CNN models, as shown in Table 1. We use to denote the node aggregators. • Connection operation: We use connection operation. zero denotes a special zero operation that represents no connection between two nodes.
Let be a set of candidate operations in , where each operation denotes some function (· ) that will be applied to (). In order to make the search space continuous, we relax the classification choice of a particular operation to the value of all possible operations: (,) () = ∑︁
︁( exp
(,))︁ ∈ ∑︀ ′∈
︁( exp ′ (,))︁ () search is then reduced to learning a set of continuous variables = {︀ (,)}︀ , as shown in Fig. 3. where a pair of nodes (, ) is parameterised by a vector (,) of dimension ||. The task of architectural (1) (2)
At the end of the search, by replacing each mixed operation (,) () with the most probable operation, i.e: (,) = argmax∈ (,) (3) Once the training is complete, the edge with the highest probability is found from all the edges to form the discrete architecture.
After relaxation, the structure and the weights (e.g.the weights of the convolutional filters) need to be learnt jointly for all hybrid operations. Similar to architectural search using RL or evolutionary algorithms, where the validation set performance is considered as a reward or fitness, the search algorithm in this paper aims to optimise the validation loss but using gradient descent. ℒtrain and ℒval denote the training loss and validation loss, respectively. Both losses depend not only on the structure , but also on the weights in the network w. The goal of the architectural search is to nfid the validation loss that makes the validation loss ℒval (︀ *, *)︀ , where the architecture-dependent weights * are obtained by minimising the training loss * = argminℒtrain (︀ , *)︀ .
The system views the search problem as a second-level optimisation problem with as the upper-level variable and as the lower-level variable: min ℒval ︁( * ( ) , ︁) s.t. * ( ) = argminℒtrain (, ) (4)
In the two-layer optimisation algorithm for gradient, the need to wait for the sub-network training to converge after each search may result in the optimisation process failing to converge to a (locally) optimal solution, resulting in a sub-optimal network framework, so we optimise the search algorithm by using ℒval (, )the idea of regularisation, using as a regular term, adding constraints to the above (a) (b) equation, where is a constant, to obtain a hybrid optimisation algorithm: (5) (6) * ( ) = arg minℒtrain(, ),
min (︀ 1 − ′)︀ ℒtrain (* ( ), ) + ′ℒ(* ( ), ) − ′,
0 ≤ ≤ 1
Lagrange multipliers and normalisation are performed to finally obtain a first order mixed layer optimisation Loss: , min [ℒtrain (* ( ), ) + ℒval (* ( ), )] where is a non-negative regularisation parameter that balances the importance of training loss and validation loss. Thus, by taking into account the potential relationship between training loss and validation loss, our hybrid-level optimisation can alleviate the overfitting problem and search the architecture with higher accuracy than the two-level optimisation.
In order to verify the model robustness of the system under diferent spatial structures, we tested the localisation stability and accuracy of NAS-FL in two typical indoor scenarios, a small laboratory with a complex environment and a relatively empty large library.
Laboratory environment: The laboratory dataset consists of CSI data collected from WiFi signals in our small lab. The CSI data acquisition device consists of a transmitter and a receiver with three antennas. RP selection is a necessary part of fingerprint positioning, and too large or too small an interval will afect the efect of the experiment. We consider positioning accuracy and data acquisition efort to evenly select RP locations at appropriate intervals. We chose a distance of 0.8 m between adjacent RPS in the laboratory and set 24 reference points. This ensures good positioning accuracy and makes ofline data collection workloads acceptable. The CSI of each reference point was collected for two diferent periods of time. These two periods each contain three diferent layouts of indoor obstacles. Each sample is composed of 30 consecutive CSI packets. The data collected in the first session was used to build an ofline training set with 40 training samples per reference point. Data from the second session were used to form an online test set, again with 40 test samples collected at each reference point. All data is searched into the final data set. The specific distribution is shown in Figure 4.
Library environment: We use the open indoor positioning dataset-10.5281/zenodo.1066040 provided by scholars Mendoza-Silva G et al. as another experimental dataset.This dataset collects the RSSI data values of the third and fifth layers of a library over a period of 15 months and contains rich environmental characteristics. It has 448 unique access Points (aps) with MAC address identifiers. At 48 reference points (RPS), measurements of signal strength were collected. In order to ensure the accuracy of the (a) (b) data, each RP is pre-assigned a serial number, and the data is collected in sequence according to the serial number. Six collections were made at each reference point, which reduced errors. The monthly data is divided into 1 training set and 5 test sets. The distribution of data collection points is shown in Figure 5.
In order to comprehensively analyse the localisation performance of the model, we considered the following evaluation metrics during the evaluation process:localisation error, average localisation error, and standard deviation. The average positioning error and standard deviation reflect the positioning accuracy and stability of the fingerprint positioning model, respectively.
For test sample i, the localisation error represents the distance between the predicted coordinates and the actual coordinates, which is calculated as error = √︁
( − )2 + (︀ − )︀ 2 where (, ) are the true coordinates of test sample i and ( , ) are the coordinates predicted by the localisation model. For all test samples, the mean error and standard deviation of localisation were calculated, respectively, by Eq:
⎯ Mean = 1 ∑︁ error, Std = ⎷⎸⎸ 1 ∑︁ (error −
Mean)2, =1 =1 Here N is the total number of test samples. The error accumulation distribution function (CDF) curve is used to represent the positioning error distribution of the test sample.
To validate the performance of our system in searching network architectures, we compared it to two other localization methods for manually designing network frameworks, including the ResNet model based on manually designed network architectures and the GraphNAS model based on graph structures for automatically searching network architectures.
The comparison of the localization results in Table 2 shows that the overall performance of the model obtained from our search calculation is better than the other two methods. Compared with the manually designed ResNet, ResNet’s model for processing WiFi signals under diferent spatial structures remains unchanged, and the ability of a single CNN model to process CSI image features is weaker.GraphNAS can extract and integrate the location information contained in the antenna link amplitude and phase, (7) (8) and make better use of the spatial diversity characteristics of CSI, but the complex changes in the spatial scene and the unchanging model structure reduce the model’s adaptability. According to the diferent spatial structures of CSI signals, NAS-FL automatically searches for the model structure that is compatible with the environment through the search algorithm, so that the feature information of CSI images can be better extracted and accurate positioning can be carried out.
Figure 6 (a) shows the cumulative positioning errors of NAS-FL, ResNet, and GraphNAS in the laboratory scenario. In the 0-2 m range, NAS-FL showed good positioning performance, with GraphNAS and ResNet slightly worse. The search algorithm in NAS-FL combined with the network structure of diferent scene spatial structure search, has a strong ability to extract the spatial location information of CSI image features, and efectively improves the generalization ability of the model. When the probability reaches 1.0, the positioning error of NAS-FL is 4.50 m, that of GraphNAS is 4.95m and that of ResNet is 5.15m. Figure 6 (b) shows the cumulative positioning error of NAS-FL, ResNet, and GraphNAS in the library scenario, which is slightly worse than the positioning error in the laboratory scenario. In general, both NAS-FL and GraphNAS have good positioning performance within 0-1m, and are better than ResNet. GraphNAS has initially performed well, but the trend has been erratic, which has created a lot of uncertainty about the positioning of practical applications. When the probability reaches 1.0, the positioning error is 4.92 m for NAS-FL, 5.36m for GraphNAS, and 5.79m for ResNet. NAS-FL has more stable performance, less positioning error, and stronger model robustness.
Figure 7(a) shows the cumulative positioning errors of NAS-FL and ENAS-FL in the laboratory scenario. In the 0-2 m range, both have good positioning ability, ENAS-FL is slightly better. The location error of NAS-FL is small, and the hybrid optimization search algorithm converges in the search process to obtain the local optimal solution, which makes the model more accurate. Figure 7(b) shows the cumulative positioning errors of NAS-FL and ENAS-FL in the laboratory scenario. In the 0-0.8m range, the positioning performance of both is very good. NAS-FL has more stable performance and less positioning error, and the hybrid optimization search network architecture efectively reduces the error lfuctuation range.
In this paper, we propose a fingerprint localization method based on automatically designed neural network architecture. The method can design an adaptive network model according to diferent spatial structures and fully mine the location information of each space. According to the WiFi signal in the input scene, the network model structure is searched based on the feedback mechanism of gradient twolayer optimization strategy. We conducted experiments in two diferent spatial structure environments with diferent signal characteristics, and NAS-FL showed good positioning accuracy and stability, which verified that the algorithm can improve the generalization ability of the positioning system in diferent positioning scenarios, and realize highly robust fingerprint positioning in complex indoor environments.
This work was financially supported by the National Natural Science Foundation of China under Grant No.62372049.