Geometric Approach to Determining the Space Object Orbit Altitude Using Angels-Only Measurements

A method for determining the altitude of a space object using angels-only measurements from a passive optical observation system is presented. The geometric relationship between the slant range, space object orbital velocity, displacement velocity in the frame plane, and the focus depth of the optical system is investigated. A final nonlinear equation is derived that relates the altitude of the space object to the angular measurements. The results of calculating the orbit altitude of the ADEOS-2 and AQUA satellites are shown based on the angular measurements from the optical observation system and the numerical solution of the nonlinear equation.