Federated learning (FL) is increasingly adopted to combine knowledge from clients in training without revealing their private data. In order to improve the performance of different participants, personalized FL has recently been proposed. However, considering the non-independent and identically distributed (non-IID) data and limited bandwidth at clients, the model performance could be compromised. In reality, clients near each other often tend to have similar data distributions. In this work, we train the personalized edge-based model in the client-edge-server FL. While considering the differences in data distribution, we fully utilize the limited bandwidth resources. To make training efficient and accurate at the same time, An intuitive idea is to learn as much useful knowledge as possible from other edges and reduce the accuracy loss incurred by non-IID data. Therefore, we devise Grouping Hierarchical Personalized Federated Learning (GHPFL). In this framework, each edge establishes physical connections with multiple clients, while the server physically connects with edges. It clusters edges into groups and establishes client-edge logical connections for synchronization. This is based on data similarities that the nodes actively identify, as well as the underlying physical topology. We perform a large-scale evaluation to demonstrate GHPFL’s benefits over other schemes.

Federated learning (FL) can be implemented in large-scale wireless networks in a hierarchical way, introducing edge servers as relays between the cloud server and devices. These devices are dispersed within multiple clusters coordinated by edges. However, the devices are typically mobile users with unpredictable trajectories, and the impact of their mobility on the model training process is not well-studied. In this work, we propose a newMobIlity-Driven feDeratedLEarning framework, namely MIDDLE. MIDDLE addresses unbalanced model updates by capitalizing on model aggregation opportunities on mobile devices due to their mobility across edges. It consists of two components: on-device model aggregation, which aggregates models from different edges carried by mobile devices as they move across edges, and in-edge device selection, adjusting the current edge optimization direction through careful device selection. Theoretical analysis emphasizes that on-device model aggregation can reduce bias in model updating on edges and the cloud, thereby accelerating the FL model convergence. Building on this analysis, we introduce on-device global control averaging, modifying the training process on mobile devices and extending MIDDLE into$\text{MIDDLE}^{+}$. Extensive experimental results validate that MIDDLE and$\text{MIDDLE}^{+}$can reduce the time steps to reach the target accuracy by 19.44% and 20.37% at least, respectively.

Multi-party training frameworks for decision trees based on secure multi-party computation enable multiple parties to train high-performance models on distributed private data with privacy preservation. The training process essentially involves frequent dataset splitting according to the splitting criterion (e.g. Gini impurity). However, existing multi-party training frameworks for decision trees demonstrate communication inefficiency due to the following issues: (1) They suffer from huge communication overhead in securely splitting a dataset with continuous attributes. (2) They suffer from huge communication overhead due to performing almost all the computations on a large ring to accommodate the secure computations for the splitting criterion.

To bring the great power of modern DNNs into mobile computing and distributed systems, current practices primarily employ one of the two learning paradigms: cloud-based learning or on-device learning. Despite their distinct advantages, neither of these two paradigms could effectively deal with highly dynamic edge environments reflected in quick data distribution shifts and on-device resource fluctuations. In this work, we propose Nebula, an edge-cloud collaborative learning framework to enable rapid model adaptation for changing edge environments. To achieve this, we first propose a new block-level model decomposition scheme to decompose the large cloud model into multiple combinable modules. With this design, we can agilely derive personalized sub-models with compact sizes for edge devices, and quickly aggregate the updated sub-models to integrate new knowledge learned on the edge into the cloud model. We further propose an end-to-end learning framework that incorporates the modular model design into an efficient model adaptation pipeline, including an offline on-cloud model prototyping and training stage, and an online edge-cloud collaborative adaptation stage. Extensive experiments demonstrate that Nebula improves model performance (e.g., 18.89% accuracy increase) and resource efficiency (e.g., 7.12 × communication cost reduction) in adapting models to dynamic edge environments.

Federated learning (FL) can achieve privacy-safe and reliable collaborative training without collecting users’ private data. Its excellent privacy security potential promotes a wide range of federated learning (FL) applications in Internet of Things (IoT), wireless networks, mobile devices, autonomous vehicles, and cloud medical treatment. However, the FL method suffers from poor model performance on non-independent and identically distributed (non-i.i.d.) data and excessive traffic volume. To this end, we propose a personalized FL algorithm using a hierarchical proximal mapping based on the moreau envelop, named sparse federated learning with hierarchical personalized models (sFedHP), which significantly improves the acrlong GM performance facing diverse data. A continuously differentiable approximated$\ell _{1}$-norm is also used as the sparse constraint to reduce the communication cost. Convergence analysis shows that sFedHP’s convergence rate is state-of-the-art with linear speedup and the sparse constraint only reduces the convergence rate to a small extent while significantly reducing the communication cost. Experimentally, we demonstrate the benefits of sFedHP compared with the federated averaging (FedAvg), hierarchical fedavg (HierFAVG), and personalized FL methods based on local customization, including FedAMP, FedProx, per- FedAvg, pFedMe, and pFedGP.

In federated learning (FL), clients may have diverse objectives, and merging all clients' knowledge into one global model will cause negative transfer to local performance. Thus, clustered FL is proposed to group similar clients into clusters and maintain several global models. In the literature, centralized clustered FL algorithms require the assumption of the number of clusters and hence are not effective enough to explore the latent relationships among clients. In this paper, without assuming the number of clusters, we propose a peer-to-peer (P2P) FL algorithm namedPANM. InPANM, clients communicate with peers to adaptively form an effective clustered topology. Specifically, we present two novel metrics for measuring client similarity and a two-stage neighbor matching algorithm based Monte Carlo method and Expectation Maximization under the Gaussian Mixture Model assumption. We have conducted theoretical analyses ofPANMon the probability of neighbor estimation and the error gap to the clustered optimum. We have also implemented extensive experiments under both synthetic and real-world clustered heterogeneity. Theoretical analysis and empirical experiments show that the proposed algorithm is superior to the P2P FL counterparts, and it achieves better performance than the centralized cluster FL method.PANMis effective even under extremely low communication budgets.

In some real-world applications, data samples are usually distributed on local devices, where federated learning (FL) techniques are proposed to coordinate decentralized clients without directly sharing users’ private data. FL commonly follows the parameter server architecture and contains multiple personalization and aggregation procedures. The natural data heterogeneity across clients, i.e., Non-I.I.D. data, challenges both the aggregation and personalization goals in FL. In this paper, we focus on a special kind of Non-I.I.D. scene where clients own incomplete classes, i.e., each client can only access a partial set of the whole class set. The server aims to aggregate a complete classification model that could generalize to all classes, while the clients are inclined to improve the performance of distinguishing their observed classes. For better model aggregation, we point out that the standard softmax will encounter several problems caused by missing classes and propose “restricted softmax” as an alternative. For better model personalization, we point out that the hard-won personalized models are not well exploited and propose “inherited private model” to store the personalization experience. Our proposed algorithm named MAP could simultaneously achieve the aggregation and personalization goals in FL. Abundant experimental studies verify the superiorities of our algorithm.

Federated learning (FL) is a collaborative machine learning technique to train a global model (GM) without obtaining clients' private data. The main challenges in FL are statistical diversity among clients, limited computing capability among clients' equipment, and the excessive communication overhead between the server and clients. To address these challenges, we propose a novel sparse personalized FL scheme via maximizing correlation (FedMac). By incorporating an approximated $\ell _{1}$ -norm and the correlation between client models and GM into standard FL loss function, the performance on statistical diversity data is improved and the communicational and computational loads required in the network are reduced compared with nonsparse FL. Convergence analysis shows that the sparse constraints in FedMac do not affect the convergence rate of the GM, and theoretical results show that FedMac can achieve good sparse personalization, which is better than the personalized methods based on the $\ell _{2}$ -norm. Experimentally, we demonstrate the benefits of this sparse personalization architecture compared with the state-of-the-art personalization methods (e.g., FedMac, respectively, achieves 98.95%, 99.37%, 90.90%, 89.06%, and 73.52% accuracy on the MNIST, FMNIST, CIFAR-100, Synthetic, and CINIC-10 datasets under non-independent and identically distributed (i.i.d.) variants).

Machine learning (ML) models have been deployed in mobile networks to deal with massive data from different layers to enable automated network management. To overcome high communication cost and severe privacy concerns of centralized ML, federated learning (FL) has been proposed to achieve distributed ML among numerous networked devices. While the computation and communication limitation has been widely studied, the impact of limited storage of mobile devices on the performance of FL is still not explored. Without an effective data selection policy to filter the massive streaming networked data on devices, classical FL can suffer from much longer model training time ($4\times$) and dramatic inference accuracy reduction ($7\%$), observed in our experiments. In this work, we take the first step to consider the online data selection for FL with limited on-device storage. We first define a new data valuation metric for data selection in FL with theoretical guarantee for simultaneously accelerating model convergence and enhancing final accuracy. We further design ODE, an Online Data sElection framework for FL, to coordinate networked devices to store valuable data samples collaboratively. Experimental results on one industrial dataset and three public datasets show the remarkable advantages of ODE over the state-of-the-art approaches. Particularly, on the industrial dataset, ODE achieves as high as$2.5\times$speedup of training time and$6\%$increase in final accuracy, and is robust to various factors in practical environments.

Federated learning (FL) in large-scale wireless networks is implemented in a hierarchical way by introducing edge servers as relays between the cloud server and devices, where devices are dispersed within multiple clusters coordinated by edges. However, the devices are usually mobile users with unpredictable mobile trajectories, whose effects on the model training process are still less studied. In this work, we propose a new MobIlity-Driven feDerated LEarning framework, namely MIDDLE in wireless networks, which can relieve unbalanced and biased model updates by leveraging the new model aggregation opportunities on mobile devices due to their mobility across edges. Specifically, mobile devices can have different models while traversing across edges, and adequately aggregate these models on the device. By theoretical analysis, we can show that this on-device model aggregation can reduce the bias of model updating on edges and cloud, and then accelerate the convergence of model training in FL. Then, we define a model similarity utility to measure the difference in gradient updates among various models, which guides the adaptive on-device model aggregation and in-edge device selection to facilitate the comprehensive information sharing between edges. Extensive experiment results validate that MIDDLE can achieve 1.51 × −6.85 × speedup on the model training, compared with the state-of-the-art model training approaches in hierarchical FL.

Many score-based active learning methods have been successfully applied to graph-structured data, aiming to reduce the number of labels and achieve better performance of graph neural networks based on predefined score functions. However, these algorithms struggle to learn policy distributions that are proportional to rewards and have limited exploration capabilities. In this paper, we innovatively formulate the graph active learning problem as a generative process, named GFlowGNN, which generates various samples through sequential actions with probabilities precisely proportional to a predefined reward function. Furthermore, we propose the concept of flow nodes and flow features to efficiently model graphs as flows based on generative flow networks, where the policy network is trained with specially designed rewards. Extensive experiments on real datasets show that the proposed approach has good exploration capability and transferability, outperforming various state-of-the-art methods.

We introduce a new problem in unsupervised domain adaptation, termed as Generalized Universal Domain Adaptation (GUDA), which aims to achieve precise prediction of all target labels including unknown categories. GUDA bridges the gap between label distribution shift-based and label space mismatch-based variants, essentially categorizing them as a unified problem, guiding to a comprehensive framework for thoroughly solving all the variants. The key challenge of GUDA is developing and identifying novel target categories while estimating the target label distribution. To address this problem, we take advantage of the powerful exploration capability of generative flow networks and propose an active domain adaptation algorithm named GFlowDA, which selects diverse samples with probabilities proportional to a reward function. To enhance the exploration capability and effectively perceive the target label distribution, we tailor the states and rewards, and introduce an efficient solution for parent exploration and state transition. We also propose a training paradigm for GUDA called Generalized Universal Adversarial Network (GUAN), which involves collaborative optimization between GUAN and GFlowNet. Theoretical analysis highlights the importance of exploration, and extensive experiments on benchmark datasets demonstrate the superiority of GFlowDA.

Consider the problem of out-of-distribution prediction given data from multiple environments. While a sufficiently diverse collection of training environments will facilitate the identification of an invariant predictor, with an optimal generalization performance, many applications only provide us with a limited number of environments. It is thus necessary to consider adapting to distribution shift using a handful of labeled test samples. We propose a constrained Bayesian approach for this task, which restricts to models with a worst-group training loss above a prespecified threshold. Our method avoids a pathology of the standard Bayesian posterior, which occurs when spurious correlations improve in-distribution prediction. We also show that on certain high-dimensional linear problems, constrained modeling improves the sample efficiency of adaptation. Synthetic and real-world experiments demonstrate the robust performance of our approach.

Machine learning models have been deployed in mobile networks to deal with massive data from different layers to enable automated network management and intelligence on devices. To overcome high communication cost and severe privacy concerns of centralized machine learning, federated learning (FL) has been proposed to achieve distributed machine learning among networked devices. While the computation and communication limitation has been widely studied, the impact of on-device storage on the performance of FL is still not explored. Without an effective data selection policy to filter the massive streaming data on devices, classical FL can suffer from much longer model training time (4 ×) and significant inference accuracy reduction (7%), observed in our experiments. In this work, we take the first step to consider the online data selection for FL with limited on-device storage. We first define a new data valuation metric for data evaluation and selection in FL with theoretical guarantees for speeding up model convergence and enhancing final model accuracy, simultaneously. We further design ODE, a framework of Online Data sElection for FL, to coordinate networked devices to store valuable data samples. Experimental results on one industrial dataset and three public datasets show the remarkable advantages of ODE over the state-of-the-art approaches. Particularly, on the industrial dataset, ODE achieves as high as 2.5 × speedup of training time and 6% increase in inference accuracy, and is robust to various factors in practical environments.

Federated learning (FL) has recently emerged as an innovative paradigm to train models among distributed agents. Conventional FL considers the center as an aggregator and trains from distributed data, while the collected global information at the center is not effectively utilized. Thus, the restricted information from local observations may limit the model accuracy. If FL can introduce data sets from the network server, the distributed models may be largely improved by the extra global information. Since network agents may not be completely trusted, the center cannot directly broadcast its raw data for security concern. Then, how to combine the central sets with FL? In this article, we propose to add a learning model at the center, which obtains the central sets as input. The outputs can be transmitted to network agents and integrated into local models instead of the raw data. The central and local models could be trained to form an integration for intelligent inference. Then, what is the integrated performance gain comparing with the original horizontal FL (HFL) and how to implement it? To figure out these two problems, we propose the vertical-HFL (VHFL) scheme, where models of the center and agents are trained collaboratively. We further analyze its convergence and the related communication channel, proposing the theoretical bounds to guide the network implementation of VHFL. Some simulation results will demonstrate the effectiveness of our proposed VHFL scheme. It is expected that VHFL will be an important block for the next generation of smart services.

Entropy search and its derivative methods are one class of Bayesian Optimization methods that achieve active exploration of black-box functions. They maximize the information gain about the position in the input space where the black-box function gets the global optimum. However, existing entropy search methods suffer from harassment caused by high dimensional optimization problems. On the one hand, the computation for estimating entropies increases exponentially as dimensions increase, which limits the applicability of entropy search to high dimensional problems. On the other hand, many high-dimensional problems have the property that a large number of dimensions have little influence on the objective function, but currently there is no compress mechanism to exclude these redundant dimensions. In this work, we propose Active Compact Entropy Search (AcCES) to fix these defects. Under the guidance of historical evaluation, AcCES actively explores the prevalent inter-dimensional correlations by maximizing the linear or non-linear relationships that may exist between dimensions in the acquisition function, which is ignored by existing Bayesian Optimization methods. In order to build a more compact input space, redundant dimensions are compressed by exploiting inter-dimensional correlations. Experiments demonstrate that AcCES achieves higher query efficiency and optimal results than existing entropy search methods.

Federated Learning (FL) fuses collaborative models from local nodes without centralizing users' data. The permutation invariance property of neural networks and the non-i.i.d. data across clients make the locally updated parameters imprecisely aligned, disabling the coordinate-based parameter averaging. Traditional neurons do not explicitly consider position information. Hence, we propose Position-Aware Neurons (PANs) as an alternative, fusing position-related values (i.e., position encodings) into neuron outputs. PANs couple themselves to their positions and minimize the possibility of dislocation, even updating on heterogeneous data. We turn on/off PANs to disable/enable the permutation invariance property of neural networks. PANs are tightly coupled with positions when applied to FL, making parameters across clients pre-aligned and facilitating coordinate-based parameter averaging. PANs are algorithm-agnostic and could universally improve existing FL algorithms. Furthermore, “FL with PANs” is simple to implement and computationally friendly.

Federated learning faces huge challenges from model overfitting due to the lack of data and statistical diversity among clients. To address these challenges, this paper proposes a novel personalized federated learning method via Bayesian variational inference named pFedBayes. To alleviate the overfitting, weight uncertainty is introduced to neural networks for clients and the server. To achieve personalization, each client updates its local distribution parameters by balancing its construction error over private data and its KL divergence with global distribution from the server. Theoretical analysis gives an upper bound of averaged generalization error and illustrates that the convergence rate of the generalization error is minimax optimal up to a logarithmic factor. Experiments show that the proposed method outperforms other advanced personalized methods on personalized models, e.g., pFedBayes respectively outperforms other SOTA algorithms by 1.25%, 0.42% and 11.71% on MNIST, FMNIST and CIFAR-10 under non-i.i.d. limited data.

Keyword spotting (KWS) aims to discriminate a specific wakeup word from other signals precisely and efficiently for different users.Recent works utilize various deep networks to train KWS models with all users' speech data centralized without considering data privacy.Federated KWS (FedKWS) could serve as a solution without directly sharing users' data.However, the small amount of data, different user habits, and various accents could lead to fatal problems, e.g., overfitting or weight divergence.Hence, we propose several strategies to encourage the model not to overfit user-specific information in FedKWS.Specifically, we first propose an adversarial learning strategy, which updates the downloaded global model against an overfitted local model and explicitly encourages the global model to capture user-invariant information.Furthermore, we propose an adaptive local training strategy, letting clients with more training data and more uniform class distributions undertake more local update steps.Equivalently, this strategy could weaken the negative impacts of those users whose data is less qualified.Our proposed FedKWS-UI could explicitly and implicitly learn user-invariant information in FedKWS.Abundant experimental results on federated Google Speech Commands verify the effectiveness of FedKWS-UI.

Federated learning (FL) has recently emerged as a transformative paradigm that jointly train a model with distributed devices while avoiding the need for central data collection. Due to the limited observation range, the devices only contain local information, which limits the quality of trained models. In this case, combining the global information into FL may be helpful. However, in horizontal FL, the central agency only acts as a model aggregator without utilizing its global observation. Meanwhile, the global data may not be directly transmitted to agents for data security. Then how to utilize the global observation residing in the central agency while protecting its safety thus rises up as an important problem in FL. In this paper, we develop a vertical-horizontal federated learning (VHFL) scheme, where the global feature is shared with the agents in a procedure similar to that of vertical FL. It is shown by experiments that the proposed VHFL could enhance the accuracy compared with horizontal FL while protecting the central data from being announced.

Collaborative multi-agent reinforcement learning (MARL) has been widely used in many practical applications, where each agent makes a decision based on its own observation. Most mainstream methods treat each local observation as an entirety when modeling the decentralized local utility functions. However, they ignore the fact that local observation information can be further divided into several entities, and only part of the entities is helpful to model inference. Moreover, the importance of different entities may change over time. To improve the performance of decentralized policies, the attention mechanism is used to capture features of local information. Nevertheless, existing attention models rely on dense fully connected graphs and cannot better perceive important states. To this end, we propose a sparse state based MARL (S2RL) framework, which utilizes a sparse attention mechanism to discard irrelevant information in local observations. The local utility functions are estimated through the self-attention and sparse attention mechanisms separately, then are combined into a standard joint value function and auxiliary joint value function in the central critic. We design the S2RL framework as a plug-and-play module, making it general enough to be applied to various methods. Extensive experiments on StarCraft II show that S2RL can significantly improve the performance of many state-of-the-art methods.

Model-based offline reinforcement learning (RL) aims to find highly rewarding policy, by leveraging a previously collected static dataset and a dynamics model. While the dynamics model learned through reuse of the static dataset, its generalization ability hopefully promotes policy learning if properly utilized. To that end, several works propose to quantify the uncertainty of predicted dynamics, and explicitly apply it to penalize reward. However, as the dynamics and the reward are intrinsically different factors in context of MDP, characterizing the impact of dynamics uncertainty through reward penalty may incur unexpected tradeoff between model utilization and risk avoidance. In this work, we instead maintain a belief distribution over dynamics, and evaluate/optimize policy through biased sampling from the belief. The sampling procedure, biased towards pessimism, is derived based on an alternating Markov game formulation of offline RL. We formally show that the biased sampling naturally induces an updated dynamics belief with policy-dependent reweighting factor, termed Pessimism-Modulated Dynamics Belief. To improve policy, we devise an iterative regularized policy optimization algorithm for the game, with guarantee of monotonous improvement under certain condition. To make practical, we further devise an offline RL algorithm to approximately find the solution. Empirical results show that the proposed approach achieves state-of-the-art performance on a wide range of benchmark tasks.

Knowledge Distillation (KD) aims at transferring the knowledge of a well-performed neural network (the {\it teacher}) to a weaker one (the {\it student}). A peculiar phenomenon is that a more accurate model doesn't necessarily teach better, and temperature adjustment can neither alleviate the mismatched capacity. To explain this, we decompose the efficacy of KD into three parts: {\it correct guidance}, {\it smooth regularization}, and {\it class discriminability}. The last term describes the distinctness of {\it wrong class probabilities} that the teacher provides in KD. Complex teachers tend to be over-confident and traditional temperature scaling limits the efficacy of {\it class discriminability}, resulting in less discriminative wrong class probabilities. Therefore, we propose {\it Asymmetric Temperature Scaling (ATS)}, which separately applies a higher/lower temperature to the correct/wrong class. ATS enlarges the variance of wrong class probabilities in the teacher's label and makes the students grasp the absolute affinities of wrong classes to the target class as discriminative as possible. Both theoretical analysis and extensive experimental results demonstrate the effectiveness of ATS. The demo developed in Mindspore is available at \url{https://gitee.com/lxcnju/ats-mindspore} and will be available at \url{https://gitee.com/mindspore/models/tree/master/research/cv/ats}.

Recently, federated learning (FL) has been treated as an important and promising learning scheme in IoT, enabling devices to jointly learn a model without sharing their data sets. Different from centralized training on some collected data sets, FL training suffers a lot of constraints from limited resources in the network. Therein, the bandwidth and package loss restrict interactions in training. Meanwhile, the highly distributed data sets and limited computation could also affect its convergence. To figure out the specific impact, we analyze the convergence rate of FL training considering both communication and training. Further taking in training costs in terms of time and power, the closed-form optimal settings for communication networks are proposed with principles to assist the parameter selection. The results build a bridge between AI and communication, giving us an intuitive knowledge of how the background system could influence the distributed training process.

Federated learning (FL) has recently emerged as an important and promising learning scheme in IoT, enabling devices to jointly learn a model without sharing their raw data sets. As FL does not collect and store the data centrally, it requires frequent model exchange through the wireless network. However, since the aggregation in FL can be partially participated with synchronized frequency, its communication pattern is different from the conventional network. Therein, limited bandwidth and package loss restrict interactions in training. Thus, the network scheduling could largely affect the FL convergence. To figure out the specific effects, we analyze the convergence rate of FL regarding the joint impact of communication and training. Combining it with the network model, we formulate the optimal scheduling problem for FL implementation. The theoretical results could guide the hyper-parameter design in the network and explain the principle of how the wireless communication could influence the FL training process.

Semi-supervised domain adaptation (SSDA) is a novel branch of machine learning that scarce labeled target examples are available, compared with unsupervised domain adaptation. To make effective use of these additional data so as to bridge the domain gap, one possible way is to generate adversarial examples, which are images with additional perturbations, between the two domains and fill the domain gap. Adversarial training has been proven to be a powerful method for this purpose. However, the traditional adversarial training adds noises in arbitrary directions, which is inefficient to migrate between domains, or generate directional noises from the source to target domain and reverse. In this work, we devise a general bidirectional adversarial training method and employ gradient to guide adversarial examples across the domain gap, i.e., the Adaptive Adversarial Training (AAT) for source to target domain and Entropy-penalized Virtual Adversarial Training (E-VAT) for target to source domain. Particularly, we devise a Bidirectional Adversarial Training (BiAT) network to perform diverse adversarial trainings jointly. We evaluate the effectiveness of BiAT on three benchmark datasets and experimental results demonstrate the proposed method achieves the state-of-the-art.

In this paper a parking space detection method is proposed. It is based on the grid map projection and utilizes the ultrasonic sensors. Firstly, it applies a virtual grid map to quantify the observing target space and build a coordinate system. Then the probable outline of the targets can be deduced from the ultrasonic wave echo signal and projected into the grid map. The boundary of the object can be obtained by comparing the overlap number of the outline in the grid with a threshold. In this way, the size of the target space can be calculated and determined whether it is proper for parking a vehicle. The method is simple while remaining effective. It can be well validated by the experimental results and the accuracy is better than 0.2m.