Integrity Monitoring for Horizontal RTK Positioning: New Weighting Model and Overbounding CDF in Open-Sky and Suburban Scenarios

Abstract

Integrity monitoring is an essential task for ensuring the safety of positioning services. Under a selected probability of hazardous misleading information, the protection levels (PLs) are computed according to a considered threat model to bound the positioning errors. A warning message is sent to users when the PL exceeds a pre-set alert limit (AL). In the short-baseline real-time relative kinematic positioning, the spatially correlated errors, such as the the orbital errors and the atmospheric delays are significantly reduced. However, the remaining atmospheric residuals and the multipath that are not considered in the observation model could directly bias the positioning results. In this contribution, these biases are analysed with the focus put on the multipath effects in different measurement environments. A new observation weighting model considering both the elevation angle and the signal-to-noise ratios is developed and their impacts on the positional results are investigated. The coefficients of the proposed weighting model are determined for the open-sky and the suburban scenarios with the positional benefits maximised. Next, the overbounding excess-mass cumulative distribution functions (EMCs) are searched on the between-receiver level for the weighted phase and code observations in these two scenarios. Based on the mean and standard deviations of these EMCs, horizontal protection levels (HPLs) are computed for the ambiguity-fixed solutions of real experiments. The HPLs are compared with the horizontal positioning errors (HPEs) and the horizontal ALs (HALs). Using the sequential exclusion algorithm developed for the ambiguity resolution in this contribution, the full ambiguity resolution can be achieved in around 100% and 95% of the time for the open-sky and the suburban scenarios, respectively. The corresponding HPLs of the ambiguity-fixed solutions are at the sub-dm to dm-level for both scenarios, and all the valid ambiguity-fixed HPLs are below a HAL of 0.5 m. For the suburban scenario with more complicated multipath environments, the HPLs increase by considering extra biases to account for multipath under a certain elevation threshold. In complicated multipath environments, when this elevation threshold is set to 30 degrees, the availability of the ambiguity-fixed solutions could decrease to below 50% for applications requiring HAL as low as 0.1 m.

Integrity Monitoring of PPP-RTK Positioning; Part I: GNSS-Based IM Procedure

“…For positioning services, users often face a much more conservative (higher) PL than the actual PE. For the dual-frequency multiconstellation (DFMC) satellite-based augmentation system (SBAS), a horizontal positioning accuracy at the sub-meter level would easily lead to horizontal protection level (HPL) above 5 m [1,2], and for the ambiguity-fixed real-time kinematic (RTK) positioning, a horizontal positioning accuracy at sub-cm to cm-level corresponds to HPL at about dm-level [3][4][5]. As such, one may expect a horizontal alert limit (HAL) of ten times (or even higher) the actual horizontal positioning accuracy.…”

“…For DFMC positioning, the IM procedure was defined for aeronautical users with the advanced receiver autonomous integrity monitoring (ARAIM) algorithm [10][11][12][13][14] and the algorithm used for the DFMC SBAS [15]. For ground-based positioning, different IM methods were also discussed for positioning techniques, such as the PPP [16][17][18] and the RTK [4,5]. For PPP-RTK, a method was proposed to detect mismodeled biases in the network corrections in [19], which could be used to validate the network corrections as part of the fault detection and exclusion (FDE) procedure.…”

A linear Kalman filter-based integrity monitoring considering colored measurement noise

“…They also require heavy computation loads with complex implementations. For the stochastic modeling approach, it mainly focuses on reducing the impact of the colored noise by adjusting the weighting of the observations according to satellite elevations (Li 2016), signalto-noise ratios (Zhu et al 2018a;Han et al 2019;Ni et al 2020), and both the elevations and signal-to-noise ratios (Wang et al 2020). They can provide realistic protection levels for integrity monitoring.…”

On the Recursive Joint Position and Attitude Determination in Multi-Antenna GNSS Platforms

“…The unknown number of integer cycles between satellite and receiver, so-called ambiguities, must be estimated to enable high-precision navigation. The ambiguities' estimation process is widely known as ambiguity resolution (AR) [2][3][4][5], which in turn results in a challenging estimation procedure.…”