Anticipation of ship behaviours in multi-vessel scenarios

COLREGs-based Situation Awareness for Marine Vessels - a Discrete Event Systems Approach

“…When using KDE based methods the choice of bandwidth h is important and often more so than the choice of kernel, with several methods availble for choosing the best bandwidth including; grid-search with cross-validation and Silverman's rule of thumb [40]. Silverman's rule is a fast algorithm for estimating the correct bandwidth, however the rule assumes that the true underlying density is a Gaussian normal distribution, which does not apply for the data transformed through (32), (34) or (35). When dealing with non-normal data the Improved Sheather-Jones (ISJ) algorithm [41] can be used, as this algorithm does not assume an underlying normal distribution in the data, the trade-off is that it requires more data for a good estimate, thereby increasing the computational time.…”

“…The grid-search based method is inherently slow, and the example shown takes around 5 minutes running on a 48 core AMD Threadripper 3960X CPU, compared to the very fast FFTbased implementation of the ISJ in [42] which takes less than a second on the same hardware. One could argue that once the bandwidth is estimated through a grid-search, the value h grid could be used for all future evaluations, however, the high non-linearities in (32), (34) and (35) does not guarantee that this choice would be valid in any scenario. Comparing to the computational cost of drawing more samples for the ISJ algorithm and re-fitting the KDE every time, to the computational cost of having to run a grid-search, the ISJ algorithm is the favorable approach.…”

“…The proposed methods will be shown to apply on any pair of vessels, and hence provides genuine situation awareness that anticipate the manoeuvres of TVs in the entire area of attention. The paper shows how this could be incorporated in an existing Discrete-Event Systems (DES)-based framework for situational awareness, [31]- [34], and illustrates how the method can increase the safety of an autonomously navigating surface vessel. The paper shows that the tracking problem is non-stationary, and highly-nonlinear due to transformations with origin in the calculation of TCPA/DCPA.…”

“…the state transition probability, and H(w|z, v) is the output relation of the stochastic automata [44]. The understanding automaton [34] illustrated in Fig. 6 implements the understanding part of the situational awareness [1], and is able to analyse a given situation between two vessels, by a interpreting Fig.…”

“…the raw state estimates of two vessels, producing a higher level abstraction which describes the situation in humaninterpretable language, thus the correct COLREGs rule can be applied accordingly. For further details of the understanding automaton, including all state definitions and output words, the reader is referred to the work presented in [31], [33], [34]. However, as each state in understanding automaton performs a specific test on some already existing data, the automaton does not have inputs in the classical sense i.e., there are no "underlying process" which is being modelled.…”