Navigation & Estimation

Multiplex Twinstar in autonomous flight

 


 

Particle Filter

Particle Distribution

A particle filter is a nonlinear probabilistic filter which generates an estimate of the probability density function (pdf) of one or more random variables. This pdf does not need to be Gaussian like for example in a Kalman Filter. The main drawback is the large amount of processing power required to run the filter in real-time due to the high number of particles that are necessary for a good approximation of the pdf.

Such a particle filter was demonstrated in flight using only IMU and GPS data to estimate the attitude and velocity of a fixed-wing UAV. The algorithm was implemented on the FPGA of the ROCS, which made it possible to run the filter in real-time onboard the UAV.

Using only IMU and GPS and avoiding potentially unreliable sensors like a magnetometer means that under certain conditions the attitude is not fully observable. An algorithm to detect this kind of situation was also developed at the institute.

  • Floarian Weimer, Michael Frangenberg, and Walter Fichter. 2013. Pipelined Particle Filter with Non-Observability Measure for On-Board Navigation with MAVs. AIAA Guidance, Navigation, and Control Conference (AIAA 2013-5247)

 


 

Vision-Aided Inertial Navigation

Non-observable and oberservable trajectories With the increasing use of small unmanned vehicles in areas where GPS cannot be relied on, navigation algorithms need to employ alternative sensors to fuse with inertial measurements. These days, visual sensing is a promising option for filling this gap. The fact that digital cameras are low-priced and lightweight while consuming little power makes them a logical choice, especially for airborne systems. An image provides plenty of information on the environment and on the camera’s pose, in which it is superior to other measurements. Taking full advantage of that information is nonetheless challenging because image analysis involves significant computational effort. Because processing power onboard small vehicles is limited, vision-based navigation algorithms have to compromise estimation accuracy in favor of real-time capability.

This work addresses the issue at an earlier stage, at the system model itself. To this end, an exact expression of the statespace model is derived, which is linear timevarying. This makes the overall problem accessible to exact and rigorous observability analysis without depending on linearization. Novel necessary and sufficient observability criteria are provided, which permit checking any given trajectory for observability deficiencies. Thanks to the linearity of the problem, a Kalman filter can be applied and is also proposed. The validity of the criteria and the effectiveness of the filter are demonstrated in simulations and flight tests.

 


 

Smooth Singularity Free Bearings-Only Tracking

Measurement error distribution in the sensor planeBearings-only tracking is the localization and tracking of a target exclusively based on a combination of bearing measurements and known maneuvers of the observer. According methods are applied in a variety of fields that employ optical or infrared sensors, passive sonar or radar under jamming conditions.

The bearings-only tracking problem was shown to be challenging since its observability is highly related to the motion of both the observer and the target and thus cannot be generally assumed. As it is furthermore severely nonlinear, estimation performance varies with the particular mathematical description being used. Consequently, several ways of stating the problem have been developed, among which the Cartesian representation and the modified spherical coordinates are the two most prominent for threedimensional scenarios. Their behavior has mostly been investigated using extended Kalman filters (EKF). One thing all these approaches have in common, is their description of the bearing information in the form of elevation and azimuth angles with respect to some reference frame either in the measurement model (Cartesian methods) or even as part of the state representation (spherical methods).

Distribution distorted by additive angular error representation

However, using angles to express a direction in three-dimensional space inevitably introduces discontinuities, singularities, and distorts error distributions, a fact widely ignored by the relevant literature. Hence, the contributions of this work are as follows: Problems related to the elevation/azimuth bearing representation are identified and it is shown under which circumstances they are likely to compromise estimation performance. Based on these considerations, requirements on a new bearings-only tracking algorithm are stated. Subsequently, a novel description of the problem yields an EKF that is smooth and free of singularities in the state equations as well as in the measurement model.

 

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