11 May 2009 The exact fundamental solution for the Benes tracking problem
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Abstract
The universal continuous-discrete tracking problem requires the solution of a Fokker-Planck-Kolmogorov forward equation (FPKfe) for an arbitrary initial condition. Using results from quantum mechanics, the exact fundamental solution for the FPKfe is derived for the state model of arbitrary dimension with Benes drift that requires only the computation of elementary transcendental functions and standard linear algebra techniques- no ordinary or partial differential equations need to be solved. The measurement process may be an arbitrary, discrete-time nonlinear stochastic process, and the time step size can be arbitrary. Numerical examples are included, demonstrating its utility in practical implementation.
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Bhashyam Balaji, "The exact fundamental solution for the Benes tracking problem", Proc. SPIE 7336, Signal Processing, Sensor Fusion, and Target Recognition XVIII, 73360V (11 May 2009); doi: 10.1117/12.817736; https://doi.org/10.1117/12.817736
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