The majority of commercial and open-source autopilot software for uncrewed aerial vehicles rely on the tried and tested extended Kalman filter (EKF) to provide the state estimation solution for the inertial navigation system (INS). While modern implementations achieve remarkable robustness, it is often due to the careful implementation of exception code for a multitude of corner cases along with significant skilled tuning effort. In this paper, we use the data wealth of the ArduPilot community to identify and highlight the most common real-world challenges in INS state estimation, including sensor self-calibration, robustness in static conditions, global navigation satellite system (GNSS) outliers and shifts, and robustness to faulty inertial measurement units (IMUs). We propose a novel equivariant filter (EqF) formulation for the INS solution that exploits a Semi-Direct-Bias symmetry group for multi-sensor fusion with self-calibration capabilities and incorporates equivariant velocity-type measurements. We augment the filter with a simple innovation-covariance inflation strategy that seamlessly handles GNSS outliers and shifts without requiring coding of a whole set of exception cases. We use real-world data from the Ardupilot community to demonstrate the performance of the proposed filter on known cases where existing filters fail without careful exception handling or case-specific tuning and benchmark against the ArduPilot’s EKF3, the most sophisticated EKF implementation currently available.

In this paper we detail the implementation of a Differential GPS system using only low-cost GPS receivers. The nature of the errors generated by low-cost modules is investigated and contrasted against typical error models of traditional, commercial DGPS systems. It is found that the error profile unique to low-cost GPS modules leads to a system that offers particular advantage in the horizontal plane compared to uncorrected receivers and as such is especially suited for tasks such as mapping and field robotics. A particular incarnation is demonstrated on a mobile robot with experimental results from static and moving tests showing an accuracy in the plane on the order of one metre.

In this paper we present TDLEAF(λ), a variation on the TD(λ) algorithm that enables it to be used in conjunction with game-tree search. We present some experiments in which our chess program “KnightCap” used TDLEAF(λ) to learn its evaluation function while playing on Internet chess servers. The main success we report is that KnightCap improved from a 1650 rating to a 2150 rating in just 308 games and 3 days of play. As a reference, a rating of 1650 corresponds to about level B human play (on a scale from E (1000) to A (1800)), while 2150 is human master level. We discuss some of the reasons for this success, principle among them being the use of on-line, rather than self-play. We also investigate whether TDLEAF(λ) can yield better results in the domain of backgammon, where TD(λ) has previously yielded striking success.

The problem of merging two sequences of elements which are stored separately in two processing elements (PEs) occurs in the implementation of many existing sorting algorithms. We describe efficient algorithms for the merging problem on asynchronous distributed-memory machines. The algorithms reduce the cost of the merge operation and of communication, as well as partly solving the problem of load balancing. Experimental results on a Fujitsu AP1000 are reported.

A parallel sorting algorithm is presented for storage-efficient internal sorting on MIMD machines. The algorithm first sorts the elements within each node using a serial based algorithm, then a two-phase parallel merge. It requires additional storage of order of the square root of the number of elements in each node. Performance of the algorithm on two general-purpose MIMD machines, the Fujitsu AP1000 and the Thinking Machines CM5, is examined. The algorithm is suitable for implementation on special-purpose parallel machines, e.g., parallel database machines.>