# smootherJIPDA

## Description

Based on the joint integrated probabilistic data association (JIPDA) algorithm,
the `smootherJIPDA`

object creates a multi-sensor multi-object fixed-interval
smoother that you can use for offline estimation of multiple objects. The smoother estimates
smoothing joint data association probabilities at each time step. These smoothing joint
association probabilities represent the data association between estimated tracks and
detections at time step *k*, given information from the preceding time steps
(1 to *k*-1) as well as succeeding time steps (*k*+1 to
*N*), where *N* is the total number of steps. By using
measurements from succeeding time steps, the smoother can estimate data associations at each
step more accurately and can resolve ambiguities more efficiently than a `trackerJPDA`

object. For more details, see Algorithms.

## Creation

### Description

creates a default
`smoother`

= smootherJIPDA`smootherJIPDA`

object. Use the `smooth`

object function to obtain smoothed tracks.

specifies properties using name-value arguments. Unspecified properties have default
values.`smoother`

= smootherJIPDA(Name=Value)

creates
a `smoother`

= smootherJIPDA(tracker)`smootherJIPDA`

object by reusing the detection-to-track assignment
properties of a `trackerJPDA`

object. You must set
the `TrackLogic`

property of the `trackerJPDA`

object
to `"Integrated"`

.

## Properties

## Object Functions

`smooth` | Smooth track estimates using JIPDA |

## Examples

## Algorithms

The `smootherJIPDA`

object goes through multiple steps to obtain the smoothed
tracks. Consider a time period from time *t*_{0} to
*t*_{N}. In this period, the
smoother is provided with detections at each *k*-th step, where
*k* = 0, 1, …, *N*.

To obtain the smoothed tracks for all the time stamps:

The smoother first performs forward JIPDA tracking by using detections from

*t*_{0}to*t*_{k-1}to obtain tracks at*t*_{k-1}. The smoother then predicts those tracks to time*t*_{k}to get forward predictions at*t*_{k}.The smoother then performs backward JIPDA tracking from

*t*_{N}to*t*_{k+1}to obtain tracks at*t*_{k+1}. The smoother also predicts those tracks backward to time*t*_{k}to get backward predictions at*t*_{k}.Next, for time step

*t*_{k}, the smoother performs JIPDA between forward predictions and backward predictions and obtain smoothing (merged) predictions at time*t*_{k}. The smoother also maintains track identities when merging forward and backward predictions.Again for time step

*t*_{k}, the smoother performs JIPDA between the obtained smoothing predictions at*t*_{k}and the detections at*t*_{k}. The smoother saves the association results called*smoothing data associations*for later use.The smoother repeats steps 1 to 4 for all

*k*= 0, 1, …,*N*.Next, the smoother updates the forward predictions to from time

*t*_{0}to*t*_{k}. In the process, the smoother exactly follows the smoothing data associations when associating tracks to detections.The smoother repeats step 6 for all

*k*= 0, 1, …,*N*.Finally, the smoother performs Rauch-Tung-Striebel (RTS) smoothing for all the obtained tracks in the time period of [

*t*_{0},*t*_{N}] and outputs the smoothed tracks.

## References

[1] Song, Taek Lyul, and Darko
Mušicki. “Smoothing Innovations and Data Association with IPDA.”
*Automatica*, vol. 48, no. 7, July 2012, pp. 1324–29.

[2] Kim, Tae Han, et al. “Smoothing
Joint Integrated Probabilistic Data Association.” *IET Radar, Sonar &
Navigation*, vol. 9, no. 1, Jan. 2015, pp. 62–66.

[3] Memon, Sufyan, et al. “Efficient
Smoothing for Multiple Maneuvering Targets in Heavy Clutter.” *2016 International
Conference on Control, Automation and Information Sciences (ICCAIS)*, IEEE, 2016,
pp. 249–54.

## Version History

**Introduced in R2023a**