David A. Haessig

Separate-bias estimation with reduced-order Kalman filters

This paper presents the optimal two-stage Kalman filter for systems that involve noise-free observations and constant but unknown bias. Like the full-order separate-bias Kalman filter, this new filter provides an alternative to state vector augmentation and offers the same potential for improved numerical accuracy and reduced computational burden. When dealing with systems involving accurate, essentially noise-free measurements, this new filter offers an additional advantage, a reduction in filter order. The optimal separate-bias reduced order estimator involves a reduced order filter for estimating the state, the order equalling the number of states less the number of observations.

STATE DEPENDENT DIFFERENTIAL RICCATI EQUATION FOR NONLINEAR ESTIMATION AND CONTROL

Abstract State-dependent Riccati equation (SDRE) methods for designing control algorithms and observers for nonlinear processes entail the use of algebraic Riccati equations. These methods have yielded a number of impressive results, however, they can be computationally quite intensive and thus far they have not yielded to those attempting to assess their stability. This paper explores an alternative, the use of state dependent differential Riccati equations and numerical integration to propagate their solutions forward in time. Stability is examined and examples illustrating the use of these methods are given.

A method for simultaneous state and parameter estimation in nonlinear systems

A new method for simultaneously estimating the state and unknown parameters in nonlinear dynamic systems is presented. The method, based on the state dependent Riccati equation (SDRE) filtering technique, is shown to work well in a number of examples, one involving friction estimation and compensation, and another being a linear system with unknown coefficients. However, when the number of states and parameters is large, the filter can become computationally overburdened. This problem is addressed by developing a two-stage form of the new state/parameter estimator for systems affine in the unknown parameters.

Modern Control Methods Applied to a Line-of-Sight Stabilization and Tracking System

Modern control methods are used to develop compensators for a precise optical positioning system designed to track a commanded line-of-sight (LOS) position while rejecting the vibrational environment of an F-16 fighter aircraft, the vehicle upon which the device will be mounted. The physical system being controlled consists of two gimbals that effect large changes in the LOS position, and a mirror assembly that is used, because of its fast dynamic response (but limited range of motion), to reduce LOS jitter (i.e. angular disturbances above 5 Hz that cause blurring). Compensators are designed that include models of the motion to reject and of the motion to track. These models become part of each compensator and enable them to distinguish aircraft vibration from aircraft maneuvers, rejecting the former and tracking the latter. The vibrational disturbance that must be rejected has a magnitude of 560 ¿rads rms, which is magnified by the optical system to 1400 ¿rads of LOS motion. Simulation of closed-loop performance with a nonlinear dynamic model of the system demonstrated that LOS jitter is reduced to about 130 ¿rads rms. A tradeoff between stabilization and tracking is demonstrated. Compensator robustness to unmodelled disturbances is increased using the Loop-Transfer-Recovery technique.

Nonlinear reduced-order state and parameter observer

A globally stable algorithm for jointly estimating the state and parameters in deterministic nonlinear dynamic systems is developed. This is accomplished by combining the concepts developed by Raghavan (1992) for the design of a full-order adaptive observer with the techniques used by Friedland (1997) for development of reduced-order estimators. The result is a method whose applicability exceeds that of many existing techniques in that it can accommodate multi-output systems. Several previously developed methods applicable to the same class of nonlinear system are restricted to single-output systems. In addition, the new method is shown to have some computational, advantages.

Maximum likelihood estimation of target acceleration

Maximum Likelihood Failure Detection (MLFD) theory is used to estimate the acceleration of a moving target performing an evasive maneuver during an air-to-air interception. Target acceleration is shown to introduce a bias in the residual of the navigation (Kalman) filter. The MLFD algorithm processes this biased residual to detect acceleration transitions, estimate the acceleration subsequent to the transition, and provide a correction term that approximately cancels the error due to target acceleration in estimating the projected miss distance. Also presented are simulation results demonstrating for a particular case that the rms terminal miss distance is reduced from 6.8 to 0.9 feet by application oF the MLFD algorithm.

“Sense and Avoid” - What's required for aircraft safety?

The safe integration of unmanned aircraft into the national airspace is a topic receiving considerable attention. The US Congress has mandated that the Federal Aviation Administration (FAA) engage in rulemaking that will allow for civil operation of unmanned aircraft in the national airspace system (NAS), with a release of those rules in 2016*. Preparations are occurring simultaneously for the implementation of the FAAs NextGEN System on 1 January 2020, changing Air Traffic Control (ATC) in the US from one that relies upon radar to a GPS-based system. The introduction of Unmanned Aerial Systems (UAS) into the NAS is expected to be integrated with NextGEN. The availability of small, light ADS-B Out equipment (Autonomous Dependent System-Broadcast) is anticipated to facilitate that, and is discussed. Further, control of UASs will likely adhere to the procedural rules present in todays ATC System and in NextGEN, rules that require a pilot in the loop, making fully autonomous operation forbidden. UASs are therefore expected to employ additional systems and equipment to enhance their sense & avoid capability. Collision avoidance in manned aircraft was improved in 2005 when certain aircraft were required to use the Traffic Collision Avoidance System, TCAS II. The sense & avoid performance of UASs within the NextGEN-controlled airspace should similarly be enhanced by a new system called the Airborne Collision Avoidance System, ACAS. This TCAS replacement will have several variants for various aircraft types including UASs, and it will be capable of accepting data from various types of onboard sensors, making “optimal” use of that data when available. Thus collision avoidance on future aircraft should benefit from enhanced sensing devices such as LIDAR, Mode-S transponder interrogation, IR sensors, and possibly from that provided by the “Due Regard” radar system currently in test on the Predator UAS.

Integrated strapdown avionics for precision guided weapons

Conventional avionic configurations for precision guided weapons are often unnecessarily costly and inefficient because of built-in (but unused) redundancy in instrumentation attributed to the present day independent systems design approach. Described in this paper is an integrated design approach using strapdown avionic components that has the potential for lowering cost, increasing realibility and improving overall performance as a result of using fewer and less costly instruments in an optimum manner.

Integrated Strapdown Avionics for Precision Guided Weapons

Conventional avionic configurations for precision guided weapons are often unnecessarily costly and inefficient because of built-in (but unused) redundancy in instrumentation attributed to the present day independent systems design approach. Described in this paper is an integrated design approach using strapdown avionic components that has the potential for lowering cost, increasing reliability, and improving overall performance as a result of using fewer and less costly instruments in an efficient manner.