cdlm_robot_twostate_2D {animalEKF}

Shiny app for simulation of 2D robot movement with CDLM and two states.

Description

Shiny app for simulation of 2D robot movement with CDLM and two states.

Usage

cdlm_robot_twostate_2D()

Details

See cdlm_robot and cdlm_robot_twostate for explanation of the basic concepts. This function simulates a 2-D moving robot with two behavioral states (1 and 2, "slow"/"fast") to model, as well as the switching probabilities between them.

The means of the log-speeds of the two behaviors are simulated by a normal distribution with two means alpha ("unknown true mean of log-speed", types 1 and 2). The variance in each case is the same and known, as before. The prior means and variances of the velocities are assigned as before.

The transition probabilities between the behaviors are given by "transition probability between type 1 and 2" and "2 and 1". If box "are transition probabilities known?" is checked, then they are known. Otherwise, the transition probabilities will be estimated by a Dirichlet prior (vector "Dirichlet prior values" of form 1->1, 1->2, 2->1, 2->2 of positive numbers, which should roughly correspond to the true probabilities in ratio). Note that the predictions in this simulation are unlikely to be as good as in the prior 1-D example since there are more parameters to learn and only a limited number of timesteps or particles.

Panel 1 shows the particles' distributions of the log-speed for each behavior. This simulation works best if the distributions are well-separated.

Panel 2 shows the location predictions (center with confidence ellipse, either solid or dashed by behavior type)

Panel 3 shows the overall resampling weights for the particles, as well as the behavior-conditional ones. The higher the behavior-conditional weight bar is, the better the particle's prediction at that behavior matches what was observed. The overall weight (top row) is the average of the conditional weight values, weighted by the transition probability into that behavior.

Panel 4 shows the resampled particles, along with their prediction of location and behavior type. Ideally, the resampled ellipses should be centered around the observed point. It is not necessarily true that the resampled (most likely) ellipses will be the smallest, since the likelihood of the behavior predicting the observed location is a combination of both the density of that location at the ellipse, as well as the likelihood (transition probability) of having that behavior, given the previous one. In panel 4, the particle predictions are shown one at a time as that particle is resampled; the weight bar in panel 3 should be in bold as that particle is selected.

Panel 5 shows convergence over time of the means of the particle distributions of log-speed (panel 1) to the true value (vertical dashed line). Ideally these should converge to the true value.

Panel 6 shows the history of predicted locations over time in terms of a spatial density plot (grayscale shading). Ideally, these should concentrate around the red overlaid trajectory of observed locations.

Panel 7 shows the estimated distributions of the behavior switching probabilities (if they are not known). The true probabilities are shown by a vertical line, and ideally the mean of the estimated distribution should be around there.

Panel 8 shows the accuracy of particle predictions of the behavior. The color (1=black, 2=gray) is the true behavior type, and the height of the bar is the fraction of particles correctly predicting it. Ideally, all bars should be high.

Note

Video explanation of simulation applet by author: https://youtu.be/4XR8eB89z7E

References

Ackerman, Samuel. "A Probabilistic Characterization of Shark Movement Using Location Tracking Data." Temple University doctoral thesis, 2018. https://digital.library.temple.edu/digital/collection/p245801coll10/id/499150

Carvalho, Carlos M., Johannes, Michael S., Lopes, Hedibert F., and Nicholas G. Polson. "Particle learning and smoothing." Statistical Science, 2010.