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When the initial heading variance becomes larger, the linear model outperforms the traditional models.
Figure 4 shows how the traditional model is advantageous only if the heading variance is small; small realized error is not enough.
This means that to gain the benefit of the known initial heading, the initial heading variance should also be set correctly.
It would also be possible to initialize the linear model with accurate heading and footstep length information, but when the initial heading variance is larger, it is not a straightforward task to select initial covariance for the linear model that is similar to the one used with nonlinear model, but that avoids the problems with linearizations.
Each simulated test track consists of 50 footsteps, and at every time step, there is a 10% probability of receiving a location measurement with variance 102m2 I. First, we test the effect of the initial heading variance on the positioning accuracy of the traditional models and comparing it with estimate obtained with linear model that does not use initial heading information.
The whale continued this strong and sustained avoidance (with rapid fluking, high ODBA and minimal heading variance) until about 1.6 h post-exposure (figure 1).
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The model assumes that uncertainty of state transition noise is equal in every direction, but our simulations show that the model is not very sensitive to different footstep length and heading variances.
When the noise level increases the linear model that uses the footstep length's variance as the σ Δ v becomes less accurate than the other methods, but the linear model that uses step vector variance computed from the heading change variance with expected footstep length (0.7 m) according to Equation 58 is either on the same level or better than traditional models without known footstep length.
The sum of node surplus head and the node surplus head variance are used as another two objective functions.
Two different strategies are followed: the design of a measurement network that aims at minimizing the log-transmissivity variance (averaged over the domain of interest) or a design that minimises the hydraulic head variance (averaged over the domain of interest).
In the first step the prior log-transmissivity and hydraulic head variances are estimated.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com