Let be a nondegenerate interval, let be an integer, and let be a continuous function.
Let k be an integer denoting the number of sensing intervals fully contained in RIDLE, i.e., k = ⌊RIDLE/TI⌋ (k = 0,1,2…) and τ be the time instant τ + T RDT + k T I = k + T RDT T I + 1 × T I ↔ τ = T RDT T I + 1 × T I − T RDT, (9). as shown in Figure 3a.
In the AMR algorithm, the regrid interval may be chosen to be an integer divisor of the refinement ratio [ 13 ], which could be any even integer number in the implementation.
Each value of the positions must be an integer.
Step 3. Obtain the envelope correlation (see (4)) between rm +1(n) and the (m+1 th-shifted range profile, with m+1 th-shiftedintegerangethe interval and N the number of range bins.
Hence, after the adjacent entries ED [ i - 1, j] and ED [ i, j] are computed, ED [ i - 1, j] - ED [ i, j] = ed (s0, i -1, t0, j ) - ed (s0, i, t0, j ) is an integer within the interval D = I a, b.
More specifically, (2) S t = ∑ l c j 0 l φ j 0, k t + ∑ k ∑ j = j 0 ∞ d j k ψ j, k t, where c j (l) = ∫ R S t) φ j, l (t) dt and d j (k) = ∫ R S t) ψ j, k (t) dt are the low-pass and high-pass coefficients, respectively; j0 is an integer to define an interval on which S t) is a piecewise constant.
GPC is designed in two cases; the first is a multirate system, where the sampling interval of a plant output is an integer multiple of the holding interval of a control input, and the second is a fast-rate single-rate system, where both the holding and sampling intervals are equivalent to the holding interval of the multirate system.
Since k is an integer and lies within the interval [1, N], it is not computationally expensive to search.
Instead of solving the problem (13) directly, we propose the algorithm that solves the problem by an exhaustive search for M. Since M is an integer and lies within the interval [1, N], the computational complexity to search the optimal M is not very high.
