Trajectory Simplification Research Articles

An adaptive trajectory segmentation and simplification algorithm based on vessel behavioral features

Existing algorithms for trajectory simplification in AIS data processing have issues such as loss of key feature points, high subjectivity in threshold selection, and incomplete consideration of factors. In this paper, an adaptive trajectory segmentation and simplification algorithm based on vessel behavioral features is proposed. The algorithm identifies behavioral feature intervals by extracting vessel behavioral features and constructs an adaptive segmentation threshold function to achieve adaptive segmentation of trajectories and extraction of key feature points. Then, considering the quality, similarity, and spatial variability of trajectory simplification, an adaptive simplification threshold function is constructed to automatically select the best threshold for each sub-trajectory to generate the simplified trajectory. Our experiments demonstrate that the algorithm maintains a high simplification rate while enabling adaptive simplification of the trajectory, and also retains the key feature points and trajectory shapes to the maximum extent. The effectiveness and robustness of the algorithm are verified through comparison with other algorithms, effectively avoiding the distortion of navigational behavior that may be caused by traditional methods. This provides reliable data support for maritime traffic management and decision-making.

Research on the Optimization of Ship Trajectory Clustering Based on the OD–Hausdorff Distance

With the growth of global trade, port shipping is becoming more and more important. In this paper, an analysis of a ship’s inbound and outbound track characteristics is conducted using the OD–Hausdorff distance. The accuracy and efficiency of trajectory data analysis have been enhanced through clustering analysis. Trajectories are arranged in a time sequence, and representative port segments are selected. An improved OD–Hausdorff distance method is employed to capture the dynamic characteristics of a ship’s movements, such as speed and heading. Additionally, the DBSCAN algorithm is utilized for clustering, allowing for the processing of multidimensional AIS data. Data cleaning and preprocessing have ensured the reliability of the AIS data, and the Douglas–Peucker algorithm is used for trajectory simplification. Significant improvements in the accuracy and efficiency of trajectory clustering have been observed. Therefore, the main channel of the Guan River and the right side of Yanwei Port are usually followed by ships greater than 60 m in length, with a lateral Relative Mean Deviation (RMD) of 7.06%. Vessels shorter than 60 m have been shown to have greater path variability, with a lateral RMD of 7.94%. Additionally, a crossing pattern at Xiangshui Port is exhibited by ships shorter than 60 m due to the extension of berths and their positions at turns. Enhanced clustering accuracy has provided more precise trajectory patterns, which aids in better channel management.

Open source map matching with Markov decision processes: A new method and a detailed benchmark with existing approaches

AbstractMap matching is a widely used technology for mapping tracks to road networks. Typically, tracks are recorded using publicly available Global Navigation Satellite Systems, and road networks are derived from the publicly available OpenStreetMap project. The challenge lies in resolving the discrepancies between the spatial location of the tracks and the underlying road network of the map. Map matching is a combination of defined models, algorithms, and metrics for resolving these differences that result from measurement and map errors. The goal is to find routes within the road network that best represent the given tracks. These matches allow further analysis since they are freed from the noise of the original track, they accurately overlap with the road network, and they are corrected for impossible detours and gaps that were present in the original track. Given the ongoing need for map matching in mobility research, in this work, we present a novel map matching method based on Markov decision processes with Reinforcement Learning algorithms. We introduce the new Candidate Adoption feature, which allows our model to dynamically resolve outliers and noise clusters. We also incorporate an improved Trajectory Simplification preprocessing algorithm for further improving our performance. In addition, we introduce a new map matching metric that evaluates direction changes in the routes, which effectively reduces detours and round trips in the results. We provide our map matching implementation as Open Source Software (OSS) and compare our new approach with multiple existing OSS solutions on several public data sets. Our novel method is more robust to noise and outliers than existing methods and it outperforms them in terms of accuracy and computational speed.

Trajectory Data Compression Algorithm Based on Ship Navigation State and Acceleration Variation

An active area of study under the dual carbon target, which is based on automatic identification systems (AIS), is the emission inventory of pollutants from ships. Data compression is required because there is currently so much data that it has become difficult to transmit, process, and store it. A trajectory simplification method considering the ship sailing state and acceleration rate of change is developed in this paper to assure the validity of the compressed data used in the emission inventory analysis. By carefully examining the integral relationship between acceleration and pollution emissions, the algorithm constructs an acceleration rate of change function for data compression and categorizes AIS data by ship navigation status. By dynamically altering the amount of acceleration change, the developed function can stabilize the pollutant emission calculation error and adaptively calculate the threshold value. The experimental results show that the emission calculation error of the proposed algorithm is only 0.185% when the compression rate is 90.28%.

AIS Trajectories Simplification Algorithm Considering Topographic Information.

With the development of maritime technology and equipment, most ships are equipped with an automatic identification system (AIS) to store navigation information. Over time, the size of the data increases, rendering its storage and processing difficult. Hence, it is necessary to transform the AIS data into trajectories, and then simplify the AIS trajectories to remove unnecessary information that is not related to route shape. Moreover, topographic information must be considered because otherwise, the simplified trajectory can intersect obstacles. In this study, we propose an AIS trajectory simplification algorithm considering topographic information. The proposed algorithm simplifies the trajectories without the intersection of the trajectory and obstacle using the improved Douglas–Peucker algorithm. Polygon map random (PMR) quadtree was used to consider topographic information on the coast, and the intersection between topographic information and simplified trajectories was efficiently computed using the PMR quadtree. To verify the effectiveness of the proposed algorithm, experiments were conducted on real-world trajectories in the Korean sea. The proposed algorithm yielded simplified trajectories with no intersections of the trajectory and obstacle. In addition, the computational efficiency of the proposed algorithm with the PMR quadtree was superior to that without the PMR quadtree.

A novel method for ship trajectory clustering

Different from trajectories in other fields, each ship trajectory has a unique direction. However, the traditional methods cannot be used to distinguish the trajectories in opposite directions. This paper presents an improved measurement with Cosine and Hausdorff distance to measure the difference between any two trajectories in different directions. In addition, to improve the efficiency of the clustering algorithm, a method named Course-Preserving Trajectory Simplification with Adaptive Compression Ratio (CPTS-ACR) has been proposed to simplify the trajectories. Ground-truth AIS data has been used to make a benchmark dataset. Experimental results show that the improved method in this paper has a better performance compared with some other existing methods.

Automatic Construction of Indoor 3D Navigation Graph from Crowdsourcing Trajectories

Lacking indoor navigation graph has become a bottleneck in indoor applications and services. This paper presents a novel automated indoor navigation graph reconstruction approach from large-scale low-frequency indoor trajectories without any other data sources. The proposed approach includes three steps: trajectory simplification, 2D floor plan extraction and 3D navigation graph construction. First, we propose a ST-Join-Clustering algorithm to identify and simplify redundant stay points embedded in the indoor trajectories. Second, an indoor trajectory bitmap construction based on a self-adaptive Gaussian filter is developed, and we then propose a new improved thinning algorithm to extract 2D indoor floor plans. Finally, we present an improved CFSFDP algorithm with time constraints to identify the 3D topological connection points between two different floors. To illustrate the applicability of the proposed approach, we conducted a real-world case study using an indoor trajectory dataset of over 4000 indoor trajectories and 5 million location points. The case study results showed that the proposed approach improves the navigation network accuracy by 1.83% and the topological accuracy by 13.7% compared to the classical kernel density estimation approach.

A Lightweight Processing Method for Hand-Drawn Pressure-Sensitive Trajectories Oriented Toward Web-Based 3D Modeling

Digital geometry processing of hand-drawn pressure-sensitive trajectories oriented toward Web-based three-dimensional (3D) modeling becomes attractive problem. Existing practices usually focus on converting raw trajectories into 3D stroke meshes with consistent line width, which the pressure information can not been fully utilized for denoising, simplification and reflecting realistic graphics of 3D stroke mesh. Also, there are little research on the high quality of trajectory with data transmission fluency and light weight in the Web environment. We propose a lightweight processing method for hand-drawn pressure-sensitive trajectories that is oriented toward Web-based 3D modeling. An angle-chord height united trajectory simplification (ACUTS) algorithm is proposed, in which the discrete points are simplified by comprehensively considering the angle deviation and chord height deviation with the sliding window mechanism. In addition, a lightweight reconstruction algorithm based on pressure -sensitivity for discrete points (LRPDP) is also proposed, in which the pressure value can be fully utilized for simplifying the redundant points while ensuring the reconstructed 3D stroke mesh more realistic. Besides, the experimental results show that compared to some other methods, we perform best in terms of data reduction using compression ratio and reduction percentages. We also perform best in terms of high accuracy of 3D stroke mesh using mean stochastic error distance, local maximum error and total length error. Although the insufficient utilization of the pressure-sensitive information limits our research to some extents, the significance of our research is to provide a new strategy to realize Web-based 3D modeling using hand drawing mode.

AIS trajectory simplification algorithm considering ship behaviours

With the establishment of satellite constellations and terrestrial networks of Automatic Identification System (AIS) receivers, an increasing number of ship trajectories have become available, and the data size of trajectories that must be recorded is increasing. As a result, transmitting, processing and storing data have become important issues. At the same time, ship behaviour information is hidden in AIS data. Hence, an effective method is required to not only compress redundant information but also maintain the main characteristic elements included in the trajectory. In this paper, a novel algorithm considering the spatial and motion features of trajectories is designed, which can compress AIS trajectories based on ship behaviour characteristics. The proposed algorithm has two main parts: the Douglas-Peucker (DP) algorithm is employed to simplify trajectories according to spatial features, and a sliding window is adopted to simplify trajectories based on motion features. Furthermore, statistical theory is applied to help determine the thresholds of motion features in sliding window algorithms. The two results are merged to form a trajectory simplification algorithm that considers ship behaviours. To verify the effectiveness of the proposed algorithm, numerical experiments are performed. The results indicate that the proposed algorithm can efficiently simplify trajectories by considering ship behaviour as needed.

Adaptive simplification of GPS trajectories with geographic context – a quadtree-based approach

ABSTRACT Big GPS trajectory datasets can have redundant spatio-temporal information for applications, which requires simplification as a key preprocessing for modeling. Many existing simplification methods focus on the geometric information from a trajectory per se. Conversely, methods considering geographic context often fail to provide spatially adaptive simplification, or require complex parameter settings to achieve this task. This study proposes a novel two-stage adaptive trajectory simplification method embedding spatial indexing, enrichment, and aggregation in an integrated process. The first stage employs a quadtree for the subdivision depending on the density of geographic context features (i.e. POIs), leading to a variable-resolution representation of the area. The second stage aggregates trajectory waypoints locating in the same quadtree leaf node into a representative point, making the aggregation adapting to the spatial layout of the geographic feature in the first stage. Evaluation with a real-world vehicle trajectory dataset shows that the proposed approach can automatically simplify trajectory segments at variable compression ratios with greater simplification in areas with sparse context features (e.g. rural) and less simplification in areas with dense context features (e.g. urban). More importantly, the method can still preserve inter-trajectory distances between original trajectories and simplified ones, while significantly reducing the computing time.

Feature-First Add-On for Trajectory Simplification in Lifelog Applications.

Lifelog is a record of one’s personal experiences in daily lives. User’s location is one of the most common information for logging a human’s life. By understanding one’s spatial mobility we can figure out other pieces of context such as businesses and activities. With GPS technology we can collect accurate spatial and temporal details of a movement. However, most GPS receivers generate a huge amount of data making it difficult to process and store such data. In this paper, we develop a generic add-on algorithm, feature-first trajectory simplification, to simplify trajectory data in lifelog applications. It is based on a simple sliding window mechanism counting occurrence of certain conditions. By automatically identifying feature points such as signal lost and found, stall, and turn, the proposed scheme provides rich context more than spatio-temporal information of a trajectory. In experiments with a case study of commuting in personal vehicles, we evaluate the effectiveness of the scheme. We find the proposed scheme significantly enhances existing simplification algorithms preserving much richer context of a trajectory.

One-pass trajectory simplification using the synchronous Euclidean distance

Various mobile devices have been used to collect, store and transmit tremendous trajectory data, and it is known that raw trajectory data seriously wastes the storage, network bandwidth and computing resource. To attack this issue, one-pass line simplification ($$\textsf {LS} $$) algorithms have been developed, by compressing data points in a trajectory to a set of continuous line segments. However, these algorithms adopt the perpendicular Euclidean distance, and none of them uses the synchronous Euclidean distance ($$\textsf {SED} $$), and cannot support spatiotemporal queries. To do this, we develop two one-pass error bounded trajectory simplification algorithms ($$\textsf {CISED} $$-$$\textsf {S} $$ and $$\textsf {CISED} $$-$$\textsf {W} $$) using $$\textsf {SED} $$, based on a novel spatiotemporal cone intersection technique. Using four real-life trajectory datasets, we experimentally show that our approaches are both efficient and effective. In terms of running time, algorithms $$\textsf {CISED} $$-$$\textsf {S} $$ and $$\textsf {CISED} $$-$$\textsf {W} $$ are on average 3 times faster than $$\textsf {SQUISH} $$-$$\textsf {E} $$ (the fastest existing $$\textsf {LS} $$ algorithm using $$\textsf {SED} $$). In terms of compression ratios, $$\textsf {CISED} $$-$$\textsf {S} $$ is close to and $$\textsf {CISED} $$-$$\textsf {W} $$ is on average $$19.6\%$$ better than $$\textsf {DPSED} $$ (the existing sub-optimal $$\textsf {LS} $$ algorithm using $$\textsf {SED} $$ and having the best compression ratios), and they are $$21.1\%$$ and $$42.4\%$$ better than $$\textsf {SQUISH} $$-$$\textsf {E} $$ on average, respectively.

Vessel Trajectory Online Multi-Dimensional Simplification Algorithm

Facilitated by the establishment of terrestrial networks and satellite constellations of Automatic Identification System (AIS) receivers, large quantities of spatial and temporal information that trace ships' paths have been collected. The exponential increase in the amount of AIS data has caused expensive and time-consuming transmission, calculation and storage problems. Using appropriate trajectory simplification methods in a timely manner to compress redundant information while minimising the loss of importation information is important. To minimise the simplification error, this paper proposes an online multi-dimensional simplification algorithm for AIS trajectory streaming data. The simplification algorithm takes into account position, direction and speed preservation. Finally, a comparison experiment with other algorithms is made to examine the effectiveness of this algorithm. The results indicate that the proposed online multi-dimensional simplification algorithm can effectively preserve a ship's motion state, including its position, speed and course.

КІНЕМАТИЧНІ ВЛАСТИВОСТІ ТРАЄКТОРІЙ, ОПИСАНИХ NURBS СПЛАЙНАМИ

The purpose of the article is to solve a number of problems of using NURBS curves in the implementation of high-speed processing of complex products on machining equipment. NURBS-splines are becoming increasingly popular among CNC specialists, which is motivated by their wide application in the modeling of the production facility in CAD/CAM systems. Advanced manufacturers of CNC devices in the number of shaping algorithms necessarily include NURBS - interpolation. But despite the extensive capabilities of CAD/CAM systems for describing the shape of products and toolpaths of processing equipment using spline curves, many manufacturers of CNC systems use more primitive methods for describing the trajectory of the tool - piecewise linear and linear-circular. This negates the benefits of using spline curves, including smooth curvature change, which is very important when moving the tool at high speed processing. Such simplification of trajectories is associated with a number of difficulties in the implementation of spline curves in modern CNC systems. In addition, the requirements for industrial cleanliness of the surfaces of the parts is information about the processing parameters, the directions of relative movements of the tool and the workpiece on the finishing operations in order to provide technological conditions to the size of the burrs formed. It is possible that the choice of strategy of processing for obtaining the minimum size of a Burr or reduction of their number. The sizes of the turned-out agnails define methods of their elimination in technological process of production of a detail. Therefore, the provision of technological information using the analytical standard of the part is a necessary condition for ensuring the quality of products and their high reliability. NURBS - interpolation allows to obtain a compact description of the tool movement in the process of forming, which allows to correctly formulate the problem of working of complex-shaped parts.

Semantically Enriched Simplification of Trajectories

Abstract. Moving objects that are equipped with GPS devices generate huge volumes of spatio-temporal data. This spatial and temporal information is used in tracing the path travelled by the object, so called trajectory. It is often difficult to handle this massive data as it contains millions of raw data points. The number of points in a trajectory is reduced by trajectory simplification techniques. While most of the simplification algorithms use the distance offset as a criterion to eliminate the redundant points, temporal dimension in trajectories should also be considered in retaining the points which convey both the spatial and temporal characteristics of the trajectory. In addition to that the simplification process may result in losing the semantics associated with the intermediate points on the original trajectories. These intermediate points can contain attributes or characteristics depending on the application domain. For example, a trajectory of a moving vessel can contain information about distance travelled, bearing, and current speed. This paper involves implementing the Synchronized Euclidean Distance (SED) based simplification to consider the temporal dimension and building the Semantically Enriched Line simpliFication(SELF) data structure to preserve the semantic attributes associated to individual points on actual trajectories. The SED based simplification technique and the SELF data structure have been implemented in PostgreSQL 9.4 with PostGIS extension using PL/pgSQL to support dynamic lines. Extended experimental work has been carried out to better understand the impact of SED based simplification over conventional Douglas-Peucker algorithm to both synthetic and real trajectories. The efficiency of SELF structure in regard to semantic preservation has been tested at different levels of simplification.

Modelling and Analysis of Semantically Enriched Simplified Trajectories Using Graph Databases

Abstract. Geospatial databases are utilized in modelling the huge volume of spatial-temporal data generated by tracking moving objects equipped with positioning devices. This data can be used in performing trajectory analysis such as optimum path finding or identification of collision risk. At the same time, this massive data becomes difficult to handle using traditional databases as raw trajectories contain a lot of unnecessary data points. Thus, trajectory simplification techniques are applied to reduce the number of vertices representing a trajectory. However, elimination of intermediate points by simplification process leads to a loss of semantics associated with the trajectories. These semantics are dependent on the application domain. For example, a trajectory of a moving vessel can convey information about time, distances travelled, bearing, or velocity. This research proposes a graph data model that enriches the simplified geometry of trajectories with the semantics lost in the simplification process. Raw trajectories, initially modelled and stored in a PostgreSQL/PostGIS database, are simplified according to both their spatial and temporal characteristics using the Synchronized Euclidean Distance (SED), while the Semantically Enriched Line simpliFication (SELF) data structure is adopted to preserve the semantics of the vertices eliminated in the simplification process. Then, enriched simplified trajectories are transferred to a Neo4j database and modelled in terms of nodes and edges using graphs. Trajectories can then be further processed using Cypher query language and Neo4j spatial procedures. A visualization tool has been developed on top of Neo4j graph database to support the semantic retrieval and visualization of trajectories.

Research on the forcefree control of cooperative robots based on dynamic parameters identification

PurposeThis paper aims to propose a forcefree control algorithm that is based on a dynamic model with full torque compensation is proposed to improve the compliance and flexibility of the direct teaching of cooperative robots.Design/methodology/approachDynamic parameters identification is performed first to obtain an accurate dynamic model. The identification process is divided into two steps to reduce the complexity of trajectory simplification, and each step contains two excitation trajectories for higher identification precision. A nonlinear friction model that considers the angular displacement and angular velocity of joints is proposed as a secondary compensation for identification. A torque compensation algorithm that is based on the Hogan impedance model is proposed, and the torque obtained by an impedance equation is regarded as the command torque, which can be adjusted. The compensatory torque, including gravity torque, inertia torque, friction torque and Coriolis torque, is added to the compensation to improve the effect of forcefree control.FindingsThe model improves the total accuracy of the dynamic model by approximately 20% after compensation. Compared with the traditional method, the results prove that the forcefree control algorithm can effectively reduce the drag force approximately 50% for direct teaching and realize a flexible and smooth drag.Practical implicationsThe entire algorithm is verified by the laboratory-developed six degrees-of-freedom cooperative robot, and it can be applied to other robots as well.Originality/valueA full torque compensation is performed after parameters identification, and a more accurate forcefree control is guaranteed. This allows the cooperative robot to be dragged more smoothly without external sensors.

Constrained trajectory simplification with speed preservation

ABSTRACTThe rapid increase in movement trajectory data causes data storage, transmission, computational processing, and visualization problems. These issues can be alleviated through trajectory simplification, which removes unnecessary details from raw trajectories. Most existing studies that focused on trajectory simplification considered freely moving objects, and they attempted to minimize position errors in their simplified representations in a two-dimensional plane. However, a large number of objects move within the constraint of road networks. In such constrained trajectory simplification, position error should be measured in the network space. Moreover, constrained trajectories contain a wealth of speed-change information that reflects the movement patterns of moving objects. In this study, we designed a data model, proposed error measurements, and developed a two-component method to simplify constrained trajectories. The geometric component in our method extended the classic Douglas–Peucker method using network distance to simplify trajectories with a guaranteed position error bound in network space. The semantic component enhanced the simplified representation by employing a data-enrichment strategy that allows users to control speed loss. Real trajectory data were used to assess the effectiveness of the proposed method. Experimental results show that our method has a lower position error than existing algorithms do when road network constrained trajectory data are simplified. The method can also preserve original speed in the simplified representation with a relatively low increase in data size. Our study thus provides an approach to simplifying trajectory data that guarantees error bounds in both location and speed.

Trajectory Extraction, Simplification and Representation Based on Phase Correlation and Dynamic Chain Code for Forward Facing Camera

Trajectory Extraction, Simplification and Representation Based on Phase Correlation and Dynamic Chain Code for Forward Facing Camera

Sunshine-Based Trajectory Simplification

Sunshine-based trajectory analysis plays a significant impact on comprehensive scenarios, including driving safety and routing planning for mobile solar collection. To the best of our knowledge, however, a little work analyzes the impact of sunshine on mobile objects on different trajectories. This paper investigates the relationship between sunshine and the trajectories of mobile objects. We introduce a sunshine orientation model to integrate sunshine information with trajectories. A sunshine-based trajectory simplification model is proposed to remove redundant points in trajectories, which carry a little sunshine-related information. The sunshine-based trajectory simplification model is indeed versatile. We apply this model to help users efficiently query the sunshine information of their trips. Our design is evaluated with extensive simulations based on three-month general transit feed specification data from August to October in 2017 in five USA cities, including Washington, DC, USA, and Minneapolis. Furthermore, we develop a sunshine query system for mobile scenarios by embedding our sunshine-based trajectory simplification model and conduct a field study to show the validity and efficiency of this model. The evaluation results show that our design reduces 87.4% position points in trajectories while only sacrificing 9.6% of sunshine information in the field tests.