Search

Regarding the terrestrial water storage anomaly (TWSA) gap between the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-on (-FO) gravity satellite missions, a BEAST (Bayesian estimator of abrupt change, seasonal change and trend)+GMDH (group method of data handling) gap-filling scheme driven by hydrological and meteorological data is proposed. Considering these driving data usually cannot fully capture the trend changes of the TWSA time series, we propose first to use the BEAST algorithm to perform piecewise linear detrending for the TWSA series and then fill the gap of the detrended series using the GMDH algorithm. The complete gap-filling TWSAs can be readily obtained after adding back the previously removed piecewise trend. By comparing the simulated gap filled by BEAST + GMDH using Multiple Linear Regression and Singular Spectrum Analysis with reference values, the results show that the BEAST + GMDH scheme is superior to the latter two in terms of the correlation coefficient, Nash-efficiency coefficient, and root-mean-square error. The real GRACE/GFO gap filled by BEAST + GMDH is consistent with those from hydrological models, Swarm TWSAs, and other literature regarding spatial distribution patterns. The correlation coefficients there between are, respectively, above 0.90, 0.80, and 0.90 in most of the global river basins. [ABSTRACT FROM AUTHOR]

The location-based smartphone service brings new development opportunities for seamless indoor/outdoor positioning. However, in complex scenarios such as cities, tunnels, overpasses, forests, etc., using only GNSS on smartphones cannot provide stable and reliable positioning results. Usually, additional sensors are needed to assist GNSS. This paper investigates the GNSS positioning algorithm assisted by pedestrian dead reckoning (PDR) in complex scenarios. First, we introduce a step detection algorithm based on the peak–valley of acceleration modulus, and the Weinberg model and the Mahony algorithm in PDR are used to estimate step length and heading. On this basis, we evaluated the performance of GNSS/PDR fusion positioning in an open scenario, a semiopen scenario, and a blocked scenario, respectively. Finally, we develop a GNSS/PDR real-time positioning software, called China University of Mining and Technology-POSitioning (CUMT-POS) version 1.0, on the Android 10 platform. By comparing GNSS solutions, PDR solutions, GNSS/PDR solutions, and real-time kinematic (RTK) solutions, we verify the potential auxiliary ability of PDR for GNSS positioning in complex environments, proving that multisource sensor fusion positioning significantly improves reliability and stability. Our research can help the realization of urban informatization and smart cities. [ABSTRACT FROM AUTHOR]

To enhance the positioning accuracy of standalone GNSS receivers in environments unable to provide precise ephemeris and clock offset, such as undeveloped forest areas that lack network communication and power supply, this study employed the Time Difference Carrier Phase (TDCP) technology to improve the positioning accuracy of Standard Point Positioning (SPP), where the Least-Squares (LS) and the extended Multi-Epoch Least Squares (MELS) method were applied in the position domain filtering for a single GNSS receiver and compare its performance with the existing observation domain filtering method. Firstly, the simulated data sets with various positioning accuracies were used to verify the effectiveness and convergence of the LS filtering methods. The results indicate that the LS filtering method produces a lower root mean square (RMS) error than the original strategy. Secondly, this study uses two kinematic GNSS data sets to evaluate the performance of the observation and position domain filtering, with an emphasis on the MELS method. The numerical experiment results show that the position domain LS filtering method outperforms the other two methods. The open environment experiments result shows that the positioning domain filtering method achieved positioning accuracies of 0.202 m, 0.843 m, and 2.036 m in the E, N, and U directions, respectively, with improvements of 68.0%, 21.6%, and 24.0%, compared to the original algorithm which achieved positioning accuracies of 0.631 m, 1.076 m, and 2.680 m. It also achieved improvements of 24.0%, 4.0%, and 18.3%, respectively, compared to the observation domain filtering method with positioning accuracies of 0.353 m, 0.886 m, and 2.526 m. The forest scenes experiments result shows that the positioning domain filtering method achieved positioning accuracies of 1.308 m, 1.375 m, and 2.133 m in the E, N, and U directions, respectively, with improvements of 42.4%, 36.2%, and 27.6%, compared to original algorithm which achieved positioning accuracies of 1.863 m, 1.873 m, and 2.722 m, and also achieved improvements of 27.0%, 19.4% and 10.6%, respectively, comparing to observation domain filtering method with positioning accuracies of 1.661 m, 1.642 m and 2.359 m. Moreover, the examination of the LS method results based on different epochs reveals that the filtering accuracy increases as more epochs are incorporated into the position domain integration and the enhancement value reaches a few millimeters. [ABSTRACT FROM AUTHOR]

Building facades has always been a challenge for feature matching in oblique photogrammetry due to weak textures, non-Lambertian objects, severe occlusion, and distortion. Plumb lines are essential building geometry structural feature lines in building facades, which show strong spatial relevance to these problems. Achieving plumb line matching has great application potential for optimizing the process and products of oblique photogrammetry. Thus, we proposed a novel matching algorithm for plumb lines based on spatial and color hybrid constraints according to its central projection imaging characteristics. Firstly, based on vanishing point theory, the plumb lines from photos were back-calculated to determine the matching target set; secondly, the property of its large elevation ranges was exploited to calculate the homonymous points as spatial constraints by projecting plumb lines onto the stratified spatial planes; thirdly, the neighboring primary colors on both sides of the plumb lines were extracted as feature descriptors and compared by colorimetry; then, the greedy strategy was employed to successively filter out the locally optimal solutions satisfying the spatial and color hybrid constraints to complete the initial matching; finally, the intersection-over-union analysis of the solution plane and the verticalness evaluation of the matching results were implemented to eliminate errors. The results show that the proposed algorithm can achieve an average accuracy of 97.29% and 78.41% in the forward and lateral overlap experiments from multi-scenes, respectively, displaying a strong adaptability to poor texture, inconsistency, and distortion. In conclusion, thanks to the plumb-line-oriented matching strategy, this algorithm owns inherent advantages in theory and computational complexity. It is suitable for all building-oriented oblique photogrammetry tasks and is highly worthy of promotion and application. [ABSTRACT FROM AUTHOR]

The high-precision building exterior facade corner point (BEFCP) is an essential element in topographic and cadastral surveys. However, current extraction methods rely on the interactions of humans with the 3D real-scene models produced by unmanned aerial vehicle (UAV) oblique photogrammetry, which have a high workload, low efficiency, poor precision, and cannot satisfy the requirements of automation. The dense point cloud contains discrete 3D building structure information. Still, it is challenging to accurately filter out the partial point cloud characterizing the building structure from it in order to achieve BEFCP extraction. The BEFCPs are always located on the plumb line of the building's exterior wall. Thus, this paper back-calculated the plumb line from the image and designed a photographic ray corresponding to the image point and point cloud intersection point calculation algorithm to recover its approximate spatial position in order to successfully extract the accurate point cloud in the building structure neighborhood. It then utilized the high signal-to-noise ratio property of the point cloud as a base to eliminate the noise points and, finally, accurately located the building exterior façade corner points by recovering the building structure through segmental linear fitting of the point cloud. The proposed algorithm conducted automated building exterior facade corner point extraction via both of planar-to-stereo and rough-to-precise strategies, reached a 92.06% correctness rate and ±4.5 cm point mean square location error in the experiment, and was able to extract and distinguish the building exterior facade corner points under eaves obstruction and extreme proximity. It is suitable for all high-precision surveying and mapping tasks in building areas based on oblique photogrammetry, which can effectively improve the automation of mapping production. [ABSTRACT FROM AUTHOR]

Physical urban boundaries (PUBs) are basic geographic information data for defining the spatial extent of urban landscapes with non-agricultural land and non-agricultural economic activities. Accurately mapping PUBs provides a spatiotemporal database for urban dynamic monitoring, territorial spatial planning, and ecological environment protection. However, traditional extraction methods often have problems, such as subjective parameter settings and inconsistent cartographic scales, making it difficult to identify PUBs objectively and accurately. To address these problems, we proposed a self-supervised learning approach for PUB extraction. First, we used nighttime light and OpenStreetMap road data to map the initial urban boundary for data preparation. Then, we designed a pretext task of self-supervised learning based on an unsupervised mutation detection algorithm to automatically mine supervised information in unlabeled data, which can avoid subjective human interference. Finally, a downstream task was designed as a supervised learning task in Google Earth Engine to classify urban and non-urban areas using impervious surface density and nighttime light data, which can solve the scale inconsistency problem. Based on the proposed method, we produced a 30 m resolution China PUB dataset containing six years (i.e., 1995, 2000, 2005, 2010, 2015, and 2020). Our PUBs show good agreement with existing products and accurately describe the spatial extent of urban areas, effectively distinguishing urban and non-urban areas. Moreover, we found that the gap between the national per capita GDP and the urban per capita GDP is gradually decreasing, but regional coordinated development and intensive development still need to be strengthened. [ABSTRACT FROM AUTHOR]

Filtering for GRACE temporal gravity fields is a necessary step before calculating surface mass anomalies. In this study, we propose a new denoising and decorrelation kernel (DDK) filtering scheme called adaptive DDK filter. The involved error covariance matrix (ECM) adopts nothing but the monthly time-variable released by several data centers. The signal covariance matrix (SCM) involved is monthly time-variable also. Specifically, it is parameterized into two parameters, namely the regularization coefficient and the power index of signal covariances, which are adaptively determined from the data themselves according to the generalized cross validation (GCV) criterion. The regularization coefficient controls the global constraint on the signal variances of all degrees, while the power index adjusts the attenuation of the signal variances from low to high degrees, namely local constraint. By tuning these two parameters for the monthly SCM, the adaptability to the data and the optimality of filtering strength can be expected. In addition, we also devise a half-weight polygon area (HWPA) of the filter kernel to measure the filtering strength of the anisotropic filter more reasonably. The proposed adaptive DDK filter and filtering strength metric are tested based on CSR GRACE temporal gravity solutions with their ECMs from January 2004 to December 2010. Results show that the selected optimal power indices range from 3.5 to 6.9, with the corresponding regularization parameters range from 1 × 1014 to 5 × 1019. The adaptive DDK filter can retain comparable/more signal amplitude and suppress more high-degree noise than the conventional DDK filters. Compared with the equivalent smoothing radius (ESR) of filtering strength, the HWPA has stronger a distinguishing ability, especially when the filtering strength is similar. [ABSTRACT FROM AUTHOR]

High-frequency and correlated noise filtering is one of the important preprocessing steps for GRACE level-2 products before calculating mass anomaly. Decorrelation and denoising kernel (DDK) filters are usually considered as such optimal filters to solve this problem. In this work, a sparse DDK filter is proposed. This is achieved by replacing Tikhonov regularization in traditional DDK filters with weighted L1 norm regularization. The proposed sparse DDK filter adopts a time-varying error covariance matrix, while the equivalent signal covariance matrix is adaptively determined by the Gravity Recovery and Climate Experiment (GRACE) monthly solution. The covariance matrix of the sparse DDK filtered solution is also developed from the Bayesian and error-propagation perspectives, respectively. Furthermore, we also compare and discuss the properties of different filters. The proposed sparse DDK has all the advantages of traditional filters, such as time-varying, location inhomogeneity, and anisotropy, etc. In addition, the filtered solution is sparse; that is, some high-degree and high-order terms are strictly zeros. This sparsity is beneficial in the following sense: high-degree and high-order sparsity mean that the dominating noise in high-degree and high-order terms is completely suppressed, at a slight cost that the tiny signals of these terms are also discarded. The Center for Space Research (CSR) GRACE monthly solutions and their error covariance matrices, from January 2004 to December 2010, are used to test the performance of the proposed sparse DDK filter. The results show that the sparse DDK can effectively decorrelate and denoise these data. [ABSTRACT FROM AUTHOR]

This paper analyzes the convergence time and the root mean square (RMS) error of single frequency (SF) precise point positioning (PPP) in the ionospheric-constrained (TIC1) and troposphere- and ionospheric-constrained (TIC2) conditions, when the stations are at a low latitude, mid-latitude, and high latitude area during the period of a magnetic storm (MS) and a non-magnetic storm (NMS). In this paper, 375 IGS (international global navigation satellite system (GNSS) service) stations were selected from all over the world for 30 days in September 2017. The 24 hour daily observations were split for each station into 8 data sets of 3 hours each, so that a total of 90,000 tests were carried out. After statistical analysis, it was concluded that: during the MS period, the percentage of TIC2 shortened compared to the TIC1 convergence time, and it was by at least 3.9%, 3.0%, and 9.3% when the station was at global, low latitude, and high latitude areas, respectively. According to the statistical analysis, during the NMS period the convergence time was shortened about at least 12.8%, 11.0%, and 30.0% with respect to the stations in the MS period at global, low, and high latitude areas, respectively. If the station was located in the mid-latitude region, the convergence time was not shortened in some modes. The ionospheric activity in the mid-latitude region was less than that in the low-latitude region, while there were more stations in the mid-latitude region, and the precision of the global ionospheric maps (GIMs) and zenith tropospheric delay (ZTD) products were also slightly higher. Overall, TIC1 and TIC2 have a greater impact on convergence time, but have less impact on positioning accuracy, and only have a greater impact in different environments during the MS and NMS periods. [ABSTRACT FROM AUTHOR]

Currently, indoor locations based on the received signal strength (RSS) of Wi-Fi are attracting more and more attention thanks to the technology's low cost, low power consumption and wide availability in mobile devices. However, the accuracy of Wi-Fi positioning is limited, due to the signal fluctuation and indoor multipath interference. In order to overcome this problem, this paper proposes a robust and accurate Wi-Fi fingerprint location recognition method based on a deep neural network (DNN). A stacked denoising auto-encoder (SDAE) is used to extract robust features from noisy RSS to construct a feature-weighted fingerprint database offline. We use the combination of the weights of posteriori probability and geometric relationship of fingerprint points to calculate the coordinates of unknown points online. In addition, we use constrained Kalman filtering and hidden Markov models (HMM) to smooth and optimize positioning results and overcome the influence of gross error on positioning results, combined with characteristics of user movement in buildings, both dynamic and static. The experiment shows that the DNN is feasible for position recognition, and the method proposed in this paper is more accurate and stable than the commonly used Wi-Fi positioning methods in different scenes. [ABSTRACT FROM AUTHOR]

An increasing number of researchers have conducted in-depth research on the advantages of low-cost single-frequency (SF) receivers, which can effectively use ionospheric information when compared to dual-frequency ionospheric-free combination. However, SF observations are bound to increase the unknown parameters and prolong the convergence time. It is desirable if the convergence time can be reduced by external information constraints, for example atmospheric constraints, which include ionosphere- or troposphere constraints. In this study, ionospheric delay constraints, tropospheric delay constraints, and their dual constraints were considered. Additionally, a total of 18,720 test experiments were performed. First, the nearest-neighbor extrapolation (NENE), bilinear- (BILI), bicubic- (BICU), and Junkins weighted-interpolation (JUNK) method of Global Ionospheric Map (GIM) grid products were analyzed. The statistically verified BILI in the percentage of convergence time, average convergence time, and computation time consumption of them shows a good advantage. Next, the influences of global troposphere- and ionosphere-constrained on the convergence time of SF Precise Point Positioning (PPP) were analyzed. It is verified that the ionosphere-constrained (TIC2) has significant influence on the convergence time in the horizontal and vertical components, while the troposphere-constrained (TIC1) has better effect on the convergence time in the vertical components within some thresholds. Of course, the dual constraint (TIC3) has the shortest average convergence time, which is at least 46.5% shorter in static mode and 5.4% in kinematic mode than standard SF PPP (TIC0). [ABSTRACT FROM AUTHOR]

With the development of global satellite navigation systems, kinematic Precise Point Positioning (PPP) is facing the increasing computational load of instantaneous (single-epoch) processing due to more and more visible satellites. At this time, the satellite selection algorithm that can effectively reduce the computational complexity causes us to consider its application in GPS/BDS/GLONASS kinematic PPP. Considering the characteristics of different systems and satellite selection algorithms, we proposed a new satellite selection approach (NSS model) which includes three different satellite selection algorithms (maximum volume algorithm, fast-rotating partition satellite selection algorithm, and elevation partition satellite selection algorithm). Additionally, the inheritance of ambiguity was also proposed to solve the situation of constantly re-estimated integer ambiguity when the satellite selection algorithm is used in PPP. The results show that the NSS model had a centimeter-level positioning accuracy when the original PPP and optimal dilution of precision (DOP) algorithm solution were compared in kinematic PPP based on the data at five multi-GNSS Experiment (MGEX) stations. It can also reduce a huge amount of computation at the same time. Thus, the application of the NSS model is an effective method to reduce the computational complexity and guarantee the final positioning accuracy in GPS/BDS/GLONASS kinematic PPP. [ABSTRACT FROM AUTHOR]

The integration of Inertial Navigation System (INS) and Global Positioning System (GPS) single-point-positioning (SPP) mode cannot meet the requirements of high-accuracy navigation. Range observation through ultra-wideband (UWB) is an effective means to enhance the reliability and accuracy of GPS/INS integrated navigation, particularly in environments where GPS availability is poor. Because it is difficult for UWB signal to achieve large-scale intervention coverage, an enhanced GPS/INS/UWB integrated scheme with positioning error correction is proposed to improve the position accuracy in the UWB signal outage scenario. The position difference between the GPS/INS integrated solution and the GPS/INS/UWB integrated solution is predicated as the error correction for GPS/INS/UWB integrated navigation in a UWB signal challenging environment. Position correction information in the north and east directions is input to the two-step filter to decrease the error of GPS/INS integrated navigation in single-point-positioning. In order to validate the proposed method, a real experiment is conducted. The results indicate that the enhanced GPS/INS/UWB integrated scheme with positioning error correction is able to improve the position accuracy of GPS/INS/UWB integrated navigation when UWB signal is unavailable. [ABSTRACT FROM AUTHOR]

In the meteorology of Global Navigation Satellite System, the weighted mean temperature (Tm) is a key parameter in the process of converting the zenith wetness delay into precipitable water vapor, and it plays an important role in water vapor monitoring. In this research, two deep learning algorithms, namely, recurrent neural network (RNN) and long short-term memory neural network (LSTM), were used to build a high-precision weighted mean temperature model for China using their excellent time series memory capability. The model needs site location information and measured surface temperature to predict the weighted mean temperature. We used data from 118 stations in and around China provided by the Integrated Global Radiosonde Archive from 2010 to 2015 to train the model and data from 2016 for model testing. The root mean square error (RMSE) of the RNN_Tm and LSTM_Tm models were 3.01 K and 2.89 K, respectively. Compared with the values calculated by the empirical GPT3 model, the accuracy was improved by 31.1% (RNN_Tm) and 33.9% (LSTM_Tm). In addition, we selected another 10 evenly distributed stations in China and used the constructed model to test the prediction capability of the weighted mean temperature from 2010 to 2016. The RMSE values were 2.95 K and 2.86 K, which proved that the model also exhibits high generalization in non-modeling sites in China. In general, the RNN_Tm and LSTM_Tm models have a good performance in weighted mean temperature prediction. [ABSTRACT FROM AUTHOR]

In complex urban environments, a single Global Navigation Satellite System (GNSS) is often not ideal for navigation due to a lack of sufficient visible satellites. Additionally, the heading angle error of a GNSS/micro-electro-mechanical system–grade inertial measurement unit (MIMU) tightly coupled integration based on the single antenna is large, and the attitude angle, velocity, and position calculated therein all have large errors. Considering the above problems, this paper designs a tightly coupled integration of GNSS/MIMU based on two GNSS antennas and proposes a singular value decomposition (SVD)-based robust adaptive cubature Kalman filter (SVD-RACKF) according to the model characteristics of the integration. In this integration, the high-accuracy heading angle of the carrier is obtained through two antennas, and the existing attitude angle information is used as the observation to constrain the filtering estimation. The proposed SVD-RACKF uses SVD to stabilize the numerical accuracy of the recursive filtering. Furthermore, the three-stage equivalent weight function and the adaptive adjustment factor are constructed to suppress the influence of the gross error and the abnormal state on the parameter estimation, respectively. A set of real measured data was employed for testing and analysis. The results show that dual antennas and dual systems can improve the positioning performance of the integrated system to a certain extent, and the proposed SVD-RACKF can accurately detect the gross errors of the observations and effectively suppress them. Compared with the cubature Kalman filter, the proposed filtering algorithm is more robust, with higher accuracy and reliability of parameter estimation. [ABSTRACT FROM AUTHOR]

As one of the atmosphere propagation delays, the tropospheric delay is a significant error source that should be properly handled in high-precision global navigation satellite system (GNSS) applications. We propose an improved zenith tropospheric delay (ZTD) modeling method whereby the piecewise model of the atmospheric refractivity is introduced. Compared with using the exponential model to fit ZTD in vertical direction, the ZTD piecewise model has a better performance. Based on ERA5 2.5° × 2.5° reanalysis data produced by the European Centre for Medium-Range Weather Forecasting (ECMWF) from 2013 to 2017, we establish the regional gridded ZTD model (RGZTD) using a trigonometric function for China and the surrounding areas, which ranges from 70° E to 135° E in longitude and from 15° N to 55° N in latitude. To verify the performance of RGZTD model, the ERA5 ZTD data in 2017–2018, the radiosonde ZTD data from 86 radiosonde stations over China in 2017–2018, and the tropospheric delay products on 251 GNSS stations from Crustal Movement Observation Network of China (CMONOC) in 2016–2017 are used as external compliance check data. The results show that the overall accuracy of RGZTD model is better than that of exponential model, UNB3m model, and GPT3 model. Moreover, the accuracy can be improved by about 13.4%, 7.1%, and 6.2% when ERA5 reanalysis data, radiosonde data, and CMONOC data are used as reference values, respectively. High-accuracy ZTD data can be provided because the RGZTD model takes into account the vertical variation of ZTD through the new piecewise model. [ABSTRACT FROM AUTHOR]

The high noise of pseudorange and the ambiguity of carrier phase observation restrain the GNSS (Global Navigation Satellite System) application in military, industrial, and agricultural, to name a few. Thus, it is crucial for GNSS technology to integrate the pseudorange and carrier phase observations. However, the traditional method proposed by Hatch has obtained only a low convergence speed and precision. For higher convergence speed and precision of the smoothed pseudorange, aiming to improve positioning accuracy and expand the application of GNSS, we introduced a new method named MELS (Multi-Epochs Least-Squares) that considered the cross-correlation of the estimating parameters inspired by DELS (Double-Epochs Least-Square). In this study, the ionospheric delay was compensated, and so its impact was limited to the performance of the filters, and then exploited the various filters to integrate carrier phase observation and pseudorange. We compared the various types of Hatch's filter and LS (Least-Square) methods using simulation datasets, which confirmed that the types of LS method provided a smaller residual error and a faster convergence speed than Hatch's method under various precisions of raw pseudorange. The experimental results from the measured GNSS data showed that LS methods provided better performance than Hatch's methods at E and U directions and a lower accuracy at N direction. Nevertheless, the types of LS method and Hatch's methods improved about 12% and 9–10% at the 3D direction, respectively, which illustrated the accumulating improvement at the enhanced directions was more than the decreased direction, proving that the types of LS method resulted to better performance than the Hatch's filters. Additionally, the curve of residual and precision based on various LS methods illustrated that the MELS only provided a millimeter accuracy difference compared with DELS, which was proved by the simulated and measured GNSS datasets. [ABSTRACT FROM AUTHOR]

Propagation path delays are a major error for the remote precise time transfer of common view; these path delays contain the ionosphere and troposphere impact, while the contributions of the ionosphere and the troposphere from common-view satellites to receivers on the ground tend to become uncorrelated when the distance between these receivers increases. In order to select the appropriate ionospheric correction method for common view under different distances between receivers, a detailed test using multi-source data under different ionosphere disturbances are carried out in this paper. Here, we choose three different ionosphere disturbance methods and analyze the advantages and disadvantages of these methods for common-view time transfer and time comparison. At last, we put forward a suitable ionospheric correction method for different distances common view. The RMS shows that the method proposed for 3000 km remote common view can achieve 2.5 ns. [ABSTRACT FROM AUTHOR]

The initial alignment of the Inertial Measurement Unit (IMU) is an important process of INS to determine the coordinate transformation matrix which is used in the integration of Global Positioning Systems (GPS) with Inertial Navigation Systems (INS). In this paper a novel alignment method for a disturbed base, such as a vehicle disturbed by wind outdoors, implemented with the aid of a Vondrak low pass filter, is proposed. The basic principle of initial alignment including coarse alignment and fine alignment is introduced first. The spectral analysis is processed to compare the differences between the characteristic error of INS force observation on a stationary base and on disturbed bases. In order to reduce the high frequency noise in the force observation more accurately and more easily, a Vondrak low pass filter is constructed based on the spectral analysis result. The genetic algorithms method is introduced to choose the smoothing factor in the Vondrak filter and the corresponding objective condition is built. The architecture of the proposed alignment method with the Vondrak low pass filter is shown. Furthermore, simulated experiments and actual experiments were performed to validate the new algorithm. The results indicate that, compared with the conventional alignment method, the Vondrak filter could eliminate the high frequency noise in the force observation and the proposed alignment method could improve the attitude accuracy. At the same time, only one parameter needs to be set, which makes the proposed method easier to implement than other low-pass filter methods.