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Since the innovation of the ubiquitous Kalman filter more than five decades back it is well known that to obtain the best possible estimates the tuning of its statistics X 0 , P 0 , Θ, R and Q namely initial state and covariance, unknown parameters, and the measurement and state noise covariances is very crucial. The earlier tweaking and other systematic approaches are reviewed but none has reached a simple and easily implementable approach for any application. The present reference recursive recipe based on multiple filter passes through the data leads to a converged 'statistical equilibrium' solution. It utilizes the pre, post, and smoothed state estimates and their corresponding measurements and the actual measurements as well as their covariances to balance the state and measurement equations and form generalized cost functions. The filter covariance at the end of each pass is heuristically scaled up by the number of data points and further trimmed to provide the P 0 for subsequent passes. A simultaneous and proper choice for Q and R based on the filter sample statistics and certain other covariances leads to a stable filter operation providing the results after few iterations. When only R is present in the data by minimizing the 'innovation' cost function J using the non filter based Newton Raphson optimization results served as an anchor for matching and tuning the filter statistics. When both R and Q are present in the data the consistency between the injected noise sequences and their statistics provided a simple route and confidence in the present approach. A typical simulation study of a spring, mass, damper system with a weak non linear spring constant shows the present approach out performs earlier techniques. The Part-2 of the paper further consolidates the present approach based on an analysis of real airplane flight test data.

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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.