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# T - James K Beard

T - James K Beard

## T - James K

Data Fusion II Radar Trackers February 16, 2006DATA FUSION II, Radar TrackersDate: February 16, 2006 Time: 5:00 – 7:30 PMInstructor: Dr. James K BeardCredits: 1 Course Code: 0901-504-04 Registration Number: 13459Today’s topics:1 Homework and Study Problems from Last Week ...................................................... 11.1 Gelb problem 3-1 ................................................................................................ 11.2 Gelb Problem 2-5................................................................................................ 21.2.1 General Scalar Solution .............................................................................. 31.2.2 General Matrix Solution ............................................................................. 32 The Kalman Filter Equations...................................................................................... 42.1.1 Summary of Equations of the Kalman Filter .............................................. 42.2 The Covariance Update and Kalman Filter Stability.......................................... 52.2.1 The Short Form........................................................................................... 52.2.2 The Joseph Stabilized Form........................................................................ 62.2.3 The Normal Form ....................................................................................... 62.2.4 Square Root Filters ..................................................................................... 73 The Kalman Filter Data Flow ..................................................................................... 74 Tracker Architectures.................................................................................................. 94.1.1 Top Level Requirements............................................................................. 94.1.2 Development Requirements........................................................................ 94.1.3 Design Requirements.................................................................................. 94.1.4 Separation of Function.............................................................................. 104.1.5 The Association Function ......................................................................... 104.1.6 The Input and Output Functions ............................................................... 125 The Radar Tracker Software Diagram...................................................................... 126 Data Fusion Considerations ...................................................................................... 137 The Quiz.................................................................................................................... 131 Homework and Study Problems from Last Week1.1 Gelb problem 3-1The linear variance equation is the differential equation for propagation of errors of anoise-driven system. This is developed in Section 3.7, Propagation of Errors, pp. 75-78.The linear variance equation is given as Equation (3.7-17) at the bottom of page 77:TP () t = F() t ⋅ P( t) + P( t) ⋅ F( t) + G( t) ⋅Q( t) ⋅G ( t)(1.1)The problem statement is to verify a solution as given:tT T TP( t) =Φ( t, t0) ⋅P( t0) ⋅Φ ( t, t0) + ∫ Φ( t, τ ) ⋅G( τ) ⋅Q( τ) ⋅G ( τ) ⋅Φ ( t,τ)⋅dτ(1.2)t0Page 1 of 14

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