郑学理 , 付敬奇 . 基于PDR和RSSI的室内定位算法研究 [J ] . 仪器仪表学报 , 2015 , 36 ( 5 ): 1177 - 1185 .

ZHENG X L , FU J Q . Study on PDR and RSSI based indoor localization algorithm [J ] . Chinese Journal of Scientific Instrument , 2015 , 36 ( 5 ): 1177 - 1185 . (in Chinese)

CHEN G L , MENG X L , WANG Y J , et al . Integrated WiFi/PDR/Smartphone using an unscented Kalman filter algorithm for 3D indoor localization [J ] . Sensors , 2015 , 15 ( 9 ): 24595 - 24614 . DOI: 10.3390/s150924595 http://doi.org/10.3390/s150924595 Because of the high calculation cost and poor performance of a traditional planar map when dealing with complicated indoor geographic information, a WiFi fingerprint indoor positioning system cannot be widely employed on a smartphone platform. By making full use of the hardware sensors embedded in the smartphone, this study proposes an integrated approach to a three-dimensional (3D) indoor positioning system. First, an improved K-means clustering method is adopted to reduce the fingerprint database retrieval time and enhance positioning efficiency. Next, with the mobile phone's acceleration sensor, a new step counting method based on auto-correlation analysis is proposed to achieve cell phone inertial navigation positioning. Furthermore, the integration of WiFi positioning with Pedestrian Dead Reckoning (PDR) obtains higher positional accuracy with the help of the Unscented Kalman Filter algorithm. Finally, a hybrid 3D positioning system based on Unity 3D, which can carry out real-time positioning for targets in 3D scenes, is designed for the fluent operation of mobile terminals.

沈世斌 , 谢非 , 赵静 , 等 . 基于相位控制的惯性与卫星超紧组合导航系统信号解调方法 [J ] . 兵工学报 , 2020 , 41 ( 3 ): 495 - 506 . DOI: 10.3969/j.issn.1000-1093.2020.03.010 http://doi.org/10.3969/j.issn.1000-1093.2020.03.010 卫星导航极易受到复杂环境下的干扰信号影响，捷联惯性导航系统（SINS）与卫星导航系统(GNSS)超紧组合导航技术可提高卫星接收机在信号干扰环境下的工作性能。在对比分析紧组合与超紧组合实现方案及北斗B1信号调制方式的基础上，提出基于相位控制的SINS与GNSS超紧组合环路信号解调方法，进一步分析SINS与GNSS超紧组合环路信号跟踪特性。对卫星信号受干扰环境及动态条件下的相位控制超紧组合与频率控制超紧组合方法的导航性能进行试验对比分析，结果表明相位控制超紧组合方法具有更稳定的定位性能，并可提高约7 dB的抗干扰能力。

SHEN S B , XIE F , ZHAO J , et al . A signal demodulation method for ultra-tightly coupled INS/GNSS navigation system based on phase control [J ] . Acta Armamentarii , 2020 , 41 ( 3 ): 495 - 506 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2020.03.010 http://doi.org/10.3969/j.issn.1000-1093.2020.03.010 Satellite navigation is easily affected by interference signals in a complicated environment. The ultra-tightly coupled strapdown inertial navigation system (SINS)/global navigation satellite system (GNSS) navigation system can improve the anti-jamming performance of receiver. On the basis of analyzing the tight integration and ultra-tight integration implementation schemes and BeiDou B1 signal modulation approach, a loop signal demodulation method of ultra-tight integration based on phase control is proposed.The tracking feature of ultra-tightly coupled SINS/GNSS loop signal is analyzed. The navigation perfor-mances of the proposed ultra-tightly coupled method based on phase control and the traditional method based on frequency control in signal jamming and high dynamic environments were test and compared. The test results indicate that the proposed ultra-tightly coupled method has a more stable positioning performance, and can improve 7 dB anti-jamming capability compared with the tightly coupled method.Key

YU Y , CHEN R Z , CHEN L , et al . A novel 3-D indoor localization algorithm based on BLE and multiple sensors [J ] . IEEE Internet of Things Journal , 2021 , 8 ( 11 ): 9359 - 9372 . DOI: 10.1109/JIOT.2021.3055794 http://doi.org/10.1109/JIOT.2021.3055794 https://ieeexplore.ieee.org/document/9343321/ https://ieeexplore.ieee.org/document/9343321/

JIANG C H , CHEN Y W , XU B , et al . Vector tracking based on factor graph optimization for GNSS NLOS bias estimation and correction [J ] . IEEE Internet of Things Journal , 2022 , 9 ( 17 ): 16209 - 16221 . DOI: 10.1109/JIOT.2022.3150764 http://doi.org/10.1109/JIOT.2022.3150764 https://ieeexplore.ieee.org/document/9711574/ https://ieeexplore.ieee.org/document/9711574/

周瑞 , 罗磊 , 李志强 , 等 . 一种基于智能手机传感器的行人室内定位算法 [J ] . 计算机工程 , 2016 , 42 ( 11 ): 22 - 26 . DOI: 10.3969/j.issn.1000-3428.2016.11.004 http://doi.org/10.3969/j.issn.1000-3428.2016.11.004 智能手机及其内置惯性传感器的普及可实现室内行人航位推算,但是由于人行走的随意性以及智能手机内置传感器精度不高,使定位精度难以满足应用要求。为此,在分析行人行走模式的基础上,基于智能手机传感器提出一种新的行人航位推算算法。对采集到的原始加速度数据进行预处理,采用基于有限状态机的行走状态转换方法识别行走周期并进行计步,利用卡尔曼滤波,结合步长-加速度关系以及连续两步步长之间的关系对步长进行估计。实验结果表明,该算法能够准确计算步数和步长,从而获得精确的室内定位结果。

ZHOU R , LUO L , LI Z Q , et al . An indoor pedestrian positioning algorithm based on smartphone sensor [J ] . Computer Engineering , 2016 , 42 ( 11 ): 22 - 26 . (in Chinese) DOI: 10.3969/j.issn.1000-3428.2016.11.004 http://doi.org/10.3969/j.issn.1000-3428.2016.11.004 Advances on smartphones and built-in inertial sensors have given rise to pedestrian dead reckoning using smartphone sensors.However,an accurate Pedestrian Dead Reckoning(PDR) system using smartphone sensors is not available yet,for smartphone sensors are not accurate enough and pedestrians have natural swings during walking.Based on the analysis of pedestrian walking patterns,a new PDR algorithm using smartphone sensors is proposed.The algorithm first preproccess the original acceleration data,then uses a finite state machine to detect walking gait and thereby counts steps.Step length is estimated by using the relationship between step length and acceleration as well as that between two consecutive steps.And the estimated result is smoothed by Kalman filtering.Experimental results show that the proposed algorithm is able to provide accurate step counts and step length,thus providing accurate location service.

肖烜 , 王清哲 , 程远 , 等 . 捷联惯导系统/里程计高精度紧组合导航算法 [J ] . 兵工学报 , 2012 , 33 ( 4 ): 395 - 400 . 针对惯导系统/里程计构成的组合导航系统，通过对陀螺仪和加速度计零偏、里程计刻度因子、惯性导航系统和里程计之间的姿态误差进行实时估计，实现了惯性导航系统和里程计信息的相互校正，有效提高了系统测量精度；同时，针对复杂应用环境下里程计测量信息不准而导致的组合导航系统精度下降的问题，利用卡尔曼滤波信息实现故障检测和隔离，从而有效提高了系统导航精度。

XIAO X , WANG Q Z , CHENG Y , et al . High accuracy navigation algorithm for tightly coupled INS/Odometer [J ] . Acta Armamentarii , 2012 , 33 ( 4 ): 395 - 400 . (in Chinese) According to the integrated navigation system which consists of inertial navigation system (INS) and odometer, the cross calibration of INS and odometer were achieved by estimating the biases of inertial sensors, scale factor of odometer, and attitude error between INS and odometer in real-time. The above tasks were resolved by a closed-loop Kalman filter, which can easily use the estimates to compensate INS and odometer. An integrated supervisory system was constructed to detect and isolate the bad data when a vehicle run in a complex environment. It helps to improve the accuracy of navigation system.

刘明雍 , 胡俊伟 , 李闻白 . 一种基于改进无迹卡尔曼滤波的自主水下航行器组合导航方法研究 [J ] . 兵工学报 , 2011 , 32 ( 2 ): 252 - 256 . 针对自主水下航行器（AUV）导航系统对稳定性、精确性针对自主水下航行器（AUV）导航系统对稳定性、精确性和实时性的需求，提出了一种基于改进无迹卡尔曼滤波(UKF)算法的捷联惯性导航系统/多普勒测速仪(SINS/DVL)组合导航新方法。通过分析中低精度组合导航系统的特点和误差模型，在系统的噪声模型为复杂加性噪声时，利用球面分布单形采样变换设计了一种简化UKF组合导航算法。仿真结果表明：与常规的比例对称采样UKF算法相比，在不损失导航系统滤波精度的情况下，基于单形采样变换的简化UKF算法有效降低了系统的计算复杂度，提高了滤波解算效率。

LIU M Y , HU J W , LI W B . Research on integrated navigation for autonomous underwater vehicle based on an improved unscented kalman filter [J ] . Acta Armamentarii , 2011 , 32 ( 2 ): 252 - 256 . (in Chinese)

徐昊玮 , 廉保旺 , 刘尚波 . 基于滑动窗迭代最大后验估计的多源组合导航因子图融合算法 [J ] . 兵工学报 , 2019 , 40 ( 4 ): 807 - 819 . DOI: 10.3969/j.issn.1000-1093.2019.04.016 http://doi.org/10.3969/j.issn.1000-1093.2019.04.016 在应用因子图算法完成多源组合导航数据融合的过程中，子系统观测噪声的时变特性将对导航状态估计的准确性产生极大影响。为解决这一问题，提出一种基于高斯模型下的子系统观测量均值向量和协方差矩阵的估计算法。该算法利用因子图最优化过程中每个迭代周期下的观测量残差，实时地更新各个子系统观测量的均值向量和协方差矩阵的最大后验估计值，从而得到更加准确的导航状态估计值，在提出新算法的同时也验证了新算法对最优化过程收敛性的影响。仿真测试与实验测试结果表明，与已有的标准因子图算法、基于最大似然估计的因子图算法和基于最大后验估计的因子图算法相比，所提出的基于迭代最大后验估计的因子图算法能够有效提高子系统观测状态变化时的多源组合导航估计精度。

XU H W , LIAN B W , LIU S B . Multi-source integrated navigation algorithm for iterated maximum posteriori estimation based on sliding-window factor graph [J ] . Acta Armamentarii , 2019 , 40 ( 4 ): 807 - 819 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2019.04.016 http://doi.org/10.3969/j.issn.1000-1093.2019.04.016 In the process of data fusion in multi-source integrated navigation using factor graph, the time-varying characteristics of the subsystem's observed noise have a great influence on the estimation accuracy of navigation state. In order to solve the problem, a Gaussian model-based method to estimate the mean vector and covariance matrix of sub-system observation is proposed. In the proposed method, the observed-measurement residuals for each iterative cycle in the process of factor graph optimization are utilized to update the maximum posteriori estimated values of mean vectors and covariance matrices. A more accurate estimated value of navigation state can be obtained by estimating the sub-system noise state. The influence of the new algorithm on the convergence of optimization process was also deduced. Both the simulated and experimental results show that, compared with the existing algorithms as factor graph, maximum likelihood estimation based factor graph and maximum posteriori based factor graph, the proposed factor graph method based on iterative maximum posteriori estimation can effectively improve the accuracy of navigation estimation when the subsystem observing state varies. Key

SUN R , ZHANG Z X , CHENG Q , et al . Pseudorange error prediction for adaptive tightly coupled GNSS/IMU navigation in urban areas [J ] . GPS Solutions , 2022 , 26 ( 1 ): 1 - 13 . DOI: 10.1007/s10291-021-01184-1 http://doi.org/10.1007/s10291-021-01184-1

吴有龙 , 王晓鸣 , 曹鹏 . 抗差估计及Allan方差在车载组合导航系统中的应用研究 [J ] . 兵工学报 , 2013 , 34 ( 7 ): 889 - 895 . DOI: 10. 3969/ j. issn. 1000-1093. 2013. 07. 015 http://doi.org/10. 3969/ j. issn. 1000-1093. 2013. 07. 015 针对组合导航系统中全球定位系统(GPS)信号易丢失和干扰、惯性导航系统(INS)无法长时间单独工作的问题,通过采用带故障检测和隔离的导航算法解决GPS 数据异常的问题,有效提高系统的可靠性;同时当GPS 卫星信号短时间丢失时,利用Allan 方差分析方法确定惯性传感器误差并进行补偿,使纯INS 能够在一定精度内独立工作相对长的一段时间。车载试验结果表明:该方法能够保证组合导航系统的可靠性,且在GPS 信号短时间丢失情况下提高了纯惯导系统的导航性能。

WU Y L , WANG X M , CAO P . The application of robust estimation and allan variance method in land vehicle navigation [J ] . Acta Armamentarii , 2013 , 34 ( 7 ): 889 - 895 . (in Chinese)

黄欣 , 熊智 , 许建新 , 等 . 基于零速/航向自观测/地磁匹配的行人导航算法研究 [J ] . 兵工学报 , 2017 , 38 ( 10 ): 2031 - 2040 . DOI: 10.3969/j.issn.1000-1093.2017.10.020 http://doi.org/10.3969/j.issn.1000-1093.2017.10.020 目前行人导航技术正发挥着越来越重要的作用，而无全球导航卫星系统（GNSS）环境下的行人导航定位成为其不可或缺的环节。以自包含传感器为硬件平台，针对无GNSS环境下的行人自主导航定位展开研究，提出一种基于“2+2”分级模式的零速判别方法，并设计一种惯性导航系统的零速修正卡尔曼滤波算法，有效提高同一参数阈值下零速判别的准确性与可靠性、抑制传感器误差发散；研究行人初始静态下磁航向误差观测算法及行人运动状态下的零速航向误差自观测算法，解决了行人长时间行走航向发散问题；提出基于多层约束和K近邻算法的地磁匹配算法，并实现基于零速修正/航向误差自观测的行人导航算法与地磁匹配算法的融合，提高了行人导航定位精度与可靠性。实际数据测试验证，所提基于零速修正/航向误差自观测/地磁匹配的行人导航算法可有效提高定位精度79%以上。

HUANG X , XIONG Z , XU J X , et al . Research on pedestrian navigation algorithm based on zero velocity update/heading error self-observation/geomagnetic matching [J ] . Acta Armamentarii , 2017 , 38 ( 10 ): 2031 - 2040 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2017.10.020 http://doi.org/10.3969/j.issn.1000-1093.2017.10.020 Nowadays, pedestrian navigation technology is playing an increasingly important role in supermarket shopping, fire rescue and field exploration, and the pedestrian navigation and positioning without global navigation satellite system (GNSS) has become an indispensable link. The self-contained sensors are used as a hardware platform for research on pedestrian autonomous navigation in non-GNSS environment. A zero-speed comprehensive discriminant algorithm based on the “2+2” hierarchical model is studied to improve the accuracy and reliability of zero velocity update (ZUPT). Kalman filter algorithm based on ZUPT designed for inertial navigation system is used to effectively suppress the sensor error divergence. To solve the problem of pedestrian long-term heading divergence, the magnetic heading error self-observation algorithm (MHESO) for pedestrian initial static state and the ZUPT heading error self-observation algorithm (ZHESO) for pedestrian movement are studied. In addition, a geomagnetic matching (GM) algorithm based on multi-layer constraint and K-nearest neighbor algorithm is proposed, and the fusion of ZUPT_HESO-pedestrian navigation algorithm and geomagnetic matching algorithm is realized, which improves the accuracy and reliability of pedestrian navigation. The actual data test proves that the proposed pedestrian navigation algorithm based on ZUPT_HESO_GM effectively improves the positioning accuracy by more than 79%. Key

KUANG J , NIU X J , CHEN X G . Robust pedestrian dead reckoning based on MEMS-IMU for smartphones [J ] . Sensors , 2018 , 18 ( 5 ): 1391 . DOI: 10.3390/s18051391 http://doi.org/10.3390/s18051391 http://www.mdpi.com/1424-8220/18/5/1391 http://www.mdpi.com/1424-8220/18/5/1391

LI X H , WEI D Y , LAI Q F , et al . Smartphone-based integrated PDR/GPS/Bluetooth pedestrian location [J ] . Advances in Space Research , 2017 , 59 ( 3 ): 877 - 887 . DOI: 10.1016/j.asr.2016.09.010 http://doi.org/10.1016/j.asr.2016.09.010 https://linkinghub.elsevier.com/retrieve/pii/S0273117716305233 https://linkinghub.elsevier.com/retrieve/pii/S0273117716305233

YE J H , LI Y X , LUO H , et al . Hybrid urban canyon pedestrian navigation scheme combined PDR, GNSS and beacon based on smartphone [J ] . Remote Sensing , 2019 , 11 ( 18 ): 2174 . DOI: 10.3390/rs11182174 http://doi.org/10.3390/rs11182174 https://www.mdpi.com/2072-4292/11/18/2174 https://www.mdpi.com/2072-4292/11/18/2174 This study presents a comprehensive urban canyon pedestrian navigation scheme. This scheme combines smart phone internal MEMS sensors, GNSS and beacon observations together. Heading estimation is generally a key issue of the PDR algorithm. We design an orientation fusion algorithm to improve smart phone heading using MEMS measurements. Static and kinematic tests are performed, superiority of the improved heading algorithm is verified. We also present different heading processing solutions for comparison and analysis. Heading bias increases with time due to error accumulation and model inaccuracy. Thus, we develop a related heading calibration method based on beacons. This method can help correct smart phone headings continuously to decrease cumulative error. In addition to PDR, we also use GNSS and beacon measurements to integrate a fusion location. In the fusion procedure, we design related algorithms to adjust or limit the use of these different type observations to constrain large jumps in our Kalman filter model, thereby making the solution stable. Navigation experiments are performed in the streets of Mong Kok and Wanchai, which are typically the most crowded areas of Hong Kong, with narrow streets and many pedestrians, vehicles and tall buildings. The first experiment uses the strategy PDR + GNSS + beacon, in east–west orientation street, in which 10 m positioning error is improved from 30 % (smart phone internal GNSS) to 80 % and in south–north orientation street, in which 15 m positioning error is improved from 20 % (smart phone internal GNSS) to 80 %. The second experiment performs two long-distance tests without any beacons, in which the fusion scheme also has significant improvement, that is, 10 m positioning error is improved from 38 % to 60 %.

HSU L T , GU Y L , KAMIJO S . Sensor integration of 3D map aided GNSS and smartphone PDR in urban canyon with dense foliage [C ] // Proceedings of IEEE/ION PLANS 2016. Savannah,GA,US:IEEE , 2016 : 85 - 90 .

REHMAN A , LIU Q , WU Z D , et al . PDR/GNSS fusion algorithm based on joint heading estimation [C ] // Proceedings of China Satellite Navigation Conference. Singapore:Springer , 2019 : 326 - 339 .

HOU X Y , BERGMANN J . Pedestrian dead reckoning with wearable sensors: a systematic review [J ] . IEEE Sensors Journal , 2022 , 21 ( 1 ): 143 - 152 . DOI: 10.1109/JSEN.7361 http://doi.org/10.1109/JSEN.7361 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=7361 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=7361

JIANG C H , CHEN Y W , CHEN C , et al . Implementation and performance analysis of the PDR/GNSS integration on a smartphone [J ] . GPS Solutions , 2022 , 26 : 81 . DOI: 10.1007/s10291-022-01260-0 http://doi.org/10.1007/s10291-022-01260-0 Pedestrian dead reckoning (PDR) is an effective technology for pedestrian navigation. In PDR, the steps are detected with the measurements of self-contained sensors, such as accelerometers, and the position is updated with additional heading angles. A smartphone is usually equipped with a low-cost microelectromechanical system accelerometer, which can be utilized to implement PDR for pedestrian navigation. Since the PDR position errors diverge with the walking distance, the global navigation satellite system (GNSS) is usually integrated with PDR for more reliable position results. This paper implemented a smartphone PDR/GNSS via a Kalman filter and factor graph optimization (FGO). In the FGO, the PDR factor is modeled, and the states are correlated with a dead reckoning algorithm. The GNSS position is modeled as the “GNSS” factor to constrain the states at each step. With a graphic model representing the states and measurements, the state estimation is converted to a nonlinear least square problem, and we utilize the Georgia Tech Smoothing and Mapping graph optimization library to implement the optimization. We tested the proposed method on a Huawei Mate 40 Pro handset with a standard playground field test, and the field test results showed that the FGO effectively improved the smartphone position accuracy. We have released the source codes and hope that they will inspire other works on pedestrian navigation, i.e., constructing an adaptive multi-sensor integration system using FGO on a smartphone.

JIANG C H , CHEN S , CHEN Y W , et al . GNSS vector tracking method using graph optimization [J ] . IEEE Transactions on Circuits and Systems II:Express Briefs , 2020 , 68 ( 4 ): 1313 - 1317 .

JIANG C H , CHEN S , CHEN Y W , et al . Superior position estimation based on optimization in GNSS [J ] . IEEE Communications Letters , 2020 , 25 ( 2 ): 479 - 483 . DOI: 10.1109/COML.4234 http://doi.org/10.1109/COML.4234 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4234 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4234