Tracking Algorithm in NEW Radars

[Muddy]

I have been taking a Radar class where the books are a little dated,
and I was wondering about some of the comments about how a standard
Kalman Filter numerical complexity was little high for many Radar
Target Tracking applications even after considerable efforts were
applied to reduce the number of targets that ever needed tracking.
The book was written in 1998, so it seems to me that in most
applications a standard (Square Root?) Kalman Filter for tracking would
now be the low complexity solution, and the other inferior solutions a
thing of the past. Hell in my research, I have 6 states and 6
measurements, and I do about 300 Unscented Kalman Filter updates a
second in a student version of relatively unoptimized Matlab. Each
Unscented Kalman filter effectively performs most of the work of 37
standard Kalman Filters. This is done as part of the overhead of
maintaining two particle filters and lots of data records.

It would seem like instead of switching between a simple and full
Linear Kalman Filter, the proper trade off would be to switch between
at least a full Linear Kalman Filter for non-maneuvering targets to an
Extended Kalman Filter, Unscented KF or Particle Filter for Maneuvering
targets. Does anyone have a modern survey paper or even a feel for
what is being done on new systems today? I am really curious about
what is being done today?

[Just Another]

Post by Muddy
I have been taking a Radar class where the books are a little dated,
and I was wondering about some of the comments about how a standard
Kalman Filter numerical complexity was little high for many Radar
Target Tracking applications even after considerable efforts were
applied to reduce the number of targets that ever needed tracking.
The book was written in 1998, so it seems to me that in most
applications a standard (Square Root?) Kalman Filter for tracking would
now be the low complexity solution, and the other inferior solutions a
thing of the past. Hell in my research, I have 6 states and 6
measurements, and I do about 300 Unscented Kalman Filter updates a
second in a student version of relatively unoptimized Matlab. Each
Unscented Kalman filter effectively performs most of the work of 37
standard Kalman Filters. This is done as part of the overhead of
maintaining two particle filters and lots of data records.
It would seem like instead of switching between a simple and full
Linear Kalman Filter, the proper trade off would be to switch between
at least a full Linear Kalman Filter for non-maneuvering targets to an
Extended Kalman Filter, Unscented KF or Particle Filter for Maneuvering
targets. Does anyone have a modern survey paper or even a feel for
what is being done on new systems today? I am really curious about
what is being done today?

I can't help you but I'm interested in learning more about the
techniques you're describing; I've never heard of "unscented" Kalman
filters (nor heard it referred to as a square-root filter). Links?

I've done some sonar work where navigation processing was enhanced using
Kalman filtering techniques (these would be called Extended Kalman
filters), using far more than six states; but only at frequencies in the
30 to 120 Hz range. In my systems, all the remaining horsepower was busy
dealing with the sonar signals themselves.

And naturally I learned all my stuff from books written prior to '98.
;-)

[подметно]

Post by Just Another
I can't help you but I'm interested in learning more about the
techniques you're describing; I've never heard of "unscented" Kalman
filters (nor heard it referred to as a square-root filter). Links?

The Unscented and Square Root forms are not the same. The Unscented
filter is the idea of Julier and Uhlman and uses the nonlinear state
model to propagate the covariance matrix.

The Square Root form is just a factorization of the Kalman filter
covariance that give better numerical properties (i.e., positive
semi-definite covariance matrix).

This is just from memory, so look these up.

[Muddy]

The Square Root Kalman filter refers to a numerical technique, that has
also been applied to Unscented Kalman Filters which are a type Sigma
point Kalman Filter, at least in the Unscented Kalman Filter its
purpose is to improve numerically accuracy, with a slight improvement
in complexity.

The short version of what a Unscented Kalman Filter does, is that it
creates a set of sigma points around your state mean on each step. They
surround the mean in a hyper ellipse, and are processed through the
full non-linear equations, and then combined in a weighted average.

Rudolph van der Merwe, Sigma-Point Kalman Filters for Probabilistic
Inference in Dynamic State-Space Models, PhD EE dissertation 2004,
Oregon Health & Science University

R. van der Merwe and E. Wan, The Square-Root Unscented Kalman Filter
for State and Parameter-Estimation, In Proceedings of the International
Conference on Acoustics, Speech, and Signal Processing (ICASSP), Salt
Lake City, Utah, May 2001

or http://cslu.cse.ogi.edu/nsel/ukf/ - Unscented Kalman Filter
http://speech.bme.ogi.edu/publications/ps/merwe01a.pdf Square Root
Unscented Kalman Filter

or
a "New" version for mixtures
http://www-sigproc.eng.cam.ac.uk/~jv211/papers/ukf_note_05.pdf

The numerical cost of these techniques is not trival, but they do
extend Kalman Filters to systems that are point linearizable, or
Gaussian. The systems need to be mono-modal however.