Elsevier

Cognitive Psychology

Volume 95, June 2017, Pages 105-144
Cognitive Psychology

Cue combination in human spatial navigation

https://doi.org/10.1016/j.cogpsych.2017.04.003Get rights and content

Highlights

  • Spatial cues were weighted in terms of their relative reliabilities in spatial navigation.

  • Landmark instability reduced reliance on landmarks by impairing cue reliability.

  • Distorted feedback influenced cue reliability.

  • Subjective evaluation of self-performance contributed to cue weighting.

Abstract

This project investigated the ways in which visual cues and bodily cues from self-motion are combined in spatial navigation. Participants completed a homing task in an immersive virtual environment. In Experiments 1A and 1B, the reliability of visual cues and self-motion cues was manipulated independently and within-participants. Results showed that participants weighted visual cues and self-motion cues based on their relative reliability and integrated these two cue types optimally or near-optimally according to Bayesian principles under most conditions. In Experiment 2, the stability of visual cues was manipulated across trials. Results indicated that cue instability affected cue weights indirectly by influencing cue reliability. Experiment 3 was designed to mislead participants about cue reliability by providing distorted feedback on the accuracy of their performance. Participants received feedback that their performance with visual cues was better and that their performance with self-motion cues was worse than it actually was or received the inverse feedback. Positive feedback on the accuracy of performance with a given cue improved the relative precision of performance with that cue. Bayesian principles still held for the most part. Experiment 4 examined the relations among the variability of performance, rated confidence in performance, cue weights, and spatial abilities. Participants took part in the homing task over two days and rated confidence in their performance after every trial. Cue relative confidence and cue relative reliability had unique contributions to observed cue weights. The variability of performance was less stable than rated confidence over time. Participants with higher mental rotation scores performed relatively better with self-motion cues than visual cues. Across all four experiments, consistent correlations were found between observed weights assigned to cues and relative reliability of cues, demonstrating that the cue-weighting process followed Bayesian principles. Results also pointed to the important role of subjective evaluation of performance in the cue-weighting process and led to a new conceptualization of cue reliability in human spatial navigation.

Introduction

The ability to navigate through the environment is a skill that our prehistoric progenitors depended upon for survival, and one that even modern humans rely upon for many daily activities. Effective navigation depends on the ability to estimate one’s position from information in the environment and from information internal to the organism. The accuracy and precision of position estimates depend on a host of factors, including the reliability of these sources of information and the manner in which they are combined.

Spatial cues to position can be divided into two categories. Internal self-motion cues (idiothetic cues) refer to bodily information generated by self-movement, such as vestibular cues and proprioceptive cues. External environmental cues (allothetic cues) refer to inputs from the outside world, such as visual and auditory cues. Environmental cues can be further subdivided into those that are not directly informative about position but can be used to estimate position (e.g., optic flow) and those that are directly informative about position in the environment (e.g., landmark beacons). Navigation using self-motion cues (e.g., vestibular cues, proprioceptive cues) and environmental cues that themselves are not directly informative about position (e.g., optic flow) is referred to as path integration (Loomis, Klatzky, Golledge, & Philbeck, 1999). Many animals demonstrate remarkable abilities to navigate using path integration (Etienne and Jeffery, 2004, Wehner and Menzel, 1969). Humans, however, are relatively poorer at path integration than are ants and rodents, in particular (Loomis et al., 1993, Loomis et al., 1999).

One heuristic to achieve better performance when multiple spatial cues are available is to combine spatial information from those cues instead of relying on one source, as every information source can be contaminated by noise and errors can be decreased by collecting multiple inputs. A second heuristic is to attend more to spatial cues considered as more reliable, so that limited cognitive resources are distributed efficiently. Bayesian principles of cue integration capture both of these heuristics.

Bayesian theory provides a systematic and quantitative method to investigate the manner in which different cues are integrated (Cheng, Shettleworth, Huttenlocher, & Rieser, 2007). Bayesian theory posits that the cue integration process involves linearly combining single-cue estimates, weighted by relative cue reliabilities,C=wA×QA+wB×QB

In this formula, C is the combined estimate, QA and QB are the estimates from single cues, and wA and wB are weights assigned to individual cues. Cue reliability is usually inferred from subjects’ performance and is inversely related to response variance,r=1/σ2

Thus, cue reliability is measured objectively and assesses the precision of the location representation associated with the cue.2 Cue reliability reflects the level of performance when a cue is used exclusively in a given task. In the example shown in Fig. 1, cue A is more reliable than cue B. Based on Bayesian principles, the weights for cues A and B are,wA=rA/(rA+rB)wB=rB/(rA+rB)Equivalently,wA=σB2/(σA2+σB2)wB=σA2/(σA2+σB2)The cue weights are therefore complementary and must sum to 1.0.

The variance of the combined estimate is,σc2=σA2×σB2/(σA2+σB2)Equivalently,1/σc2=1/σA2+1/σB2

It is clear from Eq. (8) that the variance of the combined estimate must be less than the variance of the single-cue estimates. Bayesian cue combination is optimal in the sense that the combined parameter estimate will have maximum precision mathematically (Fig. 1, red curve). This is a key prediction of optimal cue combination.

When estimates derived from single cues are in disparity, the combined mean is a compromise between the two single-cue estimates and its proximities to the two single-cue estimates are determined by the relative cue reliabilities. The combined estimate will be closer to the single-cue estimate of the more reliable cue. Thus, the manner in which weights are distributed between cue A and cue B can be measured in terms of the relative proximities between single-cue response distributions and the combined-cue response distribution. This measure of relative proximity should agree with cue relative reliability if Bayesian rules are followed. In Fig. 1, the combined distribution is closer to the cue A distribution because cue A has higher reliability than does cue B. Cue weights therefore can be estimated from relative reliabilities—which are derived from the variances of response distributions (Eqs. (2), (3), (4), (5), (6))—or from the relative proximities between response distributions (using an appropriate measure of central tendency). Cue weights estimated from relative reliabilities are typically referred to as “predicted weights” because they correspond to the weights predicted by Bayesian theory. Cue weights estimated from the relative proximities of combined-cue and single-cue response distributions are typically referred to as “observed weights” or “actual weights”. Anticipating our findings, comparisons of relative reliabilities to relative proximities—of predicted weights to observed weights—can be informative about cue-weighting processes in navigation.

In some situations, instead of combining cues, navigators alternate between cues, like children tested in the study by Nardini, Jones, Bedford, and Braddick (2008) (Fig. 1, blue line). Cue alternation refers to the use of one cue exclusively for a certain proportion of trials and use of the other cue exclusively for the remaining trials. If cues are selected based on their relative reliabilities, the alternation ratio will be equivalent to cue relative reliability. This means that the more reliable cue is used more often. Cue alternation, however, does not produce a reduction in response variability for multiple cues. Cue weights alone cannot distinguish Bayesian cue integration from cue alternation if cue selection probabilities are equal to cue relative reliabilities. To distinguish these models one must determine whether response variability reduction has occurred in multiple-cue conditions.

Researchers in several domains of investigation have demonstrated that people and non-human animals are able to combine or weight two different information sources optimally in a Bayesian manner (Butler et al., 2010, Ernst and Banks, 2002, Ernst and Bulthoff, 2004, Fetsch et al., 2009, Glennerster et al., 2006, Helbig and Ernst, 2007, Parise et al., 2012, Svarverud et al., 2010). Even when navigators do not combine cues, they appear to alternate between cues using probabilities that are consistent with optimal cue weights (Nardini et al., 2008). Such results imply that people and non-human animals might be natural Bayesian observers and that the brain might be inherently organized by Bayesian principles (Fetsch et al., 2012, Gu et al., 2008, Ma et al., 2006). However, the application of Bayesian principles to human spatial navigation is relatively limited (Bates and Wolbers, 2014, Frissen et al., 2011, Nardini et al., 2008, Petrini et al., 2016, Zhao and Warren, 2015b). Many open questions remain about cue combination in navigation, such as when optimal cue integration occurs and how other cognitive processes might influence the implementation of Bayesian rules (Ernst et al., 2000, Talsma et al., 2007). In addition, we speculate that the application of Bayesian theory to the domain of spatial navigation can be very helpful in reconciling some long-lasting debates in the spatial cognition literature and also provides new perspectives to navigational issues.

To reveal critical advantages of the Bayesian approach, we will compare it to other commonly used paradigms that have been employed in the spatial cognition domain. A frequently used paradigm is cue competition, to which the majority of the following section will be devoted. We will also discuss cue combination studies that have been conducted in the spatial navigation literature. These studies address the cue integration problem but lack key features of the Bayesian integration paradigm.

Many studies have investigated the interaction between different types of spatial cues. One extensively used paradigm is the cue competition or interference paradigm. There are two major paradigms, blocking designs and overshadowing designs. In a blocking design (Kamin, 1969), cue A is learned first. Next, both cue A and cue B are displayed. Finally, subjects are tested on their ability to use cue B alone to complete the task. Cue A is said to have blocked cue B if subjects’ performance is impaired in the cue-B-only stage. In an overshadowing design (Pavlov, 1927), first, both cue A and cue B are presented. Then only cue B is presented. If performance is impaired in the cue-B-only stage, cue A is said to have overshadowed cue B in the previous stage.

Cue competition in spatial memory and navigation tasks has been investigated primarily using visual cues. First, generally there is interference between individual landmarks. For example, landmarks closer to the target were relied on more than those farther away from the target (Goodyear and Kamil, 2004, Roberts and Pearce, 1999, Spetch, 1995). Second, interference between cues also occurs for geometric cues and non-geometric featural cues (e.g., a chamber’s shape and the color of one of the walls, respectively). Some studies found an asymmetric effect of blocking or overshadowing: the blocking/overshadowing effect of geometric cues on featural cues was greater than the blocking/overshadowing effect of featural cues on geometric cues (Wilson & Alexander, 2008). In some cases, the asymmetry was so profound that there was substantial blocking/overshadowing effect of geometric cues on featural cues but no blocking/overshadowing effect of featural cues on geometric cues (Cheng, 1986, Doeller and Burgess, 2008). These results indicated that there was at least a general preference for geometric cues over featural cues, if not to the extent of an isolated geometric module in the brain (Cheng, 1986). However, other studies demonstrated that the relative competition capacity of these two cue types was situational and species specific (Cheng and Newcombe, 2005, Lew, 2011, Twyman and Newcombe, 2010). Sometimes cue potentiation instead of cue competition was observed between geometric cues and featural cues (Pearce, Graham, Good, Jones, & McGregor, 2006). Other theories, such as the view-based matching model (Cheung et al., 2008, Stürzl et al., 2008) and the adaptive combination model (Ratliff & Newcombe, 2008), have been proposed to account for the various phenomena observed between geometric cues and featural cues (see reviews, Cheng, 2008, Cheng et al., 2013).

By comparison, relatively fewer studies have examined interference between visual cues and self-motion cues, and studies that have were conducted on non-human animals. Whereas studies contrasting different visual cues indicate that interference usually occurs, studies on competition between self-motion cues and discrete visual cues suggest that these two types of spatial cues seem to be more independent of each other and that their interaction seems to be more complicated (Shettleworth & Sutton, 2005). Such a discrepancy makes sense if one considers that different visual cues (e.g., geometric vs. featural cues) come from a single sensory modality, whereas self-motion cues and visual cues belong to different sensory modalities.

In comparison to the literature on cue competition, fewer studies directly ask the question of how different cues might be combined and what principles might govern the combination. This question is important to ask because it is likely that multiple spatial cues are employed for spatial localization. Regarding self-motion cues and visual cues, on the one hand, there is ample evidence that adding body-based self-motion cues improves navigational performance relative to visual cues alone (e.g., Kearns et al., 2002, Riecke et al., 2010, Ruddle and Lessels, 2006, Ruddle and Lessels, 2009). On the other hand, compared to self-motion cues alone, there is also evidence that adding discrete visual cues, such as landmarks and room geometry, improves navigational performance (Kelly et al., 2008, Kelly et al., 2009, Riecke et al., 2002). Such studies suggest that during navigation, both self-motion cues and external visual cues are used. However, none of these studies tested the multiple-cue condition against both single-cue conditions in ways that would allow one to determine whether cues were integrated or used independently. Similar studies have been conducted regarding various self-motion cues, such as vestibular vs. proprioceptive cues, which suffered from the same disadvantages (Allen, Kirasic, Rashotte, & Haun, 2004). It is not surprising that having more cues available leads to better navigation performance, but the key question is how different cues are combined and weighted. Most existing studies that included multiple-cue conditions in addition to single-cue conditions lacked the ability to reveal the underlying mechanisms of how cues were weighted and combined (Harris et al., 2000, Sun et al., 2004, Sun et al., 2004).

Even though the cue competition paradigm has been much more extensively used than has the cue combination paradigm (including recent studies that applied Bayesian principles) there are multiple reasons why the two paradigms might not be essentially different from each other. First, cue integration might have occurred in cue competition studies. In cue-competition studies, performance usually did not drop to a random level when only the blocked/overshadowed cue was displayed. In other words, during the preceding double-cues stage, the blocked/overshadowed cue and the blocking/overshadowing cue might have both been utilized for location representation and combined in some way. When two cues were in small conflict and a continuous response was allowed, animals usually searched for a compromise between the different dictates of the cues, suggesting that both cues were used and integrated (Chittka & Geiger, 1995). Even complete blocking/overshadowing of cue A over cue B and no blocking/overshadowing of cue B over cue A can be interpreted as extremes in the cue-integration continuum; that is, one cue is assigned a weight of 0 while the other is assigned a weight of 1. Second, cue competition and integration processes might be influenced by the same set of factors. The ability of one cue to block or overshadow another cue may depend on its intrinsic attributes (e.g., salience, stability) and the animal’s prior experiences; in a similar way, the weight assigned to one cue relative to another cue in the cue integration paradigm probably depends on the same set of factors. Compared to the overshadowing design or the integration design, in the blocking design, a cue’s competition capacity is probably strengthened by prior experiences in addition to any of its intrinsic attributes.

One limitation of cue competition studies is that they have not revealed the factors that determine a cue’s ability to compete against other cues. Researchers have examined the effects of various factors, such as cue type, cue distance, and navigation history, but they have not summarized the underlying determinants that mediate their effects. Similarly, other than those few studies that have specifically investigated Bayesian cue combination (cited previously), previous cue combination studies have shown that having more cues usually yields different patterns of behaviors or better performance than using a single cue alone, but have not determined whether and how different spatial cues are combined and weighted. As discussed in the previous paragraph, cue competition paradigms and cue integration paradigms might share some fundamental features. A cue’s competition ability as measured in cue competition tasks and a cue’s weight as measured in cue integration tasks probably derive from a common concept, namely, the capacity to gain consideration of the navigator. The Bayesian framework clearly proposes that cue reliability is one crucial determinant, meaning that the higher the cue is in reliability, the greater the cue’s ability to influence navigation decisions.

In addition, previous cue competition and combination studies have not attended to individual differences, which have been frequently observed in the spatial navigation literature (for reviews, see Allen, 1999, Hegarty et al., 2006, Wolbers and Hegarty, 2010; for recent studies, see Marchette et al., 2011, Schinazi et al., 2013, Weisberg and Newcombe, 2016, Weisberg et al., 2014). For example, both animals and humans often show different preferences in using different types of visual cues in guiding their navigation (Cheng and Spetch, 1995, Kelly et al., 2009, Spetch and Mondloch, 1993). It is also well documented that people differ greatly in path integration abilities (Loomis et al., 1999). Even single cells within a spatially sensitive brain area respond differently to the same experimental manipulations (Knierim, 2002, Neunuebel et al., 2013). However, the cue competition paradigms and the existing cue combination paradigms (not including recent studies that applied Bayesian principles) have not offered an appropriate method to incorporate individual differences into the interpretation of the roles of different cues in spatial navigation. This situation exists because those studies usually limited their focus to physical properties of spatial cues but ignored navigators’ conceptions of spatial cues and their abilities to exploit those cues. In contrast, within the Bayesian framework, cue reliability is measured in terms of the variability of performance, which is jointly determined by a cue’s physical properties, navigators’ conceptions of the cue, and navigators’ abilities to exploit the cue. The latter two factors contribute to individual differences in navigation performance. If each individual sets his or her own cue-weighting schemes and follows Bayesian principles, we would expect to observe correlations across individuals between cue relative reliabilities and response relative proximities, or equivalently, between predicted and observed cue weights. In this way, individual differences can be incorporated by applying Bayesian principles at the individual level.

As stated previously, the Bayesian approach has been employed extensively and has been proven useful in many fields of investigation, such as perception of shape from visual and haptic cues (Ernst & Banks, 2002), perception of slant from various visual cues (Nardini, Bedford, & Mareschal, 2010), perception of location from visual and auditory cues (Parise et al., 2012), and perception of object size and object distance in virtual reality (Glennerster et al., 2006, Svarverud et al., 2010). However, its application in spatial navigation is still relatively limited (Bates and Wolbers, 2014, Frissen et al., 2011, Nardini et al., 2008, Petrini et al., 2016, Zhao and Warren, 2015b). The current project had two principal goals: Since relatively few studies have investigated human navigation in the Bayesian framework, the first goal was to attempt to replicate some of the critical results of past studies (Bates and Wolbers, 2014, Nardini et al., 2008, Zhao and Warren, 2015b). We also wanted to extend the experimental design adopted by past studies. The second goal was to gain a better understanding of the Bayesian framework and expand its scope of application by asking new questions that have never been addressed in the spatial navigation literature. We focused on the interaction between idiothetic self-motion cues and allothetic visual cues, and used immersive virtual reality technologies.

These two experiments were designed to replicate and extend pioneering work in the field of human spatial navigation (Bates and Wolbers, 2014, Nardini et al., 2008, Petrini et al., 2016, Zhao and Warren, 2015b). We adopted and modified the task developed by Nardini et al. (2008). One key question addressed by these experiments is whether people integrate visual cues and self-motion cues optimally in an immersive virtual environment. A novel aspect of our experiments is that we manipulated the reliability of visual cues and of self-motion cues within-participants (in Exps. 1A & 1B, respectively). This manipulation allowed us to assess whether human navigators could flexibly adjust their strategy as the experimental setting varied.

This experiment was designed to expand the application of Bayesian theory in spatial navigation by incorporating another factor into the paradigm in addition to cue reliability. In the Bayesian framework, cue reliability is the only determinant of how weights are assigned to different cues. Hence, a natural question is whether there are other factors besides cue reliability that would also affect the weights. We hypothesize that a given factor might have its effect via two different pathways. One pathway is direct, wherein the factor affects the weights without affecting cue reliability (e.g., via a higher-order cognitive process); that is, cue reliability is short-circuited. The other is an indirect pathway, wherein the factor affects the weights by affecting cue reliability; in this case, cue reliability serves as a mediator. The Bayesian framework is suitable for distinguishing these two pathways, because cue reliability can be measured and accounted for. The indirect pathway predicts that cue weights and cue reliabilities should be congruent; that is, Bayesian principles hold true. The direct pathway, however, could cause discrepancies between cue reliabilities and cue weights, violating Bayesian principles. The direct pathway as defined here is the same as the heuristic route (Byrne & Crawford, 2010).

We studied landmark instability, which has been suggested as a factor that substantially affects navigational behaviors. For example, the general dominance of geometric cues over featural cues that has been observed in some spatial orientation paradigms has been attributed to the fact that the former are perceived to be more stable in the natural environment across time than are the latter (Gallistel, 1990). There is also a good body of empirical evidence showing that cue instability impaired navigational performance or reduced reliance on the cue in spatial memory and navigation (Burgess et al., 2004, Knierim et al., 1995, Lenck-Santini et al., 2002, Zhao and Warren, 2015a). However, it remains unclear how cue instability affects navigational behaviors. Does cue instability affect the variability of performance, and hence cue relative reliability, or does it affect reliance on the cue, as reflected in the measurement of the observed weight, or both? If results show that cue instability reduces navigators’ reliance on the cue (e.g., observed weights are smaller for unstable than for stable cues), is it necessarily the case that performance with the cue is also impaired (e.g., performance is more variable for unstable than for stable cues)? Similarly, if results show that cue instability impairs performance, is it necessarily the case that navigators rely less on the cue? Previous studies that did not incorporate Bayesian principles into their design cannot answer these questions.

In the Bayesian framework, effects on the variability of performance and on cue reliance can be dissociated quantitatively. The former effects are manifested in cue relative reliabilities and in the predicted cue weights computed from them (Eqs. (2), (3), (4), (5), (6)) and the latter effects are manifested in relative proximities of response distributions and in the observed weights computed from them (see Eqs. (11), (12) below). The indirect pathway hypothesis proposes that unstable cues should have smaller weights than stable cues because cue instability impairs the precision of performance. In this case, cue reliability is the mediator influencing cue weights. This hypothesis is supported by studies which showed that cue instability adversely affected rats’ performance on a spatial memory task, in which spatial information (e.g., distance and direction) needed to be retrieved for successful food forage (Biegler and Morris, 1993, Biegler and Morris, 1996a, Biegler and Morris, 1996b). Unstable cues might impair performance because they impose extra burden on the memory system, especially the working memory system. To take advantage of unstable spatial cues, the navigator may need to update environmental representations continuously and to coordinate the spatial correspondence between the cue’s information and other sources of spatial information, such as path integration and other visual inputs. All of these factors could increase task difficulty. The direct pathway hypothesis proposes that unstable cues might be considered less useful regardless of how precise and informative they may be, with instability not affecting the level of performance. Usually cues that have moved no longer point to the reward location. Under such circumstances, if searches still followed the moved cue, they would be centered at a reward-absent location, even though the precision of searches might remain unchanged. In addition, navigators might have had unsuccessful experiences with unstable cues and simply decide not to rely on them.

These two forms of influence have been distinguished in studies of reaching (e.g., Byrne & Crawford, 2010), but to our knowledge, they have never been investigated in the domain of spatial navigation. The current experiment was designed to test the influence of landmark stability using the cue integration paradigm. In this experiment, landmarks were unstable across trials but stable within a given trial. We expected that this form of landmark stability would influence observed cue weights via the indirect pathway hypothesis. Instability of landmarks from trial to trial would increase task difficulty and decrease cue reliability, but being stable within a given trial means that landmarks would still point to the correct target location and be considered useful. Our manipulation of landmark stability differed from the one employed by Zhao and Warren (2015a), who dissociated the cue from the correct target location within trials.

This experiment was designed to advance our understanding of cue reliability. Since cue reliability is at the core of Bayesian theory, one important question is whether it is necessary for people to acquire explicit knowledge about reliability of the cue and the ways they can be influenced by such knowledge. That is, is explicit evaluation necessary to successfully implement the weighting-by-reliability strategy? Do people need to explicitly calculate variances of sensory estimators associated with different spatial cues? This question has barely been asked or investigated in the cue integration literature. Ernst and Banks (2002) speculated that there is no need to explicitly extract cue reliability from the cue, since neural firing and inter-neuron transmission processes can accomplish it automatically and unconsciously. Their hypothesis posits that the Bayesian cue combination process is completely bottom-up, which means that performance variability and cue-weights in multiple-cue conditions can be derived purely from single-cue performance variability. However, it is still plausible that cognitive factors could exert top-down influences on the cue combination process. For example, it has been shown that active attention can affect how observers combine different cues, both in behaviors and at the neural level (Berger and Bülthoff, 2009, Mozolic et al., 2008, Talsma et al., 2007).

In this experiment, we investigated cognitive top-down influences on the cue-weighting process by manipulating the performance feedback given to participants. We speculated that one convenient way to evaluate cue reliability is to judge it by its behavioral consequences. In daily situations, we often receive feedback on our performance and we also evaluate the performance according to the feedback. Thus, feedback might be an important source of information to help people develop accurate sense of a cue’s usefulness, which could be crucial for the implementation of Bayesian principles. In Experiment 3, we provided distorted feedback on the accuracy of their performance to participants. The feedback was distorted in the sense that it never reflected the true level of accuracy. The purpose was to mislead people’s beliefs about cue reliability. Normally, feedback reflects actual performance. In this experiment, we dissociated feedback and performance by providing distorted feedback. This manipulation should help us to understand differences and interactions between the top-down influences of feedback and the bottom-up influences of performance on the cue weighting behaviors.

In Experiments 1–3, we focused on the relationship between performance with a cue (as reflected in cue reliability) and cue reliance (as reflected in observed cue weights). In daily situations, a sense of confidence accompanies almost every decision we make. The question remains unanswered whether one’s confidence also influences observed cue weights, and how it interacts with performance in this process. Past studies have shown that confidence can deviate from performance under certain situations and that human participants vary substantially on this metacognitive ability (Barttfeld et al., 2013, Fleming et al., 2010, Persaud et al., 2007). Subjective evaluation is important in guiding decisions and behaviors. The frequently observed inconsistencies between subjective evaluation and objective performance imply that it is possible that confidence in using a certain spatial cue might affect reliance on that cue even after performance has been accounted for. In the current experiment, subjects were asked to rate confidence levels while performing the homing task. This experiment represents the first time that relationships among performance, subjective evaluation, and cue reliance were examined. We speculated that distorted feedback on the accuracy of performance, which was introduced in Experiment 3, might influence participants’ subjective evaluations of cue usefulness. Therefore, as with the potential influences of feedback, we refer to influences of subjective evaluation on cue weights, if any, as a top-down process. This effect can be contrasted with the bottom-up effect of cue weights being determined by cue relative reliabilities (i.e., the variability of performance). This experiment should help us to compare further these two different types of influence. Participants also completed a battery of cognitive ability tests, and we assessed how spatial updating performance and cue-weighting strategy were related to various cognitive abilities.

In summary, this project tested two fundamental tenets of Bayesian cue combination: We sought to determine whether visual cues and self-motion cues would be assigned weights based on their relative reliabilities and whether they would be combined optimally. Cue reliability reflects the precision of performance associated with the cue, and assigned cue weights reflect navigators’ reliance on the cue. We examined individual differences in the context of this framework, because it is very likely that different navigators exhibit different levels of efficiency in utilizing visual cues vs. self-motion cues. We expanded the basic framework of Bayesian cue combination by incorporating a third factor, landmark instability, to examine whether landmark instability influenced how cues were weighted and whether it did so by influencing cue reliability. Finally, we extended previous research by investigating whether subjective evaluation of performance (or cue reliability) could influence how cues were weighted and relied upon.

Section snippets

Apparatus and materials

Virtual environments in Experiments 1–3 were displayed on an nVisor SX60 head-mounted display (HMD; NVIS, Reston, VA) with a 60° diagonal field of view. Stereoscopic images were presented at 1280 × 1024 pixel resolution, refreshed at 60 Hz. Graphics were rendered using Vizard software (WorldViz, Santa Barbara, CA) on a 3.0-GHz Pentium 4 processor with a GeForce 6800 GS graphics card. Head orientation was tracked by a 3-degrees-of-freedom orientation sensor (InertiaCube2; Intersense, Bedford, MA),

Experiment 1A

To vary reliability of visual cues in Experiment 1A, we pitted an environment rich in landmarks against an environment poor in landmarks. In Experiment 1B, to vary reliability of self-motion cues, we added different levels of body rotation into the task (Loomis et al., 1993). Participants within each experiment experienced both reliability levels of the manipulated cue. These two experiments represent the first time that the reliability of spatial cues has been manipulated in an investigation

Experiment 1B

Experiment 1B paralleled Experiment 1A but manipulated the reliability of self-motion cues within-participants. The reliability of visual cues was not manipulated.

Experiment 2

Experiment 2 was designed to test the influence of landmark stability using the cue integration paradigm (e.g., Byrne & Crawford, 2010). We wanted to know whether cue stability would affect the assignment of cue weights and whether it would do so directly without affecting cue reliability or indirectly by changing cue reliability. Half of the participants experienced landmarks changing in locations in different layouts (unstable group), whereas the other half experienced landmarks stable across

Experiment 3

Experiments 1A, 1B and 2 showed that cue reliability played an important role in cue weighting in spatial navigation. However, it remains unclear whether accurate explicit knowledge about cue reliability is necessary for the implementation of Bayesian rules and whether inaccurate explicit knowledge would cause deviations from Bayesian rules. Experiment 3 was designed to test whether subjective evaluation of response accuracy could produce a cognitive influence on cue weighting. We displayed

Experiment 4

Experiment 3 showed that explicit knowledge about cue reliability, which was distorted by false feedback, influenced navigation performance itself. Experiment 4 aimed to assess the interaction between subjective evaluation and performance in the process of cue weighting. Participants performed the same homing task, and at the same time evaluated how confident they felt about their own performance. We also compared participants’ behaviors on two consecutive days to assess stability of their

General discussion

In the current project, we applied Bayesian principles to investigate cue integration in human spatial navigation. In Experiments 1A and 1B, we extended previous pioneering work by manipulating cue reliability within-participants. There was consistent evidence of variability reduction in double-cue conditions relative to single-cue conditions, although the double-cue vs. single-cue comparisons were not always statistically reliable. Participants weighted visual cues and self-motion cues based

Conclusions and future directions

This project investigated the ways in which spatial cues are integrated in human spatial navigation. First, we found that, as in other domains of investigation, human navigators were able to integrate spatial cues from different modalities optimally or near-optimally in a Bayesian manner. Second, the very consistent pattern of positive correlations between cue relative reliability (predicted visual weights) and observed visual weights highlights the need to consider cue quality in addition to

Acknowledgements

We thank three reviewers for comments. This research was supported by research grants from the National Science Foundation (HCC-0705863) and research grant from the Human Frontiers Science Program (RGP 0062/2014, awarded to T.W.). Portions of this article were included in the dissertation submitted by Xiaoli Chen to Vanderbilt University in partial fulfillment of the degree of Doctor of Philosophy.

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