Since the altitude, airspeed, and attitude are measured by the reliable high sampling rate
IMUandADS, their performance does not change greatly when considering delayed sys- tems versus ideal non-delayed systems. As such, the below results are presented using the
test as the baseline and the 75 meter GPS/LTE/VISION/IMU to determine what, if any, effect theGPSand VISION/IMUsensors have on the accuracy of these states.
Figure 5.9 shows the altitude (Figure 5.9(a)) and airspeed (Figure5.9(b))RMSE tra- jectories for both low canyon environments. Since theADS provides high-sampling rate measurements of both states in theLTE/VISION-OF configuration, the RMS error reaches a small steady state value quickly. When adding the high-sampling rate VISION/IMU, there is a slight decrease in steady-state error for both states. This drop in error is expected
in theEKFsince two independent altitude and airspeed measurements are available at every other time step to correct the predicted estimate.
0 5 10 15 20 0 0.2 0.4 0.6 0.8 1 Time(seconds) h RMS Error (meters) EKF − LTE/VISION−OF EKF − LTE/VISION/IMU (a) Altitude 0 5 10 15 20 0 0.2 0.4 0.6 0.8 1 Time(seconds) V T RMS Error (meters/second) (b) Airspeed
Figure 5.9: RMS altitude and airspeed error trajectories for low canyon environments.
Figure5.10shows the attitude angleRMSEtrajectories for roll (Figure5.10(a)), pitch (Figure 5.10(b)), and yaw (Figure 5.10(c)). The IMU provides small steady-state RMS errors when in theLTE/VISION-OF configuration with roll and pitch error just under 0.4 degrees and yaw RMS error at 0.7 degrees. This trend of IMUroll and pitch being much more accurate than yaw is typical since yaw is primarily measured with a noisy magne-
tometer. However, once the VISION/IMUmeasurements are added, all three RMS errors drop to roughly 0.2 degrees as the VISION/IMUmeasurements are very accurate with low variances when using feature tracking-type localization algorithms.
5.3
Chapter Summary
Navigation accuracy in the open space and homogeneous urban canyon test environ-
ments was evaluated using several sensor suites that included combinations ofGPS,LTE, VISION/IMUand VISION-OF along with the traditionalIMUandADS. In the open space environment with realistic sensor delay, the addition ofLTEmade a marginal difference in lateral position navigation accuracy, but slightly decreased the estimation error covariance.
In the canyon with VISION/IMUnavigation accuracy was on the order of 0.15 meters un- der the assumed simulation conditions, with little difference when eliminatingGPS. When reverting to VISION-OF, the accuracy was on the order of 1 − 2 meters for both lateral
position states. When in the canyon using VISION-OF, the EnKF generally gave more accurate short-term results in the longitudinal direction while theEKF gave better results along the lateral direction. Longer simulations should be run in the future to determine
if theEnKF can reach a steady-state longitudinal error value. Overall, VISION/IMU in- tegrated navigation systems should be considered when possible as they are able to add
accurate high sampling rate position and attitude measurements to the state estimation fil-
ter. LTE OTDOA is still immature as a UAS positioning sensor due to its low sampling rate, high delay period, and limited availability of accuracy data in literature but it may
provide a means of detecting spoofedGPSdata on a mass level, an analysis left to future work.
0 5 10 15 20 0 0.2 0.4 0.6 0.8 1 Time(seconds) φ RMS Error (degrees) EKF − LTE/VISION−OF EKF − LTE/VISION/IMU
(a) Roll Angle
0 5 10 15 20 0 0.2 0.4 0.6 0.8 1 Time(seconds) θ RMS Error (degrees) (b) Pitch Angle 0 5 10 15 20 0 0.2 0.4 0.6 0.8 1 Time(seconds) ψ RMS Error (degrees) (c) Yaw Angle
CHAPTER 6
Accuracy of Navigation in a Heterogeneous
Urban Environment
This chapter studies navigation accuracy in a realistic urban environment using both the
exact UAS dynamics propagation model, which includes the equations of motions along
with the constant aerodynamic model parameters, and multiple randomly-generated UAS
plant dynamics propagation models where the aerodynamic model parameters are varied
from their exact values based on the literature. In the heterogeneous urban environment,
buildings of varying heights, intersections, and open spaces allow the study of sensor per-
formance in different relative location categories during straight and level flight as well
as climbing and descending flight. Since GPS availability rates are not constant within
an urban environment, these rates will be varied as a function of relative location category
throughout many of the simulations presented within the chapter. This dissertation refers to
models as matched when the same numerical values are used for constants and coefficients
in the UAS plant dynamics and state estimation filter propagation models. Unmatched
models have one or more different numerical values for the UAS plant dynamics model
versus the filter dynamics model. Unmatched models require process noise tuning to en-
sure a consistent filter. The sensor models remain unchanged. Process noise tuning is ac-
complished through the use of the average normalized estimation error squared (ANEES),
the average normalized innovation squared (ANIS), and the autocorrelation statistic, all
Specific factors affecting the accuracy of UAS state estimation in the urban environ-
ments include both sensor availability and sensor self-accuracy detection, as first discussed
in Chapter 4 as sensor accuracy mode (SAM). In reality, the UAS GPS sensor is sensitive
to its altitude in the canyon with respect to the surrounding buildings. It may generate mea-
surements when near the top of the urban canyon, but it can lose line of sight to enough
satellites to lose measurement generation capability when flying lower in the canyon. This
phenomenon can be modeled discretely by turning GPS off when the UAS is below h= 75 meters, as was the case in the previous chapter. However, a more realistic technique to
account for varying availability is to use empirical availability rates as was shown in Table
4.2. Understanding the effects of sensor self-accuracy detection for both GPS and LTE is also important. If these sensors can determine their own measurement noise covariance
values based on signal data, this information can be provided to the filter to give a more
realistic estimate of the propagated UAS states. Otherwise, if these sensors are not able
to generate this information, the filter must use estimated measurement noise covariance
values based on environmental information from previous state estimates.
The remainder of the chapter is outlined as follows: the Simulation Description sec-
tion discusses the simulation description in terms of building layout, sensors used and test
matrices. The Matched Model Results section analyzes the large pool of matched model
results where GPS availability, sensor accuracy mode, and the flight path are varied. The
Unmatched Model Results section analyzes both filter tuning and navigation accuracy for
a straight and level trajectory in the canyon. Finally, the Summary section provides overar-
ching conclusions based the simulation results.
The main contribution of this chapter is to provide navigation accuracy results for mul-
tiple trajectories in the heterogeneous urban environment with varying GPS availability for
both matched and unmatched models and filter tuning results for the unmatched model
case. The main innovations of this chapter include the incorporation of position depen-
measurement noise covariance, and using expected sensor availability in the filter tuning
process.