"Bi Directional" Kalman Filter I am working on a project in Object Tracking, i.e. need to predict the location of next bounding box.

I used a Hungarian algorithm with a Kalman Filter (which is a common method in this domain) which produced decent results. However, lots of the times detector has False Positive or False Negative detections (i.e. noise in the sensor) which limits Kalman's predictions. 

I was thinking to apply Kalman filter in the backward time direction, similar to bidirectional recurrent neural networks. This way it would utilize information in the future, of course compromising on some latency. This way we would have 2 filters, one in forward direction and another in backward both of which would predict a current location and two results will be merged using another simple method. From my understanding of Kalman filters it would only be possible to have a backward filter only if I were to recompute the full state at every sequence step given next n states.
Anuar Y, Welcome to the DSP community.

What you're talking about is called smoothing.
Let me explain, assume we have samples $ {\left\{ x \left[ n \right] \right\}}_{n = 0}^{N - 1} $ and we want to build estimator for $ x \left[ k \right] $ which we will define as $ \hat{x} \left[ k \right] $.

Now, we have 3 types of estimation:


The case $ k &gt; N - 1 $ is called prediction.
This is usually what we employ Kalman Filter for.
The case $ k = N - 1 $ is called filtration.
This is easy as we basically filter data we have.
The case $ k &lt; N - 1 $ is called smoothing.
This is basically what you're after.


So, there is plenty of information about the Kalman Filter in the Smoothing framework:


Derivation of Kalman Filtering and Smoothing Equations.
Kalman Filtering and Smoothing.
Fixed Leg Smoother.


If there is something specific you need, let us know and we'll assist you.