An enhanced least squares residual RAIM algorithm based on optimal decentralized factor

The field of GNSS integrity comprises a plethora of integrity related algorithms, each featured with different characteristics. These algorithms use a priori information of some parameters in order to provide integrity information to the user. One type of these algorithms, RAIM, is extensively used in the maritime domain in order to provide an indication if the position calculated is likely to be outside of the requirements of maritime performance standards, as it is required by IMO regulation. The term “Classical RAIM” refers to fully autonomous algorithms which can implement only one, a combination or all the following capabilities: Fault Detection, Fault Exclusion and Protection Level computation. In order to provide this indication, a GNSS receiver shall incorporate RAIM using at least Fault Detection (FD) algorithms, or similar means to determine if accuracy is within the performance standards and provide an integrity indication. In order to harmonise and ensure the correct RAIM algorithms implementation, its usage is standardised by the standard IEC 61108, in particular 1 and 3 series for GPS and Galileo constellations. The current RAIM definition in standards does not constrain the specific RAIM algorithm implementation deliberately in order to let the manufactures implement the most suitable one for their applications. In addition, in order to prove that a receiver is compliant with the requirements specified in this standard, two simple tests are proposed. The first one intends to test the performance of the receiver under safe and caution states, and the other one tests the unsafe state. However, as it is recognised by IALA in the last workshop on the future of marine radiobeacons, “current implementations of Receiver Autonomous Integrity Monitoring (RAIM) are considered inadequate due to the current lack of maritime specific RAIM algorithms.” It has been observed some limitation of current RAIM implementations beyond a specific algorithm for maritime. First of all, the relaxed requirements, in terms of high probabilities of false alarms and of not detecting an error condition, might be justified due to the limitations expected from some implementations of RAIM algorithms. In addition, requirements for GPS and Galileo RAIM differs significantly. Secondly, they are based on some hypothesis as single-failure assumption, a priory estimation of error values components (too conservative in order to provide the integrity required for any user under any condition) or the no existence of biases in faultfree measurements that may not ensure the integrity required if these hypothesis are not met in maritime domain. Finally, considering the simplicity of the aforementioned tests, which do not provides a set of parameters for testing or even assess the probabilities of miss-detection or false alarm, there is no assurance that the RAIM algorithm implemented in the receiver correctly provides the integrity required. To ensure this, it would be necessary to improve the test method in order to characterize the value of the introduced error and add new tests to evaluate the complete set of requirements to the implemented integrity algorithm. The GSA (European GNSS Agency), under GSALOT3TRANS framework contract, analysed the implementation of EGNSS in the area of transport applications. In particular, the Specific Contract 7 (SC7) MarTech it is being assessed the potential use of SBAS combined with RAIM in maritime and inland waterways (IWW) domains. The industrial partners of this specific contract are VVA Brussels (prime) and GMV. Although is not contemplated in any of the aforementioned regulations, the use of SBAS on top of other GNSS technologies that use RAIM may imply some important advantages. The first advantage and the most obvious of the SBAS corrections usage on top of RAIM is the increased performances in terms of accuracy, availability and continuity. The use of SBAS integrity information may also overcome the limitation of some RAIM algorithms that are only able to detect one faulty satellite. SBAS integrity messages also contains valuable information about the estimation of error components that may be used by the RAIM algorithm on real time with enough level of integrity to improve the performance. The aim of this paper is to provide a summary of the activities developed so far as part of GSALOT3TRANS SC7 regarding the current RAIM limitations in the maritime domain and the potential use of SBAS in combination with it to overcome some of these limitations.

Satellite Navigation Receiver Autonomous Integrity Monitoring (RAIM) is developed for detection and recognition of satellite faults using the redundant observation values of receiver itself. This article first makes a comparative analysis to the conventional and recently proposed RAIM fault detection and identification methods, and then points out that the conventional fault identification methods have such weakness as low fault detection probability and high false alarm probability in the situation of simultaneous multiple faulty satellites, while the recently proposed multi-satellite fault identification methods require excessive computation work though enjoy a higher detection probability. To solve these problems, a new RAIM multiple satellite fault detection and recognition method is proposed in this paper, which is characterized by high detection probability, low false alarm probability and low computation load, practicable for project implementation. Based on a simulation analysis, it turns out that this method has a higher detection probability without false alarm at all. This method requires so low computation work that it only needs 2 m times of least squares residuals fault detection and m times of fault identification in m (m > 0) faulty satellites situation, showing a very promising application value.

This paper evaluates the potential capacity of Receiver Autonomous Integrity Monitoring (RAIM) algorithms for Global Positioning System (GPS) and GPS Aided GEO Augmented Navigation (GAGAN) to support approach and landing phases of flight with vertical guidance. As the traditional RAIM does not support vertical guidance, Advanced RAIM (ARAIM) with potential to achieve worldwide coverage of vertical guidance, is used. These algorithms have focused on the Horizontal Protection Level (HPL) and Vertical Protection Level (VPL). User position is computed by detecting and excluding faults within the navigation solution and position accuracies are also provided. It is found that using RAIM, Position Dilution of Precision (PDOP) mean was good (1.5674) and Position Error (PE) was estimated to be 9.4042m with Fault Detection and Exclusion (FDE) implementation. While on the other hand, to increase horizontal and vertical accuracies, Advanced RAIM algorithm is implemented using GPS and GAGAN data. In case of GPS, Horizontal Protection Error (HPE) mean is 32.8541m and Vertical Protection Error (VPE) mean is 19.9901m. In case of GAGAN, HPE mean is 2.7190m and VPE mean is 3.3010m, thus achieving 95 percent accuracy requirement.

Two Receiver Autonomous Integrity Monitoring (RAIM) architectures, Advanced RAIM (A-RAIM) and Relative RAIM (R-RAIM), are compared with two different RAIM algorithms, the Classic method and the Multiple Hypothesis Solution Separation (MHSS) method. The difference between A-RAIM and R-RAIM is in the positioning methods that produce different error models and projection matrices for integrity monitoring. The difference between RAIM algorithms lies in the methods of risk distribution. The influences of different positioning methods on integrity results are analysed in this paper via a generalized RAIM framework. Simulation results for the LPV-200 service with worldwide coverage show that the R-RAIM position domain method has the best results, while the differences between these methods decrease with application of the optimization method.

With the considerable increase of visible satellites for positioning, the fault detection and identification performance of Range Consensus (RANCO) algorithm for Receiver Autonomous Integrity Monitoring (RAIM) will significantly be improved. However, the calculation amount of RANCO algorithm will exponentially increase for the sharp addition of visible satellite subsets. This paper proposes a modified RANCO algorithm based on genetic algorithm (GA-RANCO) for RAIM to inhibit the exponentially expanded calculation amount. To reduce the calculation amount in searching the optimal minimal necessary subset (MNS), the preselection step is developed to speed up the convergence process of GA-RANCO. It is executed to exclude the chromosome-represented MNS for which the count of faulty satellites will exceed the upper limit of independent simultaneous satellite faults to be monitored. Mathematical simulations are introduced to determine the GA parameters, and simulation experiments under different schemes are designed to evaluate the performance of GA-RANCO algorithm. Results illustrate that the time consumption under a large number of visible satellites of GA-RANCO is much lower than that of RANCO and the faulty detection and identification performance of GA-RANCO is the same as that of RANCO.

The space constellation of BeiDou Navigation Satellite System(BDS)has three main components, Geostationary Earth Orbits (GEOs), Medium Earth Orbits (MEOs) and Inclined Geosynchronous Satellite Orbits(IGSOs).This paper selected 6 satellite respectively in three types to simulate their exiting service, and used the statistical methods to assess receiver autonomous integrity monitoring（RAIM） availability and fault detection （FD） capability of BeiDou14（Phase Ⅱ with 14 satellites）under the circumstances. This paper assessed RAIM availability performance from satellites and constellation geometry configuration by the number of visible satellites (NVS, NVSg5) and position dilution of precision (PDOP, PDOP≤6) together. The FD capability of RAIM is assessed by the maximum minimal detectable bias (MDB) and the maximum minimal detectable effect (MDE). The analyses of simulation results testify that the exiting of single MEO or IGSO satellite have no obvious effect on RAIM availability and error detection ability. However GEO satellite’s exiting can make the number of points in where the constellation geometry is not available and maximum minimum detectable deviation and maximum minimum detectable influence significantly increase. Relative to other two satellites, GEO satellites’ health have a significant impact on the RAIM performance of BDS.

The optimum test statistic for the detection of binary sure signals in stationary Gaussian noise takes a particularly simple form, that of a correlation integral, when the solution, denoted by q(t) , of a given integral equation is well behaved (L_{2}) . For the case of a rational noise spectrum, a solution of the integral equation can always be obtained if delta functions are admitted. However, it cannot be argued that the test statistic obtained by formally correlating the receiver input with a q(t) which is not L_{2} is optimum. In this paper, a rigorous derivation of the optimum test statistic for the case of exponentially correlated Gaussian noise R(\tau) = \sigma^{2} e^{-\alpha|\tau|} is obtained. It is proved that for the correlation integral solution to yield the optimum test statistic when q(t) is not L_{2} , it is sufficient that the binary signals have continuous third derivatives. Consideration is then given to the case where a, the bandwidth parameter of the exponentially correlated noise, is described statistically. The test statistic which is optimum in the Neyman-Pearson sense is formulated. Except for the fact that the receiver employs \alpha_{\infty} (which in general depends on the observed sample function) in place of \alpha , the operations of the optimum detector are unchanged by the uncertainty in \alpha . It is then shown that almost all sample functions can be used to yield a perfect estimate of \alpha . Using this estimate of \alpha , a test statistic equivalent to the Neyman-Pearson statistic is obtained.

In family-based association studies, an optimal test statistic with asymptotic normal distribution is available when the underlying genetic model is known (e.g., recessive, additive, multiplicative, or dominant). In practice, however, genetic models for many complex diseases are usually unknown. Using a single test statistic optimal for one genetic model may lose substantial power when the model is mis-specified. When a family of genetic models is scientifically plausible, the maximum of several tests, each optimal for a specific genetic model, is robust against the model mis-specification. This robust test is preferred over a single optimal test. Recently, cost-effective group sequential approaches have been introduced to genetic studies. The group sequential approach allows interim analyses and has been applied to many test statistics, but not to the maximum statistic. When the group sequential method is applied, type I error should be controlled. We propose and compare several approaches of controlling type I error rates when group sequential analysis is conducted with the maximum test for family-based candidate-gene association studies. For a two-stage group sequential robust procedure with a single interim analysis, two critical values for the maximum tests are provided based on a given alpha spending function to control the desired overall type I error.

Kumazawa (1986) introduced a class of test statistics for testing whether a life distribution is new better than used in expectation under a random censorship model. The purpose of this paper is to give a proof of asymptotic normality of test statistics under contiguous sequence of alternatives by using a counting-process approach. For uncensored case the optimal test statistic in this class is seen to lead a locally most powerful tests for contiguous sequence of particular parametric alternatives.

Receiver Autonomous Integrity Monitoring (RAIM) has been successfully used for fault detection and exclusion in aviation applications. For airborne environment, the Geometric Dilution Of Precision (GDOP) and pseudo-range measurement quality is good. However, for urban canyon environment the GDOP may increase much and the pseudo-range measurement may contain huge multipath error. In this case, the exclusion of any pseudo-range measurement with multipath may make the GDOP increase much more and make the user position accuracy even worse. In this work, we propose an Urban Adapted-RAIM (UA-RAIM) algorithm to adjust the particular poor satellite geometry and multipath environment of urban canyon. Exclusion Accuracy Filter (EAF) is designed to check the position accuracy before and after fault exclusion. The fault satellite which can improve the positioning accuracy is processed using weighted estimation technique. Static experiment was carried out and a reflector was set to simulate the urban canyon environment. The user position errors in North, East and Up direction are 63.70%, 55.25% and 64.52% lower compared with the RAIM algorithm. From the urban vehicle tests, the vehicle positions of UA-RAIM are more like a straight line compared with RAIM. The 95% accuracy decreases from 20.32m to 16.55m using UA-RAIM and about 81.45% compared with the original.

A global navigation satellite system (GNSS)-based navigation is a challenging task in a signal-degraded environments where GNSS signals are distorted by multipath and attenuated by fading effects: the navigation solution may be inaccurate or unavailable. A possible approach to improve accuracy and availability is the joint use of measurements from different GNSSs and quality check algorithms; this approach is investigated here using live GPS and Galileo signals. A modified receiver autonomous integrity monitoring (RAIM) algorithm, including geometry and separability checks, is proposed to detect and exclude erroneous measurements: the multi-constellation approach provides redundant measurements, and RAIM exploits them to exclude distorted observations. The synergy between combined GPS/Galileo navigation and RAIM is analyzed using live data; the performance is compared to the accuracy and availability of a GPS-only solution. The tests performed demonstrate that the methods developed are effective techniques for GNSS-based navigation in signal-degraded environments. The joint use of the multi-constellation approach and of modified RAIM algorithms improves the performance of the navigation system in terms of both accuracy and availability.

In this article, the problem of detecting and excluding faulty global navigation satellite systems (GNSSs) measurements at the receiver end is formulated as a parameterized quadratic programming (PQP) problem. Compared to the existing fault detection and exclusion (FDE) methods, which mostly rely on exhaustive search, the PQP method is computationally efficient for finding the outliers even when the number of outliers is moderate or large. In the context of multiconstellation GNSS where the probability of multiple simultaneous faults is increased, the PQP method is ideal for the task of fault exclusion since the computation time does not increase with the number of fault hypotheses. It is noted that this article addresses the computational load due to the exclusion function only. The integrity risk bound and continuity risk bound are of fundamental importance to assess the performance of FDE algorithms for safety-critical applications. With the aim to benefit safety-critical applications, the PQP method is integrated with the integrity risk bound and the continuity risk bound derived for FDE using Chi-squared receiver autonomous integrity monitoring (RAIM). It is emphasized that the integration of the PQP method and the integrity and continuity risk bounds do not make the PQP method a practical integrity monitoring method. This is because the computation of the integrity risk bound is still combinatorial and the resulting integrity risk bound is rather conversative. Instead, the integration allows for the opportunity to refine the PQP method so that it can be considered a practical integrity monitoring method. In particular, improvements to reduce the computational load for the Chi-squared RAIM FDE integrity risk bound calculation can readily be applied to the integrity risk bound calculation for the PQP method. Also, further research on PQP parameter tuning can be pursued to tighten the integrity risk bound.

According to the measurement noise feature of GPS receiver and the degeneracy phenomenon of particle filter (PF), in order to alleviate the sample impoverishment problem for PF, GPS receiver autonomous integrity monitoring (RAIM) algorithm based on PF algorithm combining neural network was proposed, which was used to improve the importance state adjustment of particle filter algorithm. The PF algorithm based on neural network is analized. And the test statistic of satellite fault detection is set up. The satellite fault detection is undertaken by checking the cumulative log-likelihood ratio (LLR) of system state of GPS receiver.The proposed algorithm was Validated by the measured real raw data from GPS receiver, which are deliberately contaminated with the bias fault and ramp fault, the simulation results demonstrate that the proposed algorithm can accurately estimate the state of GPS receiver in the case of non-Gaussian measurement noise, effectively detect and isolate fault satellite by establishing log-likelihood ratio statistic for consistency test and improve the accuracy of detection performance.

In the article, we exploit the Pearson system of distributions to obtain expressions for the posterior mean and posterior variance in Tweedie’s formula. This has interesting consequences in the study of micro-array data where the interest is uncovering unusual genes. Another application deals with the development of new non-parametric tests for the two sample problems of location and of scale. These tests are based on an approximation of the locally optimal score test statistics.

The eigenvalues of the sample covariance matrix can capture signal correlations and noise characteristics well, which are widely used for spectrum sensing in cognitive radio networks. Some totally blind spectrum sensing algorithms were proposed, such as maximum eigenvalue-to-arithmetic mean (ME-AM), maximum eigenvalue-to-geometric mean (ME-GM), and arithmetic-to-geometric mean of eigenvalues (AGM) methods. This article makes full use of the advantages of these algorithms and proposes a universal spectrum sensing algorithm based on maximum eigenvalue, arithmetic mean, and geometric mean of eigenvalues. The proposed algorithm takes the weighted geometric mean of the test statistics of the ME-AM and AGM algorithms as new test statistic and includes the ME-AM, ME-GM, and AGM algorithms as special cases. Following the random matrix theory framework, in a similar vein to the ME-AM and ME-GM algorithms, we derive the analytical expressions of false alarm probability, threshold, and detection probability of the proposed method using the Tracy-Widom distribution of maximum eigenvalue. In addition, we discuss the problem of designing the optimal weighting factor through theoretical analysis and simulation experiments. Finally, simulation results verify that the universal algorithm can effectively improve the detection performance.