Current intelligent services are data-driven, and the provision and optimization of service are based on massive user data. And when service providers use user’ data, they will inevitably violate the user’s privacy. With the development of communication technology, positioning technology has been more widely applied. Mobile phones, computers, cars, and other devices, used in our daily life are all equipped with positioning technology. Newzoo Global Mobile Market Report, published in 2020, shows that The number of global smartphone users will reach 3.5 billion in 2020, up 6.7% year-on-year, and the number will reach 4.1 billion in 2023. Research on location-based services has made significant progress. Three main factors promote its rapid development. The first factor is that people are aware of the importance of human mobility research, which is very important to guide social construction, such as disease transmission, urban planning, and personal location services. The second factor is the rapid development of sensor devices. Our ability to collect location data information has been significantly improved with the rapid popularization and development of sensor devices (such as smartphones, wearable devices, onboard sensors, etc.). The third factor is the emergence of premium location services. More and more location-based services and applications, such as AutoNavi, Didi, Meituan, and others, collect users’ locations to understand their spatiotemporal mobility patterns. And they are based on location to provide users with convenient life and rich entertainment [1]. But, some malicious applications and unreliable third parties, which are mounted on these devices and provide a variety of location-based services (LBS), may violate users’ location privacy by acquiring and analyzing the subscriber’s location information [2,3]. The lawbreakers can infer the user’s sensitive information, such as a family address, medical records, religion, and other privacy. They may commit a crime based on location privacy. Therefore, a reliable and effective location privacy protection mechanism is urgently needed by users.

Trajectory generators can well solve the above problems. Namely, on the premise of guaranteeing the users’ location privacy, it can publish the highly available synthetic trajectory data [4–6]. The trajectory generators extract features and model the moving pattern of users’ to train the model. The synthetic data generated by the trained model should be highly similar to the original data, and it also could be used in data mining. At present, the main research content in trajectory generation is how to improve the availability of generated data under the premise of privacy. Researchers invest in the analysis and mining of mobile objects’ location information and produce many research results. But most of the researches focus on analyzing the historical trajectory of moving objects and mining exciting information, and there are a few types of research on trajectory generation technology.

At present, the mainstream trajectory generation method is to generate synthetic trajectory data through the statistical distribution of the data set, constructing prefix tree or the Markov model etc. Compared with the availability, researchers pay more attention to protecting the privacy of the generated data. Hence, more research on the availability of the generated data needs to be invested [7,8]. The Markov model used in the current study has some shortcomings. First, the Markov model is not enough to process some complex data, and the accuracy of the Markov model is relatively low. Second, the simple low-order Markov model works better than the high-order Markov model in the location prediction. Still, low-order Markov can not obtain the context of the high dimensional sequence [9].

To address these problems, we have presented the Trajectory Generation Model with RNNs (TGMRNN), which analyzes the historical location data of moving objects to generate synthetic trajectory data. Recursive neural networks can learn and model these hidden patterns contained in the original trajectory dataset. Trajectory data is sequential data having long-term temporal dependence. In practice, we need to analyze the trajectory data for complex and hidden movement patterns. The position sequence is sequential, and there is a context relation between the positions. The model should be able to continuously learn the characteristics of the position before and after the current position. This paper is to generate the high availability data set by processing and analyzing the historical tracks. Recurrent neural networks (RNN) can store memory through connections with feedback nerves. Besides, RNN networks have a built-in advantage in learning and generating data with long-term time dependence. Therefore, we choose to use RNNs to achieve the generation of forged data sets.

The contributions in this paper are summarized as follow:

(1) We transform location data to trajectory sequence by grid method. The location information mainly consisted of latitude and longitude, which is continuous. The grid method divides the geographic space into different cells and then takes the corresponding cell number as the number of points falling into the corresponding cell. The transformation from continuous data to discrete data is realized. And we convert the problem of continuous location generation to that of sequence generation.

(2) We adopt the GRU model to generate the trajectory, ensuring that the trajectory generator could process high-dimensional sequences and preserve the relationship between the positions. Markov model is only effective in processing low-order (1-order or 2-order) sequences relative to the GRU model. We design the training and generating process using the many-to-one pattern, combined with the N-gram method, which can customize the length of the processing sequence.

(3) We conduct experiments on a real dataset, demonstrating the effectiveness of TGMRNN compared with the mainstream model.

The rest of this paper is organized as follows: we review relevant related work in Section 2. Section 3 describes the Trajectory Generation Model using RNNs in detail. The experimental results and performance analysis are presented in Section 4. Section 5 concludes this paper.

This section describes related work on trajectory data generation based on Markov models and RNN models.

Mechanisms for generating trajectory data need to model the sequential data. Markov model is a standard sequence generation method. It models the past sequence behaviour of users to generate the next behaviour of users. Some studies use the Markov model to predict the next place for trajectory generation. Simmons et al. [10] trans the Hidden Markov Model (HMM) for each user to indicate which place the user will. Liao et al. [11] train a hierarchical Markov model on subscribers’ daily trajectories. The methods above train the model and predict the future location based on a single object’s historical trajectory. In this case, when the user reaches an area that has not been reached, the model will not predict. Xue et al. [12] propose that the collective-pattern-based method divides group tracks into sub trajectories to overcome the shortcomings of modelling individuals. These sub trajectories are combined into growth tracks, and then the Markov model is used to predict the location. However, there are also drawbacks to the collective-pattern-based method. The collective-pattern-based approach is too coarse-grained in predicting the next area, such as using a first-order Markov model that predicts the same next place for all users in the same location. In some estimation generation work based on privacy protection, Xue et al. [13] conduct a prefix-tree using individual tracks and then construct a Markov model to predict the users’ next locations. Chen et al. [14] utilize a hybrid-granularity prefix tree structure, which is efficient data-dependent yet differentially private, to generate trajectories. Chen et al. [15] proposed a novel approach, which extracts the essential information of a sequential database in terms of a set of variable-length n-grams with large counts to generate and release trajectory data. He et al. [16] took the prefix tree structure and a hierarchical reference system to model users’ moving pattern at different velocities. Wang et al. [17] proposed a private trajectories calibration and publication system (PTCP), which generates synthetic trajectories by the build noise-enhanced prefix tree. Xu et al. [18] proposed DP-LTOP, which divides the original trajectory sequence into different sub-segments, and then selects the appropriate locations and segments to form a synthetic trajectory. Wang et al. [19] proposed DP-PSP, which addresses the heterogeneity of trajectories by the anchor point clustering and road segment mechanism to better the synthetic trajectories’ usability. Gursoy et al. [20] proposed Adatrace, which consist of four steps, features extraction, feature extraction, synopsis learning, privacy and utility preserving noise injection, and generation of differentially private synthetic location traces and generates synthetic trajectory by the Markov model with noise. This paper points out three threats, Bayesian inference threat, partial sniffing threat, and outlier leakage threat which are important but many studies have overlooked. Gursoy et al. [21] proposed DP-star, similar work to Adatrace. DP-star takes the Minimum Description Length metric to normalize the trajectory data to benefit the model training process. Ou et al. [22] adopted to extract reliable segments from sub-trajectories, build an exploration tree, and generate synthetic trajectories. Ghane et al. [23] proposed TGM, which could generate trajectories with arbitrary length, could encode trajectory data into the graphical generative model effectively.

Recurrent Neural Networks (RNNs) has been not only successfully applied in Nature Language Processing but also achieve outstanding performance for sequential data, such as text generation, image captioning [24], and location prediction [25]. RNN iteratively reads the sequence, iterating through each element of the sequence and updating its representation based on the input and the previous state. The connection between the hidden units and their respective projections is preserved. Gating units are often used in RNN models to transform the information flow in a more structured manner. A critical factor in determining the applicability of RNN is the size of the data set because RNN has poor generalization performance over small data volumes [26]. Based on the application of the current research results of RNN and the characteristics of the sequence generation problem, we adopt the RNN model to achieve trajectory generation. RNNs network is practised to process sequence data with long-term space-time dependencies, and it is ideal for achieving the inherent attributes of the continuous position.

This section presents the architecture of TGMRNN.

In this section, we report experiments conducted to assess the effectiveness of our generation algorithm.

We propose TGMRNN to generate synthetic trajectory data. It could produce trajectory data for mobile service providers, who need a good deal of user data to improve the quality of their products and prevent the disclosure of users’ privacy. TGMRNN could transform continuous location data to discrete sequence data and preserve the relationship between the location of high-dimensional sequences. TGMRNN adopts the many-to-one pattern to train the model, which has fewer parameters and faster training and take the trained model to generate synthetic trajectory by predicting the next location. And experiments show that TGMRNN is effective.

In the future, trajectory generation is a hot research field. There are still many problems to be solved, such as (1) we should solve the geographic data sparsity to improve the availability of the trained model; (2) we need to improve the efficiency and effectiveness of high-dimensional sequence execution; (3) we need more measures for the availability of the trajectory data; (4) we should introduce stricter privacy mechanism in trajectory generation, such differential privacy; (5) we should eliminate some privacy threats, such as Bayesian inference threat, partial sniffing threat, and outlier leakage threat.