New method for single epoch, single frequency land vehicle attitude determination using low-end GPS receiver

Stand-alone, unaided, single frequency, single epoch attitude determination is the most challenging case of GNSS compass processing. For land vehicle applications, the baseline approximately lies in the plane of the local geodetic horizon. This provides an important constraint that can be exploited to directly aid the ambiguity resolution process. We fully integrate the constraint into the observation equations, which are transformed orthogonally. Our method can acquire the high-quality float solution by means of a heading search strategy. The fixed solution is obtained by weighted constrained integer least squares for each possible heading. The correct solution is identified by three consecutive steps: Kolmogorov?CSmirnov test, heading verification, and global minimizer of the fixed ambiguity objective function. The analysis focuses on single frequency, single epoch land vehicle attitude determination using low-end GPS receivers with very low precision of carrier phase and code measurements. The error analysis is given for choosing a proper baseline length in practical application. Experimental results demonstrate that this scheme can improve the ambiguity success rate for very short baseline.     

Testing of a new single-frequency GNSS carrier phase attitude determination method: land,ship and aircraft experiments

Global navigation satellite system (GNSS) ambiguity resolution is the process of resolving the unknown cycle ambiguities of the carrier phase data as integers. The sole purpose of ambiguity resolution is to use the integer ambiguity constraints as a means of improving significantly on the precision of the remaining GNSS model parameters. In this contribution, we consider the problem of ambiguity resolution for GNSS attitude determination. We analyse the performance of a new ambiguity resolution method for GNSS attitude determination. As it will be shown, this method provides a numerically efficient, highly reliable and robust solution of the nonlinearly constrained integer least-squares GNSS compass estimators. The analyses have been done by means of a unique set of extensive experimental tests, using simulated as well as actual GNSS data and using receivers of different manufacturers and type as well as different platforms. The executed field tests cover two static land experiments, one in the Netherlands and one in Australia, and two dynamic experiments, a low-dynamics vessel experiment and high-dynamics aircraft experiment. In our analyses, we focus on stand-alone, unaided, single-frequency, single-epoch attitude determination, as this is the most challenging case of GNSS compass processing.     

Fast integer least-squares estimation for GNSS high-dimensional ambiguity resolution using lattice theory

GNSS ambiguity resolution is the key issue in the high-precision relative geodetic positioning and navigation applications. It is a problem of integer programming plus integer quality evaluation. Different integer search estimation methods have been proposed for the integer solution of ambiguity resolution. Slow rate of convergence is the main obstacle to the existing methods where tens of ambiguities are involved. Herein, integer search estimation for the GNSS ambiguity resolution based on the lattice theory is proposed. It is mathematically shown that the closest lattice point problem is the same as the integer least-squares (ILS) estimation problem and that the lattice reduction speeds up searching process. We have implemented three integer search strategies: Agrell, Eriksson, Vardy, Zeger (AEVZ), modification of Schnorr–Euchner enumeration (M-SE) and modification of Viterbo-Boutros enumeration (M-VB). The methods have been numerically implemented in several simulated examples under different scenarios and over 100 independent runs. The decorrelation process (or unimodular transformations) has been first used to transform the original ILS problem to a new one in all simulations. We have then applied different search algorithms to the transformed ILS problem. The numerical simulations have shown that AEVZ, M-SE, and M-VB are about 320, 120 and 50 times faster than LAMBDA, respectively, for a search space of dimension 40. This number could change to about 350, 160 and 60 for dimension 45. The AEVZ is shown to be faster than MLAMBDA by a factor of 5. Similar conclusions could be made using the application of the proposed algorithms to the real GPS data.     

A constrained LAMBDA method for GPS attitude determination

An improved method to obtain fixed integer ambiguity in GPS attitude determination is presented. Known conditions are utilized as constraints to acquire attitude information when the float solution and its variance–covariance matrix are not accurate enough. The searching ellipsoidal region is first expanded to compensate for errors caused by the inaccurate float solution. Then the constraints are used to shrink the region to a proper size, which maintains the true integer ambiguity. Experimental results demonstrate that this scheme gives a fast search time and a higher success rate in determining the fixed integer ambiguity than the unconstrained method. The accuracy of attitude angles is also improved.

采用调零天线阵测向解GNSS姿态仪的整周模糊度

由多个单元天线组成的GNSS调零天线阵通常用于在大功率干扰信号来波方向上形成天线波束方向图零点,以此来抗压制性干扰。采用此调零天线阵所自然形成的二维短基线,按照电子侦察中多基线干涉仪测向原理,通过短基线的相位差测量值来解GNSS姿态仪长基线的相位差模糊,从而实现了GNSS姿态仪的整周模糊度的实时解算。该方法通过GNSS姿态仪与调零天线阵的组合应用,不仅提高了解模糊的性能,而且增强了整个系统抗干扰反欺骗的能力,从而为GNSS姿态仪和调零天线的拓展应用提供了重要参考。      

The affine constrained GNSS attitude model and its multivariate integer least-squares solution

A new global navigation satellite system (GNSS) carrier-phase attitude model and its solution are introduced in this contribution. This affine-constrained GNSS attitude model has the advantage that it avoids the computational complexity of the orthonormality-constrained GNSS attitude model, while it still has a significantly improved ambiguity resolution performance over its unconstrained counterpart. The functional and stochastic model is formulated in multivariate form, for one-, two- and three-dimensional antenna arrays, tracking GNSS signals on an arbitrary number of frequencies with two or more antennas. The stochastic model includes the capability to capture variations in the antenna-quality within the array. The multivariate integer least-squares solution of the model parameters is given and the model’s ambiguity success-rate is analysed by means of the ambiguity dilution of precision (ADOP). A general closed-form expression for the affine-constrained ADOP is derived, thus providing an easy-to-use and insightful rule-of-thumb for the ambiguity resolution capabilities of the affine constrained GNSS attitude model.     

利用迭代加权模糊度函数法的单历元模糊度固定

为提高全球导航卫星系统GNSS在复杂环境下的定向成功率，将迭代加权的思想与模糊度函数法（AFM）相结合，提出迭代加权模糊度函数法（IWAFW）。基于AFM算法，通过设计新的适应度函数，利用残差计算权重，实现对不同卫星信号权重的自动调节，并结合惯性传感器给出的姿态信息，压缩搜索空间，降低计算量。通过实测试验验证，在复杂环境中，相比于AFM和带基线长度约束的最小二乘模糊度去相关算法（CLAMBDA），该算法能够有效提高模糊度固定成功率。     

非线性基线长约束条件线性化近似对模糊度解算影响

GNSS动态相对定位中常附加非线性的基线长约束进行解算, 而LAMBDA方法只能处理无约束或者线性约束的模型, 为了应用LAMBDA方法, 应对非线性约束条件进行线性化近似。通常附加该约束后, 模糊度固定成功率会提高, 但对于超短基线有时反而会降低。何种条件下附加线性化近似的基线长约束条件可以提高模糊度固定成功率尚未有定论。本文基于附加基线长约束的GNSS相对定位数学模型, 推导基线长约束条件线性化近似余项对浮点解的最大影响值公式, 给出基线长约束能否线性化近似的诊断条件。当该条件满足时, 线性化近似余项影响可以忽略, 附加线性化近似的基线长约束可以改善浮点解解算精度, 提高模糊度固定成功率;若不满足, 则线性化近似余项影响可能不可以忽略, 附加约束会因浮点解有偏不能固定为正确的模糊度, 并通过算例验证了相关结论。     

GPS/陀螺组合测姿中整周模糊度的快速解算

采用方向余弦矩阵描述姿态,建立GPS/陀螺组合姿态确定系统模型,由矩阵Kalman滤波方法解算整周模糊度的浮点解,然后再利用MCLambda方法得到整周模糊度固定解。仿真实验结果表明,附加方向余弦矩阵约束的Kalman滤波方法可以有效地提高整周模糊度浮点解的精度,使得整周模糊度的固定成功率和效率均得到提高,尤其是在GPS观测条件较差的情况下。     

陆地导航中GNSS/陀螺仪组合实时测姿方法

在陆地导航系统中使用GNSS/INS组合导航会增加系统成本,多天线GNSS测姿精度受基线长度影响,且存在的模糊度固定问题。本文提出仅利用一个陀螺仪和单天线GNSS组合来进行实时测姿。先由单天线GNSS计算姿态角3参数,航向角为陆地导航的关键参数,为此将陀螺信息与GNSS导出的航向角进行融合。分析了单天线测姿在载体静止或低速运动时精度很差的原因,提出了在组合滤波中进行解决的方案。推导了GNSS和陀螺信息融合的滤波模型,将陀螺仪信息作为状态模型的控制输入,以GNSS航向为滤波观测值。实验结果表明,GNSS/陀螺仪组合计算的航向角精度和可靠性相对GNSS测姿结果均有很大提升。     

MLAMBDA: a modified LAMBDA method for integer least-squares estimation

The least-squares ambiguity Decorrelation (LAMBDA) method has been widely used in GNSS for fixing integer ambiguities. It can also solve any integer least squares (ILS) problem arising from other applications. For real time applications with high dimensions, the computational speed is crucial. A modified LAMBDA (MLAMBDA) method is presented. Several strategies are proposed to reduce the computational complexity of the LAMBDA method. Numerical simulations show that MLAMBDA is (much) faster than LAMBDA. The relations between the LAMBDA method and some relevant methods in the information theory literature are pointed out when we introduce its main procedures.     

FirCAR算法的OTF快速定位方法

根据GNSS不同频率间整周模糊度的约束关系,提出一种基于多频整周模糊度间关系约束的模糊度新算法(dual-frequency integer relationship constrained ambiguity resolution,FirCAR)。FirCAR可快速动态解算出高高度角卫星的整周模糊度,将已经固定的整周模糊度视为高精度的伪距观测值应用到下一步的浮点解重算中。结合模糊度搜索算法,如LAMBDA,在模糊度搜索方面的高效性,根据重算后的浮点解进一步解算其他未固定的模糊度解。模糊度固定成功后,即可实现OTF(on the fly)快速定位。实测数据表明,FirCAR算法在静态和动态观测条件下,模糊度初始化所用的平均观测历元数分别为1.04和1.10。与常规的模糊度搜索算法的对比试验表明,结合FirCAR算法模糊度固定所用的观测历元数分别减少了39%和18%。     

Single-Epoch Ambiguity Resolution for Real-Time GPS Attitude Determination with the Aid of One-Dimensional Optical Fiber Gyro

High-accuracy real-time GPS-based attitude determination requires that integer ambiguities be resolved very quickly so that the attitude angles can be output with minimum delay. This article describes an attitude determination algorithm that can resolve integer ambiguities instantaneously, relative to one antenna of a multi-antenna array configuration. The carrier phase and pseudorange observations are used with fixed baseline length constraints and fiberoptic gyro data. Real-time stochastic model improvement using empirical elevation-dependent standard deviation function and an estimated scale factor are a feature of this algorithm. Integer ambiguity search using the LAMBDA method, sophisticated validation criteria, and an adaptive procedure has also been implemented within the software. An experiment was carried out using four Leica dual-frequency GPS receivers (but only the L1 carrier phase and pseudorange data were used) and a low-cost fiberoptic on a car. The results indicate that integer ambiguities can be resolved on a single-epoch basis with a 98.9% success rate. ? 1999 John Wiley & Sons, Inc.     

基于精选基准消秩亏的GNSS参考网数据处理方法

全球导航卫星系统（GNSS）参考网多用于估计卫星轨道/钟差、监测地表形变和速度场、确定精密地球自转参数等方面。相关数据处理模式包括：双差基线解（DD）和非差精密单点定位（PPP）等。本文首先从GNSS基本观测方程出发,通过选取两组基准参数,导出了上述两模式下的列满秩观测方程,然后分析了它们的不足,例如：相位偏差在DD模式中吸收了钟差,丧失了时不变特性;模糊度在PPP模式中吸收了相位偏差,失去了整数性。基于上述分析,本文提出了一种新的参考网数据处理方案,以充分融合DD和PPP模式的优势。它的关键策略是精选基准参数,以达到消秩亏的目的,具体优点体现在：相位偏差独立可估,若合理约束为时不变参数,可充分减少参数个数,提高网解精度;待估模糊度具备整周特性,经由模糊度固定,可改善网解可靠性。     

GNSS双频整周关系约束模糊度算法研究

根据GNSS双频载波相位观测值间的特定关系,提出了一种基于双频整周关系约束的模糊度解算方法(FirCAR)。该方法在局部整数范围内可将载波相位的等效波长增长,以利于整周模糊度的快速解算。不同长度的基线数据实验证明了该算法的正确性和有效性,并分析了卫星截止高度角对解算结果的影响。     

An enhanced strategy for GNSS data processing of massive networks

Although the computational burden of global navigation satellite systems (GNSS) data processing is nowadays already a big challenge, especially for huge networks, integrated processing of denser networks with data of multi-GNSS and multi-frequency is desired in the expectation of more accurate and reliable products. Based on the concept of carrier range, in this study, the precise point positioning with integer ambiguity resolution is engaged to obtain the integer ambiguities for converting carrier phases to carrier ranges. With such carrier ranges and pseudo-ranges, rigorous integrated processing is realized computational efficiently for the orbit and clock estimation using massive networks. The strategy is validated in terms of computational efficiency and product quality using data of the IGS network with about 460 stations. The experimental validation shows that the computation time of the new strategy increases gradually with the number of stations. It takes about 14 min for precise orbit and clock determination with 460 stations, while the current strategy needs about 82 min. The overlapping orbit RMS is reduced from 27.6 mm with 100 stations to 24.8 mm using the proposed strategy, and the RMS could be further reduced to 23.2 mm by including all 460 stations. Therefore, the new strategy could be applied to massive networks of multi-GNSS and multi-frequency receivers and possibly to achieve GNSS data products of higher quality.     

Integrity monitoring of high-accuracy GNSS-based attitude determination

Global navigation satellite system (GNSS)-based attitude determination has been widely used in the navigation fields. The reliability of attitude determination is indispensable for safety-critical applications. Since the multi-antenna-based attitude determination uses ultra-short baseline carrier phase double differential processing, the incorrect ambiguity resolution and the excessive measurement error are two main factors affecting the reliability of attitude determination. Since the ambiguity correctness validation cannot guarantee the reliability of the attitude solution, therefore an integrity monitoring method is proposed for the attitude determination in the measurement domain. The proposed integrity monitoring method constructs double test statistics to satisfy the requirements of integrity risk and continuity risk, simultaneously. Furthermore, the attitude alarm limit has been derived from the required navigation performance as the threshold to test the availability of attitude determination. The performance of the proposed method is tested by conducting the static and kinematic experiments, respectively. The static results have shown that the proposed integrity monitoring method is able to monitor the ambiguity fault and the excessive measurement noise. The real-world kinematic data have indicated that the proposed method can reduce the maximum attitude error by about 2.3°, when compared with the standalone ratio-test method.     

Computed success rates of various carrier phase integer estimation solutions and their comparison with statistical success rates

The success rate of carrier phase ambiguity resolution (AR) is the probability that the ambiguities are successfully fixed to their correct integer values. In existing works, an exact success rate formula for integer bootstrapping estimator has been used as a sharp lower bound for the integer least squares (ILS) success rate. Rigorous computation of success rate for the more general ILS solutions has been considered difficult, because of complexity of the ILS ambiguity pull-in region and computational load of the integration of the multivariate probability density function. Contributions of this work are twofold. First, the pull-in region mathematically expressed as the vertices of a polyhedron is represented by a multi-dimensional grid, at which the cumulative probability can be integrated with the multivariate normal cumulative density function (mvncdf) available in Matlab. The bivariate case is studied where the pull-region is usually defined as a hexagon and the probability is easily obtained using mvncdf at all the grid points within the convex polygon. Second, the paper compares the computed integer rounding and integer bootstrapping success rates, lower and upper bounds of the ILS success rates to the actual ILS AR success rates obtained from a 24 h GPS data set for a 21 km baseline. The results demonstrate that the upper bound probability of the ILS AR probability given in the existing literatures agrees with the actual ILS success rate well, although the success rate computed with integer bootstrapping method is a quite sharp approximation to the actual ILS success rate. The results also show that variations or uncertainty of the unit–weight variance estimates from epoch to epoch will affect the computed success rates from different methods significantly, thus deserving more attentions in order to obtain useful success probability predictions.     

Development of an instantaneous GNSS/MEMS attitude determination system

Global navigation satellite systems (GNSS) are well suited for attitude determination. The key to high-precision GNSS-attitude determination is the ambiguity resolution. In case of kinematic applications, the rapidity of this process is of particular importance. We present a new instantaneous attitude determination system for GNSS-challenged environments. The single-epoch ambiguity resolution is performed by the ambiguity function method aided by a micro-electro-mechanical system (MEMS), leading to success rates above 99 %. The GNSS/MEMS fusion is realized by the use of an extended Kalman filter. When the system is stationary, a state vector augmentation with a shaping filter reduces systematic effects in the GNSS-attitudes. By means of two field experiments, the system was tested successfully. Despite poor GNSS measurement conditions, it provided reliable and accurate results, with empirical standard deviations in the range of 0.03–0.1 deg for the yaw angle.     

下三角Cholesky分解的整数高斯变换算法

针对全球导航卫星系统(GNSS)载波相位测量中,基于整数最小二乘估计准则解算整周模糊度问题。目前以LAMBDA降相关算法和Lenstra-Lenstra-Lovász(LLL)为代表的规约算法应用最为广泛。由于不同算法采用的模糊度方差-协方差阵的分解方式不同,导致难以合理地进行不同算法性能的比较。该文通过分析LAMBDA算法的降相关特点,从理论上推出基于下三角Cholesky分解多维情形下的整数高斯变换的降相关条件及相应公式,并与分解方式不同的LAMBDA和LLL算法作了对比。实验结果表明,降相关采用的分解方式将会直接影响计算复杂度和解算性能,因此该文推导的整数高斯变换算法便于今后基于下三角Cholesky分解的降相关算法间的合理比较。