Beware that if you directly uses position at time tk to set up a measurement at time tk, you miss both the uplink time and the downlink time, i.e. the time it takes for the signal to go from radar to satellite and back from satellite to Earth. Both times are used in Orekit Range measurement, so it implies what you simulate is not the same as what Orekit computes and you will not be able to get accurate results. If you also takes other modifiers in the orbit determination (like tropospheric delays), they will also not be present in your simulated data.
If you want to simulate radar measurements (which are basically two-way range) and also consider modifiers like tropospheric delays, then you should better use the measurement generation feature. The same is true for azimuth/elevation (but here you will miss only the downlink time as the measurement does not care about what the full signal path is, only the last path from satellite to ground is relevant in this measurement).
If you configure your NumericalPropagatorBuilder to use only central attraction and not any perturbation (i.e. not full Earth potential, no solara radiation pressure, no drag, no 3rd body, not anything), then it will be equivalent to a Keplerian motion.
Levenberg-Marquardt is a very robust method. Of course if there is some inconsistency in the data, it may fail to converge, but for regular solvable problems, it should solve them.
Even if you computed your measurement in a naive way (forgetting about uplink/downlink and delays), you should have converged. You should not get an accurate orbit, but you should get something sensible. So I guess there is something wrong elsewhere. Are you sure your simulated measurements are consistent with the propagation? Is the force model correct (i.e. Keplerian only) in numerical propagator? Are units corrects (remember Orekit uses SI units everywhere, i.e. meters for Range and radians for azimuth/elevation)? Are dates correct? Are the frames OK (terrestrial frame for the radar, inertial frame for the spacecraft)?
Note yet because the KeplerianPropagator that is built by KeplerianPropagatorBuilder does not compute partial derivatives. There is ongoing work (Bryan as an intern for this just now) to allow using analytical propagators in OD, but this is still Work In Progress, it will be published after the internship, perhaps near the end of the year.