State Evaluation
State estimation feasibility in multi sensor networks is determined by the mathematical relationship between physical variables and system outputs. Constructing a dynamic observability matrix provides a way to quantify whether the current trajectory and sensor set allow the complete reconstruction of the internal states of the system. This evaluation determines if additional sensors are needed to resolve ambiguities.
Matrix Formulation
Mathematical compilation involves stacking the output gradients and their Lie derivatives across the target trajectory to capture how changes in states affect the measured signals over time. The time varying nature of the trajectory means that states unobservable during straight line motion may become observable during turns or changes in speed. This trajectory dependent evaluation is performed continuously by the navigation computer to assess state tracking confidence.
Rank Determination
Determining the rank of the matrix reveals if any states are hidden from the sensor suite. A full rank result proves that every state can be uniquely recovered from the measurements, while a deficient rank indicates that some states are unobservable.
Measurement Limitation
Practical implementation of this check requires calculating singular values to measure the degree of observability, rather than relying on binary rank checks. Low singular values warn that while a state is theoretically observable, the signal to noise ratio may prevent reliable estimation in the field. This metrological limit guides the design of trajectory planners to optimize sensor performance.
