Dual-Process IMM: Hybrid Inference & Adaptation

• Dual-process IMM is a framework that integrates probabilistic filtering for continuous states with possibility-based max inference for discrete mode switching to improve dynamic state estimation.
• In tracking applications, this approach sharpens regime transitions and has demonstrated reduced errors, e.g., lowering x-RMSE from 7.0 m to 5.0 m and y-RMSE from 6.1 m to 4.2 m.
• The framework extends to reinforcement learning and computer vision, combining imitation learning with policy refinement and dynamic camera tracking for robust performance.

A dual-process Interacting Multiple Model (IMM) framework refers to any approach in which distinct but interleaved inference or learning mechanisms are combined within the IMM paradigm. Across methodologies and domains, "dual-process" IMM typically designates systems wherein two complementary processes—commonly, separate inference operators or parallel expert learners—jointly estimate or control a dynamic system under uncertainty. The framework provides robust adaptation to regime-switching or nonstationary environments, whether for continuous tracking, reinforcement learning, or combined continuous–discrete uncertainty.

1. Theoretical Foundations of the Dual-Process IMM

The canonical IMM provides Bayesian filtering in jump–Markov systems by combining parallel (E)KF filters conditioned on candidate dynamics models, mixing their state estimates and probabilities at each time increment. In classical IMM, both the continuous states $x_k$ and the discrete modes $r_k$ are treated as random variables with probabilistic transition rules, leading to posterior probabilities updated via summation and marginalization ("σ-inference") (Mei et al., 2021).

The dual-process IMM generalizes this by introducing heterogeneity in the inference operators. This is exemplified in "Hybrid IMM" (HIMM), which distinguishes:

• Randomness in state-space estimation: Continuous states $x_k$ evolve and are inferred via classical probabilistic methods (Kalman filter, additive probability mixing—σ-inference).
• Fuzziness in mode switching: Discrete model switches $r_k$ are treated under possibility theory, using max-inference for mode interaction and hard maximum a posteriori selection, rather than maintaining full probabilistic mixing. The mode transition matrix can become a possibility matrix $\Pi$ (satisfying $\max_j \Pi_{ij} = 1$) rather than a stochastic $P$ ($\sum_j P_{ij}=1$) (Mei et al., 2021).

This duality enables sharp, hard model switching and faster adaptation, contrasting with the risk of slow or diffused response inherent in pure posterior probability fusion.

2. Dual-Process IMM in Probabilistic Filtering

The archetypal implementation of the dual-process IMM in filtering tasks appears in maneuvering target tracking and multi-object tracking. The workflow is typically structured as follows (Claasen et al., 2024, Liu et al., 13 Feb 2025, Mei et al., 2021):

• Interaction/Mixing Step: Kalman-filter states and covariances for $M$ models are mixed. In the classic setting, soft mixing weights are computed with the Markov model; in the dual-process or hybrid versions, weights may use max-inference for harder model assignment.
• Model-Conditioned Prediction/Update: Each model branch proceeds with standard prediction and correction, either via linear Kalman or extended Kalman steps, depending on underlying model nonlinearities.
• Mode Probability Update: In standard IMM, posterior model probabilities are updated via joint likelihood and prior mixing. In the dual-operator scheme, possibility-based max-principles supplant this, supplementing or replacing additive fusion.
• State and Covariance Fusion: Outputs may be fused probabilistically (weighted sum) or, in strictly possibilistic settings, by selection of the single most plausible branch.

A summary of classical versus dual-process IMM mixing mechanisms:

Step	Classical IMM	Dual-Process IMM (HIMM)
Interaction	$\alpha_j = \sum_{i}\mu_i P_{ij}$	$\alpha_j = \max_{i} [\mu_i \Pi_{ij}]$
Mode Update	Soft posterior	Max-posterior or hard assignment
Output Fusion	Weighted sum	Hard selection or weighted max

This duality allows the filter to sharply represent regime changes (e.g., maneuver onsets), reducing cross-mode averaging effects that can degrade high-agility tracking (Mei et al., 2021).

3. Dual-Process IMM in Joint Homography–MOT and Camera Models

In computer vision, dual-process IMM is realized by parallelizing different model hypotheses for both geometric (e.g., homographies, dynamic/static camera motion) and kinematic objects, with likelihoood-driven adaptation. In IMM-JHSE (Claasen et al., 2024):

• State Augmentation: Each track’s state vector contains both kinematic state (position, velocity on ground plane) and full $3\times3$ homography states, representing dynamic image–world mappings.
• Two-Model IMM Structure: One branch uses a dynamic camera (affine/matrix update), permitting rapid adaptation to egomotion; the other uses a static camera assumption, favoring low-drift when the scene is stationary. Both are updated with separate EKFs and their outputs are fused according to model likelihood.
• IMM-like Association Metrics: For data association, the system combines ground-plane Mahalanobis distance with image bounding box BIoU, weighted by the predicted mode probabilities. This hybridizes association cues, supporting robust track identity maintenance across 2D/3D context switches.
• Adaptive Noise Estimation: Both process and measurement noise covariances are adapted online via windowed statistics on EKF innovations, further enhancing robustness as regime switches occur.

This approach yields improved tracking HOTA metrics over prior methods on DanceTrack and KITTI-car, confirming the effectiveness of a dual-process adaptation to camera and object dynamics (Claasen et al., 2024).

4. Dual-Process IMM in Reinforcement Learning and Market Making

The dual-process principle extends to learning-based control. In the Imitative Market Maker (IMM) for RL-based market making (Niu et al., 2023):

• Imitation Learning Bootstrapping: Policy learning is initialized by behavior cloning from a suboptimal but informative signal-driven expert (dataset $\mathcal{D}_E$), rapidly aligning exploration towards profitable regions in a high-dimensional action space.
• Reinforcement Learning Refinement: Subsequently, the policy is refined by direct RL (value-based updates, environmental interaction), moving beyond the expert toward optimality.
• Tandem Objective Function: Policy updates optimize a combined loss, $$J(\pi) = \mathbb{E}_{s\sim D}[Q(s, \pi(s))] - \lambda \mathbb{E}_{(s, \hat{a})\sim D_E}[\|\pi(s) - \hat{a}\|^2]$$, with $\lambda$ decayed over time, so that IL dominates early and RL late.
• Representation Learning: A predictive module captures short/long-term price signals (LightGBM) and latent book features (TCN+spatial attention), feeding both imitation and RL branches.
• Ablation Results: Removal of either process leads to substantial performance degradation. Omission of IL causes unstable exploration and poor convergence; omission of RL causes policies to collapse to near-expert performance, absent further improvement. Both components are empirically required for superior, stable multi-level quoting (Niu et al., 2023).

A plausible implication is that dual-process IMM learning is essential in domains where exploration is costly or unsafe and prior knowledge is informative but not sufficient.

5. Quantitative and Practical Impacts

The empirical benefits of dual-process IMM structures are well-supported across domains:

• Tracking Accuracy: In maneuvering target tracking (radar, vision), HIMM achieves lower RMSE than classic IMM, especially under matched model parameters (e.g., $x$-RMSE dropping from 7.0 m to 5.0 m, y-RMSE from 6.1 to 4.2 m for fire-control radar) (Mei et al., 2021).
• Mode Responsiveness: Dual-process (possibility) fusion yields swift regime adaptation, reducing average mode cross-time (e.g., from 85.9 to 83.8 scans) (Mei et al., 2021).
• Market Making: Dual-process RL–imitation outperforms single-process baselines in PnL, MAP, adverse-selection ratio, and stability in all tested scenarios (Niu et al., 2023).
• MOT Benchmarks: IMM-based trackers with dual camera/association models achieve state-of-the-art HOTA (e.g., +2.64 and +2.11 improvement on DanceTrack and KITTI-car in IMM-JHSE), matching or surpassing attention-based and 2D/3D competitors (Claasen et al., 2024).

Ablation studies consistently confirm that removing either process in the dual architecture results in significant, sometimes catastrophic, drops in performance across accuracy, robustness, and efficiency.

6. Limitations, Open Problems, and Future Directions

Despite empirical superiority, dual-process IMM systems are not free from trade-offs:

• Hard Decisions and Model Mismatch: Max-inference can introduce instability or mode-locking if candidate model assumptions are poor; soft inference may still be preferable in ambiguous regimes or when models cannot capture the true state transitions (Mei et al., 2021).
• Possibility Normalization Effects: When multiple modes have comparable plausibility, max-based normalization can introduce bias or abrupt regime switches.
• Non-Gaussian and High-Dimensional Scalability: While dual-process strategies have been generalized, extension to large model sets, strongly nonlinear dynamics, or non-Gaussian noise may require new theoretical advances, such as robustified or adaptive possibility mechanisms.
• Learning-Based Parameterization: There is increasing interest in learning model transition and noise parameters, or even end-to-end model set adaptation, to enhance the flexibility and applicability of the dual-process framework (Mei et al., 2021).
• Hybrid Inference in ML Systems: A plausible implication is that sigma–max inference and random–fuzzy splits could offer benefits for hybrid neural–symbolic or discrete–continuous systems in machine learning, extending beyond temporal filtering contexts (Mei et al., 2021).

7. Summary Table: Dual-Process IMM Formulations Across Domains

Domain/Problem	Main Dual Processes	Operator Types
Maneuvering Target Tracking	σ-inference (state) + max-inference (mode)	Probability (additive) + Possibility (max)
Multi-Object Tracking (IMM-JHSE)	Static/dynamic homography (mixed by likelihood); ground-plane/image-plane matching	Likelihood mixing + adaptive scoring
Market Making (RL)	Imitation (expert) + Reinforcement (environment) learning	Behaviour cloning + policy gradient

In all formulations, the unifying characteristic is the co-existence and coordinated integration of two inference or learning mechanisms, yielding robustness, adaptive behavior, and state-of-the-art performance in settings where switching, ambiguity, or nonstationarity is inherent (Niu et al., 2023, Mei et al., 2021, Claasen et al., 2024, Liu et al., 13 Feb 2025).