Improved Calibration of Numerical Integration Error in Sigma-Point Filters

Sigma-Point Filters in Robotic Applications

Sigma-Point Kalman Filters (SPKFs) are popular estimation techniques for high nonlinear system applications. The benefits of using SPKFs include (but not limited to) the following: the easiness of linearizing the nonlinear matrices statistically without the need to use the Jacobian matrices, the ability to handle more uncertainties than the Extended Kalman Filter (EKF), the ability to handle di...

Sigma-Point Kalman Filters for Integrated Navigation

Core to integrated navigation systems is the concept of fusing noisy observations from GPS, Inertial Measurement Units (IMU), and other available sensors. The current industry standard and most widely used algorithm for this purpose is the extended Kalman filter (EKF) [6]. The EKF combines the sensor measurements with predictions coming from a model of vehicle motion (either dynamic or kinemati...

Applying REC Analysis to Ensembles of Sigma-Point Kalman Filters

The Sigma-Point Kalman Filters (SPKF) is a family of filters that achieve very good performance when applied to time series. Currently most researches involving time series forecasting use the Sigma-Point Kalman Filters, however they do not use an ensemble of them, which could achieve a better performance. The REC analysis is a powerful technique for visualization and comparison of regression m...

An Error Analysis for Numerical Multiple Integration

Improved Error Estimates for First Order Sigma-delta Systems

A sigma-delta modulator converts a sequence of real numbers bounded by 1 into a digital sequence with entries +1 and 1 only. When the input sequence consists of samples of a bandlimited function, oversampled by a factor with respect to its Nyquist frequency, we prove that filtering the digital output with an appropriate kernel reproduces the original bandlimited function up to an error of at mo...