ION GNSS 2010
Session B3: Marine Navigation

Title: Reliability of an Adaptive Integrated System through Consistency Comparisons of Accelerometers and GNSS Measurements
Author(s): A. Dhital, J.B. Bancroft, G. Lachapelle, University of Calgary, Canada
Date/Time: Thursday, September 20, 2012, 11:03 a.m.

The performance of an integrated navigation system can be optimized by providing correct sensor measurement variances, as characterized by the input measurement covariance matrix. In an integrated inertial navigation system/global navigation satellite system (INS/GNSS), the quality of inertial measurement units is reflected by the noise spectral densities which are usually specified in the data sheet or measured empirically. In most cases, the sensors noise parameters remain time invariant. However, the quality of GNSS measurements varies depending upon the environment. GNSS measurements are better in open sky conditions than in areas such as urban canyons and in the indoors. In personal navigation devices, such as mobile phones or personal tracking units several methods exist to estimate the noise covariance, namely (i) a fixed value of noise covariance, (ii) an elevation weight model, and (iii) a signal to noise ratio model to characterize the noise covariance (e.g. SIGMA-? model). Often these models cannot characterize the actual measurement statistics which can lead to an unreliable navigation solution. Hence, for such cases, a suitable covariance should be adopted so that it is congruent with the actual measurement variances. Various forms of adaptive Kalman filters that optimize the filter performance through estimation of adaptive filter statistics have been proposed in the literature to address the problem of changing measurement conditions or changing dynamics of the user. However, these techniques suffer from different shortcomings. A novel approach is therefore presented herein where the accelerometer measurements are used to adjust the covariance of GNSS measurements in order to obtain a better estimate of the error covariance for GNSS measurements as per the change in GNSS signal conditions.
In indoors and urban areas, the quality of GNSS measurements degrades mainly due to signal attenuation and multipath. The stochastic characteristics of inertial sensors such as accelerometers and gyroscopes do not change whether it is open sky, indoors or other environments as they are self-contained. This robustness of stochastic characteristics of inertial sensors can be used to adjust the time variant stochastic properties of GNSS measurements and thereby improve the agreement with observed values. This is achieved by comparing accelerometer and GNSS acceleration measurements.

The first step is to obtain the range acceleration using either the time derivative of the phase measurements or Doppler measurements. In case of phase measurements, this is obtained by performing a double differentiation with respect to time, while for Doppler measurements a single time differentiation is used. The user acceleration is then obtained using a least squares technique to avoid any time correlation of the estimated acceleration. The consistency of the accelerations (AGNSS and AACCEL) can be computed by evaluating the overlapping area between of the distributions of the acceleration measurements. The intersection between the distributions is calculated using Bhattacharyya coefficient and provides a confidence level. Scaling the input covariance of the GNSS measurements to a point where both the distributions overlap to a set threshold provides the adaptive nature of the filter. In open sky conditions there will be high consistency in the acceleration measurements AGNSS and AACCEL. However in signal degraded environments, the variance will increase and likely be biased. In signal confined environments, it becomes necessary to identify the extent of degradation of GNSS measurements and to scale their covariance accordingly. This can be achieved by increasing the variance scaling factor of the GNSS measurements so that the overlapping area exceeds a threshold. This procedure will increase the covariance matrix of the GNSS observations based on the variance of the accelerometer. In the context of tightly coupled integration, the increase in variance scale factor would mean that more weight will be assigned on the IMU mechanization rather than on the GNSS updates. It should also be noted that the accelerometer biases are estimated prior to the implementation of the proposed algorithm.

The above discussed algorithm uses accelerometer measurements as a reference and it thus becomes necessary to make sure that this reference (i.e. the accelerometer) is reliable. To that purpose, a consistency comparison scheme is used where in addition to accelerometers and GNSS, barometers are also used to compute acceleration. The double derivative of the barometer measurement can be used to obtain the acceleration along vertical axis. The effect of barometer noise during this procedure can be reduced by time averaging. The vertical acceleration thus obtained, ABARO, must be consistent with the vertical acceleration obtained using accelerometers. Hence in order to validate the accelerometer measurements, the distribution of AACCEL is compared to that of AGNSS and ABARO. If the consistency of AACCEL with either of AGNSS or ABARO is larger than a certain minimum threshold, then the accelerometer is considered to be reliable.

This novel approach exploits the robustness of already existing self-contained sensors (i.e. accelerometer) in the integrated system to obtain suitable covariance for GNSS measurements, thus making it a cost effective approach. Thus this novel algorithm can be very effective in improving the reliability performance of many personal navigation applications based on INS/GNSS integrated systems and without many drawbacks of previous approaches.

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