Jan Wendel

Comparison of Extended and Sigma-Point Kalman Filters for Tightly Coupled GPS/INS Integration

This paper adresses the fusion of GPS measurements and inertial sensor data in tightly coupled GPS/INS navigation systems. Usually, an extended Kalman lter (EKF) is applied for this task. However, as the system dynamic model as well as the pseudorange and deltarange measurement models are nonlinear, the EKF is a sub-optimal choice from a theoretical point of view, as it approximates the propagation of mean and covariance of Gaussian random vectors through these nonlinear models by a linear transformation, which is accurate to rst-order only. The sigma-point Kalman lter (SPKF) family of algorithms achieve an accurate approximation to at least second-order. Therefore, the performance of EKF and SPKF applied to tightly-coupled GPS/INS integration is compared in numerical simulations. It is found that except in specic situations without practical relevance, both approaches oer an identical performance. This indicates that the SPKF may be an option considering the design of new systems, but a modication of existing EKF-based GPS/INS systems is neither required, nor appropriate to improve their performance.

Time-Differenced Carrier Phase Measurements for Tightly Coupled GPS/INS Integration

A tightly coupled GPS/INS system is characterized by the fact that pseudorange and deltarange measurements are processed in the navigation filter in order to estimate the errors of the inertial navigation solution and to calibrate the inertial measurement unit. In this paper, the usage of time differenced carrier phase measurements instead of the delta range measurements is proposed. Usually, DGPS corrections are required in order to exploit the high accuracy of the carrier phase measurements by removing the common mode errors like ionospheric errors, ephemeris errors, or satellite clock errors. Then, techniques like carrier aided smoothing or ambiguity fixing can be applied. With the approach described in this paper, DGPS corrections are not required. Additionally, a fixing of the integer ambiguities, which is especially difficult when a single frequency receiver is used, is not required either. Forming time differences of successive carrier phase measurements, the constant integer ambiguities and most of the slowly varying common mode errors are removed. These carrier phase differences do not allow for an absolute centimeter-level positioning as it can be achieved with a DGPS base station and an ambiguity fixing, but the noise in the position information is reduced and the accuracy of the velocity and attitude estimates are improved. Details of this approach are clarified and the processing of this type of measurement in the navigation filter is addressed. The improvement in performance is illustrated via hardware-in-the-loop test results and the analysis of flight test data collected with a micro aerial vehicle.

Development of a GPS/INS/MAG navigation system and waypoint navigator for a VTOL UAV

Unmanned aerial vehicles (UAV) can be used for versatile surveillance and reconnaissance missions. If a UAV is capable of flying automatically on a predefined path the range of possible applications is widened significantly. This paper addresses the development of the integrated GPS/INS/MAG navigation system and a waypoint navigator for a small vertical take-off and landing (VTOL) unmanned four-rotor helicopter with a take-off weight below 1 kg. The core of the navigation system consists of low cost inertial sensors which are continuously aided with GPS, magnetometer compass, and a barometric height information. Due to the fact, that the yaw angle becomes unobservable during hovering flight, the integration with a magnetic compass is mandatory. This integration must be robust with respect to errors caused by the terrestrial magnetic field deviation and interferences from surrounding electronic devices as well as ferrite metals. The described integration concept with a Kalman filter overcomes the problem that erroneous magnetic measurements yield to an attitude error in the roll and pitch axis. The algorithm provides long-term stable navigation information even during GPS outages which is mandatory for the flight control of the UAV. In the second part of the paper the guidance algorithms are discussed in detail. These algorithms allow the UAV to operate in a semi-autonomous mode position hold as well an complete autonomous waypoint mode. In the position hold mode the helicopter maintains its position regardless of wind disturbances which ease the pilot job during hold-and-stare missions. The autonomous waypoint navigator enable the flight outside the range of vision and beyond the range of the radio link. Flight test results of the implemented modes of operation are shown.

Sigma-Point Filter for Terrain Referenced Navigation

This paper deals with a navigation system based on inertial navigation combined with terrain referenced navigation (TRN). A TRN system is able to provide an aiding source for the inertial navigation system (INS) using radar altimeter measurements and a digital terrain elevation reference. This setup is self sucien t and does not need any external signal sources to provide a long term stable navigation solution for civil and military avionics. Especially in military applications, where GPS signals can be jammed, a combined TRN/INS system allows high performance and integrity of the navigation system. This paper describes the integration of the TRN functionality in a non-linear lter, commonly known as sigma-point lter. Furthermore, it will show the advantages this non-linear approach over the Extended Kalman lter (EKF). The sigma-point approach uses deterministically calculated and weighted points which capture the probability density function of the state. To determine the sigma points over the time, it is not necessary to calculate the linearization of the measurement and system model. Therefore, it allows the strongly non-linear measurement model of TRN-systems to be considered properly. Simulations show the superiority of the sigma-point lter compared to the extended Kalman lter. or almost all applications in civil and military avionics it is mandatory to determine position, velocity and attitude accurate and with a high update rate. These requirements cannot be sucien tly guaranteed with a single sensor. Therefore, the optimal integration of dieren t sensor signals is mandatory for navigation systems. Probably the most widely used setup is based on an inertial and a satellite navigation system like the global positioning system (GPS). The INS allows short term stable calculation of position, velocity and attitude based on acceleration and rotation rate measurements and initial position, velocity and attitude. Because of the degrading navigation solution of the INS for longer measurement periods, the satellite navigation system usually provides a position aiding using external satellite signals. Considering a situation where these external signals are disturbed, it is not possible to accomplish a long term stable navigation solution because of the failing satellite navigation system. In military applications the intentional jamming, while ying over hostile areas, has to be expected and a method has to be found to enable navigation even in this situation. Due to extensive use of satellite navigation systems in domestic applications and the simplicity to build jammers, the chances of disturbances in civil navigation has to be considered. To avoid the dependency on external signals, a self sucien t navigation system has to be used to aid the INS. A TRN system is self sucien t because it determines the position based on radar height measurements and a digital elevation reference that is stored on board of the aircraft. The dicult y by using a TRN system is based on the strong non-linearity of the measurement model. It cannot be covered properly by the Extended Kalman lter normally used to integrate the INS and GPS data. Therefore, a so called sigma-point lter is used to perform the integration for the non-linear measurement model. In the following sections a principle of terrain referenced navigation is presented and TRN algorithms based on comparison and ltering methods are introduced. Afterwards, the sigma-point lter is described and adaptations for the TRN measurement model are explained. Finally, simulation results are discussed.

Post-processing GNSS/INS Measurements Using a Tightly Coupled Fixed-Interval Smoother Performing Carrier Phase Ambiguity Resolution

This paper describes a high accurate tightly cou- pled, differentially corrected GNSS/INS system for survey appli- cations in post-processing mode. A Kalman filter is described, that calculates the navigation solution as well as the the GNSS carrier phase integer ambiguities. The LAMBDA method is used to resolve the integer ambiguities. To achieve an optimum solution based on all measurement data available, a Rauch-Tung- Striebel smoother is used. The combination of tight integration and smoothing results in a system which is capable to resolve almost all of the carrier phase ambiguities and therefore provides centimeter accuracy, even if satellites are only available for short periods. The smoother provides steady results without discontinuities and bridges GNSS outages well. Hence, the system overcomes problems which are typical for kinematic ground surveys.

Detection and tracking of objects in an image sequence captured by a VTOL-UAV

This paper focusses on the automated detection and tracking of moving objects in a camera sequence, that is provided by a small, electrically powered four-rotor helicopter in a hover-and-stare scenario. Two different algorithms for identifying independently moving areas are investigated and compared. The first approach bases on the previous compensation of the camera movement by estimation of homographies. Moving regions are extracted by robust background subtraction. The second approach bases on a dense optical flow field and needs no stabilization: Single points are identified that move not consistently with the background plane. These points are merged into objects by a cluster analysis algorithm. Furthermore, a strategy for tracking these objects over time is described including a Kalman filter. Due to several reasons, not every extracted area corresponds to an independently moving object and a heuristic rule set is used to sort artifacts out. Experimental results on in-flight images are presented and the performances of the developed algorithms are compared. Finally, first steps towards a geographic location of the tracked objects are described.

GNSS/INS Integration

This chapter discusses the role of global navigation satellite systems (GNSS s) and inertial measurements in the estimation of the state vector for a maneuvering system. The chapter considers the main objectives of accuracy, continuity, availability, and integrity; and, the contributions that the different types of sensors make toward achieving these objectives. The chapter includes an example design. Then, the chapter reviews the concepts of loose, tight, and ultratight or deeply coupled systems. Throughout, the advantages, disadvantages, and tradeoffs between alternative approaches are discussed.