arXiv subjects
Publications and source records attributed to John-Olof Nilsson.
Fourier series with power series coefficients for the normal and distance to a point from an ellipse are derived. These expressions are the first of their kind and opens up a range of analysis and computational possibilities.
A comprehensive listing of over 230 references related to Cartesian to geodetic coordinate transformations are provided. The references are coarsely sorted and DOI:s or URL:s are provided to the extent possible to facilitate studies of the material.
Minimax polynomial ECEF to geodetic coordinate transformation approximations are presented, including often preferable n-vector versions and pseudo-code implementations. The approximations provide high accuracy-to-computational-cost tunability and an unprecedented low latency down to an accuracy of $\sim10^{-5}$m, which is demonstrated in an extensive benchmark. This sets a new standard for coarse and fast ECEF to geodetic coordinate transformations and opens up a new realm of further improvement opportunities and extensions to other geodetic quantities.
Marginalization techniques are presented for the Bayesian filtering problem under the assumption of Gaussian priors and posteriors and a set of sequentially more constraining state space model assumptions. The techniques provide the capabilities to 1) reduce the filtering problem to essential marginal moment integrals, 2) combine model and numerical approximations to the moment integrals, and 3) decouple modelling and system composition. Closed-form expressions of the posterior means and covariances are developed as functions of subspace projection matrices, subsystem models, and the marginal moment integrals. Finally, we review prior work and how the results relate to Kalman and marginalized particle filtering techniques.
A maximum likelihood estimator for fusing the measurements in an inertial sensor array is presented. The maximum likelihood estimator is concentrated and an iterative solution method is presented for the resulting low-dimensional optimization problem. The Cramér-Rao bound for the corresponding measurement fusion problem is derived and used to assess the performance of the proposed method, as well as to analyze how the geometry of the array and sensor errors affect the accuracy of the measurement fusion. The angular velocity information gained from the accelerometers in the array is shown to be proportional to the square of the array dimension and to the square of the angular speed. In our simulations the proposed fusion method attains the Cramér-Rao bound and outperforms the current state-of-the-art method for measurement fusion in accelerometer arrays. Further, in contrast to the state-of-the-art method that requires a 3D array to work, the proposed method also works for 2D arrays. The theoretical findings are compared to results from real-world experiments with an in-house developed array that consists of 192 sensing elements.
The implementation challenges of cooperative localization by dual foot-mounted inertial sensors and inter-agent ranging are discussed and work on the subject is reviewed. System architecture and sensor fusion are identified as key challenges. A partially decentralized system architecture based on step-wise inertial navigation and step-wise dead reckoning is presented. This architecture is argued to reduce the computational cost and required communication bandwidth by around two orders of magnitude while only giving negligible information loss in comparison with a naive centralized implementation. This makes a joint global state estimation feasible for up to a platoon-sized group of agents. Furthermore, robust and low-cost sensor fusion for the considered setup, based on state space transformation and marginalization, is presented. The transformation and marginalization are used to give the necessary flexibility for presented sampling based updates for the inter-agent ranging and ranging free fusion of the two feet of an individual agent. Finally, characteristics of the suggested implementation are demonstrated with simulations and a real-time system implementation.
We consider the problem of estimating timing of measurements and actuation in distributed sensor and control systems with central processing. The focus is on direct timing estimation for scenarios where clock synchronization is not feasible or desirable. Models of the timing and central and peripheral time stamps are motivated and derived from underlying clock and communication delay definitions and models. Heuristics for constructing a system time is presented and it is outlined how the joint timing and the plant state estimation can be handled. For a simple set of underlying clock and communication delay models, inclusion of peripheral unit time stamps is shown to reduce jitter, and it is argued that in general it will give significant jitter reduction. Finally, a numerical example is given of a contemporary system design.
The initialization of the state estimation in a localization scenario based on ranging and dead reckoning is studied. Specifically, we start with a cooperative localization setup and consider the problem of recursively arriving at a uni-modal state estimate with sufficiently low covariance such that covariance based filters can be used to estimate an agent's state subsequently. A number of simplifications/assumptions are made such that the estimation problem can be seen as that of estimating the initial agent state given a deterministic surrounding and dead reckoning. This problem is solved by means of a particle filter and it is described how continual states and covariance estimates are derived from the solution. Finally, simulations are used to illustrate the characteristics of the method and experimental data are briefly presented.