Product

A reconstruction engine with a thin surface

Video and EDR data in; calibrated geometry, trajectories, a sensor-suite counterfactual and a hash-chained evidence bundle out. Everything with an uncertainty attached.

The product is under construction. This page describes what it is being built to do; the status table and validation page say how much of it exists. Where something is not built yet we say so.

What goes in

• Video. Dashcam, onboard camera, phone, or third-party footage (for example a fixed security camera that captured the scene). Camera make and model are optional; the engine estimates the camera model from the footage.
• EDR data. The pre-crash record — under 49 CFR Part 563, at minimum speed, accelerator and service-brake status for the 5 seconds before the trigger at 2 Hz — as exported by the retrieval tool.
• Vehicle identity. Make, model, year and trim, used to look up dimensions and the fitted assistance-sensor suite.
• Scene facts when available: survey measurements, lane widths, posted marking standards.

What comes out

Camera model

Intrinsics, distortion, rolling-shutter line delay, mount pose and per-frame timestamps, each with uncertainty.

Trajectories

Metric 6-DoF trajectories for the recording vehicle and each tracked actor; speeds, gaps, closing speed and time to collision at any instant, with intervals.

Event timing

First visibility of each actor, braking onset (changepoint detection), impact or closest approach.

EDR reconciliation

Clock offset between video and EDR, agreement of the two speed records, and flags where they conflict.

Counterfactual

For the modelled sensor suite: when each actor entered its field of view and detection envelope, the probability it would have been detected over time, and the last moment at which braking could have avoided or mitigated impact.

Evidence bundle

Inputs, intermediate results and outputs hashed and chained, so a second expert can verify nothing was changed between intake and report.

Report and replay

One written report and a 3D replay of the reconstruction. API and CLI access for experts who want the raw outputs in their own tools.

The method, in equations

Each layer is a well-posed estimation problem with an uncertainty attached. The notation follows NADIR-TR-2026-03. Badges show what exists in code today; an equation here describes the method, not a result.

1 · Self-calibrating reconstruction Planned

Project world point X_j into frame i with unknown intrinsics K, distortion δ and a rolling shutter: row v is exposed ℓ seconds per line after the frame starts, so every row has its own pose.

$$\mathbf{u}_{ij} = \pi\!\left(K, \boldsymbol{\delta};\; R(t_{ij})\,\mathbf{X}_j + \mathbf{t}(t_{ij})\right), \qquad t_{ij} = t_i + \ell\, v_{ij}$$

Metric scale comes from objects whose true size is regulated or known: a lane-marking segment of standard length L_std measured as L̂ in the reconstruction.

$$s = \frac{L_{\mathrm{std}}}{\hat{L}}$$

2 · Trajectories with uncertainty Planned

All poses and actor states are solved jointly as a maximum a posteriori problem over residuals r_k weighted by their noise Σ_k. The Laplace approximation at the optimum gives the covariance that becomes every interval in the report.

$$\mathcal{X}^{\star} = \arg\min_{\mathcal{X}} \sum_{k} \bigl\lVert r_k(\mathcal{X}) \bigr\rVert^{2}_{\Sigma_k}, \qquad \Sigma_{\mathcal{X}} \approx \left(J^{\top} \Sigma^{-1} J\right)^{-1}$$

3 · EDR fusion Planned Evidence bundles built

The EDR records speed at 2 Hz for 5 s before the trigger. The clock offset δ between the recorder and the video is the one that best reconciles the two speed traces; what is left over after alignment is the disagreement we flag.

$$\hat{\delta} = \arg\min_{\delta} \sum_{k} \frac{\bigl(v_{\mathrm{EDR}}(t_k) - \hat{v}(t_k + \delta)\bigr)^{2}}{\sigma_k^{2}}$$

4 · ADAS counterfactual Planned

For a modelled sensor suite S with detection envelope E_S for object class c_a, the probability that actor a had been continuously inside the envelope for n_min frames by time t, integrated over the trajectory posterior from layer 2:

$$p_{\mathcal{S}}(a, t) = \Pr\!\Bigl[\, \exists\, \tau \le t : \mathbf{p}^{a}(\tau') \in \mathcal{E}_{\mathcal{S}}(c_a)\ \ \forall \tau' \in [\tau, \tau + n_{\min}\Delta t] \;\Bigm|\; \text{data} \Bigr]$$

Whether the system should have acted is judged against time to collision and the last moment braking could still avoid impact, given latency t_lat and maximum deceleration a_max:

$$\mathrm{TTC}(t) = -\frac{d(t)}{\dot{d}(t)}, \qquad \dot{d}(t) < 0$$

$$t_{\mathrm{last}} = \max\Bigl\{ t : d(t) \ge v_{\mathrm{rel}}(t)\, t_{\mathrm{lat}} + \frac{v_{\mathrm{rel}}(t)^{2}}{2\, a_{\max}} \Bigr\}$$

The envelope is built from public specifications and observed behaviour. It is a model of the sensor suite, not the manufacturer's software.

5 · Published error rates Protocol in progress

Every stated interval must contain the truth as often as it claims to. Coverage is measured against instrumented ground truth; the full metric set is on the validation page.

$$\mathrm{cov}_{1-\alpha} = \frac{1}{n} \sum_{i} \mathbf{1}\bigl[\, y_i \in \hat{C}_i \,\bigr]$$

For reconstruction experts

The bottleneck in video-based reconstruction is the geometry: working out the lens and mount, fixing scale, and tracking vehicles frame by frame, usually by hand. NADIR does that part and shows its working. You get the camera solution and its residuals, the scale references it used, every trajectory with its uncertainty, and the EDR alignment. Your opinion stays yours; the engine supplies measurements and their error.

• Start from a calibrated camera rather than a guessed one.
• See which scale cues drove the solution, and override them.
• Export trajectories and intervals to your own analysis.
• Cite a published error rate for the method once the benchmark is run.

For attorneys and insurers

Early in a matter the question is whether there is an ADAS issue at all: was the hazard inside the sensors' view in time, and did the vehicle's behaviour match what the system is designed to do. The NADIR report answers that in plain language, states what the evidence cannot support, and arrives with a chain of custody. It is a triage and support tool; it is meant to be used with a retained expert, not instead of one.

• Decide sooner whether a case needs an ADAS expert.
• See the uncertainty, not just a point estimate.
• Get evidence-handling records that survive scrutiny.

For OEM product-safety teams

Later. Across many reconstructed cases, NADIR can describe how assistance systems performed in the real crashes they did not prevent: detection timing, envelope edges, scenario types. That is aggregated data, collected only with the consent of the parties, and it depends on the reconstruction itself being validated first.

Compared with the previous product

NADIR previously sold real-time ADAS sensor-drift scoring from fleet telematics. It was retired; the archive explains why.