State Estimation Using a Parametric Approximation of the Viterbi Algorithm

Abstract: In this work, a new method of approximating the Maximum-likelihood estimate has been presented. The method consists of first using the Viterbi algorithm to estimate the log likelihood of the state, and then approximating that log likelihood to keep the computational complexity down. Various methods for approximating the log likelihood are introduced, most of these using linear regression and feature vectors. The methods were compared to a Kalman filter or Extended Kalman filter (depending on wether the system was linear or nonlinear) as well as a Particle filter modified to return a maximum likelihood estimate. Two systems were used for testing, one very simple linear system as well as a complex nonlinear system. Both of these were 1-dimensional. When applied to the simple system, the presented method outperformed both the Kalman filter and the Particle filter. While many approximation methods gave a good results the best one was using a cubic spline. For the more complex system, the method presented here could not outperform the particle filter. The most promising approximation method for this system was a Chebyshev approximation.