Abstract-A framework for positioning, navigation and tracking problems using particle filters (sequential Monte Carlo methods) is developed. It consists of a class of motion models and a general non-linear measurement equation in position. A general algorithm is presented, which is parsimonious with the particle dimension. It is based on marginalization, enabling a Kalman filter to estimate all position derivatives, and the particle filter becomes low-dimensional. This is of utmost importance for highperformance real-time applications.Automotive and airborne applications illustrate numerically the advantage over classical Kalman filter based algorithms. Here the use of non-linear models and non-Gaussian noise is the main explanation for the improvement in accuracy.More specifically, we describe how the technique of map matching is used to match an aircraft's elevation profile to a digital elevation map, and a car's horizontal driven path to a street map. In both cases, real-time implementations are available, and tests have shown that the accuracy in both cases is comparable to satellite navigation (as GPS), but with higher integrity. Based on simulations, we also argue how the particle filter can be used for positioning based on cellular phone measurements, for integrated navigation in aircraft, and for target tracking in aircraft and cars. Finally, the particle filter enables a promising solution to the combined task of navigation and tracking, with possible application to airborne hunting and collision avoidance systems in cars.

Abstract-The particle filter offers a general numerical tool to approximate the posterior density function for the state in nonlinear and non-Gaussian filtering problems. While the particle filter is fairly easy to implement and tune, its main drawback is that it is quite computer intensive, with the computational complexity increasing quickly with the state dimension. One remedy to this problem is to marginalize out the states appearing linearly in the dynamics. The result is that one Kalman filter is associated with each particle. The main contribution in this paper is the derivation of the details for the marginalized particle filter for a general nonlinear state-space model. Several important special cases occurring in typical signal processing applications will also be discussed. The marginalized particle filter is applied to an integrated navigation system for aircraft. It is demonstrated that the complete high-dimensional system can be based on a particle filter using marginalization for all but three states. Excellent performance on real flight data is reported.

This paper addresses the problem of integrated aircraft navigation, and more specifically how to integrate inertial navigation with terrain aided positioning. This is a highly nonlinear and non-Gaussian recursive state estimation problem which requires state of the art methods.We propose an algorithm based on the particle filter with particular attention to the complexity of the problem. The proposed algorithm takes advantage of linear and Gaussian structure within the system and solves these parts using the Kalman filter. The remaining parts suffering from severe nonlinear and/or non-Gaussian structure is solved using the particle filter. The proposed filter is applied on a simplified integrated navigation system. The result shows that very good performance is achieved for a tractable computational load.

This paper details an approach to the integration of INS (Inertial Navigation System) and TAP (Terrain-Aided Positioning). The solution is characterized by a joint design of INS and TAP, meaning that the highly nonlinear TAP is not designed separately but jointly with the INS using one and the same lter. The applied lter extends the theory of the MPF (Marginalized Particle Filter) given by [1]. The key idea with MPF is to estimate the nonlinear part using the particle lter and the part which is linear, conditionally upon the nonlinear part, is estimated using the Kalman lter. The extension lies in the possibility to deal with a third multi-modal part, where the discrete mode variable is also estimated jointly with the linear and nonlinear parts. Conditionally upon the mode and the nonlinear part, the resulting subsystem is linear and estimated using the Kalman lter. Given the nonlinear motion equations which the INS uses to compute navigation data, the INS equations must be linearized for the MPF to work. A set of linearized equations is derived and the linearization errors are shown to be insignicant with respect to the nal result. Simulations are performed and the result indicates near-optimal accuracy when compared to the Cramer-Rao lower bound. Keywords:Terrain-aided navigation, particle lter, Kalman lter, marginalized. Filter) given by [1]. The key idea with MPF is to estimate the nonlinear part using the particle filter and the part which is linear, conditionally upon the nonlinear part, is estimated using the Kalman filter. The extension lies in the possibility to deal with a third multi-modal part, where the discrete mode variable is also estimated jointly with the linear and nonlinear parts. Conditionally upon the mode and the nonlinear part, the resulting subsystem is linear and estimated using the Kalman filter.Given the nonlinear motion equations which the INS uses to compute navigation data, the INS equations must be linearized for the MPF to work. A set of linearized equations is derived and the linearization errors are shown to be insignificant with respect to the final result. Simulations are performed and the result indicates near-optimal accuracy when compared to the Cramer-Rao lower bound.

Background The Clinical Frailty Scale (CFS) is frequently used to measure frailty in critically ill adults. There is wide variation in the approach to analysing the relationship between the CFS score and mortality after admission to the ICU. This study aimed to evaluate the influence of modelling approach on the association between the CFS score and short-term mortality and quantify the prognostic value of frailty in this context. Methods We analysed data from two multicentre prospective cohort studies which enrolled intensive care unit patients ≥ 80 years old in 26 countries. The primary outcome was mortality within 30-days from admission to the ICU. Logistic regression models for both ICU and 30-day mortality included the CFS score as either a categorical, continuous or dichotomous variable and were adjusted for patient’s age, sex, reason for admission to the ICU, and admission Sequential Organ Failure Assessment score. Results The median age in the sample of 7487 consecutive patients was 84 years (IQR 81–87). The highest fraction of new prognostic information from frailty in the context of 30-day mortality was observed when the CFS score was treated as either a categorical variable using all original levels of frailty or a nonlinear continuous variable and was equal to 9% using these modelling approaches (p < 0.001). The relationship between the CFS score and mortality was nonlinear (p < 0.01). Conclusion Knowledge about a patient’s frailty status adds a substantial amount of new prognostic information at the moment of admission to the ICU. Arbitrary simplification of the CFS score into fewer groups than originally intended leads to a loss of information and should be avoided. Trial registration NCT03134807 (VIP1), NCT03370692 (VIP2)