Ticket 047: Stochastic State Propagation for Path-Dependent Risk

Goal

Add a time-stepped stochastic propagator that carries a belief state forward through a full mission trajectory, accumulating correlated uncertainty across legs and producing a time-series of per-step risk metrics — principally the probability of reserve violation at any point mid-flight.

Current Gap

run_monte_carlo runs N fully independent deterministic estimates with perturbed scalar inputs. Each sample is a fresh deterministic execution: wind estimation error from leg 2 does not carry into leg 3, and energy shortfalls that compound across climb and cruise segments are invisible until the final reserve check. The only risk output is a distribution over total-mission scalars (total_time_s, reserve_at_landing_wh).

This means the simulator cannot produce the kind of probabilistic safety evidence needed for BVLOS operational risk assessments: "what is the probability the aircraft has insufficient reserve to reach its divert zone at any point during the mission?" The Monte Carlo gives a spread over end-states; it does not give path-dependent risk.

Scope

• Define a stochastic.v1 YAML input schema (StochasticPropagationPlan) that extends uncertainty.v1 parameters with time-step configuration and process-noise settings.
• Add a run_stochastic_propagation execution path that propagates a belief state (position, energy, wind estimate) forward at configurable Δt using Gaussian (EKF-style) representation for MVP.
• Emit a PropagationTimelinePoint at each time step recording position statistics, energy distribution, and p_reserve_violation.
• Add a propagate CLI command producing a stochastic-envelope.v1 JSON envelope and optional Markdown report.
• Preserve all existing deterministic and Monte Carlo interfaces; this is a new parallel execution mode.

Belief State

At each time step t the propagator maintains a distribution over:

StateVector:
  lat                  float   # degrees
  lon                  float   # degrees
  alt_amsl_m           float   # metres
  energy_remaining_wh  float   # Wh
  wind_east_mps        float   # m/s — estimated, not true
  wind_north_mps       float   # m/s — estimated, not true

The initial distribution is constructed from UncertaintyParameters (reuse existing schema). Wind state evolves with configurable process noise (wind_process_noise_std_mps, default 0.5 m/s) at each step to model temporal variability within the flight.

New Public API

def run_stochastic_propagation(
    plan: StochasticPropagationPlan,
    mission: MissionPlan,
    vehicle: VehicleProfile,
    *,
    wind_provider: WindProviderProtocol | None = None,
) -> StochasticPropagationResult:
    ...

Exported from estimator/__init__.py alongside the existing run_monte_carlo.

StochasticPropagationPlan (schemas/stochastic.py, stochastic.v1)

class StochasticPropagationPlan(BaseModel):
    model_config = ConfigDict(extra="forbid")
    schema_version: Literal["stochastic.v1"]
    propagation_id: str
    mission_file: str
    vehicle_file: str
    dt_s: float = 1.0              # gt=0
    samples: int                   # ge=1
    seed: int
    wind_process_noise_std_mps: float = 0.5
    parameters: UncertaintyParameters  # reuse from schemas/uncertainty.py

StochasticPropagationResult (schemas/stochastic.py)

class PropagationTimelinePoint(BaseModel):
    elapsed_time_s: float
    lat_mean: float
    lon_mean: float
    energy_remaining_wh: SampleStats
    p_reserve_violation: float     # fraction of samples with reserve < threshold

class StochasticPropagationResult(BaseModel):
    propagation_id: str
    seed: int
    dt_s: float
    sample_count: int
    timeline: list[PropagationTimelinePoint]
    reserve_at_landing_wh: SampleStats | None
    feasibility_rate: float
    baseline: MissionEstimate

CLI

New sub-command propagate:

bvlos-sim propagate stochastic.yaml [--dt 1.0] [--format json|markdown] [--output path]

Output schema: stochastic-envelope.v1. Exit codes follow the existing CliExitCode convention.

File Plan

New files:

File	Purpose
schemas/stochastic.py	StochasticPropagationPlan, StochasticPropagationResult, PropagationTimelinePoint
estimator/execution/propagator.py	Core propagation loop
estimator/execution/propagator_gaussian.py	Gaussian belief representation
adapters/stochastic_envelope.py	JSON envelope builder, STOCHASTIC_ENVELOPE_SCHEMA_VERSION
adapters/stochastic_markdown.py	Markdown report renderer
tests/test_stochastic_propagator.py	Unit and integration tests
examples/stochastic/pipeline_demo_001_stochastic.yaml	Example plan

Modified files:

• estimator/__init__.py — export run_stochastic_propagation, StochasticPropagationPlan, StochasticPropagationResult
• adapters/cli.py — add propagate command
• schemas/__init__.py — export new types

Integration Requirements

• Reuse UncertaintyParameters and SampleStats from schemas/uncertainty.py so the initial distribution is configured identically to Monte Carlo inputs.
• Reuse WindProviderProtocol for wind sampling at each step; the propagator must compose with LayeredWindProvider and SpatiotemporalWindProvider.
• The propagate CLI must accept the same mission and vehicle YAML files as the estimate and sample commands.
• run_stochastic_propagation with samples=1 and zero process noise must produce a final energy_remaining_wh.mean within 1 % of the deterministic baseline reserve_at_landing_wh (same physics, different execution path).

Acceptance Criteria

1. run_stochastic_propagation(samples=1, wind_process_noise_std_mps=0.0) produces a timeline[-1].energy_remaining_wh.mean within 1 % of the deterministic baseline reserve_at_landing_wh.
2. p_reserve_violation is monotonically non-decreasing over the timeline.
3. feasibility_rate equals the fraction of samples ending with energy_remaining_wh.mean >= reserve_threshold_wh.
4. Same seed produces identical StochasticPropagationResult across two runs.
5. Different seeds produce different p_reserve_violation timeline values.
6. propagate CLI exits 0 on the example file; JSON output has schema_version: "stochastic-envelope.v1".
7. All existing tests continue to pass.
8. uv run ruff check passes.

Out of Scope (follow-on tickets)

• Ticket 048: Observation/update step — simulated GPS fixes and battery voltage measurements narrow the belief state mid-flight.
• Ticket 049: Particle filter representation replacing the Gaussian approximation for non-linear dynamics.
• Ticket 050: Contingency trigger probability — P(lost-link policy fires before waypoint N) derived from the stochastic propagation timeline.
• Ticket 051: Integration with SITL comparison pipeline — use replay telemetry to condition the belief state retrospectively.