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A closed-form formula for GPS GDOP computation 总被引:5,自引:2,他引:5
Shing H. Doong 《GPS Solutions》2009,13(3):183-190
Geometric dilution of precision (GDOP) is often used for selecting good satellites to meet the desired positioning precision.
An efficient closed-form formula for GDOP has been developed when exactly four satellites are used. It has been proved that
increasing the number of satellites for positioning will always reduce the GDOP. Since most GPS receivers today can receive
signals from more than four satellites, it is desirable to compute GDOP efficiently for the general case. Previous studies
have partially solved this problem with artificial neural network (ANN). Though ANN is a powerful function approximation technique,
it needs costly training and the trained model may not be applicable to data deviating too much from the training data. Using
Newton’s identities from the theory of symmetric polynomials, this paper presents a simple closed-form formula for computing
GDOP with the inputs used in previous studies. These inputs include traces of the measurement matrix and its second and third
powers, and the determinant of the matrix. 相似文献
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天文定位是一种重要的导航定位方法,被广泛应用于大地天文测量、天文航海等领域。该方法中观测恒星的选择会影响最终的定位精度,目前缺少针对同时测定经纬度天文定位算法中最优选星问题的研究。随着观测仪器自动化水平的提高,观测数据的获取变得更加高效,这就要求研究最优的选星方案以达到最高的定位精度。本文借鉴卫星导航中几何精度衰减因子GDOP的概念,研究了天顶距法中恒星的数量以及分布对定位精度的影响,最后通过仿真试验和实测数据验证得到结论:在天顶距观测误差的统计特性一定时,GDOP能够用来描述恒星的分布对定位结果影响的优劣,且观测的恒星方位角均匀分布时定位误差最小。考虑到不同高度的恒星天顶距大气折射改正残差不同,在实际测量中应尽量采用等天顶距且方位角均匀分布的恒星。 相似文献
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A closed-form of Newton method for solving over-determined pseudo-distance equations 总被引:3,自引:0,他引:3
The Newton method has been widely used for solving nonlinear least-squares problem. In geodetic adjustment, one would prefer to use the Gauss–Newton method because of the parallel with linear least-squares problem. However, it is proved in theory as well as in practice that the Gauss–Newton method has slow convergence rate and low success rate. In this paper, the over-determined pseudo-distance equations are solved by nonlinear methods. At first, the convergence of decent methods is discussed after introducing the conditional equation of nonlinear least squares. Then, a compacted form of the Hessian matrix from the second partial derivates of the pseudo-distance equations is given, and a closed-form of Newton method is presented using the compacted Hessian matrix to save the computation and storage required by Newton method. At last, some numerical examples to investigate the convergence and success rate of the proposed method are designed and performed. The performance of the closed-form of Newton method is compared with the Gauss–Newton method as well as the regularization method. The results show that the closed-form of Newton method has good performances even for dealing with ill-posed problems while a great amount of computation is saved. 相似文献
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The incorrectness in the derivations of error formula (52) in Zhang's paper is pointed out and the correction is given. Table
3 [list of error formulae of Eqs (5)–(8)] in Zhang's paper is also corrected.
Received: 25 February 1998 / Accepted: 30 June 1998 相似文献
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Yanyan Liu Yidong Lou Shirong Ye Rui Zhang Weiwei Song Xing Zhang Qingquan Li 《GPS Solutions》2017,21(4):1647-1659
Although integer ambiguity resolution (IAR) can improve positioning accuracy considerably and shorten the convergence time of precise point positioning (PPP), it requires an initialization time of over 30 min. With the full operation of GLONASS globally and BDS in the Asia–Pacific region, it is necessary to assess the PPP–IAR performance by simultaneous fixing of GPS, GLONASS, and BDS ambiguities. This study proposed a GPS + GLONASS + BDS combined PPP–IAR strategy and processed PPP–IAR kinematically and statically using one week of data collected at 20 static stations. The undifferenced wide- and narrow-lane fractional cycle biases for GPS, GLONASS, and BDS were estimated using a regional network, and undifferenced PPP ambiguity resolution was performed to assess the contribution of multi-GNSSs. Generally, over 99% of a posteriori residuals of wide-lane ambiguities were within ±0.25 cycles for both GPS and BDS, while the value was 91.5% for GLONASS. Over 96% of narrow-lane residuals were within ±0.15 cycles for GPS, GLONASS, and BDS. For kinematic PPP with a 10-min observation time, only 16.2% of all cases could be fixed with GPS alone. However, adding GLONASS improved the percentage considerably to 75.9%, and it reached 90.0% when using GPS + GLONASS + BDS. Not all epochs could be fixed with a correct set of ambiguities; therefore, we defined the ratio of the number of epochs with correctly fixed ambiguities to the number of all fixed epochs as the correct fixing rate (CFR). Because partial ambiguity fixing was used, when more than five ambiguities were fixed correctly, we considered the epoch correctly fixed. For the small ratio criteria of 2.0, the CFR improved considerably from 51.7% for GPS alone, to 98.3% when using GPS + GLONASS + BDS combined solutions. 相似文献
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Nunzia Giorgia Ferrara Mohammad Zahidul H. Bhuiyan Stefan Söderholm Laura Ruotsalainen Heidi Kuusniemi 《GPS Solutions》2018,22(4):106
Due to the very low power of satellite signals when reaching the earth’s surface, global navigation satellite system receivers are vulnerable to various types of radio frequency interference, and, therefore, countermeasures are necessary. In the case of a narrowband interference (NBI), the adaptive notch filtering technique has been extensively investigated. However, the research on the topic has focused on the adaptation of the notch frequency, but not of the notch width. We present a fully adaptive solution to counter NBI. The technique is capable of detecting and characterizing any number of narrow interfered bands, and then optimizing the mitigation process based on such characterization, namely the estimates of both interference frequency and width. Its full adaptiveness makes it suitable to cope with the unpredictable and diverse nature of unintentional interfering events. In addition to a thorough performance evaluation of the proposed method, which shows its benefits in terms of signal quality improvement, an analysis of the impact of different NBI profiles on GPS L1 C/A and Galileo E1 is also conducted. 相似文献
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Changyou Zhang 《Journal of Geodesy》1995,70(1-2):51-64
A general formula is developed and presented for transformations among geoidal undulation, gravity anomaly, gravity disturbance and other gravimetric quantities. Using a spectral form of the general formula, a criterion has been built in order to classify these transformations into forward and inverse transformations in this paper. Then, the two-dimensional convolution techniques are applied to the general formula to deal with the forward transformation while the two-dimensional deconvolution techniques are employed to treat the inverse transformation and evaluate the inverse general formula. Concepts of convolution and deconvolution are also reviewed in this paper. The stability and edge effect problems related to the deconvolution techniques are investigated using simulated data and numerical tests are done to quantify the stability of the deconvolution techniques for estimated gravity information. Finally, the marine gravity information for the Norwegian-Greenland Sea area has been derived from ERS-1 altimetry data using the deconvolution techniques. 相似文献
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Journal of Geodesy - ?The application of Stokes' formula to create geoid undulations requires no masses outside the geoid. However, due to the existence of the topography, terrain... 相似文献
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Cheinway Hwang 《Journal of Geodesy》1995,70(1-2):110-116
The product of two associated Legendre functions can be represented by a finite series in associated Legendre functions with unique coefficients. In this study a method is proposed to compute the coefficients in this product-sum formula. The method is of recursive nature and is based on the straightforward polynomial form of the associated Legendre function's factor. The method is verified through the computation of integrals of products of two associated Legendre functions over a given interval and the computation of integrals of products of two Legendre polynomials over [0,1]. These coefficients are basically constant and can be used in any future related applications. A table containing the coefficients up to degree 5 is given for ready reference. 相似文献
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We propose a method for geometric areal object matching based on multi‐criteria decision making. To enable this method, we focused on determining the matched areal object pairs that have all relations, one‐to‐one relationships to many‐to‐many relationships, in different spatial data sets by fusing geometric criteria without user invention. First, we identified candidate corresponding areal object pairs with a graph‐based approach in training data. Second, three matching criteria (areal hausdorff distance, intersection ratio, and turning function distance) were calculated in candidate corresponding pairs and these criteria were normalized. Third, the shape similarity was calculated by weighted linear combination using the normalized matching criteria (similarities) with the criteria importance through intercriteria correlation method. Fourth, a threshold (0.738) of the shape similarity estimated in the plot of precision versus recall versus all possible thresholds of training data was applied, and the matched pairs were determined and identified. Finally, we visually validated the detection of similar areal feature pairs and conducted statistical evaluation using precision, recall, and F‐measure values from a confusion matrix. Their values were 0.905, 0.848, and 0.876, respectively. These results validate that the proposed classifier, which detects 87.6% of matched areal pairs, is highly accurate. 相似文献