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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

In natural and urban canyon environments, Global Navigation Satellite System (GNSS) signals suffer from various challenges such as signal multipath, limited or lack of signal availability and poor geometry. Inertial sensors are often employed to improve the solution continuity under poor GNSS signal quality and availability conditions. Various fault detection schemes have been proposed in the literature to detect and remove biased GNSS measurements to obtain a more reliable navigation solution. However, many of these methods are found to be sub-optimal and often lead to unavailability of reliability measures, mostly because of the improper characterization of the measurement errors. A robust filtering architecture is thus proposed which assumes a heavy-tailed distribution for the measurement errors. Moreover, the proposed filter is capable of adapting to the changing GNSS signal conditions such as when moving from open sky conditions to deep canyons. Results obtained by processing data collected in various GNSS challenged environments show that the proposed scheme provides a robust navigation solution without having to excessively reject usable measurements. The tests reported herein show improvements of nearly 15% and 80% for position accuracy and reliability, respectively, when applying the above approach.

While personal navigation devices, including GNSS receivers and other self-contained sensors, are capable of providing highly reliable and accurate navigation solution in open sky environments, their performance still remains limited when it comes to navigating in GNSS-challenged environments such as natural and urban canyons. In such areas, GNSS signals, when available, are significantly affected by multipath effects and if used contribute to significant errors in the navigation solution while, if not used, result in lower solution availability. Moreover, GNSS suffers from other challenges, such as limited availability leading to poor geometry, high noise due to signal attenuation, non-normality of the measurement errors. For personal navigation systems that are implemented as an integrated Global Navigation Satellite System/Inertial Navigation System (GNSS/INS), especially those using relatively low cost micro electromechanical systems (MEMS) inertial measurement units (IMUs), the quality of GNSS signals plays a significant role in the navigation solution. The absence of GNSS or the presence of biased GNSS measurements can thus result in significant errors, depending upon the quality of the IMUs and the mechanization algorithm used.

The most common approach to address these challenges is to use a suitable fault detection and exclusion (FDE) scheme to identify and reject aberrant measurements. Receiver autonomous integrity monitoring (RAIM) is the most popular technique used for that purpose. There are numerous types of RAIM methods, based on implementation particularities. Nonetheless, all of these schemes are based on some kind of self-consistency checks among the available measurements. However, in harsh GNSS signal conditions such as in urban canyons, the FDE schemes are overwhelmed with various challenges like lack of sufficient measurement redundancy and simultaneous multiple faults. As GNSS measurements are already depleted in such environments, further rejection is not desirable since it limits the overall redundancy of the estimation and solution availability. Moreover, the measurement error distribution in those environments can no longer be assumed normal nor are the measurements uncorrelated in time, thus negating fundamental requirements of the standard Kalman filter.

Improper handling of faulty measurements can result in an unreliable navigation solution. Reliability is the level of trust that can be placed on the navigation solution provided by a personal navigation device. For example, if a navigation system estimates a position with accuracy (1σ) of 2 m along a particular axis, then it means that the error along that axis is expected to be less than 6 m with a confidence of 99.7% (

In this regard, the main objective of this paper is to develop and analyze a new filtering algorithm for personal navigation systems that is more robust against outliers and optimizes the use of available GNSS measurements in harsh environments in order to obtain greater reliability. The paper identifies the significance of assumed GNSS measurement error distributions when determining the reliability of a navigation solution and proposes a method that assumes an adaptive error distribution which is more consistent with the true one. The method initially presented in [

The proposed algorithm is detailed in the following section. Several field tests were used to validate the proposed algorithm. Section 3 describes how data were collected using a specific set of equipment in various environments. The results obtained by processing the data using the proposed algorithm are then analyzed in Section 4. Finally, Section 5 summarizes the main contribution of the paper and conclusions are drawn from the analyses in the previous section.

Any FDE scheme, by definition, is reliant on statistical tests that intrinsically require an

When it comes to GNSS signal degraded environments, however, the error distributions tend to deviate from the assumed normal distribution thus deteriorating the performance of the traditional FDE schemes. The inconsistency between the assumed and the true error statistics often leads to removal of good measurements by the FDE or improper weighting of each measurement. Removing a good measurement in environments where GNSS is already depleted not only degrades the navigation solution but can also make the FDE scheme unavailable due to lack of sufficient redundancy.

In order to incorporate the GNSS measurements properly in the integrated navigation system, the FDE scheme should operate optimally. However, in harsh environments, FDE schemes face two major challenges, namely non-normality and varying error statistics. This paper, thus, attempts to address these challenges by adapting two approaches:

Use of Student's t-distribution for GNSS measurement errors.

Adaptation of GNSS covariance to the changing GNSS signal conditions.

In the Bayesian framework, the influence of measurement outliers on inferences for estimates, including population means and medians, can be reduced by replacing the normal distribution model by a heavy tailed distribution. Such heavy tailed distributions allow for the possibility of high noise and possibly biased observations. These distributions treat observations far from the regression line as high variance observations, yielding results similar to those obtained by deweighting the outliers [

The use of a heavy tailed distribution such as Student's

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The navigation filters used in personal navigation devices usually make an

The proposed method computes the user acceleration from GNSS Doppler measurements and compares its consistency with measurements from accelerometers in the IMU. With a tactical grade MEMS IMU, the user acceleration obtained using accelerometers is fairly accurate and hence is taken as a reference to compare with that obtained with GNSS Doppler measurements. Thus, during good GNSS signal conditions, the two accelerations are highly consistent whereas in GNSS signal degraded environments, the consistency between the two accelerations degrades. Based on this characteristic, a scaling factor is computed to scale the covariance of GNSS measurements thus adapting it in accordance with the changing GNSS signal conditions. A top level block diagram of the proposed method is depicted in

Firstly, the user accelerations are computed along three axes of the Earth Centered Earth Fixed (ECEF) frame using the GNSS Doppler measurements. The details on the computation of user acceleration from GNSS are given in _{IMU}_{GNSS}_{IMU}_{GNSS}

The overlap between the distributions can be calculated as a Bhattacharyya coefficient (BC) [

Then,

Generally, in open sky conditions, the consistency between these two accelerations is high. However, in areas where the GNSS measurement quality degrades, the consistency between the two accelerations decreases since the errors in the GNSS derived acceleration distributions are no longer centered on zero. Thus, in areas with a good consistency, a higher weight (lower variance) is assigned to GNSS measurement updates while in areas with poor consistency, a lower weight is used. Then a scale factor based on the consistency between the accelerations is computed, which in turn is used to scale the

As with other non-adaptive filters, initially an assumption is made about the

In order to mitigate the effect of noise in the Doppler measurements, the consistency is computed as a moving average of the consistency values at three GNSS epochs, each two typically separated by 50 ms. A buffer to store the consistency values of three consecutive epochs is thus maintained. This introduces a latency of two epochs at the beginning before the

Once the buffer is full, the current value of consistency is repeatedly computed by scaling the initial

The proposed scheme was evaluated by collecting pedestrian data in GNSS signal challenged environments. The data collection equipment setup depicted in

A reference solution was also obtained for each experimental scenario in order to evaluate the performance of the proposed scheme. The reference system consisted of a NovAtel OEMV3 receiver as a base station at a pre-surveyed location. The rover part consisted of a NovAtel SPAN-SE receiver and a tactical grade LCI IMU. The reference solution was obtained as a tightly-coupled GNSS/INS solution computed using NovAtel's Waypoint Inertial Explorer post-processing software. The accuracy of the reference trajectory was better than 0.2 m.

As shown in the block diagram of

The canyon created by the presence of tall buildings in either side of a street makes the navigation very challenging, especially for navigation systems with GNSS as a major component. The presence of multiple NLOS multipath signals with significant biases and limited visibility of the satellites degrades the quality and availability of the GNSS measurements. Hence, in order to assess the proposed scheme in GNSS challenged environments, pedestrian data was collected in downtown Calgary, Canada. The test environment presented an elevation mask angle varying from about 15 to 75 degrees. The test duration lasted over 40 min. The reference solution obtained for the urban canyon test is shown in

Unlike urban canyons where multipath is more specular, the multipath in natural canyons is generally more diffuse. The variation in the type of multipath while still limiting geometry and availability provides a unique test of the algorithms presented herein. Using a similar equipment setup as the urban scenario, data was thus collected in a natural canyon (King's Creek Canyon) in Kananaskis Country, AB, Canada. GNSS data collected using two receivers, namely OEM6 and u-blox6, were separately integrated with the IMU data collected using the ADIS16488 sensor unit. The test environment is shown in

The satellite mask angles in this environment varied between 50 and 80 degrees. The test duration was two hours. The reference trajectory obtained for the natural canyon data set is shown in

Prior to testing the proposed algorithm for an integrated navigation system, the suitability of using a heavy tailed distribution was examined through an initial test carried out using only GNSS range and Doppler measurements. GNSS data was collected in pedestrian mode under fairly open sky conditions. The OEM6 receiver inside the NavCube along with the GPS-702-GG antenna was used to collect the data. Simulated errors were added to three satellite measurements for nearly 70% of the data in order to analyze the performance of the filters in presence of known faults. The simulated errors on the three satellites consisted of uniformly distributed pseudorange (ρ) errors ranging from 10–70 m and uniformly distributed Doppler (Ø̇) errors ranging from −10 Hz to 10 Hz (±1.9 m/s). The results obtained with the navigation filter implemented with the assumption of

Taking the above result as an affirmation of the suitability of the

As discussed in Section 3, GNSS data in harsh environments such as urban and natural canyons are significantly affected by multipath. A rough idea about these measurement discrepancies would be very helpful on analyzing the results. In this regard, the approximate range errors of all the GNSS measurements were computed using the procedure described in

It can be observed that the range errors are quite significant at many epochs, exceeding well over 100 m. The presence of NLOS multipath signals and signal fading can cause the receiver to generate such erroneous measurements through shift of the NCO and distortion of the correlation function.

Additionally, the carrier to noise ratios (C/N_{o}) of available GNSS measurements are plotted in

To assess the performance of the proposed scheme in such environment, a standard tightly coupled GNSS/INS filter with residual based FDE was first implemented whereby the GNSS range and Doppler measurement errors were assumed to follow a normal distribution. The GNSS measurement distribution was then replaced by the _{o} based weighting has been found to be more robust in harsh GNSS signal conditions, the Sigma-ε variance model discussed by [

It can be observed from the above figures that the errors are smaller in the case of VB filters thus indicating the robustness of using the

As discussed in Section 1, one of the most critical parameters for many applications using personal navigation devices is the reliability of the navigation solution. In this regard, the reliability of the navigation solution along the axes of the local plane for the three cases discussed above were computed as shown in

Availability of GNSS measurements is another key parameter to be assessed in such signal deprived environment. Since the

It can be observed that there is a slight improvement in terms of availability of GNSS integrity information with the VB filters as compared to the standard filter. The improvement could very well be magnified for a user navigating through GNSS challenged environments for a longer duration of time.

As discussed in Section 3.2, the natural canyon data set includes GNSS data collected using two different receivers, namely an OEM6 and u-blox6. The data collected using these two receivers were integrated separately with the IMU in order to obtain the integrated filters for the three cases: Standard, VB and VB Adaptive filter. Using data from different GNSS receivers further validates the analysis of the performance of the proposed algorithm.

Firstly, as with the urban canyon data, the range errors were computed using a similar technique as that for the urban data using the GNSS data from the OEM6 receiver. These range errors plotted in

Moreover, a cumulative density function (CDF) of absolute values of the range errors was also plotted along with the CDF of absolute values of the normal fit to the range errors. It can be observed in

The C/N_{o} values are plotted in

The horizontal and vertical errors obtained using GNSS data from the u-blox6 receiver integrated with the IMU data are shown in

It is observed that there is a significant improvement in accuracy using the proposed scheme as compared to the standard filter. The maximum errors are also found to decrease dramatically with the proposed scheme. The reliability values for the same data set, as depicted in

The absolute values of position errors and reliability values were re-calculated by processing the GNSS data collected using OEM6 receiver tightly integrated with the IMU data. The obtained results are tabulated in

In this data set, although the accuracy improves only slightly, there is a significant improvement in reliability with the proposed scheme. This again indicates proper characterization of GNSS measurement errors through the use of adaptive

As for the urban canyon data, the availability of integrity information was also computed for the pedestrian data collected in natural canyon. The results tabulated in

A novel scheme that assumes a

The user accelerations can be obtained from GNSS using either twice differentiated phase measurements or single differentiated Doppler measurements. Due to the robustness of frequency lock loop in harsh environments, the Doppler measurements were used during this work. It follows from [_{i}_{i}^{th} satellite; _{rx}_{rx}^{th} satellite; _{i}_{i}_{i}^{th} satellite measurement, and _{i}_{i}^{th} Doppler measurement at time _{i}^{th} Doppler measurement at time

Using above equations, the user acceleration can be obtained using least-squares as:

The use of least-squares requires a minimum of four Doppler observations (or five if GLONASS is also used in addition to GPS) to be able to use the proposed scheme and thus imposes a limitation.

GNSS pseudorange measurements can be expressed as:

With the availability of an accurate reference solution for the user locations and with the knowledge of satellite positions from the ephemeris data, the true range

The clock bias can be estimated in a filter by fixing the known receiver position and velocity from the reference solution and by modeling

Thus, to mitigate the effect of multipath and other biases and noise in the estimation of

The authors declare no conflict of interest.

Block diagram of adaptive scheme.

Consistency between accelerations.

GNSS

(

Reference trajectory (urban canyon).

Data collection environment (natural canyon).

Reference trajectory (natural canyon).

Range errors in urban canyon (OEM6).

C/N_{o} values of measurements in urban canyon (OEM6).

(

Reliability of position solution (OEM6+IMU)—urban canyon.

(

C/N_{o} values of measurements in natural canyon (OEM6).

(

Reliability of the position solution (u-blox6 + IMU)—natural canyon.

IMU Specifications [

In-Run Bias Stability |
6.25°/h | |

Angular Random Walk |
0.3°/√h | |

Rate Noise Density | 23.8°/h/√Hz RMS | |

| ||

In-Run Bias Stability |
0.1 mg | |

Velocity Random Walk |
0.029 m/s/√h | |

Noise Density | 0.067 mg/√Hz RMS |

RMSE and reliability for open sky data.

3.6 | 9.0 | 9.2 | |||

2.3 | 7.9 | 7.5 | |||

3.8 | 7.0 | 8.5 | |||

2.3 | 6.9 | 6.3 | |||

| |||||

93.4 | 73.0 | 68.4 | |||

81.0 | 56.2 | 46.0 | |||

97.0 | 66.5 | 61.6 | |||

72.3 | 71.9 | 70.0 | |||

80.0 | 60.3 | 73.4 | |||

69.0 | 55.7 | 62.1 |

Availability of GNSS integrity information (OEM6)—urban canyon.

78.3 | 80.1 | 79.5 |

RMSE and reliability (OEM6 + IMU)—natural canyon.

| |||||
---|---|---|---|---|---|

17.2 | 12.1 | 32.7 | 32.5 | 36.7 | |

23.1 | 12.1 | 56.7 | 50.3 | 38.9 | |

16.9 | 11.4 | 57.7 | 50.9 | 42.4 |

Availability of GNSS integrity information—natural canyon.

71.9 | 72.0 | 71.9 | ||

65 | 74.5 | 74.5 |