Local Filter Research Articles

A local filtering approach to mitigating the GNSS multipath effects in relative precise positioning considering the multipath spatial correlation

Multipath delay is a significant error in GNSS precise positioning and affected by the station surroundings. This error cannot be effectively eliminated by observation difference techniques and must be carefully calibrated. Although the spatiotemporal correlation feature of multipath plays an important role in static multipath mitigation, this feature lacks research and needs to be thoroughly investigated. Therefore, the local filtering (LF) approach based on least square collocation (LSC) and moving average (MA) methods is proposed and investigated. The space correlation feature is characterized by covariance function or correlation function, and the residuals with small correlations are neglected while only that with relative larger correlations are used in multipath modelling and calibration. The experiments with short baseline MAT1_MATE and KERG_KRGG for both GPS and Galileo multipath calibration show that, the LF approach based on LSC, simple MA and weighted MA methods achieve better performance in multipath mitigation over short and long-time spans compared with conventional grid approach. For example, the GPS double difference (DD) residual variance reduction rates of baseline MAT1_MATE for the calibration of the next day with LF approach based on the three methods reach73.2%, 72.1% and 70.2%, respectively, which are obviously larger than 63.7% of the grid approach. The improvement reaches maximum 16.4% in the case of baseline KERG_KRGG for Galileo and the average value is around 11.5% i.e. the relatively numbers of the two values reach 29.9% and 20.2%, respectively.

Biotic and abiotic factors drive multi-trophic interactions among spiders at different spatial scales in urban greenspaces

Abstract Urbanization is often detrimental to biodiversity, yet urban greenspaces can be managed to provide habitat for many arthropods. Understanding how anthropogenic filters influence processes of community assembly in urban ecosystems will inform conservation of species such as spiders, which provide natural pest control. Spiders are abundant in urban areas, but the relative importance of biotic and abiotic factors for structuring spider communities in urban greenspaces is unclear. We initiated the Cleveland Pocket Prairie Project in the legacy city of Cleveland, Ohio, where vacant lots and urban prairies were established across eight inner-city neighborhoods. In each greenspace, spiders were collected along with landscape and local environmental data in July 2017. Using a path analysis approach, we investigated the relative importance and strength of landscape and local environmental filters for influencing the structure of spider communities during mid-summer within this system. We found that spider community assembly was influenced by multiple abiotic and biotic drivers across spatial scales related to landscape composition, soil texture and quality, prey breadth, and habitat management designs. Web-building and active hunting spiders responded differently to these landscape and local drivers, highlighting the need to incorporate a functional perspective when studying community assembly. These findings suggest that a multi-scale approach to conservation management is needed to support biodiversity and associated biological control services in urban ecosystems.

Extraction of Coastal Levees Using U-Net Model with Visible and Topographic Images Observed by High-Resolution Satellite Sensors.

Coastal levees play a role in protecting coastal areas from storm surges and high waves, and they provide important input information for inundation damage simulations. However, coastal levee data with uniformity and sufficient accuracy for inundation simulations are not always well developed. Against this background, this study proposed a method to extract coastal levees by inputting high spatial resolution optical satellite image products (RGB images, digital surface models (DSMs), and slope images that can be generated from DSM images), which have high data availability at the locations and times required for simulation, into a deep learning model. The model is based on U-Net, and post-processing for noise removal was introduced to further improve its accuracy. We also proposed a method to calculate levee height using a local maximum filter by giving DSM values to the extracted levee pixels. The validation was conducted in the coastal area of Ibaraki Prefecture in Japan as a test area. The levee mask images for training were manually created by combining these data with satellite images and Google Street View, because the levee GIS data created by the Ibaraki Prefectural Government were incomplete in some parts. First, the deep learning models were compared and evaluated, and it was shown that U-Net was more accurate than Pix2Pix and BBS-Net in identifying levees. Next, three cases of input images were evaluated: (Case 1) RGB image only, (Case 2) RGB and DSM images, and (Case 3) RGB, DSM, and slope images. Case 3 was found to be the most accurate, with an average Matthews correlation coefficient of 0.674. The effectiveness of noise removal post-processing was also demonstrated. In addition, an example of the calculation of levee heights was presented and evaluated for validity. In conclusion, this method was shown to be effective in extracting coastal levees. The evaluation of generalizability and use in actual inundation simulations are future tasks.

Cooperative target estimation of strap-down missiles considering random measurement delay

Aiming at the problem of cooperative target estimation for multiple strap-down missiles, this paper is concerned with developing a distributed cooperative estimation fusion algorithm considering the random transmission delay of observation data. As a stepping stone, the random measurement delay system with multiple strap-down missiles is transformed into a delay-free system with correlation noise in finite time intervals using the random observation delay model for strap-down missiles. Then, the distributed fusion technique without feedback is proposed based on the design of the best local filter for each strap-down sampling subsystem; To further enhance the robustness and stability of the cooperative target estimation system, the distributed fusion algorithm with feedback is suggested. Simulation in various cases and comparison studies are conducted to verify the effectiveness and robustness of the proposed scheme.

Seismic adaptive multiple subtraction using a structure-oriented matched filter

Multiple removal is a crucial step in seismic data processing prior to velocity model building and imaging. After the prediction, adaptive multiple subtraction is used to suppress multiples (considered noise) in seismic data, thereby highlighting primaries (considered signal). In practice, conventional adaptive subtraction methods fit the predicted and recorded multiples in the least-squares sense using a sliding window, formulating a localized adaptive matched filter. Subsequently, the filter is applied to the prediction to remove multiples from the recorded data. However, such a strategy runs the risk of over-attenuating the useful primaries under the minimization energy constraint. To avoid damage to valuable signals, we develop a novel approach that replaces the conventional matched filter with a structure-oriented version. From the predicted multiples, we extract the structural information to be used in the derivation of the adaptive matched filter. Our structure-oriented matched filter emphasizes the structures of predicted multiples, which helps to better preserve primaries during the subtraction. Synthetic and field data examples demonstrate the effectiveness of our structure-oriented adaptive subtraction approach, highlighting its superior performance in multiple removal and primary preservation compared with conventional methods on 2D regularly sampled data.

Performance and accuracy of cross‐section tracking methods for hydromorphological habitat assessment in wadable rivers with sparse canopy conditions

AbstractThis article investigates the performance and accuracy of continuous Real‐Time Kinematic (RTK) Global Navigation Satellite System (GNSS) position tracking for hydromorphological surveys, based on a comprehensive river restoration monitoring campaign. The aim of the research was to assess the method's suitability for efficient data collection in turbid, wadable rivers with sparse canopy conditions, and responds to the water management sector's increasing demand for efficient, low‐cost, and robust survey techniques. The methodological approach involved comparing manual, cross‐sectional water depth measurements to water depth estimations obtained by applying different interpolation methods to the continuous tracking data. The results demonstrate good agreement between both datasets (R2 = 0.77, RMSE = 0.13 m). When using a local standard deviation filter to remove noisy RTK‐GNSS measurements, estimation performance increased significantly (R2 = 0.96, RMSE = 0.06 m). The filter's influence on the hydromorphological habitat statistics mean water depth and coefficient of variation was limited but proved to be relevant for reach‐scale assessments of hydromorphological diversity. Based on a correlation analysis of >106 RTK‐GNSS position logs, we furthermore assessed the impact of tree canopy on RTK‐GNSS measurement accuracy and observed a strong influence within 6.5 m from the canopy border. Estimated accuracy deteriorated noticeably when canopy penetration exceeded 1 m, and accuracies >1 m were common beyond 4 m penetration. The study highlights the efficiency gains achieved with RTK‐GNSS tracking, and showcases its potential for hydromorphological surveys and streamgaging applications in challenging conditions, making it a promising alternative to traditional methods and remote sensing techniques.

Individual-Tree Segmentation from UAV–LiDAR Data Using a Region-Growing Segmentation and Supervoxel-Weighted Fuzzy Clustering Approach

Accurate individual-tree segmentation is essential for precision forestry. In previous studies, the canopy height model-based method was convenient to process, but its performance was limited owing to the loss of 3D information, and point-based methods usually had high computational costs. Although some hybrid methods have been proposed to solve the above problems, most canopy height model-based methods are used to detect subdominant trees in one coarse crown and disregard the over-segmentation and accurate segmentation of the crown boundaries. This study introduces a combined approach, tested for the first time, for treetop detection and tree crown segmentation using UAV–LiDAR data. First, a multiscale adaptive local maximum filter was proposed to detect treetops accurately, and a Dalponte region-growing method was introduced to achieve crown delineation. Then, based on the coarse-crown result, the mean-shift voxelization and supervoxel-weighted fuzzy c-means clustering method were used to identify the constrained region of each tree. Finally, accurate individual-tree point clouds were obtained. The experiment was conducted using a synthetic uncrewed aerial vehicle (UAV)–LiDAR dataset with 21 approximately 30 × 30 m plots and an actual UAV–LiDAR dataset. To evaluate the performance of the proposed method, the accuracy of the remotely sensed biophysical observations and retrieval frameworks was determined using the tree location, tree height, and crown area. The results show that the proposed method was efficient and outperformed other existing methods.

Resilient Multi-Sensor UAV Navigation with a Hybrid Federated Fusion Architecture

Future UAV (unmanned aerial vehicle) operations in urban environments demand a PNT (position, navigation, and timing) solution that is both robust and resilient. While a GNSS (global navigation satellite system) can provide an accurate position under open-sky assumptions, the complexity of urban operations leads to NLOS (non-line-of-sight) and multipath effects, which in turn impact the accuracy of the PNT data. A key research question within the research community pertains to determining the appropriate hybrid fusion architecture that can ensure the resilience and continuity of UAV operations in urban environments, minimizing significant degradations of PNT data. In this context, we present a novel federated fusion architecture that integrates data from the GNSS, the IMU (inertial measurement unit), a monocular camera, and a barometer to cope with the GNSS multipath and positioning performance degradation. Within the federated fusion architecture, local filters are implemented using EKFs (extended Kalman filters), while a master filter is used in the form of a GRU (gated recurrent unit) block. Data collection is performed by setting up a virtual environment in AirSim for the visual odometry aid and barometer data, while Spirent GSS7000 hardware is used to collect the GNSS and IMU data. The hybrid fusion architecture is compared to a classic federated architecture (formed only by EKFs) and tested under different light and weather conditions to assess its resilience, including multipath and GNSS outages. The proposed solution demonstrates improved resilience and robustness in a range of degraded conditions while maintaining a good level of positioning performance with a 95th percentile error of 0.54 m for the square scenario and 1.72 m for the survey scenario.

Systematising clustering techniques through cross-disciplinary research, leading to the development of new methods

Clustering algorithms can help scientists gain valuable insights from data. Thereâ–™s a variety of clustering methods in use, which means there are gaps between the methods used in different fields. Associate Professor Kohei Inoue, Department of Media Design, Kyushu University, Japan, wants to bridge these gaps by investigating the relationships among various clustering methods developed in different fields, in order to systematise the world of clustering. He is bringing two decades of research activities in pattern recognition and image processing to this work. In order to clarify the relationships between different clustering methods, Inoue and the team are conducting an interdisciplinary survey. First, the researchers are working to clarify the relationship between the technologies used across different fields. So far, they have successfully clarified the relationship between the rolling guidance filter and the local mode filter. In a previous study, Inoue and his collaborators proposed a robust K-means clustering al-algorithm. The researchers demonstrated the effectiveness of their technique utilising a BBC dataset originating from BBC News. In their work, the team is collaborating with a laboratory at a university in Japan that is studying non-photorealistic rendering. They have so far published several co-authored papers, as well as having obtained results from their joint research. Ultimately, by systemising clustering technology, Inoue believes that the characteristics of each method, as well as the interrelationships between each method, can be explained and clustering technology enhanced, as well as new clustering techniques developed.

Fluid chemistry alters faunal trophodynamics but not composition on the deep-sea Capelinhos hydrothermal edifice (Lucky Strike vent field, Mid-Atlantic Ridge)

The recently discovered deep-sea Capelinhos hydrothermal edifice, ~ 1.5 km of the main Lucky Strike (LS) vent field (northern Mid-Atlantic Ridge), contrasts with the other LS edifices in having poorly-altered end-member hydrothermal fluids with low pH and chlorine, and high metal concentrations. Capelinhos unique chemistry and location offer the opportunity to test the effects of local abiotic filters on faunal community structure while avoiding the often-correlated influence of dispersal limitation and depth. In this paper, we characterize for the first time the distribution patterns of the Capelinhos faunal communities, and analyze the benthic invertebrates (> 250 µm) inhabiting diffusive-flow areas and their trophic structures (δ13C, δ15N and δ34S). We hypothesized that faunal communities would differ from those of the nearest LS vent edifices, showing an impoverished species subset due to the potential toxicity of the chemical environment. Conversely, our results show that: (1) community distribution resembles that of other LS edifices, with assemblages visually dominated by shrimps (close to high-temperature focused-fluid areas) and mussels (at low-temperature diffuse flow areas); (2) most species from diffuse flow areas are well-known LS inhabitants, including the bed-forming and chemosymbiotic mussel Bathymodiolus azoricus and (3) communities are as diverse as those of the most diverse LS edifices. On the contrary, stable isotopes suggest different trophodynamics at Capelinhos. The high δ15N and, especially, δ13C and δ34S values suggest an important role of methane oxidation (i.e., methanotrophy), rather than the sulfide oxidation (i.e., thiotrophy) that predominates at most LS edifices. Our results indicate that Capelinhos shows unique environmental conditions, trophic structure and trophodynamics, yet similar fauna, compared to other LS edifices, which suggest a great environmental and trophic plasticity of the vent faunal communities at the LS.

Vision-aided intelligent and adaptive vehicle pose estimation during GNSS outages

In this paper, a novel multi-information fusion methodology is proposed for vehicle pose estimation. The purpose is to improve the pose estimation accuracy during global navigation satellite system (GNSS) outages, mainly from two aspects: (1) extra observations of accurate velocities and angular rates without cumulative errors; (2) adaptive and intelligent fusion. Firstly, a multidimensional motion perception network (MMPN) is designed in order to estimate the velocities and angular rates. At the same time, the motion state is also output. The inputs of the network are two consecutive images. Thus, the estimated velocities and angular rates are not affected by cumulative errors. Besides, because the corresponding velocities and angular rates measured by high-quality inertial measurement unit (IMU) with low noise and drift are used as the training samples, the accuracy of the estimated velocities and angular rates are guaranteed. Further, an unscented Kalman filter with federal structure (UKF-F) with different motion models is designed for pose estimation. The local filters of UKF-F use the current probabilities of belonging to the motion patterns output by the MMPN as the information-sharing factors. Thus, the fusion is adaptive to the actual vehicle motion state. In addition, a gate recurrent unit (GRU)-based error compensation module is introduced to further reduce the position errors during GNSS outages. The GRU-based module is trained offline with the input of MMPN and IMU observations. Due to the advantages of time series forecasting, the GRU-based module can accurately predict the position error of IMU/MMPN integration online. The KITTI dataset with different driving scenarios is used to confirm the feasibility of the proposed methodology. The results of the experiments verify that the proposed methodology can achieve precise vehicle pose estimation during GNSS outages.

Event-Triggered Distributed Fusion Estimator for Asynchronous Markov Jump Systems with Correlated Noises and Fading Measurements.

In this study, we investigate event-triggered distributed fusion estimation for asynchronous Markov jump systems subject to correlated noises and fading measurements. The measurement noises are interrelated, and they are simultaneously coupled with the system noise. The sensor samples measurements uniformly, and the sampling rates of the sensors are different. First, the asynchronous system is synchronized at state update points; then, the local filter is obtained. Furthermore, a variance-based event-triggered strategy is introduced between the local estimator and the fusion center to decrease the energy consumption of network communication. Then, a distributed fusion estimation algorithm is proposed using a matrix-weighted fusion criterion. Finally, the effectiveness of the algorithm is verified using computer simulations.

Multiple local particle filter for high-dimensional system identification

Nonlinearity and high dimensionality emerge as two primary challenges in the realm of system identification within the context of structural health monitoring (SHM) applications. Particle filter (PF) has been demonstrated efficient for nonlinear identification, but it suffers from the curse of dimensionality and behaves poorly in high-dimensional problems. The idea of state and measurement partitioning has been used in many PF algorithms to simplify high-dimensional identification problems into the identification of several lower-dimensional subgroups, but with very few applications to SHM problems. In this context, by combining multiple particle filters (MPF) with the decay of correlations property, this paper develops a novel multiple local particle filter (MLPF) for high-dimensional identification problems. A whole state vector is partitioned into several state subgroups, each consisting of fewer state components and then estimated by one PF through a novel likelihood including the local state and measurement vectors. The feasibility and efficiency of the proposed method are tested through a benchmark toy example, a case study of a twenty-story Bouc-Wen frame structure under ground motion, and an experimental study of fatigue delamination growth in composites.

ChirpTracker: A Precise-Location-Aware System for Acoustic Tag Using Single Smartphone

The increasing interest in loss prevention devices using the Internet of Things, has been driven by the convenience, low cost, and low power consumption of these devices. However, the existing technologies cannot achieve a balance between high availability over a wide area with a single smartphone and precise location awareness. In this paper, a novel Precise-Location-Aware method that integrates acoustic technology and pedestrian dead reckoning, ChirpTracker, is proposed which most smartphones support without auxiliary equipment. This system can provide wide coverage (30m) and is suitable for many scenarios such as searching for cars in underground parking or finding items indoors. ChirpTracker can detect the distance between the smartphone and a lost tag in real time using acoustic signals, it can monitor the relative position change of the smartphone based on deep learning based pedestrian dead reckoning (PDR) and update relative positioning of the lost tag though the observation from single base-station in motion. A technology that combines the local least squares method (LSM) and particle filter (PF) improves the convergence and the robustness of ChirpTracker through an identification strategy for a mirror position. This method was validated in experiments conducted in actual environments. The results demonstrate the effectiveness and positioning accuracy of ChirpTracker.

A Novel Image Segmentation Technique with N-L Means Filter Using Region Merging Strategy

Image segmentation is a branch of digital image processing which emphases on splitting an image into different fragments according to their features. This work proposes a novel image segmentation technique using fast non local (N-L) means filter with region merging approach. Here, a random noise is added to the original image and discrete wavelet transform (DWT) is applied to separate the low and high frequency bands of the digital image. The low frequency component is subjected to a fast N-L means filter and the filtered image is segmented by graph-based segmentation technique. Here, these segmented image regions are merged to reduce the over segmentation patterns. The detailed coefficients of the image component are treated with soft threshold filter to reduce the residual noise. Finally merged image is combined with preserved edge features at wavelet projection resulting in better segmented image. The results are compared with some of the best methods available in literature and are found to be significantly better. Keywords: Discrete wavelet transform (DWT), fast NL-means filter, graph-based segmentation, boundary based hierarchical region merging, soft-thresholding, peak signal to noise ratio (PSNR).

A novel robust multivariate Laplace distribution-based distributed consensus information fusion

The multivariate Laplace distribution (MLD) possesses a lesser set of prior parameters compared to the Student’s t-distribution, thus simplifying the modeling of measurement data subject to heavy-tailed noise corruption. This short communication introduces a novel distributed hybrid consensus fusion algorithm utilizing the MLD modeling and variational Bayesian approach. Firstly, we formulate the measurement noise associated with individual sensor nodes and introduce the hierarchical Gaussian form of MLD to enhance the feasibility of variational inference. Secondly, we opt for the inverse-Wishart (IW) distribution to serve as the conjugate prior to the positive definite matrix, enabling adaptive parameter learning within the MLD context. As a result, a novel hierarchical Gaussian state–space model (SSM) is established for multi-sensors network. Subsequently, we derive a novel local information filter to acquire higher precision information and innovation vector–matrix pairs, outperforming the Student’s t distribution-based filter. These derivations are grounded in the new hierarchical SSM, and the vector–matrix pairs aid in information fusion across the network. Lastly, we present a distributed robust consensus filter for fusing local information using a hybrid consensus approach that devoid of a central fusion node. Simulation results demonstrate that the proposed consensus filter can obtain better estimation accuracy under the interference of heavy-tailed measurement outliers.

Adaptive Fuzzy Decentralized Output-Feedback Control of Large-Scale Systems With Sensor Faults: A Multichannel Asynchronous Triggering Approach

This paper proposes an adaptive fuzzy decentralized output feedback control scheme for large-scale systems with multichannel asynchronous event-triggering. Uncertain system dynamics, unknown interconnections and time-varying sensor faults are handled simultaneously, even though only the corrupted measured local output is available for the design procedure. First, local state estimation filters are designed to estimate the unmeasured states. Then, considering that the resource-limited communication and computation may exist in all three types of channels including state estimation filter-to-controller channel, parameter estimator-to-controller channel and controller-to-actuator channel, an asynchronous event-triggering framework with time-varying triggering threshold is developed for multiple channels to release the communication and computation burden. Compared with the existing synchronous triggering mechanism, the proposed asynchronous one has several advantages: 1) the redundant signal transmission is reduced, 2) the triggering conditions for different channels are uncorrelated, which enables the designer to adjust the signal transmission frequency of each channel independently, and 3) the robustness could be improved in the face of noise as ideal synchronous triggering is not easy to be achieved in practice. In addition, both gain and bias faults, which are allowed to be unknown and time-varying, are covered in a unified sensor fault model. It is proved that, with the proposed control scheme, all the closed-loop signals are semi-globally uniformly ultimately bounded and the output tracking error converges into an adjustable residual set without Zeno behavior. Finally, simulation and comparison results illustrate the effectiveness and advantages of the proposed control scheme.

Robust multi-scale weighting-based edge-smoothing filter for single image dehazing

The guided image filter (GIF) and weighted guided image filter (WGIF) are local linear model-based good edge-preserving filters. However, due to fixed regularization parameter, they suffer from halo artifacts (morphological artifacts) in the sharp regions. To overcome this issue, a robust multi-scale weighting-based edge-smoothing filter (RMWEF) for single image dehazing is proposed in this paper. It removes morphological artifacts and over-smoothness strongly and preserves edge information precisely in both flat and sharp regions. The proposed dehaze method has four-steps. First, initial transmission map and atmospheric map are estimated by using a novel dark channel prior (DCP) method. Then, the morphological artifacts of initial transmission map are reduced by using non-local haze line averaging (NL-HLA) method. In the third step, transmission map is refined by using the proposed RMWEF. Finally, the haze free image is restored. Theoretical and experimental analysis proves that the proposed algorithm produce effective dehaze results quicker than the existing methods.

Linear Time Non-Local Cost Aggregation on Complementary Spatial Tree Structures

Studies on many dense correspondence tasks in the field of computer vision attempt to find spatially smooth results. A typical way to solve these problems is by smoothing the matching costs using edge-preserving filters. However, local filters generate locally optimal results, in that they only take the costs over a small support window into account, and non-local filters based on a minimum spanning tree (MST) tend to overuse the piece-wise constant assumption. In this paper, we propose a linear time non-local cost aggregation method based on two complementary spatial tree structures. The geodesic distances in both the spatial and intensity spaces along the tree structures are used to evaluate the similarity of pixels, and the final aggregated cost is the sum of the outputs from these two trees. The filtering output of a pixel on each tree can be obtained by recursively aggregating the costs along eight sub-trees with linear time complexity. The only difference between the filtering procedures on these two spatial tree structures is the order of the filtering. Experimental results in optical flow estimation and stereo matching on the Middlebury and KITTI datasets demonstrate the effectiveness and efficiency of our method. It turns out that our method outperforms typical non-local filters based on the MST in cost aggregation. Moreover, a comparison of handcrafted features and deep features learned by convolutional neural networks (CNNs) in calculating the matching cost is also provided. The code will be available soon.

Fusion filtering for rectangular descriptor systems with stochastic bias and random observation delays under weighted try-once-discard protocol

This paper studies the fusion filtering problem for a class of multi-sensor rectangular descriptor systems with stochastic bias and random observation delays under weighted try-once-discard (WTOD) protocol. In order to reflect the stochastic behavior generated by disturbances, a dynamic equation is utilized to describe the stochastic bias. The random observation delays are modeled by Bernoulli random variables with individual occurrence probability. Furthermore, the WTOD protocol is used to lessen the network traffic burden. Firstly, by introducing matrix transformation and the singular value decomposition method, the rectangular descriptor systems are transformed into two non-descriptor subsystems with lower orders, where the augmentation technique is adopted to obtain new augmented systems. Secondly, the relevant local filter gains are obtained by minimizing the filtering error covariances based on the local filters (LFs) designed by new systems. Subsequently, the local filters and the fusion filters of the original descriptor systems are obtained by state transformation and covariance intersection (CI) fusion technique, respectively. The major contribution lies in that a novel fusion filtering algorithm avoiding the calculation of error cross-covariances is proposed for rectangular descriptor systems, where special effort is devoted to handling the impacts from the WTOD protocol, stochastic bias and random observation delays. Finally, the effectiveness of the fusion algorithm is demonstrated by a simulation example.