### Smoothers and Kalman Filters

The scripts in this section demonstrate GPS, odometer zupt aided INS implementations. Each of the example is in fact a complete smoother implementation. However, the forward parts can be used as a standard Kalman filtering solution for aided INS systems.

- 2 filters Smoother
- This is a 2 filter smooter implementation. The backward part uses a backward INS to compute the reverse solution and a information form Kalman filter to compute the ML estimates.

You may use the forward filter as an example of a simple vehicular navigation system with GPS+odometer+Zupt. (The INS is mechanized in geodetic frame with quaternions. The position is updated using Cen. The system model is derived based on PSI-Formulation. The position errors are defined in meters rather than radians.) - Bryson-Frazier smoother
- Standard Bryson-Frazier smoother implementation. The forward parth demonstrates an example of a aided INS for vehicles (It is a quaternion based INS which is mechanized in geodetic frame. The position is defined in lat, lon, and height. The error model is derived based on PHI formulation.)
- Fixed Lag Smoother
- This is a fixed lag smoother based on moving window innovation approach. (That is why, it is somehow close to BF formula). In order to deal with instability problem it uses 3 INSs simultaneously.
- Rauch-Tung-Striebel Smoother
- An RTS implementation which processes real Sensor data with GPS, Odometer and ZUPT. You may use the forward path as an example for a simple vehicular INS with GPS+Odometer+Zupt.
- Weinert Smoother
- This smoother is based on complementery space approach of Weinert. This specific example processes only ZUPT instants to self calibrate the IMU data without running any INS. The self-calibrated IMU data can later be processed by any other smoother/filter. This example also derives the new time-varying error model of the generated (self-calibrated) data.