Tracking of maneuvering targets is an important area of research with applications in both the military and civilian domains. One of the most fundamental and widely used approaches to target tracking is the Kalman filter. In presence of unknown noise statistics there are difficulties in the Kalman filter yielding acceptable results. In the Kalman filter operation for state variable models with near constant noise and system parameters, it is well known that after the initial transient the gain tends to a steady state value. Hence working directly with Kalman gains it is possible to obtain good tracking results dispensing with the use of the usual covariances. The present work applies an innovations based cost function minimization approach to the target tracking problem of maneuvering targets, in order to obtain the constant Kalman gain. Our numerical studies show that the constant gain Kalman filter gives good performance compared to the standard Kalman filter. This is a significant finding in that the constant gain Kalman filter circumvents or in other words trades the gains with the filter statistics which are more difficult to obtain. The problems associated with using a Kalman filter for tracking a maneuvering target with unknown system and measurement noise statistics can be circumvented by using the constant gain approach which seeks to work only with the gains instead of the state and measurement noise covariances. The approach is applied to a variety of standard maneuvering target models.
Objective: Despite the tremendous promise of invasive brain-computer interfaces (iBCI), the associated study costs, risks, and ethical considerations limit the opportunity to develop and test the algorithms that decode neural activity into a user’s intentions. Our goal was address this challenge by designing an iBCI model capable of testing many human subjects in closed-loop. Approach: We developed an iBCI model that uses artificial neural networks to translate human finger movements into realistic motor cortex firing patterns, which can then be decoded in real time. We call the model the joint angle BCI, or jaBCI. jaBCI allows readily-recruited, healthy subjects to perform closed-loop iBCI tasks using any neural decoder, preserving subjects’ control-relevant short-latency error correction and learning dynamics. Main Results: We validated jaBCI offline through emulated neuron firing statistics, confirming that emulated neural signals have firing rates, low-dimensional PCA geometry, and rotational jPCA dynamics that are quite similar to the actual neurons (recorded in monkey M1) on which we trained the artificial neural network. We also tested jaBCI in closed-loop experiments, our single study examining roughly as many subjects as have been tested world-wide with iBCIs (n=25). Performance was consistent with that of the paralyzed, human iBCI users with implanted intracortical electrodes. jaBCI allowed us to imitate the experimental protocols (e.g., the same velocity Kalman filter decoder and center-out task) and compute the same seven behavioral measures used in three critical studies. Significance: These encouraging results suggest the jaBCI’s real-time firing rate emulation is a useful means to provide statistically robust sample sizes for rapid prototyping and optimization of decoding algorithms, the study of bi-directional learning in iBCIs, and improving iBCI control.
One of the well-known approaches to target tracking is the Kalman filter. The problem of applying the Kalman Filter in practice is that in the presence of unknown noise statistics, accurate results cannot be obtained. Hence the tuning of the noise covariances is of paramount importance in order to employ the filter. The difficulty involved with the tuning attracts the applicability of the concept of Constant Gain Kalman Filter (CGKF). It has been generally observed that after an initial transient the Kalman Filter gain and the State Error Covariance P settles down to steady state values. This encourages one to consider working directly with steady state or constant Kalman gain, rather than with error covariances in order to obtain efficient tracking. Since there are no covariances in CGKF, only the state equations need to be propagated and updated at a measurement, thus enormously reducing the computational load. The current work first applies the CGKF concept to heterogeneous sensor based wireless sensor network (WSN) target tracking problem. The paper considers the Standard EKF and CGKF for tracking various manoeuvring targets using nonlinear state and measurement models. Based on the numerical studies it is clearly seen that the CGKF out performs the Standard EKF. To the best of our knowledge, such a comprehensive study of the CGKF has not been carried out in its application to diverse target tracking scenarios and data fusion aspects.
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