Low-Complexity Tracking Algorithm

Updated 4 July 2025

Low-complexity tracking algorithms are efficient techniques that estimate and follow object states using minimal computational and memory resources.
They leverage sequential processing, problem decomposition, and rapid data association to bypass resource-intensive operations in traditional tracking methods.
These algorithms are crucial for real-time applications in computer vision, wireless communications, and sensor networks, enabling scalable and embedded tracking solutions.

A low-complexity tracking algorithm is a computational technique designed to estimate and follow the state or position of objects or signals efficiently, with minimal computational and memory resources. In diverse domains such as computer vision, communication systems, and sensor networks, these algorithms balance the need for reliable, accurate tracking with constraints on memory, processing time, or energy—making them suitable for real-time, embedded, and large-scale applications. Methods designated as “low-complexity” are distinguished by algorithmic innovations that circumvent computational bottlenecks, reduce reliance on resource-intensive operations such as matrix inversion or combinatorial hypothesis enumeration, and exploit problem structure to accelerate solution finding.

1. Foundational Principles of Low-Complexity Tracking

Low-complexity tracking solutions typically depart from traditional, computation-heavy tracking frameworks (e.g., full Bayesian multi-target filters, exhaustive data association, or large neural architectures) by pursuing one or more of these guiding principles:

Sequential or incremental processing: Algorithms update state estimates as new data arrives, avoiding storage of entire measurement histories or frames. For example, in static background estimation for surveillance, image sequences are processed block-by-block, and a “representative set” of block candidates is updated online without retaining all past frames (1303.2465).
Problem decomposition and surrogate optimization: Complex tracking objectives are split into solvable subproblems. In multi-object tracking, a global quadratic program is approximated by sequentially solving a temporal association via linear programming, followed by clustering for spatial grouping (1607.07304).
Efficient use of data association and state representation: Instead of evaluating all possible combinations, message-passing techniques (e.g., sum-product algorithm) or simplified geometric criteria are used to efficiently approximate and update associations—enabling scalability in multi-target or multi-object scenarios (2109.01490, 2208.03659).
Dimensionality reduction and feature selection: By focusing only on essential features, and employing adaptive fusion or selective updating of model components, feature space is reduced, lowering computational overhead while preserving discriminative power (2204.02054).

2. Algorithmic Methodologies

Several distinct approaches underpin the design of low-complexity tracking algorithms:

Markov Random Field (MRF) Models with Iterated Conditional Modes (ICM): In static background estimation, labeling is formulated as an MRF over spatial blocks, and optimal configurations are sought with ICM—an efficient local energy minimization scheme operating on a small label set (1303.2465).
Adaptive Filtering with Variable Forgetting Factors: In adaptive beamforming and channel estimation, recursive least squares (RLS) or least mean squares (LMS) filters are accelerated by embedding a variable forgetting factor that adapts to tracking or learning dynamics, using measures such as time-averaged constant modulus cost or instantaneous error (1406.6998, 1811.11948).
Discrete Convolutions and Fourier Techniques: To manage exponential complexity in probabilistic message passing, as in SCMA detection, high-dimensional integrals are discretized and computed efficiently using FFT-based convolution, reducing calculations that otherwise scale combinatorially (1611.08853).
First-Order Convex Optimization (Forward–Backward Splitting): For subspace estimation in massive MIMO, high-dimensional SDP optimization is cast in a convex MMV (multiple measurement vectors) form, and the solution is obtained using fast first-order iterative methods rather than matrix decomposition (1608.02477).
Non-Gaussian Measurement Handling via Analytical Approximation: For tracking with non-directional sensors where measurements yield non-Gaussian likelihoods, algorithms employ constrained Hessian searches and local coordinate transformations to maintain tractable approximations and efficient integration (2009.08310).
Geometry-based Interaction Modeling: In online multiple-object tracking, geometric cues (intersection over union, normalized spatial shifts) are used for association and occlusion reasoning, circumventing high-cost appearance-based or graph neural network interaction models (2208.03659).

3. Mathematical Formulation and Key Computational Reductions

Many low-complexity algorithms achieve their efficiency through express mathematical formulations:

Representative Set Updating in MRF Labeling:

$r_{k}^{\text{new}} = r_{k}^{\text{old}} + \frac{1}{W_k+1}(l_f - r_{k}^{\text{old}})$

This formula updates the representative mean for a block as new observations arrive, supporting online operation (1303.2465).

Variable Forgetting Factor Update in Adaptive Filtering:

$\phi(i) = \alpha \phi(i-1) + \beta (|y(i)|^2 - 1)^2$

$\lambda(i) = [1/(1+\phi(i))]^{\lambda_+}_{\lambda_-}$

These recurrent updates enable filters to track changes rapidly with minimal per-iteration computations (1406.6998).

Convex Optimization for Subspace Tracking:

$\min_{\mathbf{C}} \frac{1}{2} \|\check{\mathbf{G}}\mathbf{C} - \mathbf{X}\|^2 + \sqrt{T} \|\mathbf{C}\|_{2,1}$

Iteratively solved, this problem tracks time-varying subspaces without the need for expensive semi-definite programming (1608.02477).

Discretized Message Passing with FFT:

$g = \mathcal{F}^{-1}\left[\prod_{i} \mathcal{F}(\text{pad}(f_i))\right]$

Here, convolution over discretized PDFs replaces exhaustive sum-product operations, leading to polynomial rather than exponential complexity (1611.08853).

Sum-Product Data Association:

Posterior Multi-Bernoulli mixtures are approximated by single MB posteriors, with data association achieved by efficiently marginalizing assignment probabilities using message passing (2109.01490):

$p(\mathbf{a}_k) \approx \prod_{j=1}^{J_k} p(a_k^{\prime j})$

4. Empirical Performance and Practical Impact

Extensive empirical evaluations across surveillance, communication, and sensor tracking contexts consistently demonstrate that low-complexity tracking algorithms can achieve accuracy comparable to or exceeding more computationally intensive baselines, often with orders of magnitude less memory and computation.

In static background estimation, the proposed sequential MRF-based scheme yields lower average gray-level error (AGE) and fewer clustered error pixels compared to median filtering and ISI methods, even when using only partial data (1303.2465).
Adaptive RLS beamformers featuring low-complexity variable forgetting factor mechanisms achieve faster convergence and higher steady-state SINR than prior techniques, maintaining performance under abrupt environmental changes (1406.6998).
In multitarget tracking with non-directional sensors, the TT filter reduces optimal mass assignment error by over 36% compared to particle filters using 1,000,000 points, with at least tenfold lower computation time (2009.08310).
In neuromorphic vision sensor scenarios, the EBBIOT approach was measured to achieve 7× less memory use and 3× fewer computations than conventional mean-shift tracking, while offering higher precision and recall in real surveillance data (1910.01851).
Multi-object tracking paradigms relying on geometric association, as opposed to appearance features, achieved state-of-the-art accuracy and tracking robustness, while maintaining real-time applicability (2208.03659).

5. Limitations and Open Problems

Despite their efficiency, low-complexity tracking algorithms may exhibit limitations:

Many methods assume particular statistical or structural properties (e.g., blockwise stationarity in backgrounds, dominant geometric cues, or sparsity in target features) that may not generalize across all settings.
Discretization-based approaches introduce quantization errors dependent on sampling interval size; finer discretization narrows the gap to exact methods at the price of increased computation (1611.08853).
Handling abrupt non-stationarities, complex occlusions, or dynamic backgrounds without loss of tracking fidelity may require hybridization with more adaptive or model-rich techniques (1303.2465).
Specific recycling and approximation schemes (e.g., Bernoulli recycling in multi-Bernoulli models) may introduce information loss or bias when association uncertainties are highly coupled (2109.01490).
Some domain-specific simplifications (such as those found in MyoTracker's point tracking for myocardium motion (2503.10431)) are highly effective within their target application, but may not transfer to settings with less constrained motion dynamics.

6. Domains of Application

Low-complexity tracking is foundational in systems where computational resources and memory are at a premium or latency constraints are stringent:

Video surveillance: Block-based methods for static background estimation are directly integrated in real-time object segmentation, especially in embedded or edge camera systems (1303.2465).
Wireless and MIMO communications: Efficient subspace estimation, adaptive filtering, and beam tracking are critical to the scalability and agility of massive MIMO and mmWave systems under dynamic interference and mobility (1406.6998, 1608.02477, 1811.11948, 2007.01006).
Sensor networks: Target tracking with amplitude-only sensors using efficient Hessian-based filters enables real-time multi-target fusion in distributed sensor fields (2009.08310).
Online visual multi-object tracking: Fast geometric-based and relational tracking methods support high-accuracy target association and re-identification under limited compute budgets (1607.07304, 2208.03659).
Internet of Video Things (IoVT): Algorithms designed for extremely memory-constrained, low-power devices, such as the EBBIOT paradigm for neuromorphic vision sensors, support large-scale deployment in environmental or urban monitoring (1910.01851).
Medical imaging: Domain-adapted low-complexity neural architectures, such as MyoTracker for echocardiography point tracking, enable fast and accurate measurement of clinically relevant metrics on standard hardware (2503.10431).

7. Prospects and Research Directions

Future advances in low-complexity tracking are likely in the following areas:

Hybridization with learning-based methods: Combining lightweight deep models with domain-specific simplifications may yield the next generation of efficient trackers for high-dimensional streams and complex tasks.
Adaptive discretization and dynamic resource allocation: Techniques that modulate quantization and computation based on uncertainty, noise, or context could refine the efficiency vs. accuracy trade-off (1611.08853).
Scaling to dense and large-scale scenarios: Further algorithmic innovations will be required for robust and efficient tracking in environments with large numbers of closely spaced or highly maneuverable targets, particularly when operating under energy or bandwidth constraints.

Low-complexity tracking algorithms thus remain a cornerstone of practical systems facing stringent resource and latency requirements, with ongoing developments continuing to expand their reach and effectiveness across scientific, industrial, and societal applications.