A heuristic reference recursive recipe for adaptively tuning the Kalman filter statistics part-1: formulation and simulation studies

Ananthasayanam, M. R.; Mohan, Manikanth; Naik, Naren; Gemson, R M O

doi:10.1007/s12046-016-0562-z

Cited by 22 publications

(14 citation statements)

References 46 publications

(45 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This interpretation was given earlier in the paper by Ananthasayanam et al [54], and used by Shyam et al [55]. As mentioned earlier the importance of P0 has not been much appreciated in the literature on ET and more so in Kalman Filtering though statisticians have been discussing the philosophical and practical differences between Frequentist and Bayesian approach.…”

Section: Probability Matching Prior Interpretation For P0mentioning

confidence: 80%

A Reference Recursive Recipe for Tuning the Statistics of the Kalman Filter

Ananthasayanam¹

2018

Kalman Filters - Theory for Advanced Applications

View full text Add to dashboard Cite

The philosophy and the historical development of Kalman filter from ancient times to the present is followed by the connection between randomness, probability, statistics, random process, estimation theory, and the Kalman filter. A brief derivation of the filter is followed by its appreciation, aesthetics, beauty, truth, perspectives, competence, and variants. The menacing and notorious problem of specifying the filter initial state, measurement, and process noise covariances and the unknown parameters remains in the filter even after more than five decades of enormous applications in science and technology. Manual approaches are not general and the adaptive ones are difficult. The proposed reference recursive recipe (RRR) is simple and general. The initial state covariance is the probability matching prior between the Frequentist approach via optimization and the Bayesian filtering. The filter updates the above statistics after every pass through the data to reach statistical equilibrium within a few passes without any optimization. Further many proposed cost functions help to compare the present and earlier approaches. The efficacy of the present RRR is demonstrated by its application to a simulated spring, mass, and damper system and a real airplane flight data having a larger number of unknown parameters and statistics.

show abstract

Section: Probability Matching Prior Interpretation For P0mentioning

confidence: 80%

A Reference Recursive Recipe for Tuning the Statistics of the Kalman Filter

Ananthasayanam¹

2018

Kalman Filters - Theory for Advanced Applications

View full text Add to dashboard Cite

show abstract

“…The estimation of the system parameters X0, Θ, P0, Q and R is called filter design or filter tuning as mentioned earlier. Though there are many techniques for adaptively tuning the filter statistics [14], the recent RRR [6][7][8][9] or the heuristic approach of Myers and Tapley [15] for Q,and R, and of Gemson [16] and Gemson and Ananthasayanam [17] for P0 are perhaps the simplest ones.…”

Section: Use Of Filter Statistics In Designing the Kalman Filtermentioning

confidence: 99%

“…A careful study of data of varying length based on adaptive filtering (both by simulation and actual data) helped to assess how the estimated B, Q and R vary with data length. Recently, the RRR [6][7][8][9] has found a near optimal solution for tuning the filter statistics and thus an improvement over earlier adaptive procedures.…”

Section: Adaptive Filtering Approach For Re-entry Predictionmentioning

confidence: 99%

“…); and hence whatever the results are generated, they will be different but have to be within reasonable limits. In the RRR studies [6][7][8][9], many typical cost functions have been stated to bring home the above point. One can be around the true answer but not at the answer which is not known due to the occurrence of the random unknown sequence of the noise distribution in the data.…”

Section: Introduction To Kalman Filtermentioning

confidence: 99%

See 1 more Smart Citation

Tuning of the Kalman Filter Using Constant Gains

Ananthasayanam¹

2019

Introduction and Implementations of the Kalman Filter

View full text Add to dashboard Cite

For designing an optimal Kalman filter, it is necessary to specify the statistics, namely the initial state, its covariance and the process and measurement noise covariances. These can be chosen by minimising some suitable cost function J. This has been very difficult till recently when a near optimal Recurrence Reference Recipe (RRR) was proposed without any optimisation but only filtering. In many filter applications after the initial transients, the gain matrix K tends to a constant during the steady state, which points to design the filter based on constant gains alone. Such a constant gain Kalman filter (CGKF) can be designed by minimising any suitable cost function. 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. Though CGKF results may not be too close to those of RRR, they are acceptable. It accepts extremely simple models and the gains are robust in handling similar scenarios. In this chapter, we provide examples of applying the CGKF by ancient Indian astronomers, parameter estimation of spring, mass and damper system, airplane real flight test data, ballistic rocket, re-entry of space object and the evolution of space debris.

show abstract

“…Instead, an alternate equation for the R-adaptation scheme can be derived by using several Kalman Ąlter relations, and the necessary substitutions are shown in [20]. The desired formulation aligns with that of Maybeck [41], and has been re-derived using expectation maximization techniques [109,113]. As such, the estimated measurement noise covariance isR…”

Section: Adaptations For the Measurement Noise Covariancementioning

confidence: 99%

Adaptive Extended Kalman Filtering Strategies for Autonomous Relative Navigation of Formation Flying Spacecraft

Fraser¹

View full text Add to dashboard Cite

This research addresses the relative navigation problem for spacecraft formation Ćying missions in near-Earth orbit. Technological and economic inĆuences have expedited the miniaturization of spacecraft systems, popularizing the notion of satellite teamwork due to the potential reductions in overall costs and complexity. It is now feasible to use a coordinated group of close-proximity satellites, known as a formation, to autonomously perform rendezvous, on-orbit servicing and science-based missions for a fraction of the resources a large-scale satellite would require. Despite the growing interest in formation Ćying spacecraft however, only a limited number of applications have been Ćight validated as a result of the difficulties associated with accurately determining the relative motion of the spacecraft within a formation. To enhance the capabilities of onboard autonomous guidance, navigation and control systems, this thesis presents the development of two adaptive extended Kalman Ąlter navigation algorithms for spacecraft formation Ćying. The proposed adaptive Ąlters are capable of updating the internal noise characteristics of the Kalman Ąlter in real time, and are viable in all orbit scenarios, including highly elliptical orbits in the presence of perturbations. The Ąrst Kalman Ąlter approach uses maximum likelihood estimation techniques to derive analytical adaptations laws for the Ąlter, which are then improved through the novel inclusion of an intrinsic smoothing routine. The second approach uses an embedded fuzzy logic system based on a covariancematching analysis of the Ąlter residuals, where the fuzzy system has been speciĄcally designed for the spacecraft navigation problem at hand. Numerical simulations of three spacecraft formations are used to demonstrate that the proposed adaptive navigation algorithms are appreciably more robust to Ąlter initialization errors, dynamics modelling deĄciencies, and measurement noise than the standard Kalman Ąlter. iii To Dr. Steve Ulrich, formally my supervisor, but more importantly my mentor, my professor, and my friend; your steadfast support and leadership have made my studies in Ottawa immensely fulĄlling. Thank you for providing this opportunity to continually learn from your expertise, and for instilling conĄdence and direction throughout the span of our collaboration. The dedication you have shown to me, and all of the members of our research group, is remarkable. It has been an honor to work with you, and a whole lot of fun too. To the professors who have guided me along this journey, including Bruce Burlton, Tarik Kaya, Alex Ellery, Victor Aitken, Howard Schwartz, and many others from Carleton University. The knowledge and wisdom you have shared has been invaluable to my growth as an engineer. And from the days at Dalhousie University, my thanks in particular to Professors Darrel Doman, Jeff Dahn, Timothy Little, and Guy Kember. You managed to imbue a fascination with space elevators, the laws of nature, the rules of mathematics, and the process of learning,...

show abstract

A heuristic reference recursive recipe for adaptively tuning the Kalman filter statistics part-1: formulation and simulation studies

Cited by 22 publications

References 46 publications

A Reference Recursive Recipe for Tuning the Statistics of the Kalman Filter

A Reference Recursive Recipe for Tuning the Statistics of the Kalman Filter

Tuning of the Kalman Filter Using Constant Gains

Adaptive Extended Kalman Filtering Strategies for Autonomous Relative Navigation of Formation Flying Spacecraft

Contact Info

Product

Resources

About