**1. Introduction**

The emerging mission-critical applications in urban areas are placing more stringent requirements on the underpinning positioning, navigation, and timing (PNT) systems [1]. Due to complementary characteristics, GNSS and Inertial Measurement Unit (IMU) sensors are commonly used in an integrated architecture to support location-based services. However, in urban areas, GNSS signals are susceptible to attenuation and blockage in the built environment, resulting in multipath effects and non-line of sight (NLOS) reception. The satellite faults, defined in this paper, describe corresponding measurements that have acceptable errors, irrespective of the source and type of failure. These errors in the measurements will affect the accuracy and reliability of positioning from integrated IMU/GNSS systems. Therefore, it is particularly important to develop an effective fault detection scheme that can be applied to GNSS measurements so as to ensure quality control of integrated IMU/GNSS systems.

Fault Detection and Exclusion (FDE)-based GNSS measurements quality control has been investigated for many years. The basic FDE methods include: (1) range and position comparison [2]; (2) minimum least squares residuals [3]; (3) parity space [4]; (4) maximum slope (MS) [5]. The four methods have been shown to be largely equivalent.

The performance of FDE algorithms is related to GNSS signal quality and the number of visible satellites. With the increase in constellations beyond GPS, there are more visible satellites and better signal design, greatly improving positioning quality, and promoting the

**Citation:** Sun, R.; Qiu, M.; Liu, F.; Wang, Z.; Ochieng, W.Y. A Dual w-Test Based Quality Control Algorithm for Integrated IMU/GNSS Navigation in Urban Areas. *Remote Sens.* **2022**, *14*, 2132. https:// doi.org/10.3390/rs14092132

Academic Editors: Yuwei Chen, Changhui Jiang, Qian Meng, Bing Xu, Wang Gao, Panlong Wu, Lianwu Guan and Zeyu Li

Received: 17 March 2022 Accepted: 20 April 2022 Published: 29 April 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

development of FDE algorithms. Some new FDE algorithms have appeared, such as: GPS Integrity Channel (GIC), which is a hybrid between the GIC approach and the maximum solution separation RAIM technique [6]; Novel Integrity Optimized RAIM [7]; Optimally Weighted Average Solution [8]. Given that the probability of multiple faults in a single constellation is relatively small, the above FDE algorithms assume a single fault at a time.

In medium to high density built environments coupled with the increase in the number of constellations, the probability of simultaneous multiple faults increases. Therefore, increasing research effort is dedicated to developing algorithms for simultaneous multiple FDE. These methods include the use of statistics, calculated based on the w-test, to detect and identify outlier faults [9]. A theoretical analysis of the principle of double satellites faults in 2009, as well as their successful elimination through experiments, is presented in [10]. The Solution Separation (SS) algorithm was also applied to Advanced RAIM (ARAIM) research [11]. A point to note is that, for 4-D positioning and geometry permitting, there must be at least five visible satellites for fault detection and at least six visible satellites for fault exclusion in a single constellation. When the number of satellites is insufficient, these FDE algorithms are unavailable, thus affecting the quality of GNSS positioning with potential safety risks.

To address the problem of GNSS measurement quality, additional sensors are also used to aid GNSS FDE by considering the various error characteristics of each sensor [12].

Comparison of FDE performance, based on loosely-coupled and tightly-coupled IMU/GPS integration modes, is also analyzed in some literature [13,14]. A multiple fault detection and elimination algorithm, based on pseudorange comparison, is proposed and used for vehicle GNSS/IMU integrated navigation and positioning [15], but it needs initial database generation. In real situations, multipath effects and poor user-satellite geometry result in excessive positioning errors in urban areas, and the methods above cannot verify the correctness or reliability of the FDE algorithms. In addition, the a priori parameters of the measurement covariance matrix cannot be determined in these urban areas. This increases the probability of incorrect fault detection resulting in excessive final positioning errors. A series of adaptive Kalman filters (AKF) have been developed to overcome the limitation of using a priori statistics to model errors that have time-varying characteristics [16–18]. The adaptive indicators may take on a range of roles, including an adjustment of the covariance matrix of the state estimation vector, the covariance matrix of the process vector, and the covariance matrix of measurement vector [19–21]. None of the adaptive indicators in the above fusion methods, however, have been adjusted specifically for the errors caused by multipath signals and NLOS that are common in urban areas.

In recent years, with the continuous emergence of multi-sensors, the integrated navigation system of multi-source fusion has also ushered in a vigorous development. Altimeter, wheel odometer, magnetometer, etc., improve the accuracy and reliability of navigation information by providing additional information such as position, speed, and altitude to the GNSS/IMU integration system. From the perspective of technology integration, the research on the integration of GNSS, INS, and emerging visual navigation technology is extremely hot. Li developed a semi-tightly coupled GNSS PPP/S-VINS integration framework for better navigation performance in urban environments [22]. On this basis, Li further studied GNSS/LiDAR/INS tightly coupled integrated navigation [23]. However, the above method is in the theoretical research stage, and the high cost of the sensor is not conducive to popularization.

Another idea for quality control is to assign appropriate weights to the GNSS measurements to mitigate the effects of multipath/NLOS signals. The commonly used method is to determine weight based on the quality of GNSS signals. This usually involves the use of one or more characteristics of GNSS signals (e.g., satellite elevation angle, C/N0, or a combination of the two) to assign corresponding weights to GNSS measurements. Other weighting-based quality control methods include Huber [24], Bifactor reduction model [25], Robust estimation based on M-estimation principle [26], Robust Bayesian estimation [27], and Danish [28]. However, application of appropriate weighting, in different scenarios

in urban environments, is difficult. Given the limitations of the state-of-the-art methods above, this paper proposes a dual w-test-based quality control algorithm for integrated IMU/GNSS navigation in urban environments. The contributions are summarized below.

(1) A dual w-test is proposed, which achieves multiple fault detection from the observation domain, thus solving the problem of false alarms in the traditional w-test.

(2) A range detection is proposed to detect the subsets generated after dual w-test, and a scoring strategy is proposed to select the optimal subset. Starting from the location domain, the proposed algorithm is able to reduce the miss detection rate and, therefore, ensure the quality of the output position.
