<p>Pedestrian trajectory prediction is crucial in many fields such as autonomous driving and intelligent robot navigation. Currently, many prediction methods based on generative adversarial networks (GAN) typically model the uncertainty of the discriminator network’s output in the form of probabilities and then optimize the network using cross-entropy. However, this approach rigidly limits the network’s output to only two possibilities, yes or no, and fails to adequately express the uncertainty of the network’s output. This may result in poor adaptability of the network to unknown situations, limiting the improvement of prediction accuracy, especially in capturing predictions for complex scenarios. Evidence theory exhibits strong applicability in complex uncertain environments, able to clearly distinguish between ‘uncertainty’ and ‘ignorance.’ This distinction enables effective handling of uncertain information, which is crucial for practical applications. In evidence theory, belief entropy captures the uncertainty of information by measuring the degree of belief in propositions. Belief entropy remains usable even when prior knowledge is insufficient, demonstrating its flexibility. Inspired by this, we propose a trajectory prediction method that integrates the processing of uncertain information. This method aims to enhance the flexibility of the network, improve its ability to handle uncertain information, and thus increase prediction accuracy. Firstly, by incorporating the evidence theory, the uncertainty of the output from the discriminator network is modeled. Specifically, this is achieved by modeling the soft output state in combination with evidence theory to better express the uncertainty within the network, thus making the network more intelligent. The approach transforms the original probability output of the network into the belief output of evidence theory. Additionally, as belief entropy effectively deals with uncertain information, a new loss called fuzzy cross-belief entropy is proposed by combining belief entropy and cross-entropy based on the soft output state to optimize the network. Finally, the network’s ability to process trajectory information is improved, resulting in more reasonable trajectories. Experiments on the public datasets ETH/UCY show that compared with the baseline method, the average displacement error has been reduced by 22.22<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="521_2025_11141_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\%$</EquationSource> <EquationSource Format="MATHML"><math> <mo>%</mo> </math></EquationSource> </InlineEquation>, and the final displacement error has been reduced by 28.69<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="521_2025_11141_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\%$</EquationSource> <EquationSource Format="MATHML"><math> <mo>%</mo> </math></EquationSource> </InlineEquation>. The proposed method effectively improves the prediction accuracy of trajectories on some subsets, particularly for complex situations. In most cases, such as pedestrians in pairs, avoiding, turning sharply, stopping, and other trajectories can be effectively predicted.</p>

A new fuzzy cross-belief entropy method for trajectory prediction

期刊论文
发表日期：

2025年3月19日

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Tian Yang,
Gang Wang,
Jian Lai,
Yang Wang

摘要

Pedestrian trajectory prediction is crucial in many fields such as autonomous driving and intelligent robot navigation. Currently, many prediction methods based on generative adversarial networks (GAN) typically model the uncertainty of the discriminator network’s output in the form of probabilities and then optimize the network using cross-entropy. However, this approach rigidly limits the network’s output to only two possibilities, yes or no, and fails to adequately express the uncertainty of the network’s output. This may result in poor adaptability of the network to unknown situations, limiting the improvement of prediction accuracy, especially in capturing predictions for complex scenarios. Evidence theory exhibits strong applicability in complex uncertain environments, able to clearly distinguish between ‘uncertainty’ and ‘ignorance.’ This distinction enables effective handling of uncertain information, which is crucial for practical applications. In evidence theory, belief entropy captures the uncertainty of information by measuring the degree of belief in propositions. Belief entropy remains usable even when prior knowledge is insufficient, demonstrating its flexibility. Inspired by this, we propose a trajectory prediction method that integrates the processing of uncertain information. This method aims to enhance the flexibility of the network, improve its ability to handle uncertain information, and thus increase prediction accuracy. Firstly, by incorporating the evidence theory, the uncertainty of the output from the discriminator network is modeled. Specifically, this is achieved by modeling the soft output state in combination with evidence theory to better express the uncertainty within the network, thus making the network more intelligent. The approach transforms the original probability output of the network into the belief output of evidence theory. Additionally, as belief entropy effectively deals with uncertain information, a new loss called fuzzy cross-belief entropy is proposed by combining belief entropy and cross-entropy based on the soft output state to optimize the network. Finally, the network’s ability to process trajectory information is improved, resulting in more reasonable trajectories. Experiments on the public datasets ETH/UCY show that compared with the baseline method, the average displacement error has been reduced by 22.22 $\%$ $%$ , and the final displacement error has been reduced by 28.69 $\%$ $%$ . The proposed method effectively improves the prediction accuracy of trajectories on some subsets, particularly for complex situations. In most cases, such as pedestrians in pairs, avoiding, turning sharply, stopping, and other trajectories can be effectively predicted.