DOME: Distributed Online Learning based Multi-Estimate Fusion for Cooperative Predictive Target Tracking Using a Robotic Swarm
Authors: Shubhankar Gupta
Saksham Sharma
Suresh Sundaram
Venue: Accepted by TMLR ()

Abstract: This paper investigates cooperative predictive target tracking using a robotic swarm operating under high prediction bias and communication uncertainty. The robots interact over a randomly time-varying communication network and exhibit heterogeneity in onboard sensors and prediction algorithms. To address these challenges, a Distributed Online learning-based Multi-Estimate (DOME) fusion algorithm is proposed, which performs a collaborative weighted fusion of local and socially shared predictions. The fusion weights are adapted online using feedback from a prediction loss. Theoretical analysis establishes that conditional expectations of the fusion weights converge under reasonable assumptions. Simulation studies demonstrate that DOME outperforms both covariance-based and online learning-based decentralized fusion baselines, achieving $74\%$ and $72.4\%$ lower prediction loss in performance and scalability tests, respectively -- particularly under conditions involving significant model drift and communication unreliability. Further, DOME fusion is implemented in a ROS-Gazebo simulation environment.

Published in Transactions on Machine Learning Research (04/2026)
DOME: Distributed Online Learning based
Fusion for Cooperative Predictive Target Tracking Using a Robotic Swarm
Shubhankar Gupta
skubhaankrr@Niisc.ucc
Artificial Intelligence and Robotics Lab Deportment of Aerospace Engineering Indian Institute of Science, Bengakuru, India
Saksham Sharma
maksham.prob@gmaan
Artificial Intelligence and Robolics Lab Department of Aerospace Engineering Indian Institute of Science, Bengakuru, India
Suresh Sundaram
ussuresh occ.s.........
Artificial Intelligence and Robotics Lab Department of Aerospace Engineering Indian Institute of Science, Bengaluru, India
Reviewed on OpenReview: https: // openreview. net/ forumm id= aF5PHD6ul1
Abstract
This paper investigates cooperative predictive target tracking using a robotic swarm oper- ating under high prediction bias and communication uncertainly. The robots interact randomly fimeviarying commmication network and exhibit heterogeneity in onboard sen- sors and prediction algorithms. To address these challenges, Distributed Online learning- (DOME) fusion algorithm is proposed, which performs a collaborative weighted fusion of local and socially shared predictions. The fusion weights are adapted on- line using feedback from a prediction loss. Theoretical analysis establishes that conditional expectations of the fusion weights converge under reasonable assumptions. Simulation stud- ies demonstrate that DOME outperforms both rovariance-basee and online learning- baaning-baased docentralized fusion baselines, achieving 74% and 72.4% lower prediction loss in performance and scalability tests, respectively particularly under conditions involving significant model drift and communication unreliability. Further, DOME fusion is implemented in ROS- Gazebo simulation environment.
based
1 Introduction
With robotics technologies becoming more economical, smaller, and reliable, robotic swarms are being con- sidered attractive for use hazardous and uncertain environments (Mohiuddin al. (020).. robotic swarm has wide range of applications, such search and rescue (Scherer al. 2015). precision drug delivery (Nelson & Pané, 2023), and surveillance (Saska et al. 2016), among others, that involve tracking target one of its fundamental tasks. A key challenge in target tracking with sensor-equipped robots is the look-ahead trajectory prediction (Hao et al. 2018); robots use predicted paths to plan their motion for effective tracking performance.
Most prior work on target tracking using robotic swarm focuses on path planning and control. Approaches inchude coordinated control via formation flying (Ma & Hovakimyan 2015 Sun al. 2021) and region-based strategies (Jung & Sukhatme 2006).
Wang & Gu (2011) combined distributed Kalman filtering for target

---

simulation Published in Transactions on Machine Learning Research (04/2026)
localization with flocking control for tracking and collision avoidance. Hausman et al. (0015 presented centralized control scheme that leverages onboard sensing for target estimation. Subbarao & Ahmed (2017)
addressed tracking under dynamic network topologies using pinning control and consensus on target states [Wang& & Su 2014). In contrast, this work focuses on the estimation/prodiie prodiccion aspect of cooperative target tracking, rather than control or planning.
Heterogeneous sensors and prediction algorithms within a robotic swarmn can be systematically exploited to mitigate uncertainty in target trajectory estimation (Rizk et al. 2019 Motivated by this capability, this paper proposes the Distributed Online learning based Multi-Estimate (DOME) fusion algorithm, which employs an implicit, adaptive, consensus-like update mechanism to ensure robust performance under high uncertainly and adversarial conditions. The cooperative target-tracking problem involves robots connected over a random communication network, each running a potentially different prediction algorithm to generate look-ahead trajectories of the target. Prediction accuracy may vary over time due to algorithmic differences, scenario-specific optimizations (cf. no free lunch theorem; Murphy 2012), or environmental and system uncertainties. DOME performs a collaborative, online weighted fusion of local and social predictions. The fusion weights are learned via a prediction loss-driven process inspired by the exponentially weighted fore- caster framework (Cosa-Bianchi & Lugosi 2006). This ensures that more accurate predictions receive higher weight, thereby improving tracking performance.
A convergence analysis of DOME's learning weights is presented, demonstrating that their expected values converge over time. DOME is evaluated in simulated environment featuring random communication link failures and significant dynamic biases or drift in predictions. DOME is benchmarked against several decentralized fusion baselines, including Averaging Consensus Fusion (ACF); four covariance- based methods
Kalman Consensus Fusion (KCF), Covariance Intersection Consensus Fusion (CICF), Covariance Intersection
+ Covariance Union Consensus Fusion (CICUCF), and Separate Bias Kalman Consensus Fusion (SBKCF)
Friedland 1969 Ignagni 1990); and two decentralized online learning approaches Greedy-Local (GL) and
Distributed Mirror Descent (DMD) (Shahramoor & Jadbabaic, 2017a Simulation results show that DOME consistently outperforms all baselines, achieving at least. 74% lower prediction loss in performance evaluations. In terms of scalability, DOME also demonstrates a minimum of 72.4% reduction in prediction loss relative to the compared methods. Additionally, the algorithm is validated in environment.
Although the covariance- based baselines are derived from earlier foundational methods (e.g., Kalman Filter, Covariance Intersection, and Covariance Union), they remain widely adopted in practice due to their sim- plicity, low computational overhead, and flosed-form realizations. Recent works such as Chang et al. (2021) Daass et al.] (2021), Wang et al. (2021), and Jia et al. (2023). use these methods for multi-estimate fusion. The proposed DOME algorithm likewise lightweight and analytically tractable, yet achieves better perfor- mance without relying the consistency correlation assumptions commonly required by covarianco-basel methods.
The remainder of the paper is organized as follows: Section 2 reviews related work, Scction 3 formulates the problem, Section
g introduces the DOME fusion algorithm, and Section 5 presents its theoretical analysis. 3 reports the simulation results, and Section | concludes the paper with a summary and a broader impact statement. Nomenclature is provided in the Appendix 4A.1), along with the MATLAB simulation details (A.3), including details regarding the baselines (A.3.2p. Both MATLAB and ROS-Gazed simulation videos are provided as supplementary files. Details regarding the ROS-Gazebo simulation are included in the video itself.
Section
2 Related Works
In robotic swarm, heterogencous sensors and prediction algorithms can be leveraged to reduce uncertainty
in larget trajectory estimation (Rizk el al., 2019). Multi-sensor fusion in such systems commonly employs
established methods such as Kalman Filter/ Fusion (KF) (Maybeck) [982 Uhlmann 2003). Covariance Inter-
soction (CT) (Matzka & Altendorfer 2009 Julier & Uhlmann 2017), and Covariance Union (CU) (Matzka)
& Altendorfer] 2009: |Reece & Roberts 2010). Building on CI, Carrillo-Are et al. (2013) proposed de-
centraalized cooperative localization algorithm that reduces processing and communication overhead while
2

---

Published in Transactions on Machine Learning Research (04/2026)
maintaining consistency under asynchronous communication, Assa & Janabi-Shariti 2015 developed a non- linear KF-based fusion framework incorporating adaptive noise compensation and iterative updates for fast dynamics, Chang et al. (2021) used C1 to maintain consistency and enhance resilience in multi-robot local- ization. Daass et al. (2021) compared KF- and CI-based architectures, identifying the partially distributed approach as optimal in lerms of stability and efficiency. Wang et al.] (2021) introduced fully decentralized CU-based localization method that mitigates the effects of spurious sensor data. Jīa al. (2023) utilized CI to estimate the covariance of initialized UWB anchor positions, thereby enabling consistent data fusion in their distributed visual-inertial ranging odometry framework. However, these covariance- approaches rely on assumptions regarding consistency and inter-estimate correlations. In scenarios with significant dy- namic biases or drift, particularly when bias and covariance are uncorrelated, such methods may degrade or fail.
Unlike covariance-based methods, distributed online learning frameworks (Cesa-Bianchi & Lugosi 2006;
Chang et al., 2020) operate without requiring covariance information or assumptions about consistency
and correlation. While most existing works focus on general algorithmic seltings (Chang et. al., 2020
their application and analysis within robotics remain underexplored. (Shahrampour & Jadbabaie 2017a
introduced a mirror descent-based algorithm for tracking the minimizer of a time-varying convex function
under adversarial noise. Similarly, Shahrampour & Jadbabaie (017b) proposed a decentralized variant for multi-agent target tracking with unknown, unstructured disturbances. Eshraghi & Liang (2020) addressed heterogeneous networks with varying topology, proposing any-batch mirror descent to limit latency from slower nodes. Jiang et al.] (2021) developed an asynchronous gradient-push method using asymmetric gossip and instantaneous model averaging. [Eshraghi & Liang) (2022) extended mirror descent with multi- iteration averaging over both decisions and gradicnts to improve tracking of dynamic global minimizers over time-varying networks. These algorithms typically incorporate consensus averaging with fixed, pre-defined, or equal weights. However, the lack of adaptive weighting limits their robustness in challenging conditions involving large or time-varying biases, drift, or communccttio uncertainties.
3 Problem Formulation
The docentralized cooperative target-tracking scenario (Fig. 1 involves multiple robots predicting the tra- jectory of a largel with unknown dynamics over a random communication network. Each robot. is equipped with a sensor suite and a local prediction algorithm that relies solely on its own observations. While the target is observable to all robots, differences in sensor types and algorithms may lead to varying prediction accuracies across segments of the trajectory, particularly under system or environmental uncertaintics.
In practice, full observability of the target arises mainly in two situations. The first is when robots possess high-grade, long-range, wide field-of-view sensors capable of independently tracking the target. The second occurs when centralized sensing assets, such as ground radar networks, AWACS, or satellites, monitor the target and broadcast its position to the swarm via one-way communication. In swarm robotics, this cen- tralized sensing paradigm enhances situational awareness, reduces individual sensing demands, and enables scalable, coordinated operation over large environments. Check Appendix A.4 for more details.
Robots that share a direct communication link are referred to as neighbors. The topology of the random communication network is represented by a bi-directional random graph G(t), where t is the discrete-time variable, whose underlying base graph topology is denoted as G; the links (edges) in the digraph G drop with probability of Pia, called as the link-drop probability, thus, representing communication failure. Robots can exchange information only with their neighbors and have no knowledge of the global network structure. Let Pr denote the set of neighbors of the 4th robot at time I, as defined by the communication graph G(I). Define Ar,; == i U [i}, i.e., the set of 7t robot's neighbors including itself. Similarly, let Ωt denote the set of neighbors of the jth robot as per the base-graph topology G, and define A, =- Z. U {i}.
Let N denote the number of robots in the swarm, with each robot indexed by E [N]. The 7th robot runs a prediction algorithm A, that estimates the target's look-ahcad trajectory using real-time onboard sensor data. The set {4), may consist of non-identical algorithms either differing in type or parameterization due to heterogeneous or complementary sensors and models. Consequently, prediction accuracy may vary
3

---

Published in Transactions on Machine Learning Research (04/2026)
Target
observation
Robot #4 (5,,A4)
Robot
(SI.A]]
Robot #3 4g)
communication
Robot #2
link
(Sz. A23
Target
X Robot
S 8 robot's sensor suite
A hhh robot's prediction algorithm
Figure 1: Decentralized cooperative predictive target-tracking using robotic swarm. Each robot i E [N] is equipped with a local prediction ion algorithm A,- The robots share information over the communication network and aim to cooperatively predict the target position.
across robots and along different segments the target's trajectory. Even identical algorithms can yield varying accuracy due to system or environmental uncertainties (e.g., hardware or software failures).
Robot Model: consider the following discrete time 3DDOF kinematic model for the ith robot, where AT is the sampling period (scconds), Vi E [N]
cos Φr,i sin 0i.5
sin di,i cos Ø1.s
Xx+1,i Xt,i + AT
Vr,i
(1a)
Φ δi, + ATW
(1b)
where Nt,; E R2 is the 2-D position vector (in m), Ve, E R² is the body-axis velocity vector (m/s), 6r,s E R is the heading angle (radians), and Wr, E R is the yaw rate (rad/s) s) the ith robot at discrete-time t, respectively. Here, the body-axis velocity Ve,; and yaw rate We, are the bounded control inputs for the 7th robot.
the set of equations Q also serves as the target's kinematic model, but the target's dynamic model is unknown. The target's position vector X1,B E R (in m), heading angle Φ1,B R (radians), body- axis velocity V., E IR2 (m/s), and yaw rate Wr R (rad/s), respectively, can be represented by replacing with B (Bogey) in the set of equations [ Vr,B and B are the bounded control inputs for the target at time I, which are considered unknown to the robots because the target's 's dynamics is unknown.
Target Model:
Remark 1. While MATLAB simulations (Section 6 assume omnidirectional (holonomic) kinematic model for both robots and the target, the proposed DOME fusion framework is model-agnostic. ROS-Gazer Gazebo simulations (check supplementary video) demonstrate its applicability to non-holonomic systems.
Control Law: for the 7th robot, the translational control law consists of two terms as given below
Vi. Av.
(2)
where vR, is the 7th robot's reference command signal responsible for chasing the target by using r-step look-ahead estimate of the larget's 's trajectory, and Av,, is the ith robot's correction control signal responsible for avoiding collisions with other robots. Furthermore, consider a heading angle requirement such that the robots are required to yaw a way that their heading dircction points towards their 1-step look-ahead estimate of the target's trajectory. A detailed description of the control law used in the simulations (Section is provided in the Appendix A.3.1.
4

---

Published in Transactions on Machine Learning Research (04/2026)
Remark 2. As the focus of this work is target trajectory estimation/prediitton, simplified control strategy is employed. However, the proposed DOME fusion framework is compatible with more advanced control schemes (e.g., obstacle avoidance (Sun et al. 2014) and formation control (Cheng et al. 2005)), ) depending on application needs.
A bstract Model for Prediction Algorithm A; let & (()+))) E I denote the r-step look-ahead predic- tion of the target's position by algorithm A, at time We model this prediction
A ((+r))) X + 57,
where X a is the true larget position al time 1+T, and ST E I is the prediction drift at time L. The drift G7, models prediction inaccuracies specific to A, and is assumed to follow an arbitrary, unknown structure potentially non-Gaussian and without a known distribution capturing variability in accuracy across algorithms (E)
With the assistance of its prediction algorithm A, and its neighboring robots as per the communication seiimate/predict network G(t) at time i, each robot aims to estimate/ predict the target's position at time + T, i.e., Xt
4
Distributed Online Learning based Multi-Estimate Fusion
4.1 Conceptual Overview
The Distributed Online Learning-based Multi-Estimate (DOME) fusion framework tackles the problem of trust management in heterogeneous swarms, where robots differ in sensing and prediction quality and communication is unreliable. DOME learns which agents provide reliable predictive-tracking information and weights their contributions accordingly.
Each iteration consists four phases (see Appendix, Fig. 10 learning, local fusion, communication, and social fusion. During the learning phase, cach robot evaluates its own and neighbors' previous predictions against the current target observation and updates trust weights at two levels. Local trust balances the robot's onboard prediction with its previous social prediction, while social trust balances its local prediction against neighbors' local predictions.
In the local fusion phase, the robot combines its fresh onboard prediction with its previous social prediction using updated local trust weights to produce a robust local prediction. During the communication phase, robots share their local predictions along with associated self-trust weights with available neighbors. In the social fusion phase, each robot computes a trust-weighted average of received local predictions to generate the final social estimate for control navigation.
To handle non-stationary environments (e.g., abrupt target maneuvers or sensor occlusions), DOME incor- porates a periodic reset mechanism in its learning phase. Purely cumulative online learning can lead to weight saturation, where historically reliable robots retain excessive influence even after performance de- grades. To mitigate this historical inortia, DOME resets trust weights to a neutral bascline every (To) steps, forcing re-evaluation based on recent data and maintaining adaptability to dynamic conditions.
4.2 DOME Fusion Algorithm
Learning Phase: at the current time step I, robots observe the current position of the target, xt, The robots use this observation as the ground truth to learn the DOME fusion weights.
The DOME fusion weights (t(t) and (t)(t) are updated using bounded loss function y) [0, 1], with its arguments x E R² and y E R2.
Remark 3. The proposed algorithm applies any suitable set X with y,y E X for which the loss function y(x,y) E [0, 1] is defined. While DOME fusion extends naturally to 3-D (X' R or n-D (X RT) settings, 2-D case (X R²) is used here for simplicity.
Consider the current time step neighbor set De,s and Ar, De,s U {i] as the set of tth robot's neighbors including itself at time t.
5

---

Published in Transactions on Machine Learning Research (04/2026)
Denote (()BB_))BB as the 2th robot's 1-step look-ahead social prediction of the target's position at the previous time step t 1, calculated at time t-1 using the previous time weights Wey(t - 1) and the previous time 1-step look-ahead local predictions X (1)- where A can be given as follows:
Σ AjEA-I
wiylt 1) (1)--1),B
(4)
1)B
where the hth robot's previous time 1-step look-ahead local predictions &/ (1)t-1), calculated at time 1 using algorithm A previous time 1-step look-ahead prediction & (3,t 1-step look-ahead social prediction
&4: (((-1),B at time 2, and the previous time weights a; - 1), Vi [M], can be given as follows:
LL. (1)-1)) = as(t - 1) &4 (1) + +(1 - a1-a - 1)) 8 (111111-))
(5)
The DOME fusion's local weights (t) are updated follows:
@,(t) = á, 1) exp
(-na ((x,, B, (fft- 1).B))
(6a)
d1(()) = di(1 exp
(-na l(x,, x
(6b)
(t(
(x(() = (,( + (t(
(6c)
where Ta > 0 is the local weights' learning rate. The weights are initialized as á,(0) = 1 and d;(0) = 1.
Note that (t) E 1].
The DOME fusion's social weights (Iy(1) are updated as follows:
uu (1) wis - exp (-Tw (xx, 8 x(()-)))))
exp
(7a)
(1)
Wiy (t) 1(j E Ae.s) Eyen, (t)
(7b)
where The >> is the social weights' learning rate, and 1(.) is the indicator function; 1(j Ar,i) if the condition j E Ar, is satisfied, otherwise 1(j E Ar,)) = 0. The weights are initialized as (0: = 1. Note that (1z(1) E [0, 1] and EjEr,, Wir(t)= 1.
DOME fusion weights (t)() and wiz(() are reset every To time steps to mitigating bias accumulation under high system and environmental uncertainty. Furthermore, decentralized normalization scheme is employed to normalize the weights after each update (see Appendix A.2 for more details).
Remark 4. Note that the learning phase assumes access to the true current. target position x,,a, which is required to compute the loss used for updating the DOME fusion weights. In practical deployments, this assumption can be approximated through hierarchical perception architecture, in which nigh-precision perception module or an external sensing asset provides an accurate, current-tic reference signal that serves as ground truth for updating the DOME weights. For example, modern LiDAR-Inertia Odometry methods such as LIO-SAM (Shan et al. 2020 and FAST-LIO2 (Xu et al. 2022) achieve centimeter-level accuracy on benchmarks; their estimates can serve as proxy ground truth to compute loss and update fusion weights. Additionally, Yan al. (0022) show that networked radar resources can provide improved fused target states to distributed agents; such broadcasts can be treated as the true current target position X1,8 to update the DOME fusion weights. Check Appendix A.5 for detailed theoretical and empirical analysis of the impact of noisy observations on the DOME weight updates.
Local Prediction Fusion Phase: using the learned weights az((), the 7th robot's 7-step look-ahead local prediction of the target's position time t. ie., & ( is given
(4r10) ar(t) & & B. + (1 at)))) 8 (
(8)

---

Published in Transactions on Machine Learning Research (04/2026)
where 1((+1-1((-1).BB is the thh robot's previous time 7-step look-ahead social prediction of the target's position.
8 (141)), ox(()} with its Communication Phase: the jth robot shares the information {t, i, (1-110) B
neighbors j E Qr.i and receives {1.j, & L (1+11). & (I mz)(1)} from its neighbors j E Pt.i
Social Prediction Fusion Phase: using equation (7)) along with the received w3y (t) weights via commu- nication, get the learned weights (t)(t). Further, using the local predictions received from the neighbors, the 1t robot's r-step look-ahead social prediction at time t is calculated follows:
(L+T|0,
Σ Wes(t) x (1+T/0..B
(9)
Note that the 7th robot's r-Step look-ahead social prediction ((1r is considered the final r-step look- ahead estimate of the target's position, and thus, is used by the control law for calculating velocity reference (equation (2) and yaw-rate commands (A.3.1).
Remark 5. Note that the learning phase involves comparing previous time 1-step look-ahead predictions with the current time position of the target (using prediction loss) to update the weights. The learned weights are then used to get the current time 7-step look-ahead predictions of the target's position.
DOME fusion summarized in Algorithm
Algorithm DOME (for the hd robot, i E [N])
Choose: T.T., 7 2 1 (integers); No Tu > 0
Initialize: (0) 1, (0) = (0) =
-00 x(j0)) X (1-111-1),B 8,4 (r)0)
Iteration discrete time step t 0, 0,1,2,...
1: Observe Xt,8
2: if <>>00 > 0 then
3:
(t( = (t - 1) exp (-n 4: [r|t d1(() = d'(l 1) exp (xx
Xt,
X R))
@n(t) (t - exx (-1 (2 1) xt,
end if
Periodic Reset: re-initialize the weights (:) df((), and (1) to after every To discrete time steps 6.(()
8: a5(()= = -,(0)+4((1)
L/ (1+ (t) (++)),) 11) + (1 (1-
10: Lh (++T))) (1) (1 + (1 a; (t)
Ly 8h & (1tr)1), (t)) and receive {t.j. (1+111) (1trl)) ()){{)) from the commu-
11: transmit (t, i, (1)))))
nicating neighboring robots, Vj Uu
12: Ar, 14 U (i)
13: Wiy(() = 1(j E A1.)
(0)
MeAr, (9
14: {(+1110) Enjea,. Wir (411)))
15: & { Exjen, Wiy (t)x (1TT10)
Li (1)
5
Convergence Analysis
This section presents the theoretical convergence analysis of DOME fusion weights. Only the analysis of the social weights (t) presented; the analysis for local weights (x(t) follows a similar procedure.
Without loss of generality, the DOME weights (t)(t) are analyzed without considering periodic resets examine their convergence behavior immediately after and just before reset. Fach reset. instant can be
7

---

Published in Transactions on Machine Learning Research (04/2026)
treated t = O, making the analysis applicable to any interval between two successive resets. In practice, with periodic reset interval To, higher learning rate enables faster convergence before the next reset, while a lower rate may prevent full convergence. Nonetheless, the underlying convergence behavior remains consistent with the theoretical analysis presented.
Denote 1/, = [xx,,, x4: ( and T = -E
14. 1 Denote 14, 1(x,, ((j 1), B); and 1,, = -5,,=1111 15
Denote 16,6 = lxx1,, & ()) and T4 = E.=1 1/.0
Note that the loss function y(.,y) E [0, 1] is bounded and its arguments x E R² and y E R22
The history Hr. relevant to the jth robot's learning phase just before the communication phase occurs at time t, is defined as follows:
H4, = (192)) (8 (=t1))) Bl= (x.,B)--1 (18 s). s), Blyea,
(10)
where Q4 is the neighbor set of the it robot as per the base-graph topology G of the random commuicattion network G(t), whereas l2,E the neighbor set of the ith robot as per the random communication network G(s) at time s.
Let n, = [2,1] denote the maximum number of neighbors the tt robot can have in the base graph G, where [4 denotes the cardinality of the set f4. The time-varying communication graph G(t) is an undirected random subgraph of G, with each link independently dropping with probability Pia- At time t, robot can communicale with any subset of its n; neighbors; the number of possible neighbor sets of size l is n CkC for
n4. k = n2, Let Ofd denote the (th such subset with [ k. Further, define A R. := 2 U {i). Then
24,1 E " hnmo, Im1: and L4,i S Sz. Here, k = 0: n, implies k = 0. 1, nz and = 1 te "CC, implies [= -,,,,,, CC. C..
Let N₂(()= 1R,,i denote the number of neighbors the 7th robot has at time t. Since each link in the base graph G drops independently with probability Pıa. N:(l) follows a Binomial distribution: Ni(l) ~ B(ng. where n, = [[2.].
For some E [N], the conditional expectation of (t) can be written as follows:
([N+()) Ri CCC(1 (Pa) Pid - k (1 Pia)m;
(11)
where B[:] is the expectation operator. Note that E[N:(() independent of t. Further, note that
Cc
Pia)"PPa
Pid Tu-k +
Σ
Th CC (1a))=-
Pla ny =1
(12)
k=0
1=1
k=
Consider 0 < (0) < 1, where i E [N]. For t = 1,2, , T, based on equation (0) exp -,,,),)))) Vj E [N].
7 77),
we get w5)(()
Consider the weight wiy (t). After some mathematical manipulation, the expectation of wsy(t) conditioned on the history He Vj E As, can be written as follows:
"CC
(t)lHe)
Σ
Σ
pld) mi
w A -
(13)
where
(t;
(1) :- (1))==10) 1 E A
(14)
EgErpe way (1)
Here, 1(:) is the indicator function; 1(j E At,l) = if the condition E A is satisfied, otherwise 1(j e A k 0.
8

---

Published in Transactions on Machine Learning Research (04/2026)
Define (t) == arg mimm Lig', i..., Jo,5 (t) is the index of the robot which incurs the least cumulative loss among all other robots in the index set A,d = .2 (i) at time 4, where S2 is one of the many possible neighbor sets of the jt robot at time i, such that |s2, = k, where k = 0, 1, .. , ni, and = 1, 2, ... ni Cp- Assumption 1. For each k E (0,1,-.,,,, nh and I E (1, ".Cx} pair, lim (2 erists uniquely, such that lim, kdd (1)= ded
Remark 6. Assumption 1 implies that the performance configuration (in terms of prediction loss) gets fixed as t + 0o, i.e., for the tth robot at t + xc, there is a unique robot (either itself or its neighbor given by the index ) that incurs the least cumulative loss out of all the robots in the set A.d..
Adl
Note that the cumulative loss satisfies S L I t (since the loss function ((..) E [0, 11), Vj E ARd and L (, < L (due to (t)'s definition), Vj E A \ (1))()))
Assumption 2. 1 - T.L (1) 2 et > 0, such that 8 E (0,1] and E E (0, Vj E V.A (2100)
Remark 7. Assumption 2 implies that the cumulative loss difference between robot j and the best-performing robot (t) grows at most linearly (B = 1) or sub-linearly (0 < B < <) with time i, with both the rate and magnitude finite but arbitrarily small (0 < e < 1, < 3 < 1). In practice, this holds when the best robot (t) remains fixed for finite durations and may change intermittently.
Lemma 1. Under assumptions 1 and 2, for l = 0, 1, 1.................... ,i, and = 1,2, .., "CC, the weights wi kel (1) satisfy the following:
lim w k.l (t)= 0, Vj E d Godl
(15)
500
and
lim (0
(1)
lim w (f)=1 =1
(16)
too 12..
where (t) is the inder of the neighbor of the 8th robot whose individdull prediction incurs the least cumuulative loss among all other robots in the inder set Akd = 2.d u (i) Vi [N].
at time i, ie., (2, = arg min geAt" t.g
Proof. For some & E 10 ,..) and E 11,,.... "h Ck), consider the weight w (1), which can be re-written as follows; use (t) = ())(0) exp (k)) in eq. 14] and multiply both numerator and denom- inator by exp (Nw I,L (0) to get:
1(j E A. (0;; - nn
e0pp( (Lt - LL 1 40
wi (1)
(17)
Eyeat un (0) exp( nw (44g L. (0
In the above equation, separating the vē (0 (0) term from the summation in the denominator yields:
1(j E A/ ye -xpl-nu
y- (L - LL I (
Wij kd (t) @ 00 (0) Σ EEEAt" Wgg (0) expl - (1k -Ib (
(18)
Note that for the cumulative loss, the following holds true: 0 Li, S t (since the loss function is bounded, i.e., 1(..)) E [0, 1)), Vj E K.,, and LL 252:/11) < <Li (due to (t)ss))ss definition), Vj E Ahd \ (1)(())) Further using assumption 2, this implies that the cumulative loss for the joh robot, Vj E A (4)(())) satisfies
1 12 Lt 1 1,50/000 2 et > 0
(19)
where B E (0. 1] and e e (0, Vj A 1 (1)
9

---

Published in Transactions on Machine Learning Research (04/2026)
Using equation
19
in equation
18
get
I k. Joiy
( (xp( (xp(-
J A (0)
W (1)
(20)
KJEA - " (0) expl kw
A (0)+ ge No. 20 (0) expl nott
for Vj A/ \ (1), and
k.l (i
1000 (1) (0)
hd Mole (0)+
DexMi (st: Teu exp( T
(0) (t)
(21)
"0 (0)
s: (0)+ gent No Den (0)
Now, taking lim; (-) on equations 20 and
21
under assumption 1, leads to the desired result.
For each Ar, consider the set Mj. defined as follows:
M4 = ((k,1) bolls k E (o,...,,,,..
(22)
Further, consider the set J., which defined as
J = -:=j & (0, nnt.le E
(23)
Remark 8. The set M,, contains all the pairs (k, for which j = soo's is satisfiod. The set Jr consists of all the indices Joc,s for h = 0, May and 1,2,-.. CCk-
Theorem 1. Under assumptions and 2 (using Lemma the following:
Vj E A DOME fusion weights wey satisfy
E| (1) =0, 0, Vj $ Jj
(24)
and
lim (twsy(t) He,dl 1000
Σ
(1- 11-PP)"'i mi-k Vj E
(25)
V(KD)M,s
where pia is the communnicttio link-drop probability.
Proof. From lemma V(k,t) 0, M4i 1= 1,2,
m "OO,, using the definition of the set Jj as stated
in equation 23 note that the following holds truc:
lim w (t) Vj $ J tox
(26)
and
lim (t) lim w
kd (t) = Vj J 2.
(27)
Using equations (26) and 227 in equation along with the definition of the set M3, given in equation 22 leads to the desired result.
10

---

Published in Transactions on Machine Learning Research (04/2026)
Time 111.1 sec.
1 Prb
GL
CICF
-20
-20
Growing Bias:
1
240
53 (m)
-240
- min(s + 1mxx)
Myi = Cu drift_dir -ifitddir-s;; s; ui, (1 + pri.raatt)) u
-200
-250
X
t=t+1;
260
T.T.
R1
500
4400
480
-47
R2
-500
-490
-40
-470
01
(m)
R4
R8
IF]
(m.)
Pgb
Prb
R5
DMD
R6
DOME
T.
Receding Bias: iiassstate
s + max(s - 1,0); p4u = cu" drift_dir s; u (1 + priteett) p4:
240
5g (m))
240
x
x
XX X
t=t+1;
X
260
-280
1 Pyb
-500
-400
31
(m)
4800
-470
-500
-490
21 (m)
-480
-470
(b)
Figure (a) An event-based switching signal model for the dynamic bias term pl, for T Here, drift dii = [cos Mair sin sharrl', such that dair is sampled from Unaf. 2T) at the start of every simulation The value for prj_rate is set to 0.05. (b) Screenshot of simulation run in MATLAB for DOME and few baselines; T. is the target, T.T. is the target's 's trajectory, and Rí is the 8th robot.
6 Performance Evaluation
The DOME fusion algorithm is simulated for cooperative target tracking with N 6 robots over horizon of T 1400 steps and sampling period AT 0.1 8, using look-ahead window of 10. Robots communicate over bi-directional network with random link drops (drop probability, Pia 0.1), based on undirected connected linear graph chosen to represent the worst-case among connected topologies. Further, the loss function is set as y(x,)) = min([ y|1/50, 1), where ||- is the Euclidean norm (2-norm) and y E RR?.
The drift GT in the prediction by algorithm A; (equation is modeled as follows:
G. MI, + vl,
(28)
where vT, E IR2 is a bias term (m), and vT, E R² is zero-mean Gaussian noise (m) with covariance CT, E I222 (m²) at time t. The bias pf is modeled as event-driven switching signal (see Fig. [2), offering more realistic alternative to the ramp signal used in Cho & Jiang (2012). In the growing bias state, the bias magnitude either increases until saturation or switches to the receding bias state with probability Pro- Conversely, in the receding bias state, it decreases toward zero or switches back with probability Pzt- In Fig. h the scalar Cr,, indicative the accuracy algorithm A,, increases with prediction error. In simulations, Pyb 0.2 and Prs 0.5.
To simulate adverse system and environmental conditions, robots randomly assigned either c,2 0.01 Cr = 4 at times 0.0, 23.33, 46.67, 70, and 116.67 seconds, ensuring that 3 to 4 out of N 6 robots have inaccurate algorithms (i.c., C22 = 4). For these robots, the one-step prediction bias satisfies that each element of the vector /1,, lies in the range [0,40) m (see Fig. 22, with smax = =10). For inaccurate robots (c,, 4), the associated noise covariance C₁, is either 4 diag[[ 1]) or 0.01 diag([1 1)), each with 50% probability. For accurate robots (G.s 0.01), C₁ 0.01 diag((1 1)). For 1, the noise grows
11

---

Published in Transactions on Machine Learning Research (04/2026)
1000
Aug. Canul. Prod. Lone por Robest at 160
400
Avg. Canna. Pred. per Robot
900
GG
+DMME
350
RCP
DOME
800
Axg. Choall Pivl. Look
700
CHCUCP
Cuural Pied. Loss
800
CICDEP
GL
600
KCF
250
DMD
ACP
500
200
SRKOP
400
150
300
100
200
100
0
3
22
16
DOME, GL, 3: DMD, 4: CICUCP, CICP, 6. KCP, ACE, SDRKP
(b)
Figure 3: (a) A box plot showing the average cumulative 10-step look-ahead prediction loss per robot at 140 seconds; 500 simulation runs (points) for each method - 1: DOME, 2: GL, 3: DMD, 4: CICUCF, 5: CICF, 6: KCF, 7: ACF, 8: SBKCF. (b) Average cumulative 10-step look-ahead prediction loss per robot at 60 sec. as function of total no. of robots N, averaged over 100 simulation runs for each method.
as CT = (1 + T prij Ct This setup reflects scenarios where noise and bias are not necessarily correlated.
Remark 9. The DOME algorithm makes no structural assumptions about bias dynamics. stated in Section (Abstract Model for Prediction Algorithm), the bias modeled as arbitrary and unknown, potentially non-Gauee non-Gaussian, and without a known distribution; this arbilrariness also allows for adversarial bias. DOME employs a universal online learning update that does not depend on internal physics models (e.g., random- walk constant-bias models typically required by Kalman filter variants). The "structured" switching-bias model used in this section (Fig. 2 serves only to generate synthetic data for stress-testing under abrupt failures, and DOME was not given access to this structure.
Under this setup, DOME fusion employs learning rates Th 10 and 7a 4, with a periodic reset interval To 25, as determined through a simulation-based parametric study (see Appendix A.3.3 for more details).
Under the described communication and prediction uncertainties, DOME is evaluated against four covariance-basee based methods Kalman Consensus Fusion (KCF), Covariance Intersection Consensus Fusion (CICF), Covariance Intersection + Covariance Union Consensus Fusion (CICUCF), and Separate Bias Kalman Consensus Fusion (SBKCF), and two online learning- based mothods Greedy-Local (GL) and Dis- tributed Mirror Descent (DMD). SBKCF is inspired by the Separate Bias Kalman Filter (SBKF) (Friedland) 1969 Ignagni 1990). DMD is applied by modifying the mirror descent-based distributed online optimization algorithm proposed by Shahrampour & Jadbabaic (2017a) b) to fit the problem setting considered in this paper. An Averaging Consensus Fusion (ACF) baseline is also included. A detailed description of these methods is provided in the Appendix A.3.2
These algorithms are evaluated based on average cumulative 7-step look-ahead prediction loss for t 12:: I DENEE ((2( X.,B), with - = 10, =
N
Figure Bh presents a box plot of the average cumulative 10-step look-ahead prediction loss per robot at 140 seconds, aggregated over 500 simulation runs for each method. In each box, the central line denotes the median, while the bottom and top edges represent the 25th and 75th percentiles, respectively. Notably, DOME achieves substantially lower prediction loss compared to all other fusion algorithms. In terms of median performance, DOME reduces the average cumulative prediction loss by approximately 74% relative to the next. best. method, SBKCF. In addition to superior accuracy, DOME also demonstrates markedly lower variance, indicating greater consistency across simulation runs.
DOME fusion is further evaluated for scalability by measuring the average cumulative 10-step look-ahead prediction loss per robot at the end of 60-second horizon, averaged over 100 simulation runs, function
12

---

Published in Transactions on Machine Learning Research (04/2026)
of the total number of robots N (see Fig. 3D). Starting from N = 2, robots are incrementally added to the underlying linear graph structure without introducing random link drops. At times 0.0, 23.33, 46.67, 70, and 116.67 seconds, robots are randomly assigned either a, = 0.01 or C,, = 4 (see Fig. 22), such that at least L and at most | NN + 1 out of the total N robots use inaccurate prediction algorithms (ct,s = 4), where [i] denotes the floor function.
++++
The noise covariance behavior remains consistent with the previous simulation setup, representing scenarios where noise and bias are not necessarily correlated. As shown in Fig. Bp. DOME outperforms all other fusion algorithms in this scalability test. Its average cumulative 10-step look-ahead prediction loss per robot remains substantially lower approximately 72.4% less than the next best algorithm, SBKCF - as N increases. Moreover, beyond N = 10, DOME's performance remains nearly constant, indicating that the algorithm maintains high reliability and prediction accuracy even as the swarm size grows. This suggests that DOME enables scalable swarm behavior without compromising predictive performance.
From Figures 3a and 3p, it is evident that DOME outperforms the other fusion methods evaluated in the simulation studies. Notably, DOME, GL, and DMD do not require knowledge of prediction covariances and operate without assumptions of consistency cross-correlation. Consequently, they outperform covariance- based methods- - KCF, CICF, and CICUCF - which are sensitive to large prediction biases, particularly when such biases are not reflected in inflated covariance estimates.
SBKCF, however, achieves the strongest baseline performance due to its drift estimation mechanism inspired by the Separate Bias Kalman Filter (SBKF). By adopting a random-walk bias model, SBKCF explicitly predicts and compensates for future drift, thereby correcting biased onboard predictions. In the scalability study (Fig. B)), this modeling advantage allows SBKCF to outperform DOME for N = 2, where explicit drift estimation is beneficial. However, for N 2 3, the same modeling assumption becomes restrictive: reliance on a predefined internal drift model limits robustness under non-stationary environments with unknown or arbitrary drift dynamics. In contrast, DOME employs a model-agnostic online learning update that does not depend on internal physics assumptions (e.g., random-walk or constant-bias models), enabling greater adaptability in heterogeneous and dynamically evolving settings.
Although both ACF and DMD assign equal weights to information from neighboring robots, DMD achieves better performance due to its online error correction mechanism. In contrast, DOME surpasses both DMD and GT. by employing an adaptive weighting scheme based on an online learning process. Unlike DOME, neither ACF nor DMD includes a mechanism for adaptively filtering out biased predictions from other robots in the network. Consequently, biased information can propagate unchecked through the communication net- work, degrading the performance of even those robots with accurate prediction algorithms. GL outperforms DMD by groedily selecting the most accurate local prediction; however, it does not propagate this selection across the network.
The MATLAB simulation video is submitted a supplementary file. Furthermore, DOME is implemented in Gazebo simulation environment using ROS (a simulation video is submitted as supplementary file).
A Ablation Study: A simulation-based ablation study of DOME (Appendix A.3.5 Fig. 6 further clarifies the relative contributions of its components. The results indicate that adaptive weighting is more influential in the local fusion layer than in the social layer, whereas the social fusion layer itsclf has a greater overall effect on performance than the local fusion layer. The periodic reset mechanism, meanwhile, emerges as an essential component of the framework.
Robustness Study: Further, DOME is evaluated under varying communication link drop probabilities (Appendix A.3.6 Fig. 7 and prediction bias/drift rates (Appendix A.3.7 Fig. 8b. demonstrating that it maintains acceptable performance - remaining within the 100-loss median range- upp to Pta = 0.5 and C = 10. DOME is further evaluated under varying observation noise magnitudes ||eell2 (Appendix AA.5 Fig. . The results indicate that it maintains acceptable performance remaining within the 100-loss median range- up to ||ell22 10 meters. A detailed theoretical and empirical discussion regarding the impact of noisy observations is provided in the Appendix A.5
Sensitivity to Mismatch in T,: The convergence analysis in Theorem applies within each stationary epoch (i.e., between resets), implying that optimal performance is achieved when T, is commensurate with
13

---

Published in Transactions on Machine Learning Research (04/2026)
the environment's switching interval. If is too small, the algorithm may remain in transient high-variance regime; if too large, adaptivity lag can occur after regime shift. However, empirical results indicate a broad performance basin rather than sharp sensitivity. In the event-driven stochastic bias model (Section Fig.
2d), DOME maintains strong performance across a wide range of fixed T, values (Appendix A.3333 Table
with only gradual degradation away from the optimal setting. detailed theoretical and empirical discussion is provided in the Appendix A.6
7
Conclusion
This paper presents a Distributed Online learning- based Multi-Estimate (DOME) fusion algorithm for coop- erative predictive target tracking in robotic swarm subject to dynamic prediction bias and communication uncertainty. Designed for heterogencous teams with diverse sensors and prediction modcls, DOME performs a two-layer weighted fusion local and socially shared predictions, combined with an implicit, adaptive, consensus-like update. Fusion weights are learned online using prediction loss feedback, enabling each robot improve its own predictions while supporting its neighbors. Theoretical analysis shows convergence of the expected learning weights under reasonable assumptions. DOME is computationally lightweight and analytically tractable, making it practical for swarm deployment. Simulations under conditions of large prediction drift and random link failures show that DOME outperforms both covariance- based and online learning-based decentralized methods, achieving a 74% reduction in prediction loss compared to the next- best method, Separate Bias Kalman Consensus Fusion (SBKCF). It also scales well, with a 72.4% lower prediction loss than SBKCF as the swarm size increases. Finally, DOME is validated in a ROS-Gas Oos-Go simulation environment (check the simulation video in the supplementary zip file). This study assumes full observability of the target; future work will address the partially observable case.
Broader Impact Statement
The proposed DOME fusion algorithm enhances collaborative prediction accuracy in decentralized multi- agent systems operating under communication uncertainty and prediction biases, with particular relevance to multi-drone systems, where reliable distributed prediction and fusion are critical for applications such as surveillance, envirommental monitoring, disaster response, and autonomous navigation. For responsible deployment, strict adherence to ethical guidelines is essential when operating autonomous monitoring systems in populated areas.
While developed for cooperative predictive target tracking using robotic swarm, the DOME framework generalizes across domains requiring decentralized, privacy-preservnng. and adaptive prediction fusion. Po- tential applications span finance, where distributed trading models collaboratively forecast market trends; weather and climate forecasting, where regional prediction centers intograte heterogeneons models; urban sensing and environmental moniloring, where sensor net works fuse multi-modal data; and healthcare, where institutions jointly improve predictive diagnostics without sharing sensitive data. In smart grids and supply chains, DOME can enable robust coordination among nodes by cooperatively predicting energy availability and demand under uncertainty.
References
Akbar Assa and Farrokh Janabi-Sharif.. A kalman filter-based framework for enhanced sensor fusion. IEEE 2015.
Sensors Journal,
Luis C Carrillo-Arce, Esha D Nerurkar, José L Gordillo, and Stergios I Roumeliotis. Decentralized multi- robot cooperative localization using covariance intersection. In 2013 IEEF/RSJ International Conference on Intelligent Robots and Systems, pp. 1412 1417. IEEE, 2013.
Nicolo Cesa-Bianchi and Gábor Lugosi. Prediction, learning, and games. Cambridge university press, 2006.
Tsang- Kai Chang, Kenny Chen, and Ankur Mehta. Resilient and consistent multirobot cooperative local- isation with covariance intersection. IEFE Transactions on Robotics, 2021.
14

---

Published in Transactions on Machine Learning Research (04/2026)
Tsung-Hul Hui Chang, Mingyi Hong, Hoi-To Wai, Xinwei Zhang, and Songtao Lu. Distributed learning in the nonconvex world: From batch data to streaming and beyond. IEEE Signal Processing Magazine, 37(3): 26 26-38, 2020.
Jimming Cheng, Winston Cheng, and Radhika Nagpal. Robust and self-repairing formation control for swarms of mobile agents. In AAAI, volume 5, 2005.
Sungwhan Cho and Jin Jiang. Detection and estimation of sensor drifts using kalman filters with demon- stration pressurizer. Nuclear engineering and design, 242:389-3988 2012.
Bilal Daass, Denis Pomorski, and Kamel Haddadi. Design of multi-sensor fusion architectures based on the covariance intersection algorithm estimating calculation burdens. Journal of Intelligent Robotic Systems, (01(4): 2021.
Nima Eshraghi and Ben Liang. Distributed online optimization over heterogeneous network with any-batch mirror descent. In International Conference Machine Learning, pp. 2933 2942. PMLR, 2020.
Nima Eshraghi and Ben Liang. Improving dynamic regret in distributed online mirror descent using primal and dual information. In Learning for Dynamics and Control Conference, pp. 637-649. PMLR, 2022.
Bernard Friedland. Treatment of bias in recursive filtering. IEEE Transactions on Automatic Control, (4): 359 367, 1969.
Jingxuan Hao, Yimin Zhou, Guoshan Zhang, Qin Lv, and Qingtian Wu. A review of target tracking algorithm based on uav. In 2018 IEEE International Conference on Cyborg and Bionic Systems (CBS), pp. 2338. IEEE, 2018.
Karol Hausman, Jörg Müller, Abishek Hariharan, Nora Ayanian, and Gaurav Sukhatme. Cooperative multi-robot control for target tracking with onboard sensing. The International Journal of Robotics Re- search, 34(13):1660-166) 2015.
Mario B. Ignagni. Separate bias kalman estimator with bias state noise. IEEE Transactions on Automatic Control, 3533)3338-31 1990.
Shenhan Jia, Rong Xiong, and Yue Wang. Distributed initialization for visual-ierrtaa--raninng odometry with position-unknown uwb network. In 2023 IEEE International Conference Robotics and Aulomation (ICRA), pp. 6246 6252. IEEE, 2023.
Jiyan Jiang, Wenpeng Zhang, Jinjie Gu, and Wenwu Zhu. Asynchronous decentralized online learning. Advances in Newral Information Processing Systems, 34:20185 20196, 2021.
Simon Julier and Jeffrey K Uhlmann. General decentralized data fusion with covariance intersection. Handbook of maltisensor data fusion, pp. 339-364. CRC Press, 2017.
Boyoon Jung and Gaurav S Sukhatme. Cooperative multi-robot target tracking. In Distributed Autonomous Robolic Systems 7, pp. 31-90. Springer, 2006.
Lili Ma and Naira Hovakimyan. Cooperative larget tracking with time-varying formation radius. Tn 2015 European Control Conference (ECC), pp. 1699 1704. IEEE, 2015.
Stephan Matzka and Richard Altendorfer. A comparison of track-to-track fusion algorithms for automotive sensor fusion. In Multisensor Fusion and Integration for Intelligent Systems, pp. 69-81. Springer, 2009.
Peter S Maybeck. Stochastic models, estimation, and control. Academic press, 1982.
Abdullah Mohiuddin, Taha Tarek, Yahya Zweiri, and Dongming Gan. survey of single and multi-uav
aerial manipulation. Unmanned Systems, 1002):199-147, 2020.
Kevin P Murphy. Machine learning: probabilistic perspective. MIT press, 2012.
15

---

Published in Transactions on Machine Learning Research (04/2026)
Bradley J Nelson and Salvador Pané. Delivering drugs with microrobots. Science, (6776))) 2023.
Steven Reece and Stephen Roberts. Generalised covariance union: A unified approach to hypothesis merging in tracking. IEEE Transactions on Aerospace and Electronic Systems, 46(1):207-22) 2010.
Yara Rizk, Mariette Awad, and Edward W Tunstel. Cooperative heterogeneous multi-robot systems: A survey. ACM Compuling Surveys (CSUR), 52(2))1-33 31, 2019.
Martin Saska, Vojtéch Vonásek, Jan Chudoba, Justin Thomas, Giuseppe Loianno, and Vijay Kumar. Swarm distribution and deployment for cooperative surveillance by micro-aerial vehicles. Journal of Intelligent & Robotic Systems, 84(1):469 492, 2016.
Jürgen Scherer, Saeed Yahyanejad, Samira Hayat, Evsen Yanmaz, Torsten Andre, Asif Khan, Vladimir Vukadinovic, Christian Bettstetter, Hermann Hellwagner, and Bernhard Rinner. An autonomous multi- uav system for search and rescuc. In Proceedings of the First Workshop on Micro Aerial Vehicle Networks, Systems, and Applications for Civilian Use, pp. 33 38, 2015.
Shahin Shahrampour and Ali Jadbabaie. Distributed online optimization in dynamic environments using mirror descent. IEEE Transactions on Automatic Control, 63(3):714 725, 2017a.
Shahin Shahrampour and Ali Jadbabaie. An online optimization approach for multi-agent tracking of dy- namic parameters in the presence of adversarial noise. In 2017 American Control Conference (ACC), pp. 3306-3311. IEEE, 2017b.
Tixiao Shan, Brendan Englot, Drew Meyers, Wei Wang, Carlo Ratti, and Daniela Rus. Lio-sam: Tightly- coupled lidar inertial odometry via. smoothing and mapping. In 2020 IEEE/RSJ international conference on intelligent robots and systems (IROS), pp. 5135 5142. IEEE, 2020.
K Subbarao and M Ahmed. Target tracking using multiple unmanned acrial vehicles: Graph thcoretic nonlinear control approach. Proceedings of the Instilution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 231(3):570-586 2017.
Dali Sun, Alexander Kleiner, and Bernhard Nebel. Behavior-based multi-robot collision avoidance. In 2014 IEEE international conference on robotics and automation (ICRA), pp. 1668-1673. IEEE, 2014.
Zhiyong Sun, Hector Garcia de Marina, Brian Anderson, and Changbin Yu. Collaborative target-tracking control using multiple antonomous fixed-wing unmanned aerial vehicles with constant speeds. J. Guid. Control Dyn, 44(2):238 250, 2021.
Jeffrey Uhlmann. Covariance consistency methods for fault-tolerant distributed data fusion. Information Fusion, 4(3):201 215, 2003.
Xiaofan Wang and Housheng Su. Pinning control of complex networked systems: A decade after and beyond. Annual Reviews in Control, 38(1):103 111, 2014.
Xuedong Wang, Shudong Sun, Tiancheng Li, and Yaqiong Liu. Fault tolerant multi-robot cooperative localization based on covariance union. IEEE Robolics and Aulomation Letlers, 6(4):7799-788 7806, 2021.
Zongyao Wang and Dongbing Gu. Cooperative target tracking control of multiple robots. IEEE Transactions on Industrial Electronics, 39333 3240, 2011.
Wei Xu, Yixi Cai, Dongjiao He, Jiarong Lin, and Fu Zhang. Fast-lio2: Fast direct lidar-inertial odometry. IEEE Transactions on Robolics, 38(4):2053 2073, 2022.
Junkun Yan, Hao Jiao, Wenqiang Pu, Chenguang Shi, Jinhui Dai, and Hongwei Liu. Radar sensor network resource allocation for fused target tracking: A brief review. Information Fusion, 86:104-111 115, 2022.
16

---

Published in Transactions on Machine Learning Research (04/2026)
A
Appendix
A.1
Nomenclature
-I
2-norm
"C
choose k
(-)
transpose operation
based usage either be the cardinality of set element-wise absolute value operation for real-valued vector
E[
expectation operator
Pu
commuication link-drop probability
T
time horizon discrete-time
To
periodic reset in DOME occurs after every To discrete-tine time steps
1()
the indicator function
H
the floor function natural log
log(-)
u(-)
Th (am) aj aj@2a3.-- On.
total number of robots in the swarm
G(t)
undirected random communication connectivity graph time
2
th robot's neighbor set as per G(t) at time t
(t)
ith robot's total number of neighbors at time f, NN:(t) = [
G
base graph for the undirected random graph G(t)
Ω
neighbor set of the jth robot as per the base-graph G
maximum possible neighbors of the tt robot as per the baso-graph G, n, = =12,1
n,
A;
ith robot's prediction algorithm
Xt.
ith robot's position vector (in m)
X,
target's (Bogey's) position vector (in m)
S7,
drift in algorithm A,'s r-step look-ahead prediction
7-step look-ahead prediction of target's position given by the jth robot's algorithm A; tth robot's Local r-step look-ahead prediction of target's position given by the ith robot's 's algorithm
((+T)))
&
L
(L+T)).BB
A
(1+ 1th robot's Social 7-step look-ahcad prediction of target's position
1(5))
bounded loss function with two arguments; I(:,-) E [0,
14
algorithm A,'s prediction loss: 1(* ()
algorithm A,'s cumulative prediction loss: Σ laj
tth robot's Local prediction loss: 1(2 (1) BT
Lt.
tth robot's Local prediction's cumulative loss: Dt 1h
tth robot's Social prediction loss: 1(8) 1( Lt,B)
tth robot's Social prediction's cumulative loss: Σ.= 18 8,4
tth robot's previous-time Social prediction loss w.r.t. current target position:
1(x ()) 2t,B)
tth robot's previous-time time Social prediction's cumulative loss w.r.t. current target position: Σ1 S
He
history relevant to the 4t robot just before the communication phase begins, at time /
17

---

Published in Transactions on Machine Learning Research (04/2026)
one of the many possible neighbor sets containing k neighboring robots that the 2th robot is commu- nicating with at time where & E (0. 10,1,2,.. mii,, ,n,),, and I E (1,2,.., C.Cc]
Au,a
R4 (1)
A
[1)
2 ta U (1), where k E (0,1, and E (1,2, [CCa]
Mas nw
DOME algorithm's learning rate parameters
max. limit on the no. of neighbors any robot can have in the base graph G, such that n, S Amaz th robot's Local trust weight at time t; (+(t) E [0, 1]
Rmaa
(t
Ut,
th robot's body-axis velocity vector (in m/s) tth robot's yaw rate (in rad/s)
W1,5
AT
sampling period (in
B
positive constants governing the growth rate of cumulative loss differences (Assumption 2); E (0, E (0,1]
(t(t), (t) unnormalized weight factors used for updating the Local trust weight (;)
(1) ith robot's s unnormalized sell-trust weight
bias component of the prediction drift GT zero-mean Gaussian noise component of the prediction drift S7
de,
tth robot's heading angle (in rad)
C
scalar parameter indicating the accuracy of algorithm A; in the simulation experiments covariance matrix of the prediction noise vf, (in m²)
C
(1)
index of the best-performing robot (minimum cumulative loss) within the subset And at time t unique limit of the index (t) as - oo (Assumption 1)
k.l
Joek
Ji
set of indices of all robots that are asymptotically best for robot i across all possible neighbor subsets
set of neighbor configuration pairs (k:, 1) for which robot j is the asymptotically best source for robot M3.1
Wiy(t)
Social trust weight assigned by robot to robot at time mty(t) E [0
w (t)
intermediate weight term used in the expectation analysis of wiy conditioned on the neighbor set A
A.2 Decentralized Normalization Scheme
The weights are normalized using decentralized normalization scheme summarized as Algorithm 2 A similar procedure is used for the normalization of the weights (;(t) and at(t) as well.
A.3 MATLAB Simulation Details
In the simulations, the target (B) follows unicycle model with i B, T = O, where Vt,B = [h "/ and Dh E R, by E R. The target changes its speed after every 5 sec. intervals, such that e7 is sampled as ThB ~ (8+ (0, 4)) m/s after every 5 seconds. Further, the target also changes its yaw rate (W,,B) after every sec. intervals, such that Wr (rad./s) 6r
sampled from cither of the three expressions with equal probability: -T-AT Unif. (0, ) 0, and T-TT + Unei.. (0, T&TT). The initial position (Xo,n) and yaw angle (Wa,B) of the target randomly sampled Xo,B [Unif. (0) Uniff (0, 20)] m and Vo. ~ Unif.(-T,, x)) rad., respectively, at the start of each simulation run.
6r
For the robols, the velocity control input is bounded as /Vral < [10, 10j' m/s, and the yaw-rale control input is bounded as |wr.ul < 0.524 rad./s, where |. | is the element-wise absolute value operation. The initial position X,,; and yaw angle the of the 7th robot set be x,,; [10 i, 0j' m and th., = x/2 rad., respectively. The control law parameters are set to be ds 10 m, kn 4, ky 10, and ką 10. The loss function is defined to be y(x,y) = min([|x yl1/50, 1), where x, y E IR2.
18

---

Published in Transactions on Machine Learning Research (04/2026)
Algorithm Decentralized normalization scheme for the jth robot time 4, Vi [M]
Choose: machine's least precision 8 >>> 0
Initialize: nrment, =0 0
if (t) - 8) then
(L:(() (1)/6
nrmentu nrmenty +1 4: end if
5: send {ú, (n((), vrmenly) to and receive {i (ر,0)
(rmmnnl)))))) nrmenlyj) from neighbors j E 94
6: way(t)= (1) Vj At,i otherwise
for (t,) do
if (armentys minyeA., armentyy) then
(t:(t) +-
10: end if
11: end for
A.3.1 Control Law
Translational Control Law: for the tt robot, the translational control law consists of two terms as given below
v Av.
(29)
where v., is the 1t robot's reference command signal responsible for chasing the target, and Av., is the 7th robot's correction control signal responsible for avoiding collisions with other robots.
Denote Re E 22_2 as the 1th robot's body-global rotation matrix time t, defined as R cos Φt.2 -in cbe.z]
sin 61,5
COs 01,1
The 7th robot's reference command signal v is given
A& ( A (1
v = R
(1AAx) slll ds)
(30)
is the 2-norm, k1 > 0 is control parameter. Axi X,,B Xt,; where X, 8 is the target's position vector at time t, and x,, is the 7th robot's position vector at time t. dg > 0 (m) indicates the distance each robot should maintain from the target while chasing Here, A&i Ax( (1tr B)B is defined
where (+)' represents the transpose operation, || I|
A8 == ((141))) Xt,i
(31)
where * ((++10) is th robot's r-step look-ahead prediction of target's position time f, and xx, is 8th robot's position time
Further, assumee that each robot is equipped with a collision avoidance system, which ensures that while chasing the target, robots do not collide. Considering eq, (29), this behavior can be modeled by the correction control signal AV,, for the th robot by using an inter-robot collision avoidance control law given as follows:
X Xx,6
AV, -k2R/,
(32)
[x,,p
x
where (-y' represents the transpose operation, || is the 2-norm or the Euclidean norm, K2 0 is control parameter, pf E [N] \ {i} is the index of the robot spatially nearest to ith robot at time t, formally defined as p == arg min (iNV6 | - xx,il-- Thus, xtp; is the position vector of the robot spatially nearest to the tt robot at time f.
19

---

Published in Transactions on Machine Learning Research (04/2026)
Avg. Final Cumul. Pred. Loss at sec: for To 45
Avg. Final Cumul. Pred. Loss 140 sec. for To
309
4-
70% 80
100
100
60
0
0.6
1.5
2.5
3.5
4.6
%
Std. Dev. of Final Cumul. Pred. Loss at 140 sec. for To 45
Std. Dev. of Final Cumul. Pred. Loss at 140 sec. for To 25
2-
10
10
0.5 1.5
2.5
3
3.5
4.5 5
5.5
0 0.5
1.5
2
2.5
3.5 4.5
5.5
Rg
(a)
(b)
Figure 4: The mean and standard deviation of the average social cumulative prediction loss of all the robots at = 140 sec. (averaged over 50 sim. runs) versus the learning rates for: (a) T, = 45 and (b) To = 25.
Hcading Control Law: consider a heading angle requirement such that the robots are required yaw in way that their heading direction should point towards their 1-step look-ahead estimate of the 31
target's position & {/41)),. The angle between A&t (1+1)) (from eq 31 and the 7t robot's s heading di-
be obtained Aet Adt, atan2 (hr, x A8 h Ax{+1,B), where the first argument involves a cross-product and the second ar- gument involves dot-product. As per the heading angle requirement, 7th robot's yaw control law can be given as
rection h [cos δi,1 sin øral', with respect to the Ax 1 direction,
Wt, k3
(33)
where kg is control parameter.
A.3.2 Baselines
For the above-described simulation setup with an adverse setting, DOME is compared against four covariance-based (Kalman Consensus Fusion, Covariance Intersection Consensus Fusion, Covariance Inter- soction + Covariance Union Consensus Fusion, Separate Bias Kalman Consensus Fusion) and two online learning- (Greedy-Local Distributed Mirror Descent) decentralized prediction fusion methods, along with the Averaging Consensus Fusion baseline, which are briefly described as follows:
Averaging Consensus Fusion (ACF): instead of updating the weights Gx(t), d4(t), and (sa(t) per the DOME fusion weight update mechanism, keep them lixed á;(() 1, af(() 1, and w.(()) = 1 and calculate the predictions.
Kalman Consensus Fusion (KCF) Maybeck 1982 Uhlmann 2003 assumos that the predictions being lused are uncorrelated and their associated zero-mean Gaussian noises' covariance (CI,) are known.
Consider the covariance of &he (t+7))), and 8/1147 as Ch.
and C ((114411-1111 respectively. Con-
(b+T)t).B
sider C the covariance for & A ((+T))),
Local prediction phase:
(cL, ((
(1 +(C (C)
(34)
20

---

Published in Transactions on Machine Learning Research (04/2026)
To
Tu
f/xx
minl Ba. fh.
{1 [i
-
10
15
76.62
10
10
13.9
49.49
15
10
9.6
40.30
20
10
6.4
36.33
25
10
5.4
32.56
30
10
4.3
32.75
8.8
3.2
34.54
40
7.5
3.2
33.15
45
8.8
3.2
30.55
50
10
2.2
34.05
55
10
2.2
34.59
60
6.3
2.2
34.55
65
7.5
2.2
34.48
70
8.8
1.1
42.71
75
6.3
1.1
37.56
80
6.3
1.1
41.28
85
6.3
1.1
42.93
90
6.3
1.1
39.62
95
6.3
1.1
40.77
100
6.3
1.1
42.30
Table 1: Optimal learning rates for different To values from a simulation baseld parametric study of DOME.
((tr))) = ((C(-L4A-))))) + (CT,a)1) ((C))))) (t+r)0,B + (C (C(6-1411-1)))) (1-147/111188
(35)
(1+r R Chi ((rr)))) and receives the Communication phase: The ith robot sends the information i,,i, &
Lo ch (1)))),)) from its communcating neighbors j E S4 information [t,j, (4r11),
Social prediction phose: With ney 16,,,, we have
(C (C(4110,8)= Th,s +
Σ
(cL, ((tr1))))))
(36)
vjEAN
& (1TT0),B (Ersen, (c (C( ExeEd, (C - Ly
(37)
(1)
Covariance Intersection Consensus Fusion (CICF) Matzka & Altendorfer 2009 Julier & Uhlmann
2017): consider the equations 34
(37; each robot employs the Covariance Intersection (CI) method for the fusion of the predictions instead of Kalman Fusion. CI assumes that the predictions being fused are consistent and their associated zero-mean Gaussian noises' covariance (C7,) is known, but their cross- correlation is unknown.
Covariance Intersection Covariance Union Consensus Fusion (CICUCF) (Matzka & Altendor-
fer 2009 Reece & Roberts 2010 consider the equations 34 (37); first, each robot employs the Covariance Intersection (CI) method for the fusion in the local prediction phase instcad of Kalman fusion. After this, the oulput of CI is fused with the Cl-predictions from the neighbors in the social prediction phase using Covariance Union (CU) instead of Kalman fusion. In CU, while trying to keep the fused predictions con- sistent, the resultant fused covariance increased. Therefore, CI applied in the next itcration reduce the predictions' covariance. CU assumes that the predictions being fused can be inconsistent and their cross-correlation is unknown, but their associated zero-mean Gaussian noises' covariance (C,,)) is known.
21

---

Published in Transactions on Machine Learning Research (04/2026)
DOME: Cumul. Pred. Loes of the 3rd Robot and its Neighbors vs Time
8
Canal. Prel. Loss
6
1.53
2
0
11
13
time (sec.)
DOME Weights: otg. wha My vs time
0.8
Weight Values
0.6
0.4
0.2
0
11
13
14
15
time (sec.)
Figure 5: The first plot shows the cumulative prediction losses for selected robots for a duration of 5 seconds. The second plot illustrates how the weights change in response to the prediction losses shown in the first plot; note that random link drops occur, which means that the nominal neighbors may not be neighbors at all times.
Greedy-Local (GL): each robot uses the onc-step look-ahead prediction 8 = (411),B and the T-slep look-ahead prediction (1471).. & As. () which incurs the least cumulative loss among all the predictions that are shared by its neighbors and its own prediction algorithm, ie., j. = arg minjeA,, L E [.). Here, 4, 1(& (( B) and L -4
Distributed Mirror Descent (DMD): Mirror Descent is applied to our problem setting by modifying the Mirror Descent-based distributed online optimization algorithm proposed by SShhhrampour & Jadbabaic 2017a b leading to the following:
& & Exjeni Wor (t)
(1)-1)) + (m - Aj (1)l- 11)1_1).8)
(38)
8 (411))) -K(U). ErjEn,, (x)()(((((11))) (1-1)) -A, (1)--1)),
(39)
{11110)BB = &(10)BB ExjeAt Wo (t) (1-10)) - -(((-11),8)
(40)
Here, 7m > 0 is a learning parameter, and Wiy(t) E R20 are the weights for the cansensus-based fusion. The weights (!) are considered to be equal for all the neighbors at any time I, i.e., W,y = + 1) where n4.; = [4,,1, Vj E Ar
+
Separate Bias Kalman Consensus Fusion (SBKCF): applics the principle of bias scparation FFiedlaand 1969 Ignagni 1990) Kalman Consensus Fusion (KCF), and assumes that the predictions being fused are uncorrelated and their associated zero-mean Gaussian noises' covariance (CT,, are known. The bias drift ç)2 is modeled following Random Walk process to enable the prediction of future bias estimates.
A: Calculate the residual at time t: Yt.: = (tjt-1)) X,,. From equation B note that GL Ye.s. The drift G/ assumed to follow Random Walk process as follows:
Gt G/-,, w dritt
(41)
22

---

Published in Transactions on Machine Learning Research (04/2026)
where wfrrit NO, Qf i.., werih E I2 (in meters) is zero-mean Gaussian noise with covariance Qu E 1202 Denote the estimate of Cts Gt.. Since the drift Çt follows a Random Walk as stated in equation 411 have Ct G-1
Since the covariance matrix Qfritt is intended to capture variations in the residuals yt, under non-stationary conditions, assume Qdrift x (yr,; Y1-1.) ye-1,a)", where (-)² is the transpose operation. This formulation directly reflects the instantaneous change in the residual and is therefore well-suited for modeling drift in non-stationary environments. Consistently, the 7-step drift is modeled as S7, G. + (T - 1)(v Yt-1.), which linearly extrapolates future drift. based on the most recent residual increment.
Under the above modeling assumptions, the 7-slep drift estimate is given by E7s = 2t + (T 1)(y,, Yt-1,), which extrapolates the drift linearly based on the most recent residual increment. The corresponding covariance estimate is defined as Q (yr, - Vt-1.)(y(.; - Y1-1,)) + 2I22,, which preserves consistency with the residual-baser drift formulation while improving numerical stability. Here, 12x2 denotes the 2 x 2 identity matrix, and 0 < y < 1 is a small positive regularization (jitter) constant introduced to ensure that Quiit remains invertible.
Consider CT as the covariance for & (1+11), The onboard algorithm A, 's corrected 7-step look-ahead prediction & x (1tr))))B and the associated covariance C are calculated as:
x A:
8 4 (1+T|O,,
(14716). S7,
(42)
- + Quritt
(43)
The rest of the SBKCF algorithm is similar to that of KCF, stated as follows:
Local prediction phase:
1 (Citt1))))) = (C (Ci ( (CT,)-1)
(44)
2/ ((tr)))) = ((C(L-4T)-))))) ( (CT,)-1) -1 ((T,))**44
+ (C (C(1-1+7(-1)B)) (11--47
(45)
Chi (1 and receives the Communication phase: The tth robot sends the information {t, & (1+ information {1,j, L/ (B
Chi ((tr1),)) from communicating neighbors j E Sr.-
Social prediction phase: With ne, = 1R,, we have
(C (0(4410)))= Me,i +1
Σ (ch) ((41)))))))
(46)
AJEAe.
& (1410),
(Enjed,, ((rr))))))) EvSEA,,
- (c-T))
(47)
A.3.3 Parametric Study
Table 1 shows the optimal learning rates for which the mean of the average social cumulative prediction loss of all the robots at 140 sec. (i.e., 1 > Li is minimun for different T, values. From table the best mean performance occurs at T, = 45, with n.e 8.8 and ne 3.2. A similar study is performed to get the optimal learning rates for which the standard deviation of the average social cumulative prediction loss of all the robots at = 140 sec. (i.c., Σi= L is minimum for different T, values, which shows that the standard deviation is the least al around T. = 25, with Лı = 10.0 and 7) 5.4. Figures 4 and T show the contour plots for the mean and standard deviation the average social cumulative prediction loss all the robots at 140 sec. (i.c., 6 I versus the combination of learning parameters (1) mn) for T, 45 and T,- 25, respectively. Note the sensitivity in both the mean and standard deviation due to the learning parameter 1/a-
23

---

Published in Transactions on Machine Learning Research (04/2026)
A.3.4 DOME Weights' Behavior
A screenshot of a sample simulation run is shown Fig. 2 The dynamic behavior of DOME weights way(!), j E Ar,3 for a time duration of seconds is shown in ig. 5 along with the corresponding cumulative local prediction losses for the 3rd robot and its nominal neighbors robot and robot (note that random link drops occur, due to which the nominal neighbors may not be neighbors at all times), along with the cunulative social prediction loss for the 3rd robol.
A.3.5 DOME Ablation Study
To identify which components of the DOME fusion algorithm contribute most to the performance gains, ablation study is conducted: see Fig- 6 Without the periodic reset mechanism, the DOME algorithm's average cumulative 10-step look-ahead prediction loss (median) increases by 1025.6%, with corresponding substantial rise in loss variance. This result. highlights the periodic reset mechanism as a critical component of DOME.
Bypassing the DOME algorithm's local prediction fusion phase (i.e., ax(t) = 1) leads to an increase in the average cumulative 10-step look-ahead prediction loss (median) by 1014.4%, whereas using fixed (equal) weighting in the local prediction fusion phase (i.c., (t 0.5) leads an incrcase by 449.51%. This indicates that both the local fusion layer and its adaptive weighting are important to the performance of the DOME algorithm, with the impact of adaptive weighting being approximately half that of the local fusion layer.
Bypassing the DOME algorithm's social prediction fusion phase (i.e., wis (t) 1) leads to an increase in the average cumulative 10-step look-ahead prediction loss (median) by 1392.95%, whereas using equal weighting in the local prediction fusion phase (i.c., equal (ty(t) leads to an increase by 183.52%. This indicates that the social fusion layer has greater impact on the DOME algorithm's performance than its adaptive weighting.
Using equal weighting in both the local and social prediction fusion phases (i.e., ACF: ax(() = 0.5 and equal (t)) leads to an increase in the average cumulative 10-step look-ahead prediction loss (median) by 1232.75%. This demonstrates that adaptive weighting across both the local and social fusion layers key contributor to the DOME algorithm's performance gains.
Taken together, the results suggest muanced hierarchy of importance: adaptive weighting is more influential in the local fusion layer than in the social layer, while the social fusion layer itself has a greater overall impact on performance than the local fusion layer. The periodic reset mechanism, however, remains a critical component overall.
A.3.6 Low versus High Communication Link Drop Probability
DOME is evaluated under varying communication link drop probabilities pla see Fig. 7 The results indicate that as Pia increases from 0.01 to 0.5, the average cumulative 10-step look-ahead prediction loss (median) rises by 80.85,, yet remains within the 100-loss range (median).
A.3.7 Low versus High Prediction Bias/Drift Rate
DOME is evaluated under varying bias or drift rates Ct2 for inaccurate onboard prodiction algorithms A;; see Fig. The results indicate that as 6,2 increases from 0.01 to 10, the average cunulative 10-step look-ahead prediction loss (median) rises by 705.22%, yet remains within the 100-loss range (median).
A.4 Full Observability Assumption's Validity in Practice
The full observability assumption in DOME is practically motivated by two operational paradigms in robotic swarms (as described in Scction 3
Decentralized Sensing and Learning (costly): Robots possess high-grade (negligible noise), long- range, wide-fiele file-ffellof--iew sensors capable of independently tracking the target.
24

---

Published in Transactions on Machine Learning Research (04/2026)
DOME: Avg. Cumml. 10sttep Look ahead Pred. Loss Robot at 140 sec.
1200
DOME
No Pvd. Rot
1000
(u(f)
Ang. Ounul. Prod. Less
800
mw(())
exuun my(()
ACF
600
400
200
1: DOME, 2: No Periodie Roset, 3: a.(3) 1, 4: 0,18) - 0.5, 5 ma(0 1, oqual my(0), 7. ACF
Figure 6: Ablation study of DOME illustrating the contribution of individual components to overall per-
formance. (1) Full DOME; (2) DOME without periodic reset; (3) DOME with a;(t) 1; (4) DOME with
a1(()= = 0.5; (5) DOME with w)(()= 1; (6) DOME with equal (1) (7) ACF: DOME with az(() 0.5 and equal (t) (t).
DOME: Avg. Cumul. 10-step Look-ahend Prod. Loes per Robot at 140
900
Pir 0.01
800
Pi 0.1
700
pu
Ang. Camnl. Fred. Loss
piu
600
pau 0.7
500
0.9
Piu
400
300
200
100
3
5
6
7
1: Pa 0.01, pir 0.1, Pio 0.3, pi 0.5, 5: Pid 0.7,
6: Ph
0.9, T: pM 0.99
Figure 7: Performance of DOME under varying communication link drop probabilities pra, ranging from low
(pia = 0.01) to high (pia = 0.99).
2. Centralized Sensing with Decentralized Learning (cost-cffoctive and scalable): A subsct of "leader" robots ralizel assets (e.g., ground radar, AWACS, satellite feeds) possess high-grade (negli- gible noise), longerange, wide-fier filee-filloof-iieee sensors. These assets broadcast accurate target positions to the swarm via one-way communicttinn, providing a "teaching signal" for the decentralized DOME fusion framework.
The second paradigm (Centralized Sensing with Decentralized Learning) is particularly relevant in high- stakes surveillance disaster-management scenarios, where the swarm is often supported by high-altitude assets like AWACS (Airborne Warning and Control System) or powerful ground-based radar networks. These assets provide a global fix on the target's 's position: the centralized assets provide the "training" (ground truth), while the decentralized swarm handles the "execution" (predictive-tracking)) This setup justifies deploying DOME on simple hardware, as the expensive task of truth generation is offloaded to centralized assets, while robots perform lightweight weight updates. The resulting scalability a key practical advantage, allowing swarms to grow to hundreds of robots without saturating communication bandwidth.
25

---

Published in Transactions on Machine Learning Research (04/2026)
DOME: Avg. Cumul. 10-step Look-ahead Prod. Loss Robot 140 sec.
140
R2y
0.01
120
R2
0 9u
Avg. Cumal. Prod. Loss
100
9g
80
60
2
3
1: et 0.01, 6u 0.1, 3:
44 1,
42 5: 02 4, cq 7:
Figure 8: Performance of DOME under varying prediction bias/drift rate or for the inaccurate algorithm AG, ranging from low (c,, = 0.01) to high (ce.s = 10).
A.5 Effect of Noisy/ /Bi/sdBased Observations
Theoretical Analysis: Let the noisy observations be denoted as:
x = Xt,B + E1,s
(48)
where Et E IR2 is bounded arbitrary noise in the jth robot's observation. Given that the loss function is ((x,y) = mminn[[x-ylll Do, 1), assume Du to be sufficiently large such that ((x,y) = ||x [|x-yl y-llz/ Do. Therefore,
the noisy loss i1, is:
| Nl
||8
X1,B ec,il22
(49)
Do
Do
And the ideal loss 4f is:
1r | - x1,
(50)
Do
Using the reverse triangle incquality, get:
|Gall2 Do
17?,
14,1 s
(51)
From the above, we have:
|er,ill2 Do
|eesill Do
14,
it. it,
(52)
The weight update rule wiy(t) is given by:
wzs(t 1) exp((1nttt)
(t) EyeA,, dzzz (t 1) exp(-xpn
(53)
Consider the ratio of weights wy and wax such that ks E A
Wiy (t) wiy(t - 1) exp(-1111)
(54)
(t) wisatt - 1) exp(-n]l
26

---

Published in Transactions on Machine Learning Research (04/2026)
DOME: Avg. Cunml. 10-step Look-ahead Prod. Loss per Robos at 140 sec.
120
[bvlla
110
[[vlla 0.01
[[allaa 0.1
100
[[alla
Avg. Cumal. Pred. Loss
[|</|
[eulla
80
Ievlll
60
40
30
[eellaa 0, [oolla 0.01, 3: Ieela 0.1, [eel [lola
[|olla
T: [|alla
Figure 9: Performance of DOME under varying observation noise or bias magnitude l|aal2 (in meters),
ranging from low ([le|l22 = 0) to high (|
By substituting the bounds from equation
52 we establish the inequality:
wig(( - 1) (xeeepp(ppe exp(-n)f,)) exp(- -n | Why Way(t)
wir(( - 1) exp( exp(-ao - -n(ft) exp(n (
wos (t) S
(55)
waa(t 1) exp(-n!!;, exp(1) lec,ella) Do
tú (t 1) exp(-17((,) exp(-1) llee, la
Do
The final bounded relationship is expressed as:
wig (t 1) exp exp(-1(f;))
eep ( 1ate,lla+leees Do
Ü.s 1) exp(-n1((,))
ideal relative weight update ratio
(6)(() W
I
(56)
ر (t - 1) exp( 7
exp (n | 1latlll+tleex 12
i (1 - 1) exp(-nMii
ideal relative weight update ratio
A similar analysis be shown for the local weights (t) as well.
Empirical Analysis: Consider the operational paradigm of centralized sensing with decentralized learning, i... a centralized sensing asset broadcasting the (noisy) observed target position &, X, + 6,, where e E R2 is constant magnitude noise with randomly changing direction. The DOME algorithm is evaluated under varying observation noise magnitudes ||</||2 (see Fig. 9 As ||<e||z increases from 0 to 1 meter, the median average cumulative 10-step look-ahead prediction loss increases by only 5.83%. Tn contrast, when ||e||2 increases from 0 to 10 meters, the corresponding loss rises by 82.45%. Yet the loss remains within the 100-loss range (median) for ||e/||a 10 meters.
A.6 Implications of Fixed Periodic Reset
As noted in Section g of the paper, "the DOME weights Wiy(t) are analyzed without considering periodic resets to examine their convergence behavior immediately after and just before reset." Accordingly, the convergence result in Theorem 1 applies within each stationary epoch (i.e., the interval between resets). In practice, the learning rates are sufficiently large, DOME can identify the optimal predictor before the environment shifts, while the reset mechanism addresses the shifts themsclves. If the lcarning rates are low, the weights may not reach their convergence values before a reset occurs; however, their convergence behavior still follows the analysis in Theorem
27

---

Published in Transactions on Machine Learning Research (04/2026)
History
PHASE 1: LEARNING (Evaluate & Adapt)
PHASE 2: LOCAL FUSION (Internal Synthesis)
PHASE 4: SOCIAL FUSION (Collective Output)
Current Target
Onboard Prediction
Final Social Prediction (Navigation Control)
Evaluate Past Predictions (Calculate losses)
Onboard Past (Using Local Trust)
History for Step
Periodic Reset? (Every To steps)
PHASE 3: COMM.
Yes
Local
Trust
RESET WEIGHTS (Clear History)
Broadcast Predictions
Neighbors (Using Social Trust)
Recaive Neighbors'
Update Trust Weights (Local Social)
Social
Trust
Figure 10: Conceptual Overview of DOME Fusion Framework
Theoretical Implications of Fixed To: Theoretically, the ideal setting is for the periodic reset interval (To) to match the environment's 's switching interval (i.e., the inverse of the bias environment switching fre- quency), allowing DOME to converge within each stationary segment. If resets occur too frequently, DOME may remain in a high-variance transient state without fully converging to the best neighbor. Conversely, if resets are too infrequent, DOME can retain large weights on a now-biased neighbor, leading to adaptivity lag.
Practical Implications of Fixed To: While fixed T, might be suboptimal if the frequency of environ- mental shifts varies drastically, empirical results suggest the algorithm exhibits robust performance basin rather than sharp peak, making it resilient to such mismatches. Specifically, the simulation study (Section G utilizes an event-base based switching bias model (Fig. [b) where the bias dynamics are inherently stochastic and variable-frequency (switching probabilitics Pyb = 0.2, Prb = 0.5). Despite this variability in the 'truc' switching frequency, the parametric study (Appendix A..33.. Table [ demonstrates that the DOME algo- rithm maintains high performance across broad range of fixed T, values. As shown in Table [ (Appendix A.3.3), while the minimum for cumulative prediction loss occurs at T, 45, the performance degradation for To values ranging from 25 to 60 w.r.t. T, 45 is gradual and relatively minor (loss increases from v 30.5 to R 34.5).
28


Reviews:
[{"review_id": "6AxVCMgk8j", "reviewer": "Reviewer_ovsv", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper introduces DOME, a distributed online-learning-based fusion method, for cooperative predictive target tracking in robotic swarms. DOME uses exponentially weighted updates and adapts to biased or unreliable predictors. Notable benefits are not relying on covariance information and robustness to packet drops. The method scales well with swarm size, as demonstrated in simulations and ROS-Gazebo experiments. Key limitations are strong observability assumption for computing losses and reliance on a heuristic periodic reset not captured by the theory.", "claims_and_evidence_yn": "Yes", "claims_explanation": "Major claims of adapting to biased predictors and packet drops are supported by clear empirical evidences that show improved performance over the chosen baselines. The experimental setup is well documented. \n\nHowever, assumptions such as full observability and structured bias simplify the problem and may limit real-world generality.", "audience_yn": "Yes", "audience_explanation": "Researchers in multi-robot coordination and online learning would appreciate DOME's learning-based approach to prediction fusion, particularly as an alternative to covariance-based methods under bias. The scalable and communication-robust aspects for cooperative tracking problems could be useful to practitioners.", "requested_changes": "1. In target tracking, one rarely observes the ground truth position. Explicitly discuss how noisy or biased observations of the target instead of true $x_{t,B}$ would affect the weight updates. Or, clarify the practical implications of assuming access to the true target state. (Critical)\n\n2. The covariance-based methods are mathematically derived under the assumption of zero-mean noise. It is a known that Kalman filters fail under significant unmodeled bias. The problem formulation has a bias state where errors are up to 40m and non-zero mean. \nWhile this highlights DOME's strength, a more rigorous comparison would be an adaptive Kalman Filter or a standard KF with a bias-state augmentation. (Critical)\n\n3. Please add a brief discussion in the main text on sensitivity to mismatch in $T_o$. For example, if the bias dynamics change frequency, does the fixed $T_o$ becomes a problem? (Critical)\n\n4. In (9), the robot computes the social prediction using weighted neighbors. Is this value used only for control or is fed back into the next time step? (8) suggests the previous social prediction is used for local fusion. (Non-critical)", "broader_impact_concerns": "The work has no major ethical concerns, but its applicability to surveillance or monitoring tasks suggests potential dual-use considerations. A brief acknowledgement of responsible deployment in the existing Broader Impact Statement would be appropriate.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "lsb6At4k31", "reviewer": "Reviewer_GhzN", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper introduces DOME, an approach proposed to combat high prediction bias and uncertainty in cooperative distributed online learning system deployed for predictive target tracking. Both theoretical analysis and empirical results were presented, with DOME performing better than the reported baselines in harsh conditions where communication is highly unreliable.\n\nThe work includes sufficient baselines for comparison, with results averaged over multiple runs. Furthermore, the algorithm, hyperparameters, and source code are provided to ensure reproducibility.", "claims_and_evidence_yn": "Yes", "claims_explanation": "The claims presented in the paper were addressed via theoretical and empirical evidence.", "audience_yn": "Yes", "audience_explanation": "The paper addresses a problem that is relevant to a sub-community in TMLR as evidenced by previously published papers within the community.", "requested_changes": "Optional changes\n1. Consider moving the related works from the introduction section into a separate section. For example, paragraphs 2, 3, and 4 in Section 1 can be moved to a separate section focused on related works.", "broader_impact_concerns": "A broader impact statement of the proposed method should be discussed. Although the experiments were conducted in a simulation (ROS Gazebo), it is important to reflect on the broader impact of the algorithm in real-world domains.", "additional_comments": "N/A", "extra_scores": {}, "extra_text": {}}, {"review_id": "IlnMrjr5Jf", "reviewer": "Reviewer_sQqg", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper investigates target tracking via a fleet of robots in a cooperative multi-agent setting. Each agent has it's own sensors and individual prediction algorithm of the targets future position. All controllable agents, as well as the target, are represented by 2D position vectors and heading angles in a 2D plane. Notably the controllable agents cannot communicate with every other agent, but only those that have communication links with each other. This particular problem setting has a number of sources of error and uncertainty, including communication failures/drops and high individual prediction biases. The DOME fusion algorithm is proposed to address these challenges. The algorithm explicitly models communication failures, bias accumulation (via fusion weight resets), and more to handle these challenges. Empirical results in simulated settings demonstrate that DOME achieves better performance (measured via accumulated prediction loss over 60 seconds). Moreover, with more robots DOME performance improves, similar to the improvement shown by baselines.", "claims_and_evidence_yn": "Yes", "claims_explanation": "The algorithm looks sound and the empirical results back up the claims in the paper regarding the performance of DOME.", "audience_yn": "Yes", "audience_explanation": "Learning based methods are used in this paper to update the weights in DOME to improve tracking performance. It is interesting to see how they handle the multi-agent cooperative setting and model an incomplete communication graph setting.", "requested_changes": "For a learning based approach with empirical testing, I typically would expect there to be ablation studies on the proposed method. Part of the paper's investigation should include not just the main results, but results that highlight what exactly makes DOME better and the contributions of its various components. Another reasonable ablation would be to test DOME under specific settings to highlight how it best handles the challenges the paper proposes to address like communication failures. For example testing the performance of DOME under a high vs low communication failure rate.", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "s6omnqyyg9", "reviewer": "Reviewer_fa66", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "In this work, the authors consider the problem of a swarm of robots trying to predict the position of a target over time, when each of the robots in the swarm has access to potentially different sensors and a different trajectory computation algorithm, while having to deal with the movement of the robots. \nThe robots can communicate with their neighbours to share their trajectory updates and evaluate the relative trust they have in their own trajectories versus the trajectories of their neighbours (which might be calculated using more performant sensors/ algorithms).\n\nThe algorithm relies on exponential weights (Cesa-Bianchi and Lugosi, 2006), which is a well-studied approach in the non-stochastic learning paradigm. This structure of exponential weights is rather old and has been widely built upon in the literature, including in many applications that could be of interest to expand the current work (referring to the literature on EXP3 and bandits, which studies variants with expert advice (similar to the social structure, handling potentially changing sets of neighbours, delayed observations or faster convergence in easier environments). This being said, the structure of the problem is extremely complex and specific enough that starting with a simple version of exponential weights is probably unavoidable. \n\nIn terms of theoretical results, the authors prove that the social weights converge, which means that eventually each robot uses the prediction of the most trustworthy of them or their neighbours, even in challenging situations where the communication between robots might drop, or when the best robot changes over time (due to a problem with a sensor, for example). This robustness and adaptivity are an essential part of the exponent weights methods and could be expanded upon further. \n\nThe authors also propose a very detailed experimental setup and benchmark comparison with includes both Covariance-based methods and online learning methods. In that setting, the proposed algorithm achieves much better performance than the baselines. The experiments include validation in a ROS-Gazebo simulated environment.", "claims_and_evidence_yn": "Yes", "claims_explanation": "The claims, as stated in the theoretical results, follow detailed proofs. There is, however, a point that needs to be emphasised. In the Online Learning literature, results would typically not be stated in terms of asymptotic convergence but rather with cumulative regret guarantees, which are much stronger.\n\nRegarding the experiments, it appears that all the necessary elements have been provided to reproduce them. Some of the methods in the baseline appear fairly older, so it would be beneficial to have an additional discussion/justification for their use in practice/inexistence of other methods, to confirm that their choice is representative of the current state of the art and that the performance results announced are a fair representation to the state of the art.", "audience_yn": "Yes", "audience_explanation": "I think that the learning theory community, which is a target audience of TMLR,  could be interested in this more applied work, as there is always interest in new ways to bridge the gap between theory and practice. For example,  the early version of exponential weights used in the DOME algorithm could be replaced by a more recent and problem-specific version of the problem (for example, tailored for communication in graphs, or with faster convergence in specifically easy environments).", "requested_changes": "The algorithm has numerous elements that are difficult to keep track of; it would be helpful to have, first, a concise overview of how the algorithm functions in simple terms before introducing and defining all the specifics. Some aspects of the algorithm aren't very clear even after reading the paper: for example, figuring out why the algorithm needs to restart after T_0 steps was difficult, as the couple of lines about it on page 5 are easy to miss. \n\nSome of the variables (for example, J_i) haven't made it to the glossary, so it would be nice to add them for clarity. \n\nAs discussed in the previous section, it would be beneficial to argue that the baseline in the experiment represents the state of the art.", "broader_impact_concerns": "The most straightforward application of the project seems pretty clearly applied to drones, which could be discussed more in the broader impact statement due to the wide range of uses of drones.\nThe considerations of distributed methods for privacy in the other discussed applications are interesting.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)