RAP - Signal Processing
ARGOS localization and IMM filtering/smoothing
Within the reform of the ARGOS localization algorithm system (with CLS, www.cls.fr), we contributed to the “Interactive Multiple Model” (IMM) paradigm for nonlinear Markovian switching systems. First, we extended the IMM filter to the case when state vectors have heterogeneous sizes and meanings [LopezDanes_CDC2010]. Second, we investigated a new suboptimal solution for IMM fixed-interval or fixed-lag smoothing which is computationally cheaper and more reliable than equivalent algorithms. Therein, the smoothed mean and covariance are obtained by combining the statistics produced by a forward-time IMM filter in a backward-time recursive process based on Rauch-Tung-Striebel formulae and an original specific interaction [LopezDanes_ICASSP2012]. ARGOS location now includes the IMM filter and smoother as online and offline services.
Joint MAP estimation with "maximum Gaussian mixtures"
A recursive algorithm was proposed to the computation of the Maximum A Posteriori of the state trajectory of a dynamic system. Strikingly, it can be expressed in closed form for a linear system whose dynamics and observation pdfs take the form of “maximum Gaussian mixtures”, i.e., point-wise maximum of Gaussian pdfs [Monin_IEEE-TAC]. The method extends to nonlinear and/or hybrid systems.
Operatorial transform approach of dynamic problems
The “operatorial transform” approach of dynamic problems tackles analysis, simulation, identification, estimation or control by handling the involved signals globally as time functions (trajectories) as opposed to the conventional viewpoint of vectors depending locally on time. These problems and the underlying models are then stated into mathematical functional spaces. Trajectories are transformed by operators, either local (e.g., based on derivatives or static functions as in the conventional viewpoint) or more general (convolution-like operators, change of time, operatorial paramet-erization…). By using or combining such operators, many “difficult” problems can be turned into tractable equivalent problems: non-differential/discontinuous singularities, nonlinear control, predictive control… [MontsenyCasenave_JVC2013]