Error Accumulation Problem Research Articles

Generative adversarial network for semi-supervised image captioning

Traditional supervised image captioning methods usually rely on a large number of images and paired captions for training. However, the creation of such datasets necessitates considerable temporal and human resources. Therefore, we propose a new semi-supervised image captioning algorithm to solve this problem. The proposed method uses a generative adversarial network to generate images that match captions, and uses these generated images and captions as new training data. This avoids the error accumulation problem when generating pseudo captions with autoregressive method and the network can directly perform backpropagation. At the same time, in order to ensure the correlation between the generated images and captions, we introduced the CLIP model for constraints. The CLIP model has been pre-trained on a large amount of image–text data, so it shows excellent performance in semantic alignment of images and text. To verify the effectiveness of our method, we validate on MSCOCO offline “Karpathy” test split. Experiment results show that our method can significantly improve the performance of the model when using 1% paired data, with the CIDEr score increasing from 69.5% to 77.7%. This shows that our method can effectively utilize unlabeled data for image caption tasks.

Progressive Decision Boundary Shifting for Unsupervised Domain Adaptation.

Unsupervised domain adaptation (UDA) is attracting more attention from researchers for boosting the task-specific generalization on target domain. It focuses on addressing the domain shift between the labeled source domain and the unlabeled target domain. Recent biclassifier-based UDA models perform category-level alignment to reduce domain shift, and meanwhile, self-training is used for improving the discriminability of target instances. However, the error accumulation problem of instances with high semantic uncertainty may cause discriminability degradation and category-level misalignment. To solve this issue, we design the progressive decision boundary shifting algorithm, where stable category information of target instances is explored for learning a discriminability structure on target domain. Specifically, we first model the semantic uncertainty of instances by progressively shifting decision boundaries of category. Then, we introduce the uncertainty decoupling in a contrastive manner, where the discriminative information is learned from the source domain for instance with low semantic uncertainty. Furthermore, we minimize the predictive entropy of instances with high semantic uncertainty to reduce their prediction confidence. Extensive experiments on three popular datasets show that our model outperforms the current state-of-the-art (SOTA) UDA methods.

Short-term water demand prediction based on decomposition technique optimization and a multihead attention mechanism

ABSTRACT Short-term water demand prediction is crucial for real-time optimal scheduling and leakage control in water distribution systems. This paper proposes a new deep learning-based method for short-term water demand prediction. The proposed method consists of four main parts: the variational mode decomposition method, the golden jackal optimization algorithm, the multihead attention mechanism, and the bidirectional gated recurrent unit (BiGRU) model. Furthermore, a seq2seq strategy was adopted for multistep prediction to avoid the error accumulation problem. Hourly water demand data collected from a real-world water distribution system were applied to investigate the potential of the proposed method. The results show that the proposed method can yield remarkably accurate and stable forecasts in single-step prediction (i.e., the mean absolute percentage error (MAPE) reaches 0.45%, and the root mean squared error (RMSE) is 25 m3/h). Moreover, the proposed method still achieves credible performance in 24-step prediction (i.e., the MAPE reaches 2.12%, and the RMSE is 126 m3/h). In general, for both single-step prediction and multistep prediction, the proposed method consistently outperforms other BiGRU-based methods. These findings suggest that the proposed method can provide a reliable alternative for short-term water demand prediction.

Heterogeneous Interaction Modeling With Reduced Accumulated Error for Multiagent Trajectory Prediction.

Dynamical complex systems composed of interactive heterogeneous agents are prevalent in the world, including urban traffic systems and social networks. Modeling the interactions among agents is the key to understanding and predicting the dynamics of the complex system, e.g., predicting the trajectories of traffic participants in the city. Compared with interaction modeling in homogeneous systems such as pedestrians in a crowded scene, heterogeneous interaction modeling is less explored. Worse still, the error accumulation problem becomes more severe since the interactions are more complex. To tackle the two problems, this article proposes heterogeneous interaction modeling with reduced accumulated error (HIMRAE) for multiagent trajectory prediction. Based on the historical trajectories, our method infers the dynamic interaction graphs among agents, featured by directed interacting relations and interacting effects. A heterogeneous attention mechanism (HAM) is defined on the interaction graphs for aggregating the influence from heterogeneous neighbors to the target agent. To alleviate the error accumulation problem, this article analyzes the error sources from the spatial and temporal perspectives, and proposes to introduce the graph entropy and the mixup training strategy for reducing the two types of errors, respectively. Our method is examined on three real-world datasets containing heterogeneous agents, and the experimental results validate the superiority of our method.

Research on a Low-Cost High-Precision Positioning System for Orchard Mowers

To regulate the energy flow in orchard ecosystems and maintain the environment, weeding has become a necessary measure for fruit farmers, and the use of automated mowers can help reduce labor costs and improve the economic efficiency of orchards. However, due to the complexity of the geographic and spatial environment of the orchard, in particular, the loose and undulating road surface, the interference of satellite signals by large trees, etc., which decreases the positioning accuracy and stability of the positioning system of the mower, and the high cost of the sensor also affect the popularization of intelligent mowers for these applications. To address the above problems, this paper constructs a positioning system through a low-cost global navigation satellite system (GNSS), inertial measurement unit (IMU), and odometry, and utilizes the Kalman filter algorithm based on the error state for a combined GNSS/IMU positioning so that the inertial navigation system can maintain a more accurate positioning when the GNSS signals are poor. Considering the side-slip and error accumulation problems of the odometry of the traction mower, the combined GNSS/IMU positioning information is used to optimize the odometry model and improve the navigation and positioning accuracy. To reduce the measurement error of the IMU and the problem of error accumulation, this paper utilizes the nonholonomic constraint (NHC) of a lawn mower to suppress the dispersion of IMU measurement errors and constructs periodic and nonperiodic zero-velocity updating (ZUPT) strategies in combination with the travel paths of lawn mower navigation operations in the region to update the IMU data to improve the positioning accuracy and stability of the positioning system. The experiments show that the average error of the constructed positioning system is controlled within 0.15 m, the maximum error is maintained at approximately 0.3 m, and the positioning system constructed by using low-cost sensors can achieve a positioning accuracy similar to that of the differential global navigation satellite system (DGNSS), which is beneficial for the promotion and application of intelligent mowers in orchards.

Simultaneously Calibration of Multi Hand–Eye Robot System Based on Graph

Precise calibration is the basis for the vision-guided robot system to achieve high-precision operations. Systems with multi-eyes (cameras) and multi-hands (robots) are particularly sensitive to calibration errors. Most existing methods focus on the calibration of a single unit of the whole system, such as poses between hand and eye, or between two hands. These methods can be used to determine the pose between each unit, but the serialized incremental calibration strategy cannot avoid the error accumulation problem in a large-scale system. Instead of focusing on a single unit, this paper models the multi-eye and multi-hand system calibration problem as a graph and proposes a method based on the minimum spanning tree and graph optimization. This method can automatically plan the serialized optimal calibration strategy in accordance with the system settings to get coarse calibration results initially. Then, with these initial values, the closed-loop constraints are introduced to carry out global optimization with different sensor's accuracy considered. As a general calibration method, it can be applied to different multi-robot systems. Simulation experiments demonstrate the performance of the proposed algorithm under different noises and various hand-eye configurations. In addition, experiments on real robot systems are presented to further verify the proposed method.

Fast fluid–structure interaction simulation method based on deep learning flow field modeling

The rapid acquisition of high-fidelity flow field information is of great significance for engineering applications such as multi-field coupling. Current research in flow field modeling predominantly focuses on low Reynolds numbers and periodic flows, exhibiting weak generalization capabilities and notable issues with temporal inferring error accumulation. Therefore, we establish a reduced order model (ROM) based on Convolutional Auto-Encoder (CAE) and Long Short-Term Memory (LSTM) neural network and propose an unsteady flow field modeling method for the airfoil with a high Reynolds number and strong nonlinear characteristics. The attention mechanism and weak physical constraints are integrated into the model architecture to improve the modeling accuracy. A broadband excitation training strategy is proposed to overcome the error accumulation problem of long-term inferring. With only a small amount of latent codes, the relative error of the flow field reconstructed by CAE can be less than 5‰. By training LSTM with broadband excitation signals, stable dynamic evolution can be achieved in the time dimension. CAE-LSTM can accurately predict the forced response and complex limit cycle behavior of the airfoil in a wide range of amplitude and frequency under subsonic/transonic conditions. The relative errors of predicted variables and integral force are less than 1%. The fluid–structure interaction framework is built by coupling the ROM and motion equations of the structure. CAE-LSTM predicts the time series response of pitch displacement and moment coefficient at different reduced frequencies, which is in good agreement with computational fluid dynamics, and the simulation time savings exceed one order of magnitude.

FlightBERT++: A Non-autoregressive Multi-Horizon Flight Trajectory Prediction Framework

Flight Trajectory Prediction (FTP) is an essential task in Air Traffic Control (ATC), which can assist air traffic controllers in managing airspace more safely and efficiently. Existing approaches generally perform multi-horizon FTP tasks in an autoregressive manner, thereby suffering from error accumulation and low-efficiency problems. In this paper, a novel framework, called FlightBERT++, is proposed to i) forecast multi-horizon flight trajectories directly in a non-autoregressive way, and ii) improve the limitation of the binary encoding (BE) representation in the FlightBERT. Specifically, the FlightBERT++ is implemented by a generalized encoder-decoder architecture, in which the encoder learns the temporal-spatial patterns from historical observations and the decoder predicts the flight status for the future horizons. Compared with conventional architecture, an innovative horizon-aware contexts generator is dedicatedly designed to consider the prior horizon information, which further enables non-autoregressive multi-horizon prediction. Moreover, a differential prompted decoder is proposed to enhance the capability of the differential predictions by leveraging the stationarity of the differential sequence. The experimental results on a real-world dataset demonstrated that the FlightBERT++ outperformed the competitive baselines in both FTP performance and computational efficiency.

A Model-Based Reinforcement Learning Method with Conditional Variational Auto-Encoder

Model-based reinforcement learning can effectively improve the sample efficiency of reinforcement learning, but the environment model in this method has errors. The model errors can mislead the policy optimization, leading to suboptimal policy. To improve the generalization ability of the environment model, existing methods often use ensemble models or Bayesian models to build the environment model. However, these methods are computationally intensive and complex to update. Since the generated model can describe the stochastic nature of the environment, this paper proposes a model-based reinforcement learning method based on a conditional variational auto-encoder. In this paper, we use a conditional variational auto-encoder to learn task-related representations and apply the generative model to predict environmental changes. Considering the problem of multi-step error accumulation, model adaptation is utilized to minimize the difference between simulated and real data distributions. Furthermore, the experiments verified that the proposed method can learn task-relevant representations and accelerate policy learning.

Multistep traffic speed prediction: A sequence-to-sequence spatio-temporal attention model

Multistep traffic speed prediction plays a crucial role in alleviating road congestion and improving transport efficiency. In actual traffic networks, the spatio-temporal dependence among roads dynamically changes over time due to factors such as road conditions and unforeseen incidents, which brings great challenges to multistep traffic speed prediction. Additionally, multistep traffic speed prediction commonly faces the problem of error accumulation, resulting in a loss of prediction accuracy. To address these issues, we propose a Sequence-to-Sequence Spatio-Temporal Attention model (STSSTA) for multistep traffic speed prediction. Specifically, we build an adaptive tuning module to select road preferences and automatically obtain global information about the roads. Then we construct a Sequence-to-Sequence architecture for spatio-temporal feature learning and multistep traffic speed prediction. In particular, in the encoder, we design a Diffusion Graph Convolutional Network (DGCN) and combine it with a Gated Recurrent Unit (GRU) to effectively capture the complex spatio-temporal features within the traffic networks. In the decoder, we introduce a Recalling attention mechanism to alleviate the problem of local information loss caused by encoder compression, thereby reducing error accumulation in multistep prediction. Experiments on METR-LA and PeMS-BAY datasets demonstrate that STSSTA outperforms the baseline models in long-term prediction.

CoreDiff: Contextual Error-Modulated Generalized Diffusion Model for Low-Dose CT Denoising and Generalization.

Low-dose computed tomography (CT) images suffer from noise and artifacts due to photon starvation and electronic noise. Recently, some works have attempted to use diffusion models to address the over-smoothness and training instability encountered by previous deep-learning-based denoising models. However, diffusion models suffer from long inference time due to a large number of sampling steps involved. Very recently, cold diffusion model generalizes classical diffusion models and has greater flexibility. Inspired by cold diffusion, this paper presents a novel COntextual eRror-modulated gEneralized Diffusion model for low-dose CT (LDCT) denoising, termed CoreDiff. First, CoreDiff utilizes LDCT images to displace the random Gaussian noise and employs a novel mean-preserving degradation operator to mimic the physical process of CT degradation, significantly reducing sampling steps thanks to the informative LDCT images as the starting point of the sampling process. Second, to alleviate the error accumulation problem caused by the imperfect restoration operator in the sampling process, we propose a novel ContextuaL Error-modulAted Restoration Network (CLEAR-Net), which can leverage contextual information to constrain the sampling process from structural distortion and modulate time step embedding features for better alignment with the input at the next time step. Third, to rapidly generalize the trained model to a new, unseen dose level with as few resources as possible, we devise a one-shot learning framework to make CoreDiff generalize faster and better using only one single LDCT image (un)paired with normal-dose CT (NDCT). Extensive experimental results on four datasets demonstrate that our CoreDiff outperforms competing methods in denoising and generalization performance, with clinically acceptable inference time. Source code is made available at https://github.com/qgao21/CoreDiff.

An $\omega$-Free Accelerometer Array Method for 2-D Trajectory Reconstruction

A trajectory can be reconstructed by integrating acceleration and angular velocity (i.e. <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\omega$</tex-math></inline-formula> ) sampled by a single inertial measurement unit (IMU) which consists of an accelerometer (ACC) and gyroscope (GYRO). To reduce the system power consumption, a GYRO-free-IMU (GF-IMU) method was proposed which disabled the more power-consuming GYRO and utilized only an ACC array (AA) to obtain acceleration and calculate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\omega$</tex-math></inline-formula> . To alleviate the error accumulation problem in the GF-IMU method, we previously proposed an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\omega$</tex-math></inline-formula> -free ACC pair (OFAP) method which doesn't require the calculation of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\omega$</tex-math></inline-formula> and can estimate the trajectory by solving a constrained optimization problem. However, the constrained problem makes it computationally expensive to generalize the proposed approach for different AA setups with more ACCs. To enhance the scalability and robustness of the system, this paper proposes a new <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\omega$</tex-math></inline-formula> -free inertia-based method, namely <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\omega$</tex-math></inline-formula> -free AA (OFAA), which transforms the constrained problem into an unconstrained one, and derives its scalable and computational-efficient closed-form solution. In both physical experiments and simulations, compared with conventional inertial methods, the proposed OFAA method has a lower trajectory-reconstruction error per distance traveled and is more robust to errors in raw inertial data, while still having a low energy consumption.

Image emotion multi-label classification based on multi-graph learning

Images contain rich information and can induce various emotions in the audience. Image emotion classification aims to identify the emotion categories that images can evoke. It is widely used in mental health assessment, human–computer interaction, etc. There are two main problems in existing image emotion classification methods: (1) Most of them only focus on a single emotion label; (2) The global structural relationship among semantic objects in the image is ignored. Therefore, this paper proposes an Image Emotion classification method based on Multi-Graph Multi-Label learning (IE-MGML). In contrast to the existing approaches, the image is transformed into a graph-based representation by extracting the emotional features of semantic objects and calculating the similarity between the features. The local (semantic objects) features and global structure (relationship among semantic objects) features of the image are fused by the relationship between nodes. Furthermore, the graph representation of an image from the perspective of multiple emotional features is pooled and modeled as a graph bag containing multiple graphs (i.e., multi-graph). In multi-graph learning, the graph kernel directly evaluates a graph-label dependency score to avoid the loss of structural information caused by graph-instance degradation. The bag(image)-label dependency score is obtained by aggregating the graph-label dependency score from different perspectives through the aggregation function. The problem of error accumulation in the learning process is handled by proposing a threshold-based ranking loss objective function. Moreover, the non-convex optimization problem is addressed using a subgradient descent algorithm to deal with the required high-dimensional space computation. Experimental results on three general image emotion datasets show that the proposed method outperforms the state-of-the-art methods.

MuA-SAR Fast Imaging Based on UCFFBP Algorithm with Multi-Level Regional Attention Strategy

Multistatic airborne SAR (MuA-SAR) benefits from the ability to flexibly adjust the positions of multiple transmitters and receivers in space, which can shorten the synthetic aperture time to achieve the required resolution. To ensure both imaging efficiency and quality of different system spatial configurations and trajectories, the fast factorized back projection (FFBP) algorithm is proposed. However, if the FFBP algorithm based on polar coordinates is directly applied to the MuA-SAR system, the interpolation in the recursive fusion process will bring the problem of redundant calculations and error accumulation, leading to a sharp decrease in imaging efficiency and quality. In this paper, a unified Cartesian fast factorized back projection (UCFFBP) algorithm with a multi-level regional attention strategy is proposed for MuA-SAR fast imaging. First, a global Cartesian coordinate system (GCCS) is established. Through designing the rotation mapping matrix and phase compensation factor, data from different bistatic radar pairs can be processed coherently and efficiently. In addition, a multi-level regional attention strategy based on maximally stable extremal regions (MSER) is proposed. In the recursive fusion process, only the suspected target regions are paid more attention and segmented for coherent fusion at each fusion level, which further improves efficiency. The proposed UCFFBP algorithm ensures both the quality and efficiency of MuA-SAR imaging. Simulation experiments verified the effectiveness of the proposed algorithm.

Joint Channel Estimation and Data Detection for IRS-Assisted OFDM Systems

Intelligent reconfigurable surface (IRS) becomes a promising technology for improving spectrum efficiency and reducing the energy consumption in the next-generation networks. To reap the passive beamforming gain of IRS, accurate channel estimation is essentially required. However, the existing channel estimation methods for the IRS-assisted orthogonal frequency division multiplexing (OFDM) systems suffer from serious performance loss, due to using the least-squares (LS) estimator and ignoring the channel sparsity in the time domain. Another drawback of the existing methods is that the channel estimation and data detection are separated from each other so that any inaccurate channel estimation would cause an error accumulation problem for the data detection. To overcome these drawbacks, we propose a novel joint sparse channel estimation and data detection method for the IRS-assisted OFDM systems. The novelties of the proposed method are twofold: (i) present a new common sparse representation model for the joint channel estimation and data detection, which can utilize the common channel sparsity between the pilots and data streams to significantly improve the channel estimation performance and reduce the training overhead; and (ii) propose an efficient variational Bayesian inference (VBI) framework to simultaneously perform the Bayesian inference for the sparse channel recovery and data detection, where the coupling effect caused by the reflection pattern is trickly evaded by adopting an additional column-independent factorization. Besides exploiting the common sparsity for the channel estimation and data detection, the proposed method also avoids using the LS estimator, and thus its performance can be greatly enhanced. Simulation results verify the superiority of the proposed method.

Directed Acyclic Transformer Pre-training for High-quality Non-autoregressive Text Generation

Abstract Non-AutoRegressive (NAR) text generation models have drawn much attention because of their significantly faster decoding speed and good generation quality in machine translation. However, in a wider range of text generation tasks, existing NAR models lack proper pre-training, making them still far behind the pre-trained autoregressive models. In this paper, we propose Pre-trained Directed Acyclic Transformer (PreDAT) and a novel pre-training task to promote prediction consistency in NAR generation. Experiments on five text generation tasks show that our PreDAT remarkably outperforms existing pre-trained NAR models (+4.2 score on average) and even achieves better results than pre-trained autoregressive baselines in n-gram-based metrics, along with 17 times speedup in throughput. Further analysis shows that PreDAT benefits from the unbiased prediction order that alleviates the error accumulation problem in autoregressive generation, which provides new insights into the advantages of NAR generation.1

Decorate the Newcomers: Visual Domain Prompt for Continual Test Time Adaptation

Continual Test-Time Adaptation (CTTA) aims to adapt the source model to continually changing unlabeled target domains without access to the source data. Existing methods mainly focus on model-based adaptation in a self-training manner, such as predicting pseudo labels for new domain datasets. Since pseudo labels are noisy and unreliable, these methods suffer from catastrophic forgetting and error accumulation when dealing with dynamic data distributions. Motivated by the prompt learning in NLP, in this paper, we propose to learn an image-layer visual domain prompt for target domains while having the source model parameters frozen. During testing, the changing target datasets can be adapted to the source model by reformulating the input data with the learned visual prompts. Specifically, we devise two types of prompts, i.e., domains-specific prompts and domains-agnostic prompts, to extract current domain knowledge and maintain the domain-shared knowledge in the continual adaptation. Furthermore, we design a homeostasis-based adaptation strategy to suppress domain-sensitive parameters in domain-invariant prompts to learn domain-shared knowledge more effectively. This transition from the model-dependent paradigm to the model-free one enables us to bypass the catastrophic forgetting and error accumulation problems. Experiments show that our proposed method achieves significant performance gains over state-of-the-art methods on four widely-used benchmarks, including CIFAR-10C, CIFAR-100C, ImageNet-C, and VLCS datasets.

Multi-UAV Cooperative Air Combat Decision-Making Based on Multi-Agent Double-Soft Actor-Critic

Multiple unmanned aerial vehicle (multi-UAV) cooperative air combat, which is an important form of future air combat, has high requirements for the autonomy and cooperation of unmanned aerial vehicles. Therefore, it is of great significance to study the decision-making method of multi-UAV cooperative air combat since the conventional methods are challenging to solve the high complexity and highly dynamic cooperative air combat problems. This paper proposes a multi-agent double-soft actor-critic (MADSAC) algorithm for solving the cooperative decision-making problem of multi-UAV. The MADSAC achieves multi-UAV cooperative air combat by treating the problem as a fully cooperative game using a decentralized partially observable Markov decision process and a centrally trained distributed execution framework. The use of maximum entropy theory in the update process makes the method more exploratory. Meanwhile, MADSAC uses double-centralized critics, target networks, and delayed policy updates to solve the overestimation and error accumulation problems effectively. In addition, the double-centralized critics based on the attention mechanism improve the scalability and learning efficiency of MADSAC. Finally, multi-UAV cooperative air combat experiments validate the effectiveness of MADSAC.

Overview of Multi-Robot Collaborative SLAM from the Perspective of Data Fusion

In the face of large-scale environmental mapping requirements, through the use of lightweight and inexpensive robot groups to perceive the environment, the multi-robot cooperative (V)SLAM scheme can resolve the individual cost, global error accumulation, computational load, and risk concentration problems faced by single-robot SLAM schemes. Such schemes are robust and stable, form a current research hotspot, and relevant algorithms are being updated rapidly. In order to enable the reader to understand the development of this field rapidly and fully, this paper provides a comprehensive review. First, the development history of multi-robot collaborative SLAM is reviewed. Second, the fusion algorithms and architectures are detailed. Third, from the perspective of machine learning classification, the existing algorithms in this field are discussed, including the latest updates. All of this will make it easier for readers to discover problems that need to be studied further. Finally, future research prospects are listed.

A Novel Ranging and IMU-Based Method for Relative Positioning of Two-MAV Formation in GNSS-Denied Environments.

Global Navigation Satellite Systems (GNSS) with weak anti-jamming capability are vulnerable to intentional or unintentional interference, resulting in difficulty providing continuous, reliable, and accurate positioning information in complex environments. Especially in GNSS-denied environments, relying solely on the onboard Inertial Measurement Unit (IMU) of the Micro Aerial Vehicles (MAVs) for positioning is not practical. In this paper, we propose a novel cooperative relative positioning method for MAVs in GNSS-denied scenarios. Specifically, the system model framework is first constructed, and then the Extended Kalman Filter (EKF) algorithm, which is introduced for its ability to handle nonlinear systems, is employed to fuse inter-vehicle ranging and onboard IMU information, achieving joint position estimation of the MAVs. The proposed method mainly addresses the problem of error accumulation in the IMU and exhibits high accuracy and robustness. Additionally, the method is capable of achieving relative positioning without requiring an accurate reference anchor. The system observability conditions are theoretically derived, which means the system positioning accuracy can be guaranteed when the system satisfies the observability conditions. The results further demonstrate the validity of the system observability conditions and investigate the impact of varying ranging errors on the positioning accuracy and stability. The proposed method achieves a positioning accuracy of approximately 0.55 m, which is about 3.89 times higher than that of an existing positioning method.