Stability analysis, for example. But it has been already done in "Stochastic Stability of the Discrete-Time Extended Kalman Filter" (1999) by Reif, for example. KF is quite often a subject of numerous modifications. If you did one, provide a stability analysis. If you didn't, then you may rely on the existing analyses. It is up to you to figure out what a merit of our work is. It is also worth to provide a comparison study. Use something as a baseline. It might be simple RLS, for instance (KF is a type of RLS filter), or MLE.

Generally EKF is used to estimate unknown plant parameters. You  can apply EKF to estimate coefficients of A  matrix of the state equation: X (k+1) = AX (k) + Bu( k),   Y(k) = CX(k)+ Du(k)

If you want further validation you should check the residuals or output predictions errors for whiteness. If the filters works as good as an ideal linear KF the output prediction errors will we white noise.

I heartily recommend you use about 100 Monte Carlo runs of your filter and publish the Root Mean Squared errors (RMSE) of your state vector estimates over  the Monte Carlo runs as a performance measure of your filter. Look in the book "Bayesian Estimation and Tracking: A Practical Guide" for explicit description of this method. You could also compute the Cramer-Rao lower bound (CRLB) of the problem to compare with the RMSE.

You can study further the complexity of the resulting algorithm.  As such, the EKF algorithm complexity scale linearly with the size of the covariance matrix. 

unless your covariance matrix is a low-dimensional and fixed in size

thank you all dear colleagues for your help.

Dear Torben, 

I checked the errors for whiteness and the result was positive. Would you please show me a reference to cite for this assertion. 

Thank you for your help. 

One other thing you can do it plot the RMS errors along with the estimated covariance diagonals. If they match it means your filter is consistent. Usually, with an EKF, the covariances are smaller than the RMS errors showing that the EKF is not a consistent estimator.