In this paper, we investigate the problem of robust state estimation in time-difference-of-arrival (TDOA) localization systems under scenarios involving random measurement loss. Traditional TDOA localization methods typically rely on the extended Kalman filter (EKF), which performs local linearization of the nonlinear system model using a first-order Taylor expansion. However, the EKF relies on a first-order linearization of the system model, which inevitably introduces approximation errors and compromises the accuracy of state estimation. In addition, when the fusion center is subject to Denial-of-Service (DoS) attacks, communication interruptions, or data tampering, measurement data may be lost or corrupted, further compromising the stability and reliability of the state estimation process. To address these challenges, we augment the EKF cost function with a penalty term on the innovation sensitivity to modeling errors, thereby proposing a robust state estimation algorithm with enhanced resilience to disturbances and system uncertainties. Under certain assumptions, it is theoretically established that the proposed robust estimator guarantees bounded estimation error. Numerical simulations indicate that, in three-dimensional TDOA-based localization scenarios, the proposed algorithm achieves improved estimation accuracy compared to the standard EKF.
{"title":"Robust State Estimation for Time-Difference-of-Arrival Localization Systems Under Measurement Loss","authors":"Yuhao Cui;Huabo Liu;Keke Huang;Yao Mao;Haisheng Yu","doi":"10.1109/TSP.2026.3658065","DOIUrl":"10.1109/TSP.2026.3658065","url":null,"abstract":"In this paper, we investigate the problem of robust state estimation in time-difference-of-arrival (TDOA) localization systems under scenarios involving random measurement loss. Traditional TDOA localization methods typically rely on the extended Kalman filter (EKF), which performs local linearization of the nonlinear system model using a first-order Taylor expansion. However, the EKF relies on a first-order linearization of the system model, which inevitably introduces approximation errors and compromises the accuracy of state estimation. In addition, when the fusion center is subject to Denial-of-Service (DoS) attacks, communication interruptions, or data tampering, measurement data may be lost or corrupted, further compromising the stability and reliability of the state estimation process. To address these challenges, we augment the EKF cost function with a penalty term on the innovation sensitivity to modeling errors, thereby proposing a robust state estimation algorithm with enhanced resilience to disturbances and system uncertainties. Under certain assumptions, it is theoretically established that the proposed robust estimator guarantees bounded estimation error. Numerical simulations indicate that, in three-dimensional TDOA-based localization scenarios, the proposed algorithm achieves improved estimation accuracy compared to the standard EKF.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"74 ","pages":"471-482"},"PeriodicalIF":5.8,"publicationDate":"2026-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146089995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-30DOI: 10.1109/TSP.2026.3659721
Daniel Cederberg
Over the past decades, there has been a surge of interest in studying low-dimensional structures within high-dimensional data. Statistical factor models (i.e., low-rank plus diagonal covariance structures) offer a powerful framework for modeling such structures. However, traditional methods for fitting statistical factor models, such as principal component analysis (PCA) or maximum likelihood estimation assuming the data is Gaussian, are highly sensitive to heavy tails and outliers in the observed data. In this paper, we propose a novel expectation-maximization (EM) algorithm for robustly fitting statistical factor models for elliptical distributions. Our approach is based on Tyler’s M-estimator of the scatter matrix and consists of solving Tyler’s maximum likelihood estimation problem while imposing a structural constraint that enforces the low-rank plus diagonal covariance structure. We present numerical experiments on both synthetic and real examples, demonstrating the robustness of our method for direction-of-arrival estimation in nonuniform noise and subspace recovery.
{"title":"T-Rex: Fitting a Robust Factor Model via Expectation-Maximization","authors":"Daniel Cederberg","doi":"10.1109/TSP.2026.3659721","DOIUrl":"10.1109/TSP.2026.3659721","url":null,"abstract":"Over the past decades, there has been a surge of interest in studying low-dimensional structures within high-dimensional data. Statistical factor models (<italic>i.e.,</i> low-rank plus diagonal covariance structures) offer a powerful framework for modeling such structures. However, traditional methods for fitting statistical factor models, such as principal component analysis (PCA) or maximum likelihood estimation assuming the data is Gaussian, are highly sensitive to heavy tails and outliers in the observed data. In this paper, we propose a novel expectation-maximization (EM) algorithm for robustly fitting statistical factor models for elliptical distributions. Our approach is based on Tyler’s M-estimator of the scatter matrix and consists of solving Tyler’s maximum likelihood estimation problem while imposing a structural constraint that enforces the low-rank plus diagonal covariance structure. We present numerical experiments on both synthetic and real examples, demonstrating the robustness of our method for direction-of-arrival estimation in nonuniform noise and subspace recovery.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"74 ","pages":"561-571"},"PeriodicalIF":5.8,"publicationDate":"2026-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146089993","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-28DOI: 10.1109/tsp.2026.3659022
Mohammad Taha Shah, Gourab Ghatak, Ankit Kumar, Shobha Sundar Ram
{"title":"Modeling and Statistical Characterization of Large-Scale Automotive Radar Networks","authors":"Mohammad Taha Shah, Gourab Ghatak, Ankit Kumar, Shobha Sundar Ram","doi":"10.1109/tsp.2026.3659022","DOIUrl":"https://doi.org/10.1109/tsp.2026.3659022","url":null,"abstract":"","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"15 1","pages":""},"PeriodicalIF":5.4,"publicationDate":"2026-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146070288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-27DOI: 10.1109/tsp.2026.3655687
Qiankun Diao, Dongpo Xu, Shuning Sun, Danilo P. Mandic
{"title":"QLMS-QHM: Accelerated Quaternion LMS Algorithm with Quasi-Hyperbolic Momentum","authors":"Qiankun Diao, Dongpo Xu, Shuning Sun, Danilo P. Mandic","doi":"10.1109/tsp.2026.3655687","DOIUrl":"https://doi.org/10.1109/tsp.2026.3655687","url":null,"abstract":"","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"293 1","pages":"1-11"},"PeriodicalIF":5.4,"publicationDate":"2026-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146056016","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-26DOI: 10.1109/TSP.2026.3657751
Mingjing Cui;Dongyuan Lin;Lei Li;Yunfei Zheng;Shiyuan Wang
Adaptive filters, constrained by a linear filtering framework, often struggle with nonlinear modeling in complex processes. Kernel adaptive filters (KAFs) offer a promising solution by mapping input signals into diverse feature spaces. However, their computational efficiency and filtering accuracy may still not meet the demands of practical applications. To this end, based on Kolmogorov-Arnold (KA) representation theorem, this paper proposes a novel nonlinear filtering framework by treating filter weights as learnable functions. Specifically, the learnable functions are represented as a linear combination of multiple Gaussian basis functions with different centers. To determine the coefficients that define these learnable functions, the weight-learning-based least mean square (WL-LMS) and weight-learning-based recursive least squares (WL-RLS) algorithms are further proposed based on minimum mean square error (MMSE). In addition, to ensure convergence and assess the steady-state and transient performance of proposed algorithms, a thorough theoretical analysis of the convergence conditions and excess mean square error (EMSE) is provided. Finally, linear-in-parameters system identifications validate the correctness of theoretical analysis, while chaotic time-series prediction and nonlinear system identifications demonstrate the superiorities of the proposed WL-LMS and WL-RLS algorithms.
{"title":"Treating the Filter Weights as Learnable Functions: An Efficient Nonlinear Filtering Framework and Its Adaptive Algorithms","authors":"Mingjing Cui;Dongyuan Lin;Lei Li;Yunfei Zheng;Shiyuan Wang","doi":"10.1109/TSP.2026.3657751","DOIUrl":"10.1109/TSP.2026.3657751","url":null,"abstract":"Adaptive filters, constrained by a linear filtering framework, often struggle with nonlinear modeling in complex processes. Kernel adaptive filters (KAFs) offer a promising solution by mapping input signals into diverse feature spaces. However, their computational efficiency and filtering accuracy may still not meet the demands of practical applications. To this end, based on Kolmogorov-Arnold (KA) representation theorem, this paper proposes a novel nonlinear filtering framework by treating filter weights as learnable functions. Specifically, the learnable functions are represented as a linear combination of multiple Gaussian basis functions with different centers. To determine the coefficients that define these learnable functions, the weight-learning-based least mean square (WL-LMS) and weight-learning-based recursive least squares (WL-RLS) algorithms are further proposed based on minimum mean square error (MMSE). In addition, to ensure convergence and assess the steady-state and transient performance of proposed algorithms, a thorough theoretical analysis of the convergence conditions and excess mean square error (EMSE) is provided. Finally, linear-in-parameters system identifications validate the correctness of theoretical analysis, while chaotic time-series prediction and nonlinear system identifications demonstrate the superiorities of the proposed WL-LMS and WL-RLS algorithms.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"74 ","pages":"545-560"},"PeriodicalIF":5.8,"publicationDate":"2026-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146056290","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-23DOI: 10.1109/tsp.2026.3657395
Haoxiang Ye, Tao Sun, Qing Ling
{"title":"Generalization Error Analysis for Attack-Free and Byzantine-Resilient Decentralized Learning with Data Heterogeneity","authors":"Haoxiang Ye, Tao Sun, Qing Ling","doi":"10.1109/tsp.2026.3657395","DOIUrl":"https://doi.org/10.1109/tsp.2026.3657395","url":null,"abstract":"","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"7 1","pages":""},"PeriodicalIF":5.4,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146042847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-23DOI: 10.1109/tsp.2026.3657342
Zijian Zhang, Mingyao Cui
{"title":"Observation Matrix Design for Densifying MIMO Channel Estimation via 2D Ice Filling","authors":"Zijian Zhang, Mingyao Cui","doi":"10.1109/tsp.2026.3657342","DOIUrl":"https://doi.org/10.1109/tsp.2026.3657342","url":null,"abstract":"","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"8 1","pages":""},"PeriodicalIF":5.4,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146042845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-23DOI: 10.1109/TSP.2026.3657434
Tran Thien Dat Nguyen;Ba Tuong Vo;Ba-Ngu Vo;Hoa Van Nguyen;Changbeom Shim
This paper introduces the concept of a mean for trajectories and multi-object trajectories (defined as sets or multi-sets of trajectories) along with algorithms for computing them. Specifically, we use the Fréchet mean, and metrics based on the optimal sub-pattern assignment (OSPA) construct, to extend the notion of average from vectors to trajectories and multi-object trajectories. Further, we develop efficient algorithms to compute these means using greedy search and Gibbs sampling. Using distributed multi-object tracking as an application, we demonstrate that the Fréchet mean approach to multi-object trajectory consensus significantly outperforms state-of-the-art distributed multi-object tracking methods.
{"title":"The Mean of Multi-Object Trajectories","authors":"Tran Thien Dat Nguyen;Ba Tuong Vo;Ba-Ngu Vo;Hoa Van Nguyen;Changbeom Shim","doi":"10.1109/TSP.2026.3657434","DOIUrl":"10.1109/TSP.2026.3657434","url":null,"abstract":"This paper introduces the concept of a mean for trajectories and multi-object trajectories (defined as sets or multi-sets of trajectories) along with algorithms for computing them. Specifically, we use the Fréchet mean, and metrics based on the optimal sub-pattern assignment (OSPA) construct, to extend the notion of average from vectors to trajectories and multi-object trajectories. Further, we develop efficient algorithms to compute these means using greedy search and Gibbs sampling. Using distributed multi-object tracking as an application, we demonstrate that the Fréchet mean approach to multi-object trajectory consensus significantly outperforms state-of-the-art distributed multi-object tracking methods.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"74 ","pages":"531-544"},"PeriodicalIF":5.8,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146042846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-23DOI: 10.1109/tsp.2026.3656119
Zhongtao Chen, Lei Cheng, Yik-Chung Wu, H. Vincent Poor
{"title":"Rank-Revealing Bayesian Block-Term Tensor Completion with Graph Information","authors":"Zhongtao Chen, Lei Cheng, Yik-Chung Wu, H. Vincent Poor","doi":"10.1109/tsp.2026.3656119","DOIUrl":"https://doi.org/10.1109/tsp.2026.3656119","url":null,"abstract":"","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"4 1","pages":""},"PeriodicalIF":5.4,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146042848","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-22DOI: 10.1109/tsp.2026.3656887
Thu Ha Phi, Alexandre Hippert-Ferrer, Florent Bouchard, Arnaud Breloy
{"title":"Leveraging Low-rank Factorizations of Conditional Correlation Matrices in Graph Learning","authors":"Thu Ha Phi, Alexandre Hippert-Ferrer, Florent Bouchard, Arnaud Breloy","doi":"10.1109/tsp.2026.3656887","DOIUrl":"https://doi.org/10.1109/tsp.2026.3656887","url":null,"abstract":"","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"40 1","pages":""},"PeriodicalIF":5.4,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146042745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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