<p>A critical feature in particle filtering that determines its tracking accuracy is the choice of the proposal distribution. A good choice of the proposal is one that leverages the incoming observation from the sensor(s) because it leads to particles being placed in regions of high importance that fully contribute to the posterior density. The auxiliary particle filter accomplishes this using a clever lookahead scheme. However this filter and its recent variants suffer from over-estimation of the probability mass in the tails of the posterior, especially in low noise scenarios. This over-estimation leads to many particles having low probability mass and adversely affects the tracking accuracy. In this paper, we propose a particle filtering method with an auxiliary sampling scheme with multiple disturbances and a fully deterministic resampling scheme that treats the tails of the posterior fully and accurately, with no over-estimation nor under-estimation, for any observation noise. The properties of the proposed scheme are evaluated empirically and the method is applied to (a) target tracking using nonlinear image measurements from camera sensors, and (b) cardiac health monitoring using electrocardiograms.</p>