基于移动参考站的GPS动态相对定位算法研究
|
摘要
相对于一个移动参考站的GPS动态相对定位简称为动对动定位,具有广泛应用,如舰队管理、战场指挥、编队飞行、运动车辆相对定位、卫对卫定轨、飞行器安全接近、载体免撞、自动驾驶等。在这些场合中难以建立不动的参考站,传统定位方法(比如雷达/激光测距),或是精度不高或是限制条件严格,不能完全满足要求。在这些应用中,物体的绝对位置重要性远小于相对位置的重要性,因此有精确已知坐标的参考站的配置不是强求的,而高的相对定位精度和可靠性是必须的。大多数相对定位方法假定参考站的精密位置是预先给定的,因此,相对定位精度主要依赖于测量误差。然而,在动对动定位中,这一先决条件是没有的,因此那些已有算法难以直接用于动对动定位,需要作适当修改,本文将对此作深入研究。
高精度动对动定位需要使用载波相位观测值,当平台间距离很短,双差处理可以削弱相位观测值中的空间相关误差,卫星和接收机钟差可以消除掉。当残余误差很小,模糊度固定后定位精度可以达到厘米级。高精度相对定位主要地依赖于模糊度成功解算及模糊度保持为常数,然而,在动态情形下,由于接收机振荡器、遮挡和多路径等因素会引起周跳,即相位观测值的整周跳跃,周跳改变了相位观测值表达的距离值进而影响了以相位为基础的定位精度,因此,整周模糊度解算和周跳探测与修复是高精度动对动定位的核心问题。
观测值是用来获得所需要的参数,由于观测值含有偏差和误差,为了削弱误差的影响和提高解的精度,需要有多余观测数,即实际的独立观测值数多于估计未知参数所必须的观测值数。由于误差存在使得观测值间不相容,为了消除不相容并获得待估参数,通常要应用最小二乘估计,即残差平方和加权最小原理。由于最小二乘估计仅能处理线性系统,而所需的流动站坐标未知参数包含在站星几何距离中,观测方程线性化就是GPS数据处理的基本内容。在现有的参考文献中,所给出的线性化方式可以分为两类,一是以流动站坐标为参数进行线性化,未知参数是流动站坐标改正量;另一线性化方法是以流动站到参考站的基线向量为参数,未知参数是基线向量的改正数。前一种线性化方法无疑作了三个前提假设:参考站坐标精确已知、参考站坐标与观测数据在同一坐标系、流动站近似坐标也在同一坐标系中。显然,在动对动定位中,以上假设是不存在的,因此以测站坐标为参数线性化单差、双差观测方程是不行的。后一种线性化方法在有的参考文献中介绍了很复杂的双差观测方程线性化推导过程,为此,本文给出了一种简单易行的观测方程线性化方法,在此基础上指出了动对动定位与其它定位模式在方程线性化方面的不同与相同之处。
On-the-fly GPS positioning relative to a moving reference, referred to as KINRTK in, this thesis, has many applications, such as fleet management, battlefield command, formation flying, vehicles positioning, satellite-to-satellite orbit determination, aerocraft safety approach, and others, where a static reference is difficult to establish. In this application, the absolute positions of the objects are not important but rather their relative positions, so that the configuration of the reference station with precisely known coordinates is not mandatory. High relative positioning accuracy and reliability are required. Most of the existing methods of relative positioning assume that the precise position of a reference station is given a priori. Thus, the accuracy of the relative positioning only depends on the measurement errors. However, in this research, such a precondition is not given. Therefore, those previous approaches cannot be directly used for this research. Modifications are required to process the kinematic data simultaneously. The impact of these modifications on the effectiveness of relative positioning is to be investigated in this thesis.To achieve high positioning accuracy, the double-differenced GPS carrier phase method is usually adopted. When the inter-platform distances are short, e.g., less than 10 km, double differencing can largely reduce spatially correlated errors in the carrier phase measurements. Satellite and receiver clock errors are cancelled, regardless of the inter-platform distance. When the remaining errors are small, centimeter-level accuracy relative positions can be obtained with fixed integer ambiguities. High accuracy relative positioning depends mostly on successful integer ambiguity resolution of the double-differenced carrier phase measurements. Before the carrier phase observable can be utilized as a precise range information its inherent integer cycle ambiguity must be resolved and carrier phase positioning rely on the ambiguities being constant. Unfortunately, high user dynamics, the receiver's oscillator, shadowing and multipath can cause cycle slips, i.e. jumps of the carrier phase observable by an integer multiple of wavelengths. Every cycle slip would deteriorate the high accuracy of the affected carrier phase range and also that of the position derived from such carrier phase observables. Therefore, integer ambiguity resolution and cycle slips detection and repairing are two of the crucial problems to resolve for high accuracy relative positioning.Observations are made to derive certain parameters. However, observations often contain biases and errors. To reduce the effect of the errors and assess the accuracy of the solution, redundancy is required. That is, more than the minimum number of observations is required to determine the estimated parameters. These observations must be adjusted so that the solution will be consistent with these adjusted observations. To adjust observations and to obtain the desired parameters, the method of least-squares estimation is often used. In least-squares estimation, parameters and corrected observations are derived by minimizing the weighted sum of the squared residuals. As well known, least-squares estimation can only process a linear system, while the desired parameters, rover station coordinates, are contained in the geometric range between the satellite and the receiver
antenna. Therefore, linearization is the basic work in GPS data processing. Two modes of linearization can be found in the GPS literature. In the first approach, observation equation is linearized by rover station coordinates, whose estimated parameters are the correction to the approximated station coordinates. The other one linearizes the equations with baseline vector between rover station and the reference, whose estimated parameters are the correction to the approximated baseline vector. There are three presupposition assumptions in the former approach, i.e., known precise reference station coordinates, the coordinates and observables are in the same coordinate system, and the approximated rover station coordinates are also in the system. Obviously, these assumptions do not exist in KINRTK, and the equation must be linearized by the latter. A simple and efficient linearization method is presented, and the differences between KINRTK and other GPS positioning modes are analyzed.Most receivers attempt to keep their internal clocks synchronized to GPS Time. This is done by periodically adjusting the clock by inserting time jumps. Two typical examples of receiver clock jumps exist in different manufacturer's receivers. The first example is a millisecond jump which occurs when the clock offset becomes larger than ± 1 millisecond, the receiver corrects the clock by ± 1 millisecond. The second example is a very small clock jump which occurs every second and the jumps are often small. At the moment of the clock correction, two main effects are transferred into the code and phase observables. The effects of the geometric range corresponding to the clock jump are common to all measurements at the moment of the clock jump at one receiver. By single-differencing (SD) the measurements between satellites or double-differencing (DD) the measurements (that is, differencing between receivers followed by differencing between satellites or vice versa), the common effects can be removed. However, the effects of the geometric range rate corresponding to the jump are different for each observation. They cannot be removed by the SD or DD operation. However, like cycle slips, their effects on the code and phase observables are more or less known to users and hence it is possible to detect and remove their effects almost completely in both the measurement and parameter domains.The quality of GPS positioning is dependent on a number of factors. For attaining high-precision positioning results, we need to identify the main error sources impacting on the quality of the observations. In terms of data processing, cycle slips, receiver clock jumps and quasi-random errors are the main sources which can deteriorate the quality of the observations and subsequently, the quality of positioning results. Cycle slips are discontinuities of an integer number of cycles in the measured (integrated) carrier phase resulting from a temporary loss-of-lock in the carrier tracking loop of a GPS receiver. In this event, the integer counter is reinitialized which causes a jump in the instantaneous accumulated phase by an integer number of cycles. The detection and correction of cycle slips is needed if accurate positioning is to be carried out. Cycle slip detection and correction requires the location of the jump and the determination of its size. It can be completely removed once it is correctly detected and identified. Slip detection and repair still represents a challenge to carrier phase data processing even after years of research. For completeness, a short description of the development of strategies for detecting and determining cycle slips over the past two decades or so is presented. For the most part, techniques used in the detection and determination of cycle slips have not changed drastically since the first methods were devised in the early 1980s. The focus has always
been on attempting to develop a reliable, somewhat automatic detection and repair procedure. All methods have the common premise that to detect a slip at least one smooth (i.e., low noise) quantity derived from the observations must be tested in some manner for discontinuities that may represent cycle slips. The derived quantities usually consist of linear combinations of the undifferenced or double-differenced L1 and L2 carrier-phase and possibly pseudorange observations. Examples of combinations useful for kinematic data are. the geometry-free phase (a scaled version of which is called the ionospheric phase delay), and widelane phase minus narrowlane pseudorange. Once the time series for the derived quantities have been produced, the cycle-slip detection process (that is, the detection of discontinuities in the time series) can be initiated. Of the various methods available, a novel approach, called Non-integer Linear Combination (NLC), is proposed.Time-relative positioning is a recently developed method for processing GPS observations. Observe first carrier phases at a station of known coordinates (a geodetic point, for example) for a short period of time (1-2 min). Preferably, the observation rate must be high—e.g., 1 s. The user then moves the receiver and the antenna quickly (e.g., 30 s) toward the station of unknown coordinates located about a hundred meters (depending on the type of transportation) away from the first one, while continuously observing carrier phases. At the second station, phase observations are recorded again for a short period of time (1-2 min). Relative positioning is then obtained by processing carrier phase observations taken at different epochs (and different stations)with a single GPS receiver. The main distinction between time-relative positioning and conventional relative positioning is that in the former there is a combination of observations taken at two different epochs and two different stations with the same receiver to detennine the position of the unknown station with respect to the known station. In other words, simultaneous observations using a second GPS receiver at a reference station are not required, unlike conventional relative positioning. The disadvantage of time-relative positioning compared to conventional relative positioning is that, since observations at both stations are not obtained simultaneously, it is also affected by the temporal "decorrelation" of errors (time variation of errors) in addition to the spatial "decorrelation" of errors also present in conventional relative positioning. In most GPS applications, regardless of surveying modes (static and kinematic) and baseline lengths (short, medium and long), the effects of the epoch-differenced biases and noise (i.e., atmospheric delay, satellite orbit bias, multipath, and receiver system noise) are more or less below a few centimetres as long as observation sampling interval is relatively short (e.g., sampling interval less than 1 minute). Based on high sampling interval assumption, time-relative positioning observation equation is further analyzed, the concept of virtual measurement is applied, which results in a robust linearization scheme. A new cycle slip detection approach based on time-relative positioning theory is studied for the first time, and valuable unrecognized knowledge of relation between satellites geometry and cycle slip detection is obtained.GPS carrier phase positioning has a higher accuracy than code positioning, assuming the integer ambiguity is correctly fixed. OTF ambiguity resolution refers to the case when the ambiguities are resolved when at least one receiver is moving, i.e., when the receiver is in kinematic mode. It differs from the static ambiguity resolution in two ways: In kinematic applications, errors of measurement cannot be reduced by time averaging because the movement of platforms can significantly change the testing environment; In kinematic
applications, the position and velocity of the object is required for every epoch, so the batch processing cannot be adopted if real-time processing is required. Since less information is available and larger errors occur, OTF ambiguity resolution is more difficult in kinematic than in static mode. Here are some major factors affecting the OTF ambiguity resolution: Selection of observables; Inter-receiver distance; Number and geometry of satellites; Magnitude of GPS errors; Ambiguity search method; Performance required, etc. The major challenges of OTF ambiguity resolution are relative error modeling, and the efficiency and reliability of the ambiguity search technique. There are many methods that have been developed for solving On-The-Fly (OTF) ambiguity since the 1980's. Basically, they have the same strategies to fix ambiguities, namely, float ambiguity resolution, integer ambiguity searching, and the use of a distinguishing test. The float ambiguity and its variance are used to define the initial search point, and the search range of the integer candidates. Therefore, float solution is more important than anything else in ambiguity resolution. In static mode, float solution can be obtained by only processing carrier phase observables, while in the KINRTK application, although redundancy number exists with epochs increasing, no robust float solution can be achieved, and pseudo-range measurements must be added to the adjustment system.In the GPS literature there are two of the many different approaches proposed for integer ambiguity estimation, which have drawn much interest. The two approaches differ in the model used for integer ambiguity estimation. In the first approach, which is the common mode of operation for most surveying applications, an explicit use is made of the available relative receiver-satellite'geometry, named the "geometry-based" model. Integer ambiguity estimation is also possible however, when one opts for dispensing with the relative receiver-satellite geometry, and is named the "geometry-free" model. In fact from the conceptual point of view, this is the simplest approach to integer ambiguity estimation. The pseudo-range data are directly used to determine the unknown integer ambiguities of the observed phase data. Of particular interest here is the shape and orientation of the ellipsoid of standard deviation for the ambiguities. The orientation for the geometry-free model does not change as the number of epoch increases. The orientation of LI and L2 for the same satellite is exactly 37.93°, i.e., the slope is k = XLXI A.12, and the semi-minor axes for the geometry-based are equal to those of the geometry-free model, while the semi-major axes for the geometry-free model are longer than those of the geometry-based model, which means that the ellipse for the geometry-free model always contains the ellipse for the geometry-based model. The geometry is the same for every epoch solution, as long as the stochastic model remains unchanged. The orientation for the geometry-free model does not change for every epoch, while the orientation of two different satellites for the geometry-based model is closer to the axes as the number of epoch increases, which means that these two ellipses overlap each other partly. Combining these two models' advantages, a new concept for ambiguity resolution, called Dual-space Ambiguity Resolution Approach (DARA), involving a search in both spaces at the same time, is proposed.
高精度动对动定位需要使用载波相位观测值,当平台间距离很短,双差处理可以削弱相位观测值中的空间相关误差,卫星和接收机钟差可以消除掉。当残余误差很小,模糊度固定后定位精度可以达到厘米级。高精度相对定位主要地依赖于模糊度成功解算及模糊度保持为常数,然而,在动态情形下,由于接收机振荡器、遮挡和多路径等因素会引起周跳,即相位观测值的整周跳跃,周跳改变了相位观测值表达的距离值进而影响了以相位为基础的定位精度,因此,整周模糊度解算和周跳探测与修复是高精度动对动定位的核心问题。
观测值是用来获得所需要的参数,由于观测值含有偏差和误差,为了削弱误差的影响和提高解的精度,需要有多余观测数,即实际的独立观测值数多于估计未知参数所必须的观测值数。由于误差存在使得观测值间不相容,为了消除不相容并获得待估参数,通常要应用最小二乘估计,即残差平方和加权最小原理。由于最小二乘估计仅能处理线性系统,而所需的流动站坐标未知参数包含在站星几何距离中,观测方程线性化就是GPS数据处理的基本内容。在现有的参考文献中,所给出的线性化方式可以分为两类,一是以流动站坐标为参数进行线性化,未知参数是流动站坐标改正量;另一线性化方法是以流动站到参考站的基线向量为参数,未知参数是基线向量的改正数。前一种线性化方法无疑作了三个前提假设:参考站坐标精确已知、参考站坐标与观测数据在同一坐标系、流动站近似坐标也在同一坐标系中。显然,在动对动定位中,以上假设是不存在的,因此以测站坐标为参数线性化单差、双差观测方程是不行的。后一种线性化方法在有的参考文献中介绍了很复杂的双差观测方程线性化推导过程,为此,本文给出了一种简单易行的观测方程线性化方法,在此基础上指出了动对动定位与其它定位模式在方程线性化方面的不同与相同之处。
On-the-fly GPS positioning relative to a moving reference, referred to as KINRTK in, this thesis, has many applications, such as fleet management, battlefield command, formation flying, vehicles positioning, satellite-to-satellite orbit determination, aerocraft safety approach, and others, where a static reference is difficult to establish. In this application, the absolute positions of the objects are not important but rather their relative positions, so that the configuration of the reference station with precisely known coordinates is not mandatory. High relative positioning accuracy and reliability are required. Most of the existing methods of relative positioning assume that the precise position of a reference station is given a priori. Thus, the accuracy of the relative positioning only depends on the measurement errors. However, in this research, such a precondition is not given. Therefore, those previous approaches cannot be directly used for this research. Modifications are required to process the kinematic data simultaneously. The impact of these modifications on the effectiveness of relative positioning is to be investigated in this thesis.To achieve high positioning accuracy, the double-differenced GPS carrier phase method is usually adopted. When the inter-platform distances are short, e.g., less than 10 km, double differencing can largely reduce spatially correlated errors in the carrier phase measurements. Satellite and receiver clock errors are cancelled, regardless of the inter-platform distance. When the remaining errors are small, centimeter-level accuracy relative positions can be obtained with fixed integer ambiguities. High accuracy relative positioning depends mostly on successful integer ambiguity resolution of the double-differenced carrier phase measurements. Before the carrier phase observable can be utilized as a precise range information its inherent integer cycle ambiguity must be resolved and carrier phase positioning rely on the ambiguities being constant. Unfortunately, high user dynamics, the receiver's oscillator, shadowing and multipath can cause cycle slips, i.e. jumps of the carrier phase observable by an integer multiple of wavelengths. Every cycle slip would deteriorate the high accuracy of the affected carrier phase range and also that of the position derived from such carrier phase observables. Therefore, integer ambiguity resolution and cycle slips detection and repairing are two of the crucial problems to resolve for high accuracy relative positioning.Observations are made to derive certain parameters. However, observations often contain biases and errors. To reduce the effect of the errors and assess the accuracy of the solution, redundancy is required. That is, more than the minimum number of observations is required to determine the estimated parameters. These observations must be adjusted so that the solution will be consistent with these adjusted observations. To adjust observations and to obtain the desired parameters, the method of least-squares estimation is often used. In least-squares estimation, parameters and corrected observations are derived by minimizing the weighted sum of the squared residuals. As well known, least-squares estimation can only process a linear system, while the desired parameters, rover station coordinates, are contained in the geometric range between the satellite and the receiver
antenna. Therefore, linearization is the basic work in GPS data processing. Two modes of linearization can be found in the GPS literature. In the first approach, observation equation is linearized by rover station coordinates, whose estimated parameters are the correction to the approximated station coordinates. The other one linearizes the equations with baseline vector between rover station and the reference, whose estimated parameters are the correction to the approximated baseline vector. There are three presupposition assumptions in the former approach, i.e., known precise reference station coordinates, the coordinates and observables are in the same coordinate system, and the approximated rover station coordinates are also in the system. Obviously, these assumptions do not exist in KINRTK, and the equation must be linearized by the latter. A simple and efficient linearization method is presented, and the differences between KINRTK and other GPS positioning modes are analyzed.Most receivers attempt to keep their internal clocks synchronized to GPS Time. This is done by periodically adjusting the clock by inserting time jumps. Two typical examples of receiver clock jumps exist in different manufacturer's receivers. The first example is a millisecond jump which occurs when the clock offset becomes larger than ± 1 millisecond, the receiver corrects the clock by ± 1 millisecond. The second example is a very small clock jump which occurs every second and the jumps are often small. At the moment of the clock correction, two main effects are transferred into the code and phase observables. The effects of the geometric range corresponding to the clock jump are common to all measurements at the moment of the clock jump at one receiver. By single-differencing (SD) the measurements between satellites or double-differencing (DD) the measurements (that is, differencing between receivers followed by differencing between satellites or vice versa), the common effects can be removed. However, the effects of the geometric range rate corresponding to the jump are different for each observation. They cannot be removed by the SD or DD operation. However, like cycle slips, their effects on the code and phase observables are more or less known to users and hence it is possible to detect and remove their effects almost completely in both the measurement and parameter domains.The quality of GPS positioning is dependent on a number of factors. For attaining high-precision positioning results, we need to identify the main error sources impacting on the quality of the observations. In terms of data processing, cycle slips, receiver clock jumps and quasi-random errors are the main sources which can deteriorate the quality of the observations and subsequently, the quality of positioning results. Cycle slips are discontinuities of an integer number of cycles in the measured (integrated) carrier phase resulting from a temporary loss-of-lock in the carrier tracking loop of a GPS receiver. In this event, the integer counter is reinitialized which causes a jump in the instantaneous accumulated phase by an integer number of cycles. The detection and correction of cycle slips is needed if accurate positioning is to be carried out. Cycle slip detection and correction requires the location of the jump and the determination of its size. It can be completely removed once it is correctly detected and identified. Slip detection and repair still represents a challenge to carrier phase data processing even after years of research. For completeness, a short description of the development of strategies for detecting and determining cycle slips over the past two decades or so is presented. For the most part, techniques used in the detection and determination of cycle slips have not changed drastically since the first methods were devised in the early 1980s. The focus has always
been on attempting to develop a reliable, somewhat automatic detection and repair procedure. All methods have the common premise that to detect a slip at least one smooth (i.e., low noise) quantity derived from the observations must be tested in some manner for discontinuities that may represent cycle slips. The derived quantities usually consist of linear combinations of the undifferenced or double-differenced L1 and L2 carrier-phase and possibly pseudorange observations. Examples of combinations useful for kinematic data are. the geometry-free phase (a scaled version of which is called the ionospheric phase delay), and widelane phase minus narrowlane pseudorange. Once the time series for the derived quantities have been produced, the cycle-slip detection process (that is, the detection of discontinuities in the time series) can be initiated. Of the various methods available, a novel approach, called Non-integer Linear Combination (NLC), is proposed.Time-relative positioning is a recently developed method for processing GPS observations. Observe first carrier phases at a station of known coordinates (a geodetic point, for example) for a short period of time (1-2 min). Preferably, the observation rate must be high—e.g., 1 s. The user then moves the receiver and the antenna quickly (e.g., 30 s) toward the station of unknown coordinates located about a hundred meters (depending on the type of transportation) away from the first one, while continuously observing carrier phases. At the second station, phase observations are recorded again for a short period of time (1-2 min). Relative positioning is then obtained by processing carrier phase observations taken at different epochs (and different stations)with a single GPS receiver. The main distinction between time-relative positioning and conventional relative positioning is that in the former there is a combination of observations taken at two different epochs and two different stations with the same receiver to detennine the position of the unknown station with respect to the known station. In other words, simultaneous observations using a second GPS receiver at a reference station are not required, unlike conventional relative positioning. The disadvantage of time-relative positioning compared to conventional relative positioning is that, since observations at both stations are not obtained simultaneously, it is also affected by the temporal "decorrelation" of errors (time variation of errors) in addition to the spatial "decorrelation" of errors also present in conventional relative positioning. In most GPS applications, regardless of surveying modes (static and kinematic) and baseline lengths (short, medium and long), the effects of the epoch-differenced biases and noise (i.e., atmospheric delay, satellite orbit bias, multipath, and receiver system noise) are more or less below a few centimetres as long as observation sampling interval is relatively short (e.g., sampling interval less than 1 minute). Based on high sampling interval assumption, time-relative positioning observation equation is further analyzed, the concept of virtual measurement is applied, which results in a robust linearization scheme. A new cycle slip detection approach based on time-relative positioning theory is studied for the first time, and valuable unrecognized knowledge of relation between satellites geometry and cycle slip detection is obtained.GPS carrier phase positioning has a higher accuracy than code positioning, assuming the integer ambiguity is correctly fixed. OTF ambiguity resolution refers to the case when the ambiguities are resolved when at least one receiver is moving, i.e., when the receiver is in kinematic mode. It differs from the static ambiguity resolution in two ways: In kinematic applications, errors of measurement cannot be reduced by time averaging because the movement of platforms can significantly change the testing environment; In kinematic
applications, the position and velocity of the object is required for every epoch, so the batch processing cannot be adopted if real-time processing is required. Since less information is available and larger errors occur, OTF ambiguity resolution is more difficult in kinematic than in static mode. Here are some major factors affecting the OTF ambiguity resolution: Selection of observables; Inter-receiver distance; Number and geometry of satellites; Magnitude of GPS errors; Ambiguity search method; Performance required, etc. The major challenges of OTF ambiguity resolution are relative error modeling, and the efficiency and reliability of the ambiguity search technique. There are many methods that have been developed for solving On-The-Fly (OTF) ambiguity since the 1980's. Basically, they have the same strategies to fix ambiguities, namely, float ambiguity resolution, integer ambiguity searching, and the use of a distinguishing test. The float ambiguity and its variance are used to define the initial search point, and the search range of the integer candidates. Therefore, float solution is more important than anything else in ambiguity resolution. In static mode, float solution can be obtained by only processing carrier phase observables, while in the KINRTK application, although redundancy number exists with epochs increasing, no robust float solution can be achieved, and pseudo-range measurements must be added to the adjustment system.In the GPS literature there are two of the many different approaches proposed for integer ambiguity estimation, which have drawn much interest. The two approaches differ in the model used for integer ambiguity estimation. In the first approach, which is the common mode of operation for most surveying applications, an explicit use is made of the available relative receiver-satellite'geometry, named the "geometry-based" model. Integer ambiguity estimation is also possible however, when one opts for dispensing with the relative receiver-satellite geometry, and is named the "geometry-free" model. In fact from the conceptual point of view, this is the simplest approach to integer ambiguity estimation. The pseudo-range data are directly used to determine the unknown integer ambiguities of the observed phase data. Of particular interest here is the shape and orientation of the ellipsoid of standard deviation for the ambiguities. The orientation for the geometry-free model does not change as the number of epoch increases. The orientation of LI and L2 for the same satellite is exactly 37.93°, i.e., the slope is k = XLXI A.12, and the semi-minor axes for the geometry-based are equal to those of the geometry-free model, while the semi-major axes for the geometry-free model are longer than those of the geometry-based model, which means that the ellipse for the geometry-free model always contains the ellipse for the geometry-based model. The geometry is the same for every epoch solution, as long as the stochastic model remains unchanged. The orientation for the geometry-free model does not change for every epoch, while the orientation of two different satellites for the geometry-based model is closer to the axes as the number of epoch increases, which means that these two ellipses overlap each other partly. Combining these two models' advantages, a new concept for ambiguity resolution, called Dual-space Ambiguity Resolution Approach (DARA), involving a search in both spaces at the same time, is proposed.
引文
[1] 刘基余,李征航,王跃虎,桑吉章(1993).全球定位系统原理及其应用.测绘出版社,1993.10,北京.
[2] Parkinson, B W, James J, Spilker J Jr(1996) Global Positioning System: Theory and Applications. Volume Ⅰ, American Institute of Aeronautics and Astronautics. Inc.793pages.
[3] Parkinson, B W, James J, Spilker J Jr(1996) Global Positioning System: Theory and Applications. Volume Ⅱ, American Institute of Aeronautics and Astronautics. Inc.643pages.
[4] Hofmann-Wellenhoh B, Lichtenegger H, Collins J(1994), Global Positioning System Theory and Pracice, Third revised edition, Springer-verlag wien, 1994, 382pages, Fifth revised edition, 2001.
[5] Olynik M C(2002). Temporal Characteristics of GPS Error Sources and Their Impact on Relative Positioning. Doctor Thesis, UCGE Report 20162, Geomatics Engineering, The University of Calgary, 122pages.
[6] Radovanovic R S(2002). Adjustment of Satellite-based Ranging Observations for Precise Positioning and Deformation Monitoring. Doctor Thesis, UCGE Report 20166, Geomatics Engineering, The University of Calgary, 195pages.
[7] Shin T Y, Shin H Y, Yang M(2001). The Performance of GPS Standard Positioning Service Without Selective Availability. Survey Review, Vol.36, No.281, pp 192-201, 2001.
[8] Satirapod, C, Rizos C, Wang J(2001). GPS Single Point Positioning with SA OFF: How Accurate Can We get. Survey Review, Vol.36, No.282, pp255-262, 2001
[9] Luo N(2001). Precise Relative Positioning of Multiple Moving Platforms Using GPS Carrier Phase Observables.Doctor Thesis. University of Calgary, 217pages.
[10] Hermann B R, Evans A G, and Law C S, Remondi B W(1995). Kinematic on the fly GPS Positioning Relative to a Moving reference. NAVAGATION: Journal of the Institute of Navigation, Vol.42,No.3,Fall 1995,pp487-501.
[11] 葛茂荣,过静王君.GPS相对导航在航天器交会对接中的应用.测绘通报,No.5 MAY 1998,pp6-7.
[12] Lu, G. (1995) Development of a GPS Multi-antenna System for Attitude Determination. Pd. D. Thesis, UCGE Report 20073, Geomatics Engineering, The University of Calgary, 179pages.
[13] Weisenburger, S. D. (1997) Effect of Constraints and Multiple Receivers for On-the-fly Ambiguity Resolution. Master Thesis, UCGE Report 20109, Geomatics Engineering, The University of Calgary, 125pages.
[14] 刘经南,施闯,陈俊勇(1998).‘92’、‘96’国家高精度GPSA级网整体结果分析与我国块体运动模型研究,武汉测绘科技大学学报,1998,No.4
[15] 刘大杰,胡丛玮(1999).应用GPS监测城市地表形变的初步分析,地壳形变与地震,Vol.19,No.1,Feb.,1999
[16] Collier P A(1997). Kinematic GPS for Deformation Monitoring. Geomatica, No.2, 1997, pp157-168.
[17] Kalber S, Jager R and Schwable R(2000). A GPS-based Online Control and Alarm System. GPS Solution, Vol.3, No.3 pp19-25.
[18] 熊永良.黄丁发,张献洲.一种可靠的含约束条件的GPS变形监测单历元求解算法.武汉大学学报.信息科学版,2001,26(1):51-57
[19] Binning P W(1997). Absolute and Relative Satellite to Satellite Navigation Using GPS. Ph.D. Thesis, University of Colorado, 1997, 162pages.
[20] Isao Kawano, Masaaki Mokuno, Toru Kasai, Takashi Suzuki(2001). First Autonomous Rendezvous Using Relative GPS Navigation By ETS_Ⅶ. NAVAGATION: Journal of the Institute of Navigation, Vol.48,No.1, Spring 2001, pp49-56.
[21] LUO N. (2000) Centimeter-Level Relative Positioning of Multiple Moving Platforms Using Ambiguity Constraints. Proceedings of GPS2000 (Session B3, Salt Lake City, 19-22 September), The Institute of Navigation, Alexandria, VA., 113-122.
[22] 刘广军,曾纪斌.GPS动态相对导航用于航天器交会对接的研究及其OTF解算方法.飞行器测控学报,Vol.19.No.2,2000,pp86-93
[23] Teunissen P J G(1995). The Least-squares Ambiguity Decorrelation Adjustment: A Method for GPS Integer Ambiguity Estimation. Journal of Geodesy. Vol.70, No. 1-2, 1995, pp65-82.
[24] Chen D S(1994). Development of a Fast Ambiguity Search Filtering (FASF) Method for GPS Carrier Phase Ambiguity Resolution. Pd. D. Thesis, UCGE Report 20071, Geomatics Engineering, The University of Calgary, 110pages.
[25] Raquet, J.F. (1998) Development of a Method for Kinematic GPS Carrier-phase Ambiguity Resolution Using Multiple Reference Receivers. Ph.D. Thesis,UCGE Report 20116, Geomatics Engineering, The University of Calgary, 259pages.
[26] Fortes, L P S, Cannon, M E, and Lachapelle, G(2000). Testing a Multi-Reference GPS Station Network for OTF Positioning in Brazil, In Proceedings of the 13th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GPS-00). Salt Lake City, Utah.
[27] Alfred Kleusberg, P J G Teunissen(1996). GPS for Geodesy. Springer, 1996, 407pages.
[28] Alfred Leick(1995), GPS Satellite Surveying, second edition John wiley&sons.inc. 1995,560pages
[29] Frei E, Beutler G(1990). Rapid Static Positioning Based On The Fast Ambiguity Resolution Approach "FARA": Theory and First Results. Mannscripta Geodaetica, Vol. 15,No.6 1990, pp325-356.
[30] Al-Hafi Y M, Corbett S J, Cross P A(1997). Performance Evaluation of GPS Single Epoch on the Fly Ambiguity Resolution. NAVAGATION: Journal of the Institute of Navigation, Vol.44,No.3, Winter 1997,pp479-487.
[31] 李淑慧(2002).整周模糊度搜索方法的比较研究.武汉大学硕士学位论文,2002.5,60pages.
[32] 高星伟(2002).GPS/GLONASS网络RTK的算法研究与程序实现.武汉大学博士学位论文,2002.5,142pages.
[33] Lichtenegger H and Hofmann-Wellenhof B(1990). GPS-data preprocessing for cycle-slip detection[C]. Global Positioning System: an overview. Bock Y and Leppard N (Eds.), International Association of Geodesy Symposia 102, Edinburgh, Scotland, 2-8 August, 1989. 57-68.
[34] Mader G L(1986). Dynamic Positioning Using GPS Carrier Phase Measurements. Manuscripta Geodaetica, 1986, Vol. 17, No.4, pp272-277.
[35] Bastos L and Landau H(1988). Fixing cycle slips in dual-frequency kinematic GPS-applications using Kalman filtering. Mannscripta Geodaetica, 1988, Vol.13, No.4 pp249-256.
[36] Bisnath S B(2000). Efficient, automated cycle-slip correction of dual-frequency kinematic GPS-data[C]. Proceedings of ION GPS 2000, the 13th International Technical Meeting of The Institute of Navigation, Salt Lake City, Utah, 19-22 September 2000, pp145-154.
[37] Kim D. and Langley-R B (2001).Instantaneous realtime cycle-slip correction of dual-frequency GPS Data[C]. Proceedings of the International Symposium on Kinematic Systems in Geodesy, Geomatics and Navigation, Banff, Alberta, Canada, 5-8 June 2001, pp. 255-264.
[38] 袁洪,万卫星,宁百齐,李静年.基于三差解检测与修复GPS载波相位周跳新方法[J].测绘学报,1998,Vol.27,No.3,pp189-194.
[39] Lu G, Lachapelle G(1992). Statistical Quality Control for Kinematic GPS Positioning. Manuscripta Geodaetica, 1992, Vol. 17,No.6, pp270-281.
[40] Collin F, Warnant R(1995). Application of the wavelet transform for GPS cycle slip correction and comparison with Kalman filter. Manuscripta Geodaetica, 1995, Vol.20, No.3, pp161-172.
[41] 何海波,杨元喜(1999).GPS动态测量连续周跳检验[J].测绘学报.1999,Vol.28,No.3,pp199-203
[42] 黄丁发,卓健成(1997).GPS相位观测值周跳检测的小波分析法.测绘学报,Vol.26,No.4,1997,pp352-357.
[43] Teunissen P J G(1997). Minimal Detectable Biases of GPS data. Journal of Geodesy, 1998, Vol.72, No.4 pp236-244.
[44] Blewitt G(1990). An automatic editing algorithm for GPS data[J]. Geophysical Research Letters, 1990, Vol. 17, No.3, pp199-202.
[45] Gao Y and Li Z (1999). Cycle slip detection and ambiguity resolution algorithms for dual-frequency GPS data processing[J]. Marine Geodesy, 1999, Vol.22, No.4, pp169-181.
[46] 胡丛玮,刘大杰,姚连壁.高精度动态GPS定位中的一种周跳修复方法[J].同济大学学报,1998,Vol.26,No.6,pp686-690.
[47] Altmayer C(2000). Improving Availability And Reliability of High Accuracy Integrated Systems. Presented at the IFAC Symposium on Transportation Systems 2000, Braunschweig, Germany, 15th July 2000.
[48] SchUler T(2001). On Ground-Based GPS Tropospheric Delay Estimation. Heft 73, Neubiberg,2001,364pages.
[49] 周忠谟,易杰军(1992).GPS卫星测量原理与应用.测绘出版社,1992.北京
[50] 黄维彬(1992).近代平差理论及其应用.解放军出版社,1992.7,北京.
[51] Teunissen P J G(2000). Testing Theory—An Introduction. Delft University Press,2000,the Netrerlands.
[52] Barnes J B, and Cross P A(1998), Processing Models for Very High Accuracy GPS Positioning, Journal of Navigation, Vol.51,No.2,1998, pp180-193.
[53] Bassiri S and Hajj G A(1993). Higher Order Ionospheric Effects on The Global Positioning System Observables and Means of Modelling. Manuscrpta Geodetica, Vol.18, No.5, 1993,pp 280-289.
[54] Liu G C(2001). Ionosphere Weighted Global Positioning System Carrier Phase Ambiguity Resolution. Master Thesis, UCGE Report 20155, Geomatics Engineering, The University of Calgary, April, 2001, 157pages.
[55] Schaer, S. (1997). How to Use CODE's Global Ionosphere Maps. http://www.aiub.unibe.ch/ionosphere.html, Astronomical Institute, University of Berne.
[56] Shen X B(2002). Improving Ambiguity Convergence in Carrier Phase-based Precise Point Positioning. Master Thesis, UCGE Report 20170, Geomatics Engineering, The University of Calgary, April, 2002, 143pages.
[57] 柳响林(2002).精密GPS动态定位的质量控制与随机模型精化.博士学位论文,武汉大学,2002.
[58] Shi J(1994). High Accuracy Airborne Differential GPS Positioning Using A Multi-receiver Configuration. Pd. D. Thesis, UCGE Report 20061, Geomatics Engineering, The University of Calgary, April, 1994, 131pages.
[59] Nayak, R. (2000) Reliable and Continuous Urban Navigation Using Multiple GPS Antennas and Low Cost IMU. Master Thesis, UCGE Report 20144, Geomatics Engineering, The University of Calgary, 167pages.
[60] Georgiodou, Y and A. Kleusberg (1988) On Carrier Signal Multipath Effects in Relative GPS Positioning. Manuscripts Geodaetica, Vol. 13, No. 3: 172-179.
[61] 夏林元(2001).GPS观测值中的多路径效应理论研究及数值结果.博士学位论文,武汉大学,2001.10,154pages.
[62] Ray, J. K. (2000) Mitigation of GPS Code and Carrier Phase Multipath Effects Using a Multi-Antenna System. Ph.D. Thesis, UCGE report 20136. Geomatics Engineering, The University of Calgary, 260pages.
[63] De Jong K(1999). The Influence of Code Multipath on The Estimated Parameters of Geometry-free GPS Model. GPS Solutions Vol.3 No.2 pp11-18,1999.
[64] Chen C S and Lee H C(2002). A Study on The Multipath Effect of the GPS Antenna. Geomatics Research Australia. No.76, pp37-58, June 2002.
[65] Han S and Rizos C(2000). GPS Multipath Mitigation Using Fir Filters. Surv Rev, Vol.35,No.277, 2000.
[66] Kim, D. and R.B. Langley (2001). "Estimation of the stochastic model for long-baseline kinematic GPS applications." Proceedings of The Institute of Navigation 2001 National Technical Meeting, Long Beach, CA, U.S.A., 22-24 January, 2001, pp 586-595
[67] Key K W(1997). Theory and Applications of Using GPS Equipped Buoys for the Accurate Measurement of Sea Level. Ph.D. Thesis, University of Colorado, 1997, 185pages.
[68] Bock, Y., Gourevitch, S.A., Counselman Ⅲ, C.C., King, R.W. and Abbot, R.I., (1986), lnterferometric Analysis of GPS Phase Observations, Manuscripta Geodaetica, 11,282-288.
[69] Gao Y, Lahaye F, Heroux P, Liao X, Beck N, and Olynik M(1999). Investigation of Measurement Inconsistency in Dual-Frequency GPS Receivers. Proceedings of the 12th Internationa Technical Meeting of the Satellite Divisionof the Institute of Navigation,September 14-17, 1999, Nashville, Tennessee, 251-258.
[70] Lin L, Rizos C(1996). An Algorithm to Estimate GPS Satellite and Receiver L1/L2 Differential Delays and its Application to Regional Ionosphere Modelling. Geomatics Research Australasia, 65, pp1-26.
[71] Satirapod C and Wang J(2000). Comparing the Quality Indicators of GPS Carrier Phase. Geomatics Research Australia, 73, December 2000, 75-92.
[72] Wang J(1998). Stochastic Assessment of the GPS Measurements for Precise Positioning, 11th Int. Tech. Meeting of the Satellite Division of the U.S. Inst. Of Navigation GPS ION'98, Nashville, Tennessee, 15-18 September, 81-89.
[73] Brunner, F.K., Hartinser, H., and Troyer, L.,(1999), GPS Signal Diffraction Modelling: The Stochastic SIGMA-△ Model, Journal of Geodesy, 73,259-267.
[74] Euler, H-J(2000), Advances in Ambiguity Resolution for Surveying Type Applications, Proceedings of ION GPS-2000, Salt Lake City, Utah, September 19-22, 95-103.
[75] Han S. Quality-control Issues Relating To Instantaneous Ambiguities Resolution for Real-time GPS Kinematic Positioning. Journal of Geodesy. 1997 Vol.71, No.6, pp351-361.
[76] 李庆海,陶本藻(1990).概率统计原理和在测量中的应用.测绘出版社,1990.6,北京,370pages.
[77] Teunissen P J G(1995). The invertible GPS ambiguity transformations. Manuscripta geodaetica, Vol.20, No.6, 1995, pp489-497.
[78] Michaud S, Santeree R(2001).Time-Relative Positioning with a Single Civil GPS Receiver. GPS Solutions, Vol. 5, No. 2, 2001, pp71-77
[79] De Jong K(2002). Precise GNSS Positioning Threats and Opportunities. Simposio Brasileiro de Geomatica UNESP, Presidente Prudente, July 2002
[80] Masson A,Burtin D and Sebe M(1997). Kinematic DGPS and INS Hybridizaition for precise Trajectory Determination. NAVIGATION: Journal of The Institute of Navigation, Fall, 1997, Vol.44, No.3, pp313-321.
[81] Teague E H(1997). Flexible Structure Estimation and Control Using The Global Positioning System. Stanford University. Ph.D. Thesis, 1997,160pages.
[82] 姬生月,胡国荣(2000).一种新的GPS整周模糊度快速解算方法.铁道学报,Vol.22,No.6,2000,pp95-98.
[83] 魏子卿,葛茂荣(1998).GPS相对定位数学模型.测绘出版社,1998.2,北京,182pages.
[84] Teunissen P J G(1997). Some Remarks on GPS Ambiguity Resolution. presented at the symposium of the 'Geodatische Woche', 6-11 Oct. 97, Berlin, Germany.
[85] Wang J, Stewart M and Tsakiri M(1995). A discrimination test procedure for ambiguity resolution on-the-fly, Journal of Geodesy,1998(72), 644-653.
[86] Wang J, Stewart M P, and Tsakiri M(2000). A comparative study of the integer ambiguity validation procedures. Earth Planets Space, 2000(52): 813-817.
[87] Teunissen P J G(2000). The Success Rate and Precission of GPS Ambiguities. Journal of Geodesy, 74, 2000, pp.321-326.
[88] 刘经南,陈俊勇,张燕平,李毓麟,葛茂荣(1999).广域差分GPS原理和方法.测绘出版社,1999年1月.北京
[89] Horemuz. M, Sjoberg L E(2002). Rapid GPS Ambiguity Resolution For Short And Long Baselines. Journal of Geodesy, vol.76, No.6-7,2002, pp381-391.
[90] Euler H J and Goad C C(1991). On Optimal Filtering of GPS Dual Frequency Observations Without Using Orbit Information. Bull.Geod, Vol.63,No.2,1991, pp 130-143.
[91] Grass F V and Lee S(1995). High-Accuracy Differential Positioning for Satellite-Based System Without Using Code-phase Measurements. NAVAGATION: Journal of the Institute of Navigation, Vol.42,No.4, Winter 1995,pp605-618.
[92] Sjoberg L E(1996). Application of GPS in Detailed Surveying. Z.F.Verm.wesen. Vol.121, No.10, 1996, pp485-491.
[93] Sjoberg L E(1995). A new method for GPS phase base ambiguity resolution by combined phase and code observables. Surv Rev Vol.34, No.268,1998,pp363-372.
[94] Teunissen P J G(1996). On The Geometry of the Ambiguity Search Space with and Without Ionosphere. Z.F.Verm.wesen. Vol. 121, No.7, 1996, pp332-341.
[95] Teunissen P J G(1997). GPS Double Difference Statistics: With and Without Using Satellite Geometry. Journal of Geodesy. Vol.71,No.3,1997,pp137-145.
[96] Huang D, Ding X, Chen Y(2001). Ambiguity Online Estimation By Combining Dual-Frequency Phase and Carrier Smothed Code Measurements: Performance On Short Baseline. Survey Review, Vol.36, No.253, pp263-272.
[97]Kleusberg A(1986). Ionospheric Propagation Effects In Geodetic Relative GPS Positioning. Manuscripta Geodaetica, Vol.11,No.4 1986,pp256-261.
[98]Lz H B, Ge M, Chen Y Q(1998). Grid Point Search Algorthm for Fast Integer Ambiguity Resolution. Journal of Geodesy, 1998(72),pp639-643.
[99]Kim D, Langley R(2000).A search space optimization technique for improving ambiguity resolution and computational efficiency.Earth Planets Space,2000, 52, pp807-812
[100] Shaw M, Sandhoo K, and Turner D(2000):Modernization of the Global Positioning System, GPS World, September 2000, pp. 36-44.
[101]Hein G. et al., (2001): The Galileo Frequency Structure and Signal Design, Proc. ION GPS 2001, Salt Lake City.September 11-14.
[102]Eissfeller B. et al(2001). Real-Time Kinematic in the Light of GPS Modernization and Galileo. ION GPS 2001, Salt Lake City.September 11-14.
[103]Hatch R(1996). The Promise of a Third Frequency. GPS World, May 1996,pp55-58. Sjoberg L E(1998). On The Estimation of GPS Phase Ambiguities By Triple Frequency Phase And Code Data. Z.F.Verm.wesen. Vol.123, No.5, 1998, pp162-165.
[104]Vollath U, Birnbach S, Landau H, et al(1996). Analysis of Three-Carrier Ambiguity Resolution Technique for Precise Relative Positioning in GNSS-2. NAVIGATION: Journal of The Institute of Navigation, 1999, Vol.46, No.1,pp13-23.
[105]Hatch R, Jung J, Enge P, Pervan B(2000). Civilian GPS:The Benefits of Three Frequencies. GPS solutions ,Vol.3, No.4 ,pp1-9.
[106]Han S, Rizos C(1999). The Impact of Two Additional Civilian GPS Frequencies on Ambiguity Resolution Strategies. 55th National Meeting U.S. Institute of Navigation, "Navigational Technology for the 21st Century". Cambridge, Massachusetts, 28-30 June, 1999,pp315-321
[107]Han S Rizos C(1999). Single-epoch Ambiguity Resolution for Real-time GPS Attitude Determination With The Aid of One-dimensional Optical Fiber Gyro. GPS Solution, Vol.3,No 1, 1999,pp5-12.
[108] 李志林,朱庆(2001).数字高程模型. 武汉大学出版社,2001年7月,武汉.
[2] Parkinson, B W, James J, Spilker J Jr(1996) Global Positioning System: Theory and Applications. Volume Ⅰ, American Institute of Aeronautics and Astronautics. Inc.793pages.
[3] Parkinson, B W, James J, Spilker J Jr(1996) Global Positioning System: Theory and Applications. Volume Ⅱ, American Institute of Aeronautics and Astronautics. Inc.643pages.
[4] Hofmann-Wellenhoh B, Lichtenegger H, Collins J(1994), Global Positioning System Theory and Pracice, Third revised edition, Springer-verlag wien, 1994, 382pages, Fifth revised edition, 2001.
[5] Olynik M C(2002). Temporal Characteristics of GPS Error Sources and Their Impact on Relative Positioning. Doctor Thesis, UCGE Report 20162, Geomatics Engineering, The University of Calgary, 122pages.
[6] Radovanovic R S(2002). Adjustment of Satellite-based Ranging Observations for Precise Positioning and Deformation Monitoring. Doctor Thesis, UCGE Report 20166, Geomatics Engineering, The University of Calgary, 195pages.
[7] Shin T Y, Shin H Y, Yang M(2001). The Performance of GPS Standard Positioning Service Without Selective Availability. Survey Review, Vol.36, No.281, pp 192-201, 2001.
[8] Satirapod, C, Rizos C, Wang J(2001). GPS Single Point Positioning with SA OFF: How Accurate Can We get. Survey Review, Vol.36, No.282, pp255-262, 2001
[9] Luo N(2001). Precise Relative Positioning of Multiple Moving Platforms Using GPS Carrier Phase Observables.Doctor Thesis. University of Calgary, 217pages.
[10] Hermann B R, Evans A G, and Law C S, Remondi B W(1995). Kinematic on the fly GPS Positioning Relative to a Moving reference. NAVAGATION: Journal of the Institute of Navigation, Vol.42,No.3,Fall 1995,pp487-501.
[11] 葛茂荣,过静王君.GPS相对导航在航天器交会对接中的应用.测绘通报,No.5 MAY 1998,pp6-7.
[12] Lu, G. (1995) Development of a GPS Multi-antenna System for Attitude Determination. Pd. D. Thesis, UCGE Report 20073, Geomatics Engineering, The University of Calgary, 179pages.
[13] Weisenburger, S. D. (1997) Effect of Constraints and Multiple Receivers for On-the-fly Ambiguity Resolution. Master Thesis, UCGE Report 20109, Geomatics Engineering, The University of Calgary, 125pages.
[14] 刘经南,施闯,陈俊勇(1998).‘92’、‘96’国家高精度GPSA级网整体结果分析与我国块体运动模型研究,武汉测绘科技大学学报,1998,No.4
[15] 刘大杰,胡丛玮(1999).应用GPS监测城市地表形变的初步分析,地壳形变与地震,Vol.19,No.1,Feb.,1999
[16] Collier P A(1997). Kinematic GPS for Deformation Monitoring. Geomatica, No.2, 1997, pp157-168.
[17] Kalber S, Jager R and Schwable R(2000). A GPS-based Online Control and Alarm System. GPS Solution, Vol.3, No.3 pp19-25.
[18] 熊永良.黄丁发,张献洲.一种可靠的含约束条件的GPS变形监测单历元求解算法.武汉大学学报.信息科学版,2001,26(1):51-57
[19] Binning P W(1997). Absolute and Relative Satellite to Satellite Navigation Using GPS. Ph.D. Thesis, University of Colorado, 1997, 162pages.
[20] Isao Kawano, Masaaki Mokuno, Toru Kasai, Takashi Suzuki(2001). First Autonomous Rendezvous Using Relative GPS Navigation By ETS_Ⅶ. NAVAGATION: Journal of the Institute of Navigation, Vol.48,No.1, Spring 2001, pp49-56.
[21] LUO N. (2000) Centimeter-Level Relative Positioning of Multiple Moving Platforms Using Ambiguity Constraints. Proceedings of GPS2000 (Session B3, Salt Lake City, 19-22 September), The Institute of Navigation, Alexandria, VA., 113-122.
[22] 刘广军,曾纪斌.GPS动态相对导航用于航天器交会对接的研究及其OTF解算方法.飞行器测控学报,Vol.19.No.2,2000,pp86-93
[23] Teunissen P J G(1995). The Least-squares Ambiguity Decorrelation Adjustment: A Method for GPS Integer Ambiguity Estimation. Journal of Geodesy. Vol.70, No. 1-2, 1995, pp65-82.
[24] Chen D S(1994). Development of a Fast Ambiguity Search Filtering (FASF) Method for GPS Carrier Phase Ambiguity Resolution. Pd. D. Thesis, UCGE Report 20071, Geomatics Engineering, The University of Calgary, 110pages.
[25] Raquet, J.F. (1998) Development of a Method for Kinematic GPS Carrier-phase Ambiguity Resolution Using Multiple Reference Receivers. Ph.D. Thesis,UCGE Report 20116, Geomatics Engineering, The University of Calgary, 259pages.
[26] Fortes, L P S, Cannon, M E, and Lachapelle, G(2000). Testing a Multi-Reference GPS Station Network for OTF Positioning in Brazil, In Proceedings of the 13th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GPS-00). Salt Lake City, Utah.
[27] Alfred Kleusberg, P J G Teunissen(1996). GPS for Geodesy. Springer, 1996, 407pages.
[28] Alfred Leick(1995), GPS Satellite Surveying, second edition John wiley&sons.inc. 1995,560pages
[29] Frei E, Beutler G(1990). Rapid Static Positioning Based On The Fast Ambiguity Resolution Approach "FARA": Theory and First Results. Mannscripta Geodaetica, Vol. 15,No.6 1990, pp325-356.
[30] Al-Hafi Y M, Corbett S J, Cross P A(1997). Performance Evaluation of GPS Single Epoch on the Fly Ambiguity Resolution. NAVAGATION: Journal of the Institute of Navigation, Vol.44,No.3, Winter 1997,pp479-487.
[31] 李淑慧(2002).整周模糊度搜索方法的比较研究.武汉大学硕士学位论文,2002.5,60pages.
[32] 高星伟(2002).GPS/GLONASS网络RTK的算法研究与程序实现.武汉大学博士学位论文,2002.5,142pages.
[33] Lichtenegger H and Hofmann-Wellenhof B(1990). GPS-data preprocessing for cycle-slip detection[C]. Global Positioning System: an overview. Bock Y and Leppard N (Eds.), International Association of Geodesy Symposia 102, Edinburgh, Scotland, 2-8 August, 1989. 57-68.
[34] Mader G L(1986). Dynamic Positioning Using GPS Carrier Phase Measurements. Manuscripta Geodaetica, 1986, Vol. 17, No.4, pp272-277.
[35] Bastos L and Landau H(1988). Fixing cycle slips in dual-frequency kinematic GPS-applications using Kalman filtering. Mannscripta Geodaetica, 1988, Vol.13, No.4 pp249-256.
[36] Bisnath S B(2000). Efficient, automated cycle-slip correction of dual-frequency kinematic GPS-data[C]. Proceedings of ION GPS 2000, the 13th International Technical Meeting of The Institute of Navigation, Salt Lake City, Utah, 19-22 September 2000, pp145-154.
[37] Kim D. and Langley-R B (2001).Instantaneous realtime cycle-slip correction of dual-frequency GPS Data[C]. Proceedings of the International Symposium on Kinematic Systems in Geodesy, Geomatics and Navigation, Banff, Alberta, Canada, 5-8 June 2001, pp. 255-264.
[38] 袁洪,万卫星,宁百齐,李静年.基于三差解检测与修复GPS载波相位周跳新方法[J].测绘学报,1998,Vol.27,No.3,pp189-194.
[39] Lu G, Lachapelle G(1992). Statistical Quality Control for Kinematic GPS Positioning. Manuscripta Geodaetica, 1992, Vol. 17,No.6, pp270-281.
[40] Collin F, Warnant R(1995). Application of the wavelet transform for GPS cycle slip correction and comparison with Kalman filter. Manuscripta Geodaetica, 1995, Vol.20, No.3, pp161-172.
[41] 何海波,杨元喜(1999).GPS动态测量连续周跳检验[J].测绘学报.1999,Vol.28,No.3,pp199-203
[42] 黄丁发,卓健成(1997).GPS相位观测值周跳检测的小波分析法.测绘学报,Vol.26,No.4,1997,pp352-357.
[43] Teunissen P J G(1997). Minimal Detectable Biases of GPS data. Journal of Geodesy, 1998, Vol.72, No.4 pp236-244.
[44] Blewitt G(1990). An automatic editing algorithm for GPS data[J]. Geophysical Research Letters, 1990, Vol. 17, No.3, pp199-202.
[45] Gao Y and Li Z (1999). Cycle slip detection and ambiguity resolution algorithms for dual-frequency GPS data processing[J]. Marine Geodesy, 1999, Vol.22, No.4, pp169-181.
[46] 胡丛玮,刘大杰,姚连壁.高精度动态GPS定位中的一种周跳修复方法[J].同济大学学报,1998,Vol.26,No.6,pp686-690.
[47] Altmayer C(2000). Improving Availability And Reliability of High Accuracy Integrated Systems. Presented at the IFAC Symposium on Transportation Systems 2000, Braunschweig, Germany, 15th July 2000.
[48] SchUler T(2001). On Ground-Based GPS Tropospheric Delay Estimation. Heft 73, Neubiberg,2001,364pages.
[49] 周忠谟,易杰军(1992).GPS卫星测量原理与应用.测绘出版社,1992.北京
[50] 黄维彬(1992).近代平差理论及其应用.解放军出版社,1992.7,北京.
[51] Teunissen P J G(2000). Testing Theory—An Introduction. Delft University Press,2000,the Netrerlands.
[52] Barnes J B, and Cross P A(1998), Processing Models for Very High Accuracy GPS Positioning, Journal of Navigation, Vol.51,No.2,1998, pp180-193.
[53] Bassiri S and Hajj G A(1993). Higher Order Ionospheric Effects on The Global Positioning System Observables and Means of Modelling. Manuscrpta Geodetica, Vol.18, No.5, 1993,pp 280-289.
[54] Liu G C(2001). Ionosphere Weighted Global Positioning System Carrier Phase Ambiguity Resolution. Master Thesis, UCGE Report 20155, Geomatics Engineering, The University of Calgary, April, 2001, 157pages.
[55] Schaer, S. (1997). How to Use CODE's Global Ionosphere Maps. http://www.aiub.unibe.ch/ionosphere.html, Astronomical Institute, University of Berne.
[56] Shen X B(2002). Improving Ambiguity Convergence in Carrier Phase-based Precise Point Positioning. Master Thesis, UCGE Report 20170, Geomatics Engineering, The University of Calgary, April, 2002, 143pages.
[57] 柳响林(2002).精密GPS动态定位的质量控制与随机模型精化.博士学位论文,武汉大学,2002.
[58] Shi J(1994). High Accuracy Airborne Differential GPS Positioning Using A Multi-receiver Configuration. Pd. D. Thesis, UCGE Report 20061, Geomatics Engineering, The University of Calgary, April, 1994, 131pages.
[59] Nayak, R. (2000) Reliable and Continuous Urban Navigation Using Multiple GPS Antennas and Low Cost IMU. Master Thesis, UCGE Report 20144, Geomatics Engineering, The University of Calgary, 167pages.
[60] Georgiodou, Y and A. Kleusberg (1988) On Carrier Signal Multipath Effects in Relative GPS Positioning. Manuscripts Geodaetica, Vol. 13, No. 3: 172-179.
[61] 夏林元(2001).GPS观测值中的多路径效应理论研究及数值结果.博士学位论文,武汉大学,2001.10,154pages.
[62] Ray, J. K. (2000) Mitigation of GPS Code and Carrier Phase Multipath Effects Using a Multi-Antenna System. Ph.D. Thesis, UCGE report 20136. Geomatics Engineering, The University of Calgary, 260pages.
[63] De Jong K(1999). The Influence of Code Multipath on The Estimated Parameters of Geometry-free GPS Model. GPS Solutions Vol.3 No.2 pp11-18,1999.
[64] Chen C S and Lee H C(2002). A Study on The Multipath Effect of the GPS Antenna. Geomatics Research Australia. No.76, pp37-58, June 2002.
[65] Han S and Rizos C(2000). GPS Multipath Mitigation Using Fir Filters. Surv Rev, Vol.35,No.277, 2000.
[66] Kim, D. and R.B. Langley (2001). "Estimation of the stochastic model for long-baseline kinematic GPS applications." Proceedings of The Institute of Navigation 2001 National Technical Meeting, Long Beach, CA, U.S.A., 22-24 January, 2001, pp 586-595
[67] Key K W(1997). Theory and Applications of Using GPS Equipped Buoys for the Accurate Measurement of Sea Level. Ph.D. Thesis, University of Colorado, 1997, 185pages.
[68] Bock, Y., Gourevitch, S.A., Counselman Ⅲ, C.C., King, R.W. and Abbot, R.I., (1986), lnterferometric Analysis of GPS Phase Observations, Manuscripta Geodaetica, 11,282-288.
[69] Gao Y, Lahaye F, Heroux P, Liao X, Beck N, and Olynik M(1999). Investigation of Measurement Inconsistency in Dual-Frequency GPS Receivers. Proceedings of the 12th Internationa Technical Meeting of the Satellite Divisionof the Institute of Navigation,September 14-17, 1999, Nashville, Tennessee, 251-258.
[70] Lin L, Rizos C(1996). An Algorithm to Estimate GPS Satellite and Receiver L1/L2 Differential Delays and its Application to Regional Ionosphere Modelling. Geomatics Research Australasia, 65, pp1-26.
[71] Satirapod C and Wang J(2000). Comparing the Quality Indicators of GPS Carrier Phase. Geomatics Research Australia, 73, December 2000, 75-92.
[72] Wang J(1998). Stochastic Assessment of the GPS Measurements for Precise Positioning, 11th Int. Tech. Meeting of the Satellite Division of the U.S. Inst. Of Navigation GPS ION'98, Nashville, Tennessee, 15-18 September, 81-89.
[73] Brunner, F.K., Hartinser, H., and Troyer, L.,(1999), GPS Signal Diffraction Modelling: The Stochastic SIGMA-△ Model, Journal of Geodesy, 73,259-267.
[74] Euler, H-J(2000), Advances in Ambiguity Resolution for Surveying Type Applications, Proceedings of ION GPS-2000, Salt Lake City, Utah, September 19-22, 95-103.
[75] Han S. Quality-control Issues Relating To Instantaneous Ambiguities Resolution for Real-time GPS Kinematic Positioning. Journal of Geodesy. 1997 Vol.71, No.6, pp351-361.
[76] 李庆海,陶本藻(1990).概率统计原理和在测量中的应用.测绘出版社,1990.6,北京,370pages.
[77] Teunissen P J G(1995). The invertible GPS ambiguity transformations. Manuscripta geodaetica, Vol.20, No.6, 1995, pp489-497.
[78] Michaud S, Santeree R(2001).Time-Relative Positioning with a Single Civil GPS Receiver. GPS Solutions, Vol. 5, No. 2, 2001, pp71-77
[79] De Jong K(2002). Precise GNSS Positioning Threats and Opportunities. Simposio Brasileiro de Geomatica UNESP, Presidente Prudente, July 2002
[80] Masson A,Burtin D and Sebe M(1997). Kinematic DGPS and INS Hybridizaition for precise Trajectory Determination. NAVIGATION: Journal of The Institute of Navigation, Fall, 1997, Vol.44, No.3, pp313-321.
[81] Teague E H(1997). Flexible Structure Estimation and Control Using The Global Positioning System. Stanford University. Ph.D. Thesis, 1997,160pages.
[82] 姬生月,胡国荣(2000).一种新的GPS整周模糊度快速解算方法.铁道学报,Vol.22,No.6,2000,pp95-98.
[83] 魏子卿,葛茂荣(1998).GPS相对定位数学模型.测绘出版社,1998.2,北京,182pages.
[84] Teunissen P J G(1997). Some Remarks on GPS Ambiguity Resolution. presented at the symposium of the 'Geodatische Woche', 6-11 Oct. 97, Berlin, Germany.
[85] Wang J, Stewart M and Tsakiri M(1995). A discrimination test procedure for ambiguity resolution on-the-fly, Journal of Geodesy,1998(72), 644-653.
[86] Wang J, Stewart M P, and Tsakiri M(2000). A comparative study of the integer ambiguity validation procedures. Earth Planets Space, 2000(52): 813-817.
[87] Teunissen P J G(2000). The Success Rate and Precission of GPS Ambiguities. Journal of Geodesy, 74, 2000, pp.321-326.
[88] 刘经南,陈俊勇,张燕平,李毓麟,葛茂荣(1999).广域差分GPS原理和方法.测绘出版社,1999年1月.北京
[89] Horemuz. M, Sjoberg L E(2002). Rapid GPS Ambiguity Resolution For Short And Long Baselines. Journal of Geodesy, vol.76, No.6-7,2002, pp381-391.
[90] Euler H J and Goad C C(1991). On Optimal Filtering of GPS Dual Frequency Observations Without Using Orbit Information. Bull.Geod, Vol.63,No.2,1991, pp 130-143.
[91] Grass F V and Lee S(1995). High-Accuracy Differential Positioning for Satellite-Based System Without Using Code-phase Measurements. NAVAGATION: Journal of the Institute of Navigation, Vol.42,No.4, Winter 1995,pp605-618.
[92] Sjoberg L E(1996). Application of GPS in Detailed Surveying. Z.F.Verm.wesen. Vol.121, No.10, 1996, pp485-491.
[93] Sjoberg L E(1995). A new method for GPS phase base ambiguity resolution by combined phase and code observables. Surv Rev Vol.34, No.268,1998,pp363-372.
[94] Teunissen P J G(1996). On The Geometry of the Ambiguity Search Space with and Without Ionosphere. Z.F.Verm.wesen. Vol. 121, No.7, 1996, pp332-341.
[95] Teunissen P J G(1997). GPS Double Difference Statistics: With and Without Using Satellite Geometry. Journal of Geodesy. Vol.71,No.3,1997,pp137-145.
[96] Huang D, Ding X, Chen Y(2001). Ambiguity Online Estimation By Combining Dual-Frequency Phase and Carrier Smothed Code Measurements: Performance On Short Baseline. Survey Review, Vol.36, No.253, pp263-272.
[97]Kleusberg A(1986). Ionospheric Propagation Effects In Geodetic Relative GPS Positioning. Manuscripta Geodaetica, Vol.11,No.4 1986,pp256-261.
[98]Lz H B, Ge M, Chen Y Q(1998). Grid Point Search Algorthm for Fast Integer Ambiguity Resolution. Journal of Geodesy, 1998(72),pp639-643.
[99]Kim D, Langley R(2000).A search space optimization technique for improving ambiguity resolution and computational efficiency.Earth Planets Space,2000, 52, pp807-812
[100] Shaw M, Sandhoo K, and Turner D(2000):Modernization of the Global Positioning System, GPS World, September 2000, pp. 36-44.
[101]Hein G. et al., (2001): The Galileo Frequency Structure and Signal Design, Proc. ION GPS 2001, Salt Lake City.September 11-14.
[102]Eissfeller B. et al(2001). Real-Time Kinematic in the Light of GPS Modernization and Galileo. ION GPS 2001, Salt Lake City.September 11-14.
[103]Hatch R(1996). The Promise of a Third Frequency. GPS World, May 1996,pp55-58. Sjoberg L E(1998). On The Estimation of GPS Phase Ambiguities By Triple Frequency Phase And Code Data. Z.F.Verm.wesen. Vol.123, No.5, 1998, pp162-165.
[104]Vollath U, Birnbach S, Landau H, et al(1996). Analysis of Three-Carrier Ambiguity Resolution Technique for Precise Relative Positioning in GNSS-2. NAVIGATION: Journal of The Institute of Navigation, 1999, Vol.46, No.1,pp13-23.
[105]Hatch R, Jung J, Enge P, Pervan B(2000). Civilian GPS:The Benefits of Three Frequencies. GPS solutions ,Vol.3, No.4 ,pp1-9.
[106]Han S, Rizos C(1999). The Impact of Two Additional Civilian GPS Frequencies on Ambiguity Resolution Strategies. 55th National Meeting U.S. Institute of Navigation, "Navigational Technology for the 21st Century". Cambridge, Massachusetts, 28-30 June, 1999,pp315-321
[107]Han S Rizos C(1999). Single-epoch Ambiguity Resolution for Real-time GPS Attitude Determination With The Aid of One-dimensional Optical Fiber Gyro. GPS Solution, Vol.3,No 1, 1999,pp5-12.
[108] 李志林,朱庆(2001).数字高程模型. 武汉大学出版社,2001年7月,武汉.