Moving horizon estimation

A constrained state-estimation method that repeatedly optimizes model fit over a finite recent measurement window and summarizes earlier data in an arrival cost.

Version

v1 · 2026-09-08 · History

Domain-specific #

5682

Origin domain

control and state estimation

Subdomain

control and state estimation

Core Idea

MHE estimates current states and parameters by solving a rolling nonlinear or quadratic program subject to process dynamics, measurement models, bounds, and disturbances. Each new measurement advances the window, an arrival cost compresses information from the discarded past, constraints prune infeasible trajectories, and optimization selects the best recent state path. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.

Scope of Application

Moving horizon estimation belongs to control and state estimation and is useful where the analyst can specify the typed control and state estimation carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate the dynamic and measurement models, horizon length, arrival cost, noise or loss model, constraints, solver, update timing, and observability assumptions are declared. The scope is broad within that domain but bounded by the need for the dynamic and measurement models, horizon length, arrival cost, noise or loss model, constraints, solver, update timing, and observability assumptions are declared. Conceptual estimator identity only; safety-critical process or vehicle control requires validated models, timing guarantees, fault analysis, and qualified engineering review.

Clarity

The abstraction clarifies a crowded vocabulary by making the dynamic and measurement models, horizon length, arrival cost, noise or loss model, constraints, solver, update timing, and observability assumptions are declared the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name Moving horizon estimation can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.

Manages Complexity

Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Moving horizon estimation. Moving horizon estimation compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.

Abstract Reasoning

1. Identify the carrier. State what the elements, states, objects, or observations are: the typed control and state estimation carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the dynamic and measurement models, horizon length, arrival cost, noise or loss model, constraints, solver, update timing, and observability assumptions are declared independently of one notation or implementation.

Knowledge Transfer

Knowledge transfers strongly among subfields of control and state estimation because they reuse the typed control and state estimation carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, Each new measurement advances the window, an arrival cost compresses information from the discarded past, constraints prune infeasible trajectories, and optimization selects the best recent state path., and type the carrier, state every parameter and convention in the definition, test that the dynamic and measurement models, horizon length, arrival cost, noise or loss model, constraints, solver, update timing, and observability assumptions are declared, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions

Current abstraction Moving horizon estimation Domain-specific

Parents (1) — more general patterns this builds on

• Moving horizon estimation is a kind of Estimation Prime

  The proposed strict upward parent is prime:estimation.

Hierarchy path (1) — routes to 1 parentless root

• Moving horizon estimation → Estimation → Approximation → Representation → Abstraction

Neighborhood in Abstraction Space

Moving horizon estimation sits in a crowded region of the domain-specific corpus (24^th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Model Estimation & Numerical Diagnostics (15 abstractions)

Nearest neighbors

• Recursive Bayesian estimation — 0.91
• Separation principle — 0.91
• Trajectory optimization — 0.91
• Optimal control — 0.91
• System identification — 0.91

Computed from structural-signature embeddings · 2026-09-08