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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.
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When the initial heading variance becomes larger, the linear model outperforms the traditional models.
This means that to gain the benefit of the known initial heading, the initial heading variance should also be set correctly.
Figure 4 shows how the traditional model is advantageous only if the heading variance is small; small realized error is not enough.
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.
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.
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).
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.
In the first step the prior log-transmissivity and hydraulic head variances are estimated.
We solve the mean head up to fourth-order in σY and the head variances up to third-order in σY2.
The sum of node surplus head and the node surplus head variance are used as another two objective functions.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com