Relative Frame Bootstrap Without Absolute Reference

Mechanism

Each mesh node carries a ranging radio that produces inter-node range estimates with each of its in-radio-horizon neighbours. The collection of pairwise ranges across the mesh forms an incomplete distance matrix. The bootstrap procedure begins by selecting a seed triplet of nodes whose pairwise ranges are mutually consistent within the ranging error budget. The seed triplet is assigned coordinates in a synthetic local frame: one node is placed at the origin, a second on the positive x-axis at the measured range, and the third in the upper half-plane at the position dictated by its two ranges. This choice fixes the four gauge degrees of freedom — origin translation, axis rotation, and reflection parity — that are intrinsically unobservable from range data alone.

Once the seed is fixed, additional nodes are admitted to the frame one at a time using multilateration against already-placed neighbours. A node with three or more ranges to placed neighbours yields a determined or overdetermined position estimate; the estimate is accepted if its residual against the observed ranges is below a threshold drawn from the ranging error model. Nodes that cannot be uniquely placed are deferred until additional ranges arrive. The result of the bootstrap pass is a local-frame position assignment for each mesh member, together with a per-node covariance estimate that reflects the cumulative error in the chain of multilaterations that placed it.

After the initial bootstrap, the local frame is maintained by a continuous estimator that consumes new range observations, tracks node motion, and refines the position estimates. The estimator is a sparse non-linear least-squares solver over the position state of all mesh members, optionally augmented with inertial measurement data when nodes carry the requisite sensors. The frame is internally self-consistent: every pairwise distance and every triangulated direction within the mesh is correct to the precision of the ranging system, even though the orientation of the frame relative to any external reference is undefined.

Operations that require only intra-mesh geometry — formation maintenance, collision avoidance among mesh members, relative navigation, and intra-mesh routing — execute against the local frame from the moment the bootstrap completes. Such operations are unaware of, and indifferent to, the absence of an absolute reference.

When an anchor observation becomes available, it is used to estimate the rigid-body transform between the local frame and the corresponding global frame. A single anchor observation of one node's global position constrains three of the seven parameters of a similarity transform; additional anchor observations resolve rotation and, if the ranging system did not previously fix scale, the scale factor. Anchor sources include opportunistic global-navigation-satellite fixes acquired by any mesh member, surveyed reference markers identified by any mesh member's perception system, and external position reports relayed into the mesh by an outside coordination element. Each anchor observation is admitted to the transform estimator as a credentialed observation, signed by the originating node and tagged with the policy reference under which the anchor was acquired.

The transform estimator maintains the local-to-global rigid-body transform and its covariance. When the covariance falls below a policy-defined threshold, the mesh declares itself absolute-bound and emits a frame-promotion event into the governance lineage. Operations that require absolute coordinates — geofence enforcement against externally specified boundaries, coordination with non-mesh systems, reporting of mesh state to external command — admit the frame-promotion event before activating. Operations that require only the relative frame remain unaffected by the promotion.

Operating Parameters

The bootstrap procedure is parameterised by the ranging error budget, the seed-triplet consistency threshold, the multilateration residual threshold, the maximum admissible position covariance for a node to be considered placed, and the minimum number of placed neighbours required to admit a candidate node. The continuous estimator is parameterised by the process-noise covariance for node motion, the measurement-noise covariance for ranging, and the time horizon over which range observations are retained.

The transform estimator is parameterised by the minimum number of independent anchor observations required for transform admission, the maximum admissible transform covariance for declaring absolute binding, and the policy reference under which anchor observations are credentialed. The frame-promotion event is parameterised by the declared uncertainty of the transform at promotion time.

All parameters are bound to the mesh's active governance policy. Mid-mission mutation of these parameters is forbidden so that the conditions under which the local frame was constructed and under which absolute binding was admitted can be reconstructed from the lineage alone. The lineage records the policy reference active at each event so that the parameter set governing any historical observation is recoverable.

Alternative Embodiments

The seed-triplet construction may be replaced by a multidimensional-scaling pass over the full distance matrix when a sufficient density of pairwise ranges is available at bootstrap time. Multidimensional scaling yields a global solution to the placement problem in a single step, at the cost of computational complexity that scales superlinearly with mesh size. For small meshes the trade-off favours multidimensional scaling; for large meshes the incremental seed-and-extend procedure remains preferred.

The continuous estimator may be implemented as a centralised sparse solver running on a designated mesh master, as a decentralised consensus-based solver in which each node maintains and exchanges only its own state, or as a hybrid in which a slow centralised pass periodically reconciles the faster decentralised local updates. The disclosure contemplates each topology.

The transform estimator may be implemented as a closed-form similarity-transform solver when sufficient anchor observations are available simultaneously, or as a sequential estimator that incorporates anchors as they arrive. A particle-filter realisation is admissible when the ranging error distribution is heavy-tailed and a Gaussian assumption is unsafe.

Anchor observations may originate from satellite navigation receivers, from inertial-aided dead-reckoning bridges, from optical recognition of surveyed markers, from radio-frequency ranging to external beacons, or from manually entered coordinates relayed by an operator. The credentialing of the observation is independent of its physical origin: any source admissible under the policy yields a usable anchor.

The two-stage relative-then-absolute construction may be inverted in environments where a coarse absolute fix is available immediately but inter-node ranges are sparse. In that embodiment the absolute frame seeds the local frame, and the relative-frame bootstrap reduces to a refinement pass.

Composition With Other Mechanisms

The relative-frame bootstrap composes with the mesh's governance lineage by emitting credentialed observation records at every significant event: seed selection, node placement, transform admission, and frame promotion. These records are anchored into the lineage on the same substrate that anchors any other mesh observation, so that an auditor reviewing the mesh's history can determine when each node entered the frame, on whose ranges, and under what policy.

The bootstrap composes with downstream coordinated-action mechanisms by exposing two distinct frame-state signals: a relative-frame-ready signal raised at the completion of the initial bootstrap, and an absolute-bound signal raised at frame promotion. Coordinated actions subscribe to whichever signal corresponds to their requirement; intra-mesh formation actions subscribe to the relative-frame-ready signal, while external-coordination actions subscribe to the absolute-bound signal.

The bootstrap also composes with the mesh's permission machinery. Operations that are admissible only inside a known absolute frame, such as engagement against an externally specified geofence, hold a permission predicate that evaluates the absolute-bound signal and the freshness of the underlying anchor observations. Operations admissible in either frame, such as intra-mesh formation, hold a predicate that evaluates only the relative-frame-ready signal. The permission-evaluation logic is uniform across both classes and is itself part of the governance lineage.

Composition with the mesh's resilience mechanisms is direct. If a node fails or leaves the mesh, the continuous estimator drops its state without disrupting the frame; if the anchor source fails after promotion, the absolute binding is preserved at its last covariance and downstream operations may be permitted or denied based on the staleness of the binding under the active policy.

Prior-Art Distinction

Cooperative localization in sensor networks contemplates inter-node ranging and incremental position assignment, and simultaneous-localization-and-mapping techniques contemplate relative-frame construction with delayed global registration. The novelty claimed here lies in the explicit two-stage operating model in which the relative frame is treated as a first-class operating substrate rather than as a transient intermediate, in the credentialing of every observation through a governance policy reference, and in the explicit frame-promotion event that gates external-coordination operations on a covariance-bounded transform.

Prior anchor-based localization typically conditions all operations on the availability of anchors and degrades to no-operation when anchors are absent. The mechanism described here decouples internal operations from anchor availability by design, so that internal operations begin at deployment minute zero and external operations engage only when the absolute binding meets the policy-declared uncertainty bound.

Prior work on graph-based pose-graph optimisation provides the mathematical machinery that any embodiment of the continuous estimator may use, but does not articulate the governance and credentialing structure that distinguishes the present disclosure.

Prior cooperative-localization literature also tends to treat the gauge ambiguity of a pure-range solution as a nuisance to be eliminated by the introduction of anchors. The present disclosure inverts that posture by treating the gauge-ambiguous local frame as the primary operating substrate and the anchor-derived transform as a secondary, gated capability whose admission to operations is itself an auditable event.

Disclosure Scope

This disclosure covers the seed-triplet bootstrap, the incremental multilateration extension, the continuous local-frame estimator, the transform estimator that attaches the local frame to a global frame, the credentialed observation format used for ranges and anchors, the two-stage frame-state signalling, the policy-bound parameter set, and the lineage records that anchor each significant frame event. Implementations contemplated include centralised, decentralised, and hybrid topologies, and applications contemplated include forward-deployed defence operations, disaster-response deployments, subterranean and indoor robotics, and any other operating context in which a mesh must begin work before any absolute reference is available. The disclosure extends to any embodiment in which a self-consistent relative coordinate frame is constructed from observed inter-node ranges, used as the operating substrate for intra-mesh actions, and subsequently attached to a global frame by a credentialed transform whose uncertainty is governance-anchored.