Selective resetting position and heading estimations while driving in a large-scale immersive virtual environment

Abstract

Two experiments investigated how self-motion cues and landmarks interact in determining a human’s position and heading estimations while driving in a large-scale virtual environment by controlling a gaming wheel and pedals. In an immersive virtual city, participants learned the locations of five buildings in the presence of two proximal towers and four distal scenes. Then participants drove two streets without viewing these buildings, towers, or scenes. When they finished driving, either one tower with displacement to the testing position or the scenes that had been rotated reappeared. Participants pointed in the directions of the five buildings. The least squares fitting method was used to calculate participants’ estimated positions and headings. The results showed that when the displaced proximal tower reappeared, participants used this tower to determine their positions, but used self-motion cues to determine their headings. When the rotated distal scenes reappeared, participants used these scenes to determine their headings. If they were instructed to continuously keep track of the origin of the path while driving, their position estimates followed self-motion cues, whereas if they were not given instructions, their position estimates were undetermined. These findings suggest that when people drive in a large-scale environment, relying on self-motion cues, path integration calculates headings continuously but calculates positions only when they are required; relying on the displaced proximal landmark or the rotated distal scenes, piloting selectively resets the position or heading representations produced by path integration.

Appendix

Derivation of homing error = position error – heading error (i.e., b_ PO′ – b_PO = (b_OP′ − b_OP) – (h’ − h)) (see Fig. 5).

Fig. 5

A hypothetic participant while standing at the testing position (P) with the testing heading (h) points to the location of the origin (O). Suppose that the judged location of O is O′. The angular error of homing is b_ PO′ – b_PO. b_AB refers to a bearing from positions A to B relative to an horizontal allocentric reference direction in the environment. Suppose that this participant’s estimates of his or her testing position and heading are P′ and h′. The angular error of heading is h′ – h. Both h and h′ are specified by the angular distance from the allocentric reference direction. The angular error of position is b_OP′ − b_OP. As derived in the “Appendix”, homing error = position error – heading error. Position errors and heading errors cannot be dissociated with the measured homing errors. If this participant also learns an addition location X and then replaces X in the position of X′, then position errors can be measured by (b_OX – b_PO) – (b_O′X′– b_PO′) [see Mou and Zhang (2014) for derivation] and heading errors can also be measured given the measured position errors and homing errors (heading error = position error – homing error)

We assume that this participant uses the represented spatial relations between the origin (O), the estimated testing position (P′), and the estimated testing heading (h′) in his or her spatial memory to judge the relations between replaced location of the origin (O′), the testing position (P), and the testing heading (h) during response. Hence the relations between the elements in the memory (O, P′, h′) should be the same as the relations between the elements in the response (O′, P, h).

We obtain

$$h^{\prime }- b\_{\text{OP}}^{\prime} = h-b\_{\text{O}}^{\prime}{\text{P}}$$

(1)

All headings (h and h′) and bearings (i.e., b_AB) are defined as the angular distance from a fixed allocentric direction in the environment. We further define the clockwise direction as the positive direction to specify an angular distance. As signed angles belong to real numbers, all the mathematical principles for read numbers should be applied to headings and bearings.

Equation 1 can be rewritten as

$$h^{\prime } - h = {\text{ b}}\_{\text{OP}}^{\prime } - {\text{ b}}\_{\text{O}}^{\prime } {\text{P}}$$

(2)

Therefore,

$$\begin{aligned} {\text{b}}\_{\text{OP}}^{\prime } - {\text{ b}}\_{\text{OP }}-{\text{ }}\left( {{\text{h}}^{\prime } - {\text{ h}}} \right){\text{ }} & ={\text{ b}}\_{\text{OP}}^{\prime } - {\text{ b}}\_{\text{OP }}-{\text{ }}\left( {{\text{b}}\_{\text{OP}}^{\prime }{\text{ }}-{\text{ b}}\_{\text{O}}^{\prime }{\text{P }}} \right) \\ ={\text{ b}}\_{\text{O}}^{\prime }{\text{P }} - {\text{ b}}\_{\text{OP}} \\ \end{aligned}$$

We obtain

$${\text{b}}\_{\text{OP}}^{\prime } - {\text{ b}}\_{\text{OP }}-{\text{ }}\left( {{\text{h}}^{\prime } - {\text{ h}}} \right){\text{ }}={\text{ b}}\_{\text{O}}^{\prime }{\text{P }} - {\text{ b}}\_{\text{OP}}$$

(3)

Because b_AB = b_BA − 180, we rewrite Eq. 3 as

$$\begin{aligned} {\text{b}}\_{\text{OP}}^{\prime } - {\text{ b}}\_{\text{OP }}-{\text{ }}\left( {{\text{h}}^{\prime } - {\text{ h}}} \right){\text{ }} & ={\text{ b}}\_{\text{PO}}^{\prime }{\text{ }} - {\text{18}}0{\text{ }}-{\text{ }}\left( {{\text{b}}\_{\text{PO }} - {\text{ 18}}0} \right) \\ ={\text{ b}}\_{\text{PO}}^{\prime } - {\text{ b}}\_{\text{PO}}. \\ \end{aligned}$$

We obtain

b_PO′ − b_PO = b_OP′ − b_OP – (h′ − h) or homing error = position error – heading error.