The tilt will inevitably occur due to the carrier motion when the bioinspired polarization compass is attached to the mobile carrier (such as a drone), which brings about the zenith position in AoP images collected by the polarization imaging system to be changed. The error of fitting the solar meridian causes the AoP calculated error, decreasing the orientation accuracy for the bioinspired polarized compass dramatically. In addition, we have found in a large number of dynamic experiments that the coupling between the solar meridian and the carrier body axis angle (A-SMBA) and the inclination angle also produces very significant orientation errors. Therefore, this chapter first comprehensively analyzes the influence of the changed attitude angles by the polarization compass (including A-SMBA, pitch angle and roll angle) on the heading error. Next, the Gated Recurrent Unit (GRU) neural network is introduced to model and compensate for the orientation error caused by the changed attitude angles by the polarization compass so as to improve the orientation accuracy during the carrier actual motion.

This book focuses on the issue of autonomous orientation error facing unmanned sports platform in situations such as satellite signal rejection and the accumulated error in inertial navigation system working alone over time. This book provides a detailed introduction to the basic theory and current research status of bioinspired polarized light orientation, the error processing methods of the bioinspired polarized light compasses and the PC/INS seamless integrated orientation method and system. The effectiveness and practicality of the PC/INS integrated orientation error processing method proposed in this book have been verified through various experiments. The main research results and conclusions are summarized as follows.

Biological research results demonstrate that insects such as sand ants and bees not only possess the ability to be highly sensitive to polarization information, but also can determine their own movement direction through the distribution of polarization patterns in the sky. The highly autonomous sky polarization pattern is one of the inherent resources in nature, which is basically not damaged and interfered by human subjective factors. It is very suitable to provide orientation information for carriers in the environment of weak or no satellite signals. Consiquently, the orientation method based on the atmospheric polarization pattern has a good application prospect for autonomous orientation. This chapter focuses on the vector-oriented methods and systems based on atmospheric polarization patterns.

According to the static and dynamic test results for the bioinspired polarization compass, the heading accuracy is seriously affected by the compass noise. This noise comes not only from the AoP image acquired by the compass polarization image sensor, but also from the compass circuit. Therefore, this chapter concentrates the noise analysis and denoising methods for the bioinspired polarization compass. Firstly, different types of noise and their generation mechanism of the bioinspired polarization compass are explored and the noise characteristics are analyzed. Secondly, the denoising algorithm based on Multi-scale Transform (MST) is presented for the bioinspired polarization compass. Finally, the denoising methods for AoP image and heading angle data in significantly improving the orientation accuracy of the polarization compass are verified and analyzed in detail in the way of various experiments.

Compared with modern orientation methods such as inertial and satellite navigation, the bioinspired polarization orientation is based on the principle of insect navigation. Not only does it possess strong autonomy, good concealment, large working range, and long working time, but its error also does not accumulate over time. This book takes the application background as six rotor small unmanned aerial vehicles (UAVs) performing low altitude unmanned missions, and carries out research on the challenges faced by the autonomous orientation technology for small UAVs. Although the directional signals originate from natural polarization and are generally not affected by modern information warfare, the bioinspired polariztion compass is temporarily unavailable under complex environmental conditions such as encountering obstacles from clouds, tunnels, and buildings. Accordingly, the integrated orientation technique of the bioinspired polarization compass and inertial navigation system displays great significances in exploiting the natural polarization orientation principle and multi-source information fusion algorithms for fulfillong the autonomous orientation requirements of small UAVs and promoting their combat capabilities.

The accuracy of the bioinspired polarization compass (PC) is easily affected by complex environmental conditions such as cloudy weather, tunnels, building occlusion, and so on. It is difficult to provide continuous orientation information, while the error of inertial navigation system (INS) is easy to diverge over time. As a result, the two orientation means above mentioned can be integrated through information fusion methods such as Kalman filter to improve the performance of the entire integrated orientation system with its good autonomy and complementarity with each other. This chapter focuses on the research of a bioinspired polarized light compass/inertial navigation system (PC/INS) seamless integrated orientation method and system based on self-learning multi-frequency residual correction. First, a integrated orientation model for PC and INS is constructed using a multi-frequency volumetric Kalman filter (CKF-MR) fusion algorithm. Secondly, a Cubature Kalman filter (CKF-MRC) fusion algorithm based on multi-frequency residual correction is proposed to address the issues of low data output frequency and overall system orientation accuracy in the PC/INS integrated orientation system when PC information is not affected. Finally, when the PC is temporarily unavailable due to occlusion or other factors, a self-learning seamless integrated orientation method based on long short-term memory (LSTM) neural network is proposed for the PC/INS integrated orientation system. The seamless integrated orientation method based on CKF-MRC proposed in this book has been validated through UAV test. This integrated orientation method is able to effectively improve the data output frequency and orientation accuracy for the PC/INS system when the PC is not affected. When the PC is temporarily unavailable due to occlusion or other factors, it can still maintain high orientation accuracy and ultimately improve the robustness of the entire integrated orientation system.

As the most important high technology national strategic field in the twenty-first century, earth observation consists of two elements, one is the physical and chemical characteristics of the observed object (What), namely remote sensing: the other is four-dimensional time and space, namely navigation and position (Where, When). Thus, navigation is an old and young science. Before the appearance of satellite position systems, radio navigation systems were mainly used for remote navigation and position. Radio navigation position has played a very important role in the history of navigation through methods such as Roland-C, Omega and Doppler systems. However, it covers a small working area. This has largely limited its development and application, because radio wave propagation is affected by the atmosphere, the position accuracy and other factors. It was not until the development of global navigation position in the 1990s, which can provide continuous and high-precision three-dimensional position velocity and time information to users at sea, on land, in air and space in around the clock on a global scale and can lead to epoch-making changes in the navigation and position of carriers such as ships, aircraft and automobiles. However, globle position system also has some shortcomings, such as satellite signals which are susceptible to be interfered, poor reception in hidden areas, no in-water capability, and some difficulty in underwater position. And being controlled by the military of the country where the system is located, the application can be very limited at critical times. On the other hand, although the instantaneous position accuracy of inertial navigation system is high, the error will accumulate over time. Based on this consideration, it is particularly important to study new technologies for independent navigation and position in environments where satellite signals do not cover or are subject to electromagnetic interference. This monograph is the mathematical-physical basis of passive navigation and positioning based on natural vector fields as the main source.

The irregularity of the earth's shape and the non-uniformity of density lead to different gravity fields at various points of the earth, which are expressed as a function of spatial position (longitude, latitude, height). Therefore, during navigation, the submersible can collect the gravity data of the route through the gravity measuring instrument, match it with the pre stored gravity data, obtain the current positioning information of the submersible, and then correct the position error accumulated by the inertial navigation system. Gravity assisted navigation system in the process of measuring gravity field data, the submersible does not need to be exposed to or close to the water surface, and the measuring instrument does not need to send or receive external signals to the outside. The system can carry out passive and covert navigation and positioning, and the submersible can still achieve the purpose of autonomous covert navigation in the special case of satellite and radio positioning system failure or damage. With the development of gravity measurement instruments and space measurement technology [Chen et al. in Advances in Earth Sciences. 16:1–13, 2001], it has become a reality to obtain gravity data quickly and accurately all over the world, which makes the mapped gravity aided navigation system have the ability to correct ins accumulated position error. There are mainly two representative systems of the charted gravity assisted navigation system, both developed by Bell aerospace, namely, the gravity gradient navigation system developed in 1990 and the gravity assisted inertial navigation system developed in 1991. The gravity assisted positioning system can be divided into four main parts: inertial navigation system, gravity measurement instrument, digital gravity reference map and matching positioning algorithm. The performance difference of each part has an important impact on the performance of the gravity assisted positioning system. Gravity model (benchmark map) is the basis of gravity assisted positioning. Whether the description of gravity model is accurate, whether the gravity features contained are rich, and whether the resolution meets the requirements will affect the performance of gravity assisted positioning system. Based on the external gravity model J2 gravity field model, this chapter discusses the calculation method of normal gravity on the surface of rotating ellipsoid, and establishes a small depth underwater three-dimensional gravity field model and the corresponding underwater inertial navigation system INS combined model, which provides a basic theoretical method for the application of gravity assisted positioning system.

Over 3.5 billion years of evolution, about 2 million kinds of organisms have gradually formed.

When solar radiation enters the earth, it will be affected by the refraction, scattering and reflection of atmospheric particles and the ground surface.

The geomagnetic field is a fundamental geophysical field (M.-L. Zhang, in Introduction to geophysics. Petroleum Industry Press, pp. 23–25, 2019), which consists of the Earth's internal and external magnetic field. Among them, the internal magnetic field mainly consists of the main magnetic field formed by the Earth's core and the crustal anomalous field formed by the lithosphere, which accounts for more than 99% of the geomagnetic field. The external magnetic field is mainly composed of the magnetic field superposition, which is generated by the solar activity acting on the atmospheric ionosphere and magnetosphere (Y. Kamide, A. C. L. Chian, in Handbook of the solar-terrestrial environment. J.-L. Jian. Science Press, pp. 91–96, 2010). The geomagnetic field has the following characteristics: (1) It continuous distribution in the near-Earth space; (2) It differences in the geomagnetic field in various regions due to the distribution of the Earth's magnetic materials;(3) It is strong near the ground and gradually decays with the increase of height; (4) The change period of the main magnetic field originating from the Earth's core is measured in centuries, and the change of the anomalous field originating from the Earth's crust is recorded in geological ages, so the main magnetic field and the anomalous field are stable; (5) The changing magnetic field mainly originates from outside the Earth, and the trend of change is consistent within hundreds of kilometers of geography. The geomagnetic field has been widely used for orientation navigation of ships and airplanes, and the geomagnetic field orientation information is measured using compasses and magnetic compasses to obtain a stable north pointing of the Earth (K. Liu, in Research on long-distance geomagnetic navigation based on magnetotactic search. NorthWestern Polytechnical University, pp. 45–50, 2019). Geomagnetic positioning navigation technology, unlike orientation measurement technology, uses the characteristic that the intensity of the geomagnetic field has different distributions with geospatial location to achieve the positioning of the motion platform. Through magnetic field sensors installed on the motion platform, the geomagnetic field data on the motion track is measured in real-time. Features are extracted and matched with the geomagnetic field model or geomagnetic reference map obtained and stored in advance to determine the real-time position of the motion platform (K. Chen et al., in Journal of Zhejiang University-Science A (Applied Physics & Engineering), 22(5):357–368, 2021; Feng-Min et al. in Journal of Projectiles, Rockets, Missiles and Guidance 41:10–14, 2021; G.-G. Wang et al. in A geomagnetic localization method based on road magnetic field characteristics. Beijing: CN107621263B, 2019–12-27; X. Li et al., in Chinese Journal of Sensors and Actuators, 30(12):1869–1875, 2017; Zhuang-Sheng et al. in Progress in Geophysics 26:1473–1477, 2011). Ultimately, a high-precision local three-dimensional spatial reference geomagnetic field that meets the requirements of geomagnetic positioning and navigation can be constructed.

At present, the inertial navigation system (hereinafter referred to as “inertial navigation system” and “INS”) is the core navigation system of the underwater vehicle. However, due to the problem that the positioning error of the inertial navigation system accumulates with the increase of the running time, it is necessary to use other external information to regularly correct the inertial navigation system, that is, auxiliary navigation technology. Gravity-assisted navigation technology uses the sensors installed on the carrier that can accurately measure the earth's gravity field and the accurate earth's gravity field map, and uses modern optimal control theory and methods to regularly determine the position of the carrier. It is one of the technical ways to modify the inertial navigation system, and is especially suitable for underwater vehicles (Zhao, X., & Chen, G. (2020). Development status and trend of ship navigation. Navigation and control, 19(z1), 82–87; Wei, B., Lv, W., Fan, X., Zhu, Y., & Guo, Y. (2019). AUV navigation technology development status and prospects. Journal of Underwater Unmanned Systems, 27(01), 9; Zhou, B., & Liu, S. (2012). Research on underwater navigation technology. Modern navigation, 3(01), 19–23; Xiong, Z., Cai, K., & Fengde, W., et al. (2002). A summary of the development of navigation technology of U.S. strategic submarines in the 21st century. Ship science and technology, 24(3), 30−37; Feizhou, Z. (2003). Research on underwater passive navigation technology [postdoctoral report]. Beijing Peking University.). The basic principle of the gravity aided navigation system is that the gravity sensor measures the gravity characteristic data in real time during the movement of the carrier; At the same time, the gravity data is read from the gravity map according to the position information of the inertial navigation system. The two data are sent to the matching solution computer, and the matching solution software is used to solve the problem to obtain the best matching position. Using this information to correct the inertial navigation system can suppress the inertial navigation error and improve the navigation accuracy (Moryl, J., Rice, H., & Shinners, S. (1998). The universal gravitymodule for enhanced submarine navigation. In Position Location and Navigation Symposium 1998 (pp. 324−331). IEEE; Feng, H., Yan, L., Ge, Y. et al. (2004). Real time gravity correction of underwater vehicle based on INS. Journal of Wuhan University (Engineering Edition), 37(3), 135−138.). To sum up, the gravity assisted navigation system mainly includes gravimeter, gravity field model and gravity data processing, gravity map matching theory and matching algorithm, and correction theory and method of various system errors. The second chapter focuses on the gravity field model and gravity data processing method. The underwater application is the most important application scenario of gravity assisted navigation. When introducing the specific methods of gravity assisted navigation, the application is gravity. From the perspective of application, this chapter focuses on the moving base gravity sensor, the moving base marine gravity real-time measurement, providing relevant theoretical basis and technical support for the final gravity assisted inertial navigation system (Zhang, H. (2013). Research on key technologies of underwater gravity field aided navigation and positioning (pp. 56–60). Doctoral dissertation of Harbin Engineering University; Javed, W., Ghani, S., & Elmqvist, N.: GravNav conference (pp. 217–224). In Advanced Visual Interfaces; Zhu, Z., & Zhou, P. (2011). Research on multi-scale characteristics of gravity field in gravity assisted inertial navigation. Progress in geophysics, 26(05), 1868–1873.).

Topographic elevation navigation positioning is a navigation method that uses the specificity and uniqueness of elevation differences at each point in space for positioning. Because it is a passive navigation method that does not depend on external signals, it is not easily affected by objective factors such as electromagnetic interference and weather and is valued in existing combined navigation methods. The basic principle of topographic elevation navigation and positioning is that the geographic coordinates of any location on the earth's surface can be determined singularly based on the contours or landforms of its surrounding territory. Firstly, the terrain elevation model (map) along the route is stored in the motion carrier, and when the motion carrier flies over an area with known terrain elevation, the current terrain elevation is measured by the altimetric (depth) sensor on the motion carrier, and the measured data is correlated and analyzed with the pre-stored terrain elevation model (map) to determine the corresponding grid position of the motion carrier in the terrain elevation model (map) because the terrain The latitude and longitude corresponding to the grid position in the elevation model (map) is known in advance so that the position of the motion carrier can be determined. Although the combination of inertial navigation and positioning system (INS) and satellite navigation and positioning system (GNSS) navigation can meet the requirements of high precision positioning, this combination of navigation autonomy is insufficient and easy to expose the target. The combination of INS and terrain elevation navigation and positioning meets various navigation requirements and does not depend on an artificial satellite navigation system. In addition to the navigation and positioning of motion carriers, terrain elevation positioning navigation also has many functions such as terrain tracking/terrain avoidance, rational routing, threat avoidance, obstacle alert, ground alert, target interception, marine exploitation, marine wreck salvage, and underwater launch. Terrain elevation navigation and positioning are most widely used in air vehicles and underwater vehicles because it is easier to obtain airborne terrain elevation maps, so the application of terrain elevation navigation and positioning is more mature in air vehicles; underwater artifacts are the least, and satellite positioning is limited, so it is the easiest background condition for terrain elevation navigation and positioning to work, so the academic research is focused on underwater terrain. Regardless of underwater and aviation, the basic theory of terrain elevation positioning navigation and positioning navigation methods are common, only in the means of terrain elevation map acquisition, altimetry (depth) sensors exist differently: this chapter will be developed to describe respectively.

The core of the electrostatic gyro is to levitate the rotor in the spherical cavity by the electrostatic force in the electrostatic field, which causes the change of the gap between the rotor and the spherical cavity due to the change of the external field environment, gyro attitude, etc., thus causing the change of the gyro output signal for navigation and positioning.

Chapter 4 introduces the composition of the geomagnetic field and the basic principles of the geomagnetic field that can be used for navigation and positioning, as well as the method of creating geomagnetic reference maps for navigation and positioning. This chapter focuses on the process and method of implementing navigation and positioning on the basis of geomagnetic reference maps. As one of the important technologies in the multi-source fusion navigation and positioning system, geomagnetic navigation and positioning have the advantages of a wide range of applications, strong anti-electromagnetic interference capability, and the ability to work around the clock, providing a passive and autonomous navigation and positioning technology path for motion carriers in underground, underwater, and other scenarios where satellite signal reception is limited (Fisher and Raquet in Air & Space Power Journal, 24 –33, 2011; Goldenberg et al. in Location, And Navigation Symposium, 684–694, 2006; Wilson et al. in Proceedings of the 2006 National Technical Meeting of The Institute of Navigation, Monterey, CA, January 2006, pp. 770–779; Li et al. in A geomagnetic positioning method suitable for indoor free motion carriers, Beijing, 2018). Geomagnetic navigation and positioning use the characteristic that the geomagnetic field intensity has a different distribution with a change in geospatial location to achieve the positioning of the motion carrier. The geomagnetic navigation and positioning system obtains the geomagnetic field characteristic data on the motion trajectory through the magnetometer installed on the motion carrier and matches it with the pre-stored geomagnetic field model or geomagnetic reference map to determine the real-time position and correct the inertial guidance error. All seven geomagnetic elements of the geomagnetic field described in Chap. 4 can be used as geomagnetic feature data or a combination of them. The selection of geomagnetic positioning feature data mainly requires the following considerations: (1) significant spatial variation; (2) slow change with time; (3) accurate measurement by measuring instruments; and (4) low influence by external interference. According to the basic principle of geomagnetic navigation and positioning, which is similar to the gravity aided navigation and positioning method. Two working systems are required: a pre-processing system and a real-time positioning system. The pre-processing system is mainly based on the process introduced in Chap. 4 to complete the preparation of geomagnetic reference data. This chapter introduces the implementation process of the real-time positioning system, which mainly includes real-time measurement of geomagnetic fields and positioning calculation. The implementation of geomagnetic navigation and positioning focuses on three aspects: (1) magnetometer sensors; (2) real-time measurement methods; and (3) navigation and positioning algorithms. According to the different carriers and scenarios of geomagnetic positioning applications, there are certain differences in the process of geomagnetic navigation and positioning implementation, which are mainly reflected in the above three aspects. In this chapter, different application scenarios of geomagnetic positioning are categorized, and the specific implementation process for different application scenarios is given (Jun et al. in Journal of Astronautics 05:1467–1472, 2008). For the convenience of description, “geomagnetic navigation and positioning” is referred to as “geomagnetic positioning” in this chapter.

The terrain elevation field navigation and positioning can overcome the shortcomings of inertial navigation accuracy which decreases with time accumulation and meet the needs of long-time and high-precision navigation of motion carriers by comprehensive correction of inertial navigation (INS) errors with terrain elevation field information.

The characteristic of inertial navigation technology is that it does not need to provide the position data of the carrier without external reference and signal, and its core is precision and autonomy.

Until now, in the satellite-denied environment, there is no mature and stable universal solution for high-precision Location Based System (LBS) similar to the Global Navigation Satellite System, making it still an open field. Near-ultrasonic positioning, as an emerging medium-range positioning technology, has natural advantages such as low synchronization costs, strong compatibility with smart devices, independence from image acquisition, and signals that are not easily obstructed by rooms, making it an optimal solution for low-cost, high-precision safety positioning. This chapter focuses on positioning in the practical and complex satellite-denied environments, based on portable smart terminal platforms, leveraging the complementary advantages of near-ultrasonic and inertial navigation technologies. It combines positioning data with theoretical and practical requirements for training privacy-secure solutions, aiming to provide novel and practical robust positioning schemes. By diverging from conventional electromagnetic wave-based methods for indoor positioning, it offers innovative perspectives and approaches.

Sparse Bayesian learning (SBL) is a millimeter-wave (mmWave) positioning method that leverages the sparsity of channels to estimate parameters such as angle of arrival (AOA) and time delay for positioning. Compared to other parameter estimation algorithms, such as the Multi-signal classification (MUSIC) algorithm, Expectation–Maximization (EM) algorithm, and Space-alternating Generalized Expectation–Maximization (SAGE) algorithm, SBL demonstrates superior performance and robustness in millimeter wave scenarios. However, most existing SBL solutions only account for angle sparsity. In this chapter, we address the joint sparsity of both the angle domain and time delay domain, and propose a new two-dimensional adaptive grid refinement method to enhance the existing SBL framework. To address the grid mismatch problem common in all sparse estimation algorithms, we have also introduced a low-complexity grid evolution algorithm. Additionally, we derive the Cramer-Rao bound (CRB) for AOA, time delay, and position estimation based on the mmWave multipath signals from base stations (BS), and subsequently analyze estimation errors. Simulation results indicate that the proposed algorithm outperforms existing algorithms and approaches the CRB. Simulations using real-world datasets also confirm these findings.

Understanding the floor-level location of a user in a multi-storey building is crucial for various applications, including emergency response and shopping guides. Current floor identification systems face several challenges, such as low accuracy, the requirement for time-consuming site surveys, assumptions about user encounters, initial floor knowledge, and poor generalization. In this chapter, we present UnFI, a novel floor identification system that is both scalable and accurate, eliminating the need for site surveys, initial floor knowledge, and other assumptions. The system leverages widely-available smartphone sensors to determine a user's floor location. By automatically recognizing the ground floor and utilizing the stable pressure difference between floors, we avoid the need for cumbersome site surveys for fingerprint association. To ensure precise floor identification, we have developed deep learning-based methods for indoor/outdoor detection and floor identification. Experimental results demonstrate that UnFI outperforms existing systems and shows great potential for large-scale deployment.

The low-cost inertial navigation system (INS) suffers from bias and measurement noise, which would result in poor navigation accuracy during the global positioning system (GPS) outages. Aiming to bridge the GPS outages duration and enhance the navigation performance, a deep learning network architecture named GPS/INS neural network (GI-NN) is proposed to assist the INS. The GI-NN combines a convolutional neural network and a gated recurrent unit neural network to extract the spatial features from the inertial measurement unit (IMU) signals and track their temporal characteristics. The relationship among the attitude, specific force, angular rate and the GPS position increment is modelled, while the current and previous IMU data are used to estimate the dynamics of the vehicle via the proposed GI-NN. Numerical simulations, real field tests and public data tests are performed to evaluate the effectiveness of the proposed algorithm. Compared with the traditional machine learning algorithms, the results illustrate that the proposed method can provide more accurate and reliable navigation solution in the GPS denied environments.

Real-time precise tropospheric corrections are critical for global navigation satellite system (GNSS) data processing. This chapter aims to develop a new tropospheric delay model over China with advanced machine learning method. Compared with previous models, the new model has features such as high accuracy, a small number of coefficients and good continuity of service, showing a good performance in severe weather conditions. The new model utilizes the complementary advantages of numerical weather prediction (NWP) forecasts and real-time GNSS observations with the aid of machine learning, which alleviates the high-dependency on the dense GNSS network and allows for the ease of generating tropospheric corrections. The results can provide a new insight into augmenting tropospheric delays for BeiDou Satellite-Based PPP service across China.

The spatially discernible indoor magnetic field indicates locations through different magnetic readings at various positions. Therefore, magnetic positioning has garnered attention due to its promising localization accuracy and infrastructure-free nature, significantly reducing the investment in localization. Since the magnetic field covers all indoor environments, magnetic positioning holds the potential to create a ubiquitous indoor positioning system. This chapter investigates the stability of the magnetic field concerning factors such as devices, testers, materials, and dates. Compensation methods for different types of magnetic features are studied based on fluctuation patterns to achieve accurate positioning results. Evolutionary algorithm-based optimization strategies are proposed for online localization, tailored to the types of used magnetic features. Testing experiments validate the feasibility and efficiency of utilizing evolutionary algorithms to enhance magnetic positioning performance.

Global Navigation Satellite System (GNSS) time series prediction plays a significant role in monitoring crustal plate motion, landslide detection, and maintenance of the global coordinate framework. Long Short-Term Memory (LSTM), a deep learning model has been widely applied in the field of high-precision time series prediction especially when combined with Variational Mode Decomposition (VMD) to form the VMD-LSTM hybrid model. To further improve the prediction accuracy of the VMD-LSTM model, this paper proposes a dual variational modal decomposition long short-term memory (DVMD-LSTM) model to effectively handle the noise in GNSS time series prediction. This model extracts fluctuation features from the residual terms obtained after VMD decomposition to reduce the prediction errors associated with residual terms in the VMD-LSTM model. Daily E, N, and U coordinate data recorded at multiple GNSS stations between 2000 and 2022 are used to validate the performance of the proposed DVMD-LSTM model. The experimental results demonstrate that compared to the VMD-LSTM model, the DVMD-LSTM model achieves significant improvements in prediction performance across all measurement stations. The average root mean squared error (RMSE) is reduced by 9.86%, and the average mean absolute error (MAE) is reduced by 9.44%, and the average R2 increased by 17.97%. Furthermore, the average accuracy of the optimal noise model for the predicted results is improved by 36.50%, and the average velocity accuracy of the predicted results is enhanced by 33.02%. These findings collectively attest to the superior predictive capabilities of the DVMD-LSTM model, thereby enhancing the reliability of the predicted results.