cramer rao lower bound for the ml direct position estimator
Báo cáo hóa học: " Autonomous Positioning Techniques Based on ´ Cramer-Rao Lower Bound Analysis" pot
... other nodes in transmission range of the kernel (iii) For each positioned node outside the kernel, estimate the accuracy in relative coordinates If the accuracy is found to be inadequate for the ... information If the data is preprocessed in some way, we can measure the “information-loss” due to the preprocessing operation in terms of the Fisher information If the Fisher information about ... kernel estimators For comparison purposes, we also plot the performance of an approximation to the ML estimator of relative node coordinates, given by (21), discussed in [1] and also in [4] The...
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Báo cáo toán học: "A LOWER BOUND FOR THE NUMBER OF EDGES IN A GRAPH CONTAINING NO TWO CYCLES OF THE SAME LENGTH" pptx
... 17t+1 Then f (n) ≥ n + 32t − 1, for n ≥ nt This completes the proof of the theorem From the above theorem, we have f (n) − n 2562 √ ≥ 2+ , n 6911 √ 487 which is better than the previous bounds ... i ≤ 31t + 799) Now we define these Bi ’s These subgraphs all have a common vertex x, otherwise their vertex sets are pairwise disjoint For 7t+1 ≤ i ≤ t − 742, let the subgraph B19t+2i+1 consist ... (G) denote the number of edges In this paper, we construct a graph G having no two cycles with the same length which leads to the following result Theorem Let t = 27720r + 169 (r ≥ 1), then f (n)...
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Báo cáo toán học: "Lower Bound for the Size of Maximal Nontraceable Graphs." pot
... n ≥ 10 has at least 3n−2 edges The first one concerns the lower bound for the number of edges of MNH graphs It is the combination of results proved in [2] and [7] Theorem (Bondy and Lin, Jiang, ... now give a lower bound for g(n) for n ≥ Theorem If G is a MNT graph of order n, then if n = 10 12 if n = e(G) ≥ 3n−2 if n ≥ 10 Proof If G is not connected, then G = Kk ∪ Kn−k , for some positive ... (v) = 2, then the neighbours of v are adjacent Also, one of the neighbours has degree at least and the other neighbour has degree or at least Proof Let NG (v) = {x1 , x2 } and let Q be the path...
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Báo cáo toán học: "Sharp lower bound for the total number of matchings of tricyclic graphs" doc
... sharp bounds for the Hosoya index of connected graphs [25] In [30], Ren and Zhang determined the sharp upper bound for the Hosoya index of double hexagonal chains In [31], Shiu studied the extremal ... minimal Hosoya index As for n-vertex unicyclic graphs, Deng and Chen [6] gave the sharp lower bound on the Hosoya index of unicyclic graphs In [15], Hua determined the minimum of the Hosoya index within ... give the following proposition Proposition 3.2 Let G ∈ Tn4 , then z(G) if G ∼ A3,3,3,2 ; see Figure = n−6 n−6 z(A3,3,3,2 ), and the equality holds if and only Proposition 3.3 Let G ∈ Tn6 , then...
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Báo cáo toán hoc:"A New Lower Bound on the Density of Vertex Identifying Codes for the Infinit" doc
... improve the lower bound to 12/29 Before we prove our main result, which is Theorem 1, we first prove a weaker lower bound, given in Proposition The proof of Proposition is instructive, because the ... uncrowded and they each have both leaves within distance three of the other cluster, then neither cluster sends charge to the other We say that such C1 and C2 are paired with each other Note that ... #R113 the discharging argument We separate these lemmas from the rest of the present proof because they make no mention of discharging rules Thus, they may be useful in proving a stronger lower bound...
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Báo cáo toán học: "A tight lower bound for convexly independent subsets of the Minkowski sums of planar point sets" potx
... slopes As before we sort the lines in L in the increasing order by their slopes For the second issue, we apply the following transform to P and L (after the projective transformation and the rotation ... and asked whether a superlinear lower bound exists for M (n, n) The quantity M (n, n) gives an upper bound for the largest convexly independent subset of P ⊕ P , and it is related to the convex ... proved that this bound is the e best possible, confirming Erd˝s’ conjecture (see [4] for the currently known best constant o coefficients) Sort the lines in L by the increasing order of their slopes...
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Báo cáo hóa học: "Cramer-Rao-Type Bounds for Localization Cheng Chang and Anant Sahai" ppt
... interpreted as the CRB given perfect knowledge of the positions of all other nodes.5 We can use more information to tighten the bound The lower bound using two-hop information is the CRB given the positions ... decays, the less the CRB benefits from faraway information A heuristic argument reveals the basic scaling laws involved Section studies the bound for anchor-free localization The rank of the FIM for ... Obviously, the N-hop bound is nondecreasing with N, and the ∞-hop bound is the same as the CRB for the original estimation problem In our simulation, we have 200 nodes and 10 anchors all uniformly randomly...
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Báo cáo toán học: "A Lower Bound for Schur Numbers and Multicolor Ramsey Numbers of K3" doc
... is the objective function for our maximization problem In practice, we make c1 relatively large and c2 relatively small so that the f1 term is the more important term in the function For the ... modified the objective function so as to prefer partitions having one large set The idea was to find a partition with a set large enough to improve the lower bound for R4 (3) However, the largest ... 160]; of these, four are symmetric These 10,000 partitions are all “close” to each other In other words, one can begin with one of the partitions, move an integer from one set to another, and...
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Báo cáo toán học: "New lower bound for multicolor Ramsey numbers for even cycle" doc
... analogously We refer the reader to [6] for a survey The Ramsey numbers for even cycles Up to now, there have been known only two exact values for 3-color Ramsey numbers for even cycles More precisely, ... vertices the electronic journal of combinatorics 12 (2005), #N13 G1 G2 G = K15 v1 v2 v3 S G4 G3 Figure 1: An illustration of coloring from the proof of Theorem for the case m = and k = To make the ... and V with the color i, and for any pair {i, j} such that j > i > 0, color edge {vi , vj } with the color i (thus there are no monochromatic cycles in the subgraph induced by S.) More formally,...
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Báo cáo toán học: "A sharp bound for the reconstruction of partitions" ppt
... (and the definitions of r and c) we see that the only possibility for λ/µ is (r, c), completing the proof of this case and the theorem Acknowledgements I would like to thank the referee for several ... that the conjugate of a partition λ is the partition λ obtained by flipping the diagram of λ across the NW-SE axis; it follows that λi counts the number of entries of λ which are at least i Before ... r and c intersect at the cell (i, j) It follows from the maximality of r and c that i, j < k, and thus the cell (k, k) does not lie in µ Were the cell (k, k) to lie in λ then, because |λ| ≥ k...
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Báo cáo toán học: "Lower bounds for the football pool problem for 7 and 8 matches" pdf
... = resp k = 5) In the case n = the best previously known lower bound k3 (7) ≥ 153 is due to Habsieger [5] We show Theorem k3 (7) ≥ 156 For the case of matches the best lower bound k3 (8) ≥ 398 ... lower bounds, Discr Mathematics 256 (2002), 161-178 [4] L Habsieger, Lower bounds for q-ary coverings by spheres of radius one, J Comb Theory Ser A 67 (1994), 199-222 [5] L Habsieger, A new lower ... A new lower bound for the football pool problem for matches, J de Th des Nombres de Bordeaux (1996), 481-484 [6] L Habsieger, A Plagne, New lower bounds for covering codes, Discr Mathematics 222...
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Báo cáo toán học: "Lower Bounds for the Size of Random Maximal H-Free Graphs" pdf
... given at Section 3.1, we lower bound the probability of the event E1 In the second part we lower bound the probability of the event E2 (f ) Since these two lower bounds would be shown to be − ... given√ the proposition, implies the validity of the claim for j in Next, assume j ≤ δ + δ 1/4 Crudely, qg,d (0, j) is lower bounded by the probability of the event that for every G ∈ ΓT (g) there ... −2)/(eH −1) ) Note that the above lower bounds trivially imply similar lower bounds on the expectation of e(Mn (H)) It is worth mentioning that all of the above lower bounds on the expectation of...
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Báo cáo toán học: "Lower Bounds for the Average Genus of a CF-graph" doc
... obtained the following result for the maximum genus of a CF-graph Theorem 1.3 (See [9]) Let G be a CF-graph with minimum degree at least Then lower bounds on the maximum genus are given in Table The ... show a lower bound for the average genus of a CF-graph which is a linear function of its Betti Number Theorem 1.4 Let G be a CF-graph with minimum degree at least Then lower bounds on the average ... empty, the theorem is true Otherwise B1 is nonempty, for any x2 ∈ B1 , on the basis of orientability and x2 and x1 parallel, the only possibility is x− ∈ B1 From the known condition, there is...
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Lower bounds for the integration error for multivariate functions with mixed smoothness and optimal Fibonacci cubature for functions on the square
... the method Q The the cubature error for a non-periodic function f ∈ Bp,θ N following theorem gives an upper bound for the worst-case cubature error of the method QN with α (I2 ) respect to the ... estimate the remaining terms in (3.31) in a similar fashion Altogether we end up with (3.19) which concludes the proof Lower bounds for optimal cubature This section is devoted to lower bounds for the ... proves the theorem for the case θ ≥ To prove the theorem for the case θ < 1, we take k ∈ Zd+ with |k|1 = m + 1, and consider the function on Td gk := C 2−αm g˜k,s s∈S∗ (k) Similarly to the argument...
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Báo cáo hóa học: " Research Article An ML-Based Estimate and the Cramer-Rao Bound for Data-Aided Channel Estimation in KSP-OFDM" pdf
... Gaussian Cramer- Rao bound First, let us determine the Cramer- Rao bound of the estimation of h from the observation r The Cramer- Rao bound is defined by Rh−h − J−1 ≥ [9], where Rh−h is the autocorrelation ... not the case), the latter estimator is derived based on the ML estimation rule It is clear that the estimator proposed in this paper outperforms the estimator from [8] Further, in the latter estimator ... for large block size) for the Cramer Rao bound, that is, the Gaussian Cramer- Rao bound, related to for data-aided channel estimation in KSP-OFDM, when the pilot symbols are distributed over the...
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Báo cáo hóa học: " Statistical resolution limit for the multidimensional harmonic retrieval model: hypothesis test and Cramér-Rao Bound approaches" docx
... variable formula, closed-form expression of the MSRL are given Finally, note that the concept of the MSRL can be used to optimize, for example, the waveform and/or the array geometry for a specific ... based on the hypothesis test approach to a new extension of the SRL based on the Cramér -Rao bound approach Using the Cramér -Rao bound and a in which ξ = g(ξ ) = [δ ϑ T ]T (P) )T ]T Thanks to the Jacobian ... derive the MSRL using the lk norm for a given integer k ≥ The aim of this part is to support the endnote a, which stays that using the l1 norm computing the MSRL using the l1 norm is for the calculation...
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Báo cáo hóa học: " The Cramer-Rao Bound and DMT Signal Optimisation for the Identification of a Wiener-Type Model" pptx
... [n] The Cramer- Rao bound is the theoretical lower bound for ˆ the variance of all unbiased estimators θ for the model parameters θ and is determined by the diagonal elements of the inverse of the ... likelihood estimator is a minimum variance estimator [1], thus the variance of this estimator coincides with the Cramer- Rao bound VERIFICATION OF THE THEORETICAL RESULT The above result (24) for the ... and on the used excitation signal If the estimator is a minimum variance estimator, then its parameter variance achieves the lower bound, that is, the Cramer- Rao bound Thus, to even further decrease...
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Báo cáo hóa học: " Research Article The Best Lower Bound Depended on Two Fixed Variables for Jensen’s Inequality with Ordered Variables" pot
... holds for a1 a2 · · · an If i √ ak , ak ak a1 a2 · · · , · · · ak−1 Remark 2.9 For p1 a1 a2 ··· p2 pn with equality if and only if a1 n 1, then equality holds again for · · · an 1/n, from Proposition ... ··· p2 2.30 ≥ pn Then, Qi Rk ak − , ak Qi Rk ak 2.31 with equality for ··· a2 a1 ai Qi Qi ··· an , 2.32 Rk ak Rk Using Corollary 2.12, we can prove the following proposition Proposition 2.13 Let ... p 5.4 If p ≥ 1, then − x−2/ p ≥ 0, 5.5 and if p ≤ 1, then g x 2p − p −2/ p x p 1 ≥ Since g x ≥ for x ≥ 1, and g x is increasing, g x ≥ g hence g x ≥ g for x ≥ This concludes the proof 5.6 0,...
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Methods of Policy Accommodation at the Interest-Rate Lower Bound ppt
... at the interest-rate lower bound, the experience of reaching the lower bound has undoubtedly increased the willingness of central banks like the Fed to experiment with more explicit forms of forward ... paths, but now in the direction of anticipating a lower future path for the repo rate than the Riksbank For example, Figure 12 shows the market expected forward paths before and after the Riksbank’s ... Criterion for “Lift-Off ” from the Lower Bound? In the case of a central bank at the lower bound for its policy rate, it is important to discuss what will determine the date T at which “lift-off” from the...
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WORKING PAPER NO. 218 THE ZERO-INTEREST-RATE BOUND AND THE ROLE OF THE EXCHANGE RATE FOR MONETARY POLICY IN JAPAN potx
... downward bias in the variability of the real rate depending on the level of the nominal equilibrium rate of interest The downward bias in the variability of the real rate accounts for the reduced ... data The structural shocks differ from the estimated residuals to the extent of agents’ forecast errors We obtained the structural shocks by solving the model algebraically for the reduced form ... the role of the exchange rate for monetary policy by exploring the performance of the three different proposals for avoiding or escaping the liquidity trap by means of depreciation of the domestic...
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