Thomas Higginbotham, Kestrel Intelligence
https://doi.org/10.64861/CUYC2247
Keywords: Space Situational Awareness (SSA), Space Domain Awareness (SDA), Dynamic sensor tasking, Conjunction assessment, Collision risk management, Value of Information (VoI), Expected Value of Sample Information (EVSI), Bayesian decision theory
Abstract:
Conjunction assessment is increasingly defined by a saturation regime: many candidate events arrive in tight temporal clusters while observation windows, slews, and processing capacity remain finite. In this regime, fixed revisit policies and catalog-wide proxy objectives can systematically misallocate sensor time, over-collecting on cases where additional measurements do not change the operational decision while under-collecting on cases where one high-quality observation would materially alter collision-risk classification, screening prioritization, or maneuver recommendation. This mismatch is not only an algorithmic scheduling issue but an objective-function issue: “maximize tracking accuracy” is not equivalent to “maximize decision quality,” especially near decision thresholds and under asymmetric consequences.
Recent SSA scheduling approaches have productively shifted toward information-centric figures of merit, including predicted covariance at a decision epoch and thresholded final-orbit-accuracy constraints, implemented through EKF or batch/epoch-state formulations with explicit process-noise growth. These improve rigor but still value observations through estimation-centric proxies (covariance decrement, KL divergence) rather than the decision value of reducing the probability of taking the wrong action.
We propose an information-theoretic framework in which the objective is explicitly conditioned on the operational decision context and therefore changes as a conjunction evolves. The central construct is a belief state over conjunction-relevant latent variables (object states propagated to time of closest approach with process noise, encounter geometry, and nuisance variables). Actions select a sensor, mode, and window; defer collection; or escalate. Decisions represent the operational choice set (dismiss, monitor, prepare, maneuver), and an asymmetric loss encodes unnecessary-maneuver cost, missed-collision penalty, and latency-to-commit penalties.
We value a candidate observation by its Expected Value of Sample Information (EVSI): the preposterior expected reduction in Bayes risk obtained by collecting it before deciding — an information price denominated in decision-loss units. The general result that decision value subsumes information measures is classical (Howard 1966; Krause and Guestrin 2005); our contribution is its explicit instantiation for orbital estimation — the covariance/mutual-information mapping as the quadratic-loss special case — and an analytic location of the estimation-to-decision crossover where the decision boundary meets the operational collision-probability threshold, so value concentrates near decision boundaries under asymmetric loss.
A key contribution is making objective switching explicit and principled through a composite objective Jₜ(a) = αₜ·IG(a) + βₜ·EVSI(a) − γₜ·C(a), whose weights are functions of decision proximity and time-to-decision rather than free tuning knobs. We characterize the switching empirically as an operational regime map over loss asymmetry, threshold proximity, prior realism, and sensor saturation — identifying where decision-value tasking separates from covariance/MI proxies and where it collapses to them.
Exact value-of-information is computationally hard (#P to evaluate; NP^PP to optimize), so we make decision-centric pricing tractable with a tiered, anytime stack: Gaussian-closure surrogates for all candidates; selective importance-sampled Monte Carlo reserved for near-threshold, high-consequence, or non-Gaussian cases; and anytime escalation with runtime-versus-quality curves and bounded optimality gaps on solvable instances. We further evaluate online receding-horizon operation and report a design insight rather than an assumed win: under loose, realistic priors a first observation of a neglected object can carry near-zero immediate decision value yet high enabling value for subsequent observations, so myopic online selection over-concentrates depth and underperforms breadth-preserving static allocation — a first-look unlock-value effect. Evaluating a family of five planners against it yields a sharper result: the failure is one of breadth, not horizon. An explicit first-look coverage term restores breadth and matches or outperforms static allocation at negligible cost, whereas two-step rollout and sparse-tree (Monte-Carlo tree search) planning return identical allocations and costs at up to an order of magnitude more compute. Lookahead does not buy what breadth does.
We evaluate on public conjunction geometries (CelesTrak general-perturbations catalogs; SOCRATES screenings) under controlled truth-plus-noise simulation, with paired-seed comparisons, bootstrap confidence intervals, and calibration diagnostics, plus replay on real screened conjunctions for allocation-path realism (no ground-truth outcomes are claimed). Metrics are decision-native: time-to-stable risk classification, incorrect-maneuver rate, missed-high-risk rate, expected decision cost, and compute/anytime profiles. Findings: decision-value scoring robustly improves on fixed-revisit baselines under realistic kilometre-scale priors and dominates covariance-based tasking, while against mutual-information tasking it is statistically indistinguishable across most of the operating envelope we sweep. We pre-registered the hypothesis that separation would appear where decision proximity is heterogeneous across the portfolio, tested it, and falsified it — 0 of 6 cells in the named regime, all contested. The separation that does exist lies elsewhere and is operationally meaningful: in the false-alarm-avoidance regime, where a loose catalog-quality prior over-alarms on clearly-safe events at high loss asymmetry, decision-value pricing separates in 14 of 30 swept cells and dismisses every clearly-safe event, declining collections that cannot change the call while estimation objectives continue to spend capacity on them. We identify the structural cause of the null: under a loose prior the posterior is measurement-dominated, so decision value and information gain coincide; separation requires a prior informative enough for the two to come apart. The contribution is therefore the map rather than a dominance claim — we characterize where decision-value pricing changes allocation and where a cheaper estimation objective suffices, an outcome consistent with value-of-information theory. The framework is additionally exercised end-to-end in a working prototype that carries recommendations through guidance capture (threshold, loss asymmetry, and objective weights as commander’s-guidance parameters), tasking-order production, execution tracking, and multi-phenomenology assessment over live public catalogs; its information-gain and cost terms already serve custody and maneuver-candidate events, with decision-value pricing for those event types identified as the next extension.
The broader contribution is a reusable formulation for tasking problems in which what is optimized is not fixed but adapts rigorously to mission phase, consequence, and time-to-decision — together with an honest map of when the added machinery matters and when simple estimation-centric tasking suffices
Date of Conference: September 15-18, 2026
Track: Astrodynamics