Performance Improvement of Laser TRN using Particle Filter incorporating Gaussian Mixture Noise Model and Novel Fault Detection Algorithm
Kyung-Jun Han, Chang-Ky Sung, Myeong-Jong Yu, Agency for Defense Development, Republic of Korea
Location: Big Sur
GNSS is a key player in modern navigation systems, however more and more threats to week satellite signals are emerging such as jamming and spoofing. Alleviating the risk, terrain referenced navigation (TRN) has been actively researched as an alternative to the GNSS denied environment. The operation principle of the TRN algorithm is to estimate the current position by comparing the difference between the altitude measured by the barometric altimeter (BA) and the altitude measurement from the radar altimeter (RA) with the digital elevation map (DEM). The problem of RA is the large footprint that induces large measurement errors. This problem can be eliminated by replacing the RA with a laser altimeter (LA). Typical laser rangefinder produces a laser pulse that is several feet footprint in diameter and can distinguish the forest canopy and the ground. This indicates that more accurate TRN is possible with LA than with RA. F. Neregard et al. (2006) showed that the performance of TRN using LA was improved about 50% compared to that of RA-based TRN. This paper aims to further improve the performance of laser TRN.
In this paper, we propose two methods to improve the accuracy of the laser TRN algorithm. The first is to model the LA measurement error with Gaussian mixture noise model (GMNM). TRN is suitable for mountainous areas and mountains are generally forests. Laser pulse reflections are concentrated around the forest canopy and the ground. In this case, measurement error modeling using multimodal probability density function (PDF) is more suitable than modeling with single Gaussian PDF. Referring the experimental data presented in the existing literatures, we arbitrarily model the output of the laser altimeter in the forested mountain area and show that the performance is improved by applying the GMNM-based likelihood function through simulation. Second, we suggest an effective fault detection algorithm to eliminate the outliers in measured altitude. Large, irregular measurement errors severely degrade TRN performance and impair system stability. Proper rejection of outliers is a crucial factor for improving TRN performance. The proposed error detection algorithm works in the sequential Monte Carlo framework. The residual sequence defined by the predicted measurement cumulative distribution is formulated taking into account GMNM. The residual sequence is then converted to a Gaussian sequence using the inverted standard Gaussian CDF. The transformed Gaussian sequence can be used to validate the measured data. Also, if the particle cloud is properly positioned and the measurement is normal, it can also be assumed that the minimum absolute value of the predicted measurement errors of particle cloud should be within a certain stochastic upper limit. The error detection logic is constructed by monitoring the residual sequence and the minimum absolute value of the predicted measurement. If an error is detected, the measurement update is prohibited and only the time update is performed to prevent the wrong correction. Through simulation experiment we show that the proposed fault detection algorithm effectively eliminates singularities and improves the performance and reliability of TRN.
In conclusion, we propose to apply the Gaussian mixture noise model to the laser TRN. This approach show better performance than using a single Gaussian noise model. We develop novel fault detection algorithm in the particle filter framework and show that it is effective method to eliminate measurement outliers. The proposed fault rejection scheme is applicable to any kind of nonlinear Bayesian state estimators.