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Estimating location without external cues.

Cheung A - PLoS Comput. Biol. (2014)

Bottom Line: Surprisingly, localization does not require the sensing of any external cue, including the boundary.Optimal localization performance was found to depend on arena shape, arena size, local and global rotational asymmetry, and the structure of the path taken during localization.Based on these results, experiments are suggested to identify if and where information fusion occurs in the mammalian spatial memory system.

View Article: PubMed Central - PubMed

Affiliation: The University of Queensland, Queensland Brain Institute, Brisbane, Queensland, Australia.

ABSTRACT
The ability to determine one's location is fundamental to spatial navigation. Here, it is shown that localization is theoretically possible without the use of external cues, and without knowledge of initial position or orientation. With only error-prone self-motion estimates as input, a fully disoriented agent can, in principle, determine its location in familiar spaces with 1-fold rotational symmetry. Surprisingly, localization does not require the sensing of any external cue, including the boundary. The combination of self-motion estimates and an internal map of the arena provide enough information for localization. This stands in conflict with the supposition that 2D arenas are analogous to open fields. Using a rodent error model, it is shown that the localization performance which can be achieved is enough to initiate and maintain stable firing patterns like those of grid cells, starting from full disorientation. Successful localization was achieved when the rotational asymmetry was due to the external boundary, an interior barrier or a void space within an arena. Optimal localization performance was found to depend on arena shape, arena size, local and global rotational asymmetry, and the structure of the path taken during localization. Since allothetic cues including visual and boundary contact cues were not present, localization necessarily relied on the fusion of idiothetic self-motion cues and memory of the boundary. Implications for spatial navigation mechanisms are discussed, including possible relationships with place field overdispersion and hippocampal reverse replay. Based on these results, experiments are suggested to identify if and where information fusion occurs in the mammalian spatial memory system.

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Related in: MedlinePlus

Failure of localization using only path integration.Examples of the first 20 true steps along random trajectories (red), using iPI only (A) or aPI only (B) to track the position (cyan), starting at the arena centre fully oriented. The estimated final position (cyan, with bivariate Gaussian fit showing 1, 2 and 3 SDs) following 48 minutes for 103 independent trials differed markedly from the true positions (red, approximately uniformly random within the arena). (C) Initially oriented, Ip (solid lines, median; shaded, IQR) decayed more rapidly using iPI (blue,  by 3:07) than aPI (orange,  by 5:33). V(θ) increased using iPI (blue dotted line), but V(θ) remained constant during aPI (orange dotted line). The Ip distributions (right) showed that all position estimates were below chance (0.5) at 48 minutes. (D) Simulated grid cell spikes using iPI (top row) and aPI (bottom row) had insufficient spike count (averaging <1 spike per analysis pixel) to obtain reliable measures of information content. (E) Initially disoriented,  throughout the 48 minute period (lower than (C), Wilcoxon test: iPI, p = 1.4×10−4; aPI, p = 3.3×10−5), and no grid firing pattern formed. Stable V(θ) showed no gain or loss of directional information.
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pcbi-1003927-g001: Failure of localization using only path integration.Examples of the first 20 true steps along random trajectories (red), using iPI only (A) or aPI only (B) to track the position (cyan), starting at the arena centre fully oriented. The estimated final position (cyan, with bivariate Gaussian fit showing 1, 2 and 3 SDs) following 48 minutes for 103 independent trials differed markedly from the true positions (red, approximately uniformly random within the arena). (C) Initially oriented, Ip (solid lines, median; shaded, IQR) decayed more rapidly using iPI (blue, by 3:07) than aPI (orange, by 5:33). V(θ) increased using iPI (blue dotted line), but V(θ) remained constant during aPI (orange dotted line). The Ip distributions (right) showed that all position estimates were below chance (0.5) at 48 minutes. (D) Simulated grid cell spikes using iPI (top row) and aPI (bottom row) had insufficient spike count (averaging <1 spike per analysis pixel) to obtain reliable measures of information content. (E) Initially disoriented, throughout the 48 minute period (lower than (C), Wilcoxon test: iPI, p = 1.4×10−4; aPI, p = 3.3×10−5), and no grid firing pattern formed. Stable V(θ) showed no gain or loss of directional information.

Mentions: As a baseline, both iPI and aPI (allothetic PI implies PI using a compass) performance were quantified without arena memory, in a kite-shaped arena. Even for the simplified task of PI initially orientated, localization failed (Fig. 1A, 1B). The median place stability index, , fell below 0.5 (chance level) in 3 minutes using iPI alone, and under 6 minutes using aPI alone (Fig. 1C), consistent with the generally-accepted idea that cumulative PI errors degrade location estimates over time. Using iPI, the circular variance which measures the particle filter's directional performance across trials, increased from 0 (no error) to close to 1 (uniformly random orientation). In contrast, remained close to 0 using aPI since the compass continually reset orientation errors. Using either type of PI, spatially-selective firing patterns could not be maintained beyond 1–2 minutes (Fig. 1D). The more general task of localization initially disoriented (Fig. 1E) further increased localization difficulty, with throughout the simulation period, and no grid-like firing pattern was observed. Taken together, it was clear that neither aPI or iPI alone could enable localization. Next, idiothetic self-motion cues were combined with arena memory information.


Estimating location without external cues.

Cheung A - PLoS Comput. Biol. (2014)

Failure of localization using only path integration.Examples of the first 20 true steps along random trajectories (red), using iPI only (A) or aPI only (B) to track the position (cyan), starting at the arena centre fully oriented. The estimated final position (cyan, with bivariate Gaussian fit showing 1, 2 and 3 SDs) following 48 minutes for 103 independent trials differed markedly from the true positions (red, approximately uniformly random within the arena). (C) Initially oriented, Ip (solid lines, median; shaded, IQR) decayed more rapidly using iPI (blue,  by 3:07) than aPI (orange,  by 5:33). V(θ) increased using iPI (blue dotted line), but V(θ) remained constant during aPI (orange dotted line). The Ip distributions (right) showed that all position estimates were below chance (0.5) at 48 minutes. (D) Simulated grid cell spikes using iPI (top row) and aPI (bottom row) had insufficient spike count (averaging <1 spike per analysis pixel) to obtain reliable measures of information content. (E) Initially disoriented,  throughout the 48 minute period (lower than (C), Wilcoxon test: iPI, p = 1.4×10−4; aPI, p = 3.3×10−5), and no grid firing pattern formed. Stable V(θ) showed no gain or loss of directional information.
© Copyright Policy
Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC4214594&req=5

pcbi-1003927-g001: Failure of localization using only path integration.Examples of the first 20 true steps along random trajectories (red), using iPI only (A) or aPI only (B) to track the position (cyan), starting at the arena centre fully oriented. The estimated final position (cyan, with bivariate Gaussian fit showing 1, 2 and 3 SDs) following 48 minutes for 103 independent trials differed markedly from the true positions (red, approximately uniformly random within the arena). (C) Initially oriented, Ip (solid lines, median; shaded, IQR) decayed more rapidly using iPI (blue, by 3:07) than aPI (orange, by 5:33). V(θ) increased using iPI (blue dotted line), but V(θ) remained constant during aPI (orange dotted line). The Ip distributions (right) showed that all position estimates were below chance (0.5) at 48 minutes. (D) Simulated grid cell spikes using iPI (top row) and aPI (bottom row) had insufficient spike count (averaging <1 spike per analysis pixel) to obtain reliable measures of information content. (E) Initially disoriented, throughout the 48 minute period (lower than (C), Wilcoxon test: iPI, p = 1.4×10−4; aPI, p = 3.3×10−5), and no grid firing pattern formed. Stable V(θ) showed no gain or loss of directional information.
Mentions: As a baseline, both iPI and aPI (allothetic PI implies PI using a compass) performance were quantified without arena memory, in a kite-shaped arena. Even for the simplified task of PI initially orientated, localization failed (Fig. 1A, 1B). The median place stability index, , fell below 0.5 (chance level) in 3 minutes using iPI alone, and under 6 minutes using aPI alone (Fig. 1C), consistent with the generally-accepted idea that cumulative PI errors degrade location estimates over time. Using iPI, the circular variance which measures the particle filter's directional performance across trials, increased from 0 (no error) to close to 1 (uniformly random orientation). In contrast, remained close to 0 using aPI since the compass continually reset orientation errors. Using either type of PI, spatially-selective firing patterns could not be maintained beyond 1–2 minutes (Fig. 1D). The more general task of localization initially disoriented (Fig. 1E) further increased localization difficulty, with throughout the simulation period, and no grid-like firing pattern was observed. Taken together, it was clear that neither aPI or iPI alone could enable localization. Next, idiothetic self-motion cues were combined with arena memory information.

Bottom Line: Surprisingly, localization does not require the sensing of any external cue, including the boundary.Optimal localization performance was found to depend on arena shape, arena size, local and global rotational asymmetry, and the structure of the path taken during localization.Based on these results, experiments are suggested to identify if and where information fusion occurs in the mammalian spatial memory system.

View Article: PubMed Central - PubMed

Affiliation: The University of Queensland, Queensland Brain Institute, Brisbane, Queensland, Australia.

ABSTRACT
The ability to determine one's location is fundamental to spatial navigation. Here, it is shown that localization is theoretically possible without the use of external cues, and without knowledge of initial position or orientation. With only error-prone self-motion estimates as input, a fully disoriented agent can, in principle, determine its location in familiar spaces with 1-fold rotational symmetry. Surprisingly, localization does not require the sensing of any external cue, including the boundary. The combination of self-motion estimates and an internal map of the arena provide enough information for localization. This stands in conflict with the supposition that 2D arenas are analogous to open fields. Using a rodent error model, it is shown that the localization performance which can be achieved is enough to initiate and maintain stable firing patterns like those of grid cells, starting from full disorientation. Successful localization was achieved when the rotational asymmetry was due to the external boundary, an interior barrier or a void space within an arena. Optimal localization performance was found to depend on arena shape, arena size, local and global rotational asymmetry, and the structure of the path taken during localization. Since allothetic cues including visual and boundary contact cues were not present, localization necessarily relied on the fusion of idiothetic self-motion cues and memory of the boundary. Implications for spatial navigation mechanisms are discussed, including possible relationships with place field overdispersion and hippocampal reverse replay. Based on these results, experiments are suggested to identify if and where information fusion occurs in the mammalian spatial memory system.

Show MeSH
Related in: MedlinePlus