Measurement Jacobian

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A matrix describing the local sensitivity of measurements to system states, defined as the partial derivatives of the measurement function with respect to the state vector. In the observability gramian P(x₀) = ∫₀ᵀ Φ'(t)H'(t)H(t)Φ(t)dt, H is the measurement Jacobian which, together with the fundamental matrix solution Φ, determines the gramian elements.

Application Value

该矩阵在可观测性分析和滤波器设计中起关键作用。在编目系统中，该技术可提高对空间目标的探测、跟踪和编目能力。

Related Concepts

• Hill Sphere Radius
• Pseudospectral Convex Optimization
• Poincaré Map Representation
• Minimum Norm Targeting

References

• Observability metrics for space-based cislunar domain awareness (Fowler & Paley, 2023)